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GraFit version 4 - Erithacus Software

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1. 239 GraFit User s Guide IC 50 This fits data to a full 4 parameter equation The binding or inhibition is then characterized in terms of an IC5o value using the following equation R eee background 1 i IC so A graph is made of the fitted data as shown below 240 Chapter Error AutoText entry not defined Standard Templates Ligand Binding This template analyzes ligand binding data to single site saturation equation L Cap RA A graph is made of the fitted data together with an inset Scatchard plot as shown below m py ma gg B ILC KE pS See gt AA E 241 GraFit User s Guide Linear Regression This template allows data to be fitted using linear regression and the results plotted BH A m m gt 242 Chapter Error AutoText entry not defined Standard Templates Single Exponential This template fits data to a single exponential decay function using the following equation y A e A graph is created showing the fit ES KS 243 GraFit User s Guide 244 APPENDIX 1 GraFit Symbols Font GraFit Symbols Font GraFit is supplied with a font that can be used to represent the various graph drawing symbols used by the program This can be useful when annotating graphs for example when labeling axes The font is called GraFit Symbols and ca
2. E ICs 225 GraFit User s Guide In this equation s is a slope factor The equation assumes that y falls with increasing x IC50 0 100 show IC50 Displays the Csy value on the plot For best results set the curve resolution to High when using this transformation IC50 background corrected This equation fits inhibition data to a 3 parameter equation where the lower data limit is O i e the data are background corrected 10046 7 IC 5 In this equation s is a slope factor The equation assumes that y falls with increasing x IC50 background corrected show IC50 Displays the ICs value on the plot For best results set the curve resolution to High when using this transformation IC50 background corrected show limit Displays the limit value on the plot IC50 full 4 param Fits data to a full 4 parameter equation which is usually the best way to fit results from RIA analysis or inhibition data see Halfman 198116 The binding or inhibition is then characterized in terms of an IC value Hesponse o B e BBP R y o background iS ICs Here Range is the maximum y range and s is a slope factor The x axis represents the concentration of analyte Data fitted to this equation are usually displayed with a logarithmically scaled x axis For convenience the equation as defined attempts to provide initial estimates for the parameter values 16 Halfman C
3. sse 193 Worked Data Fitting Examples ocococococncnonononononanananarararannnnnnnnnrnrnrnrncnnasa 195 Using One of the Equations Provided ssssssseeme 195 Fitting the Data ep Oed trot be T ets 196 Checking the Weighting sssssssssses mme 199 Drawing Residual Plots sssssssssseee emm 199 Using Robust Weighting rettet E RR ER ERE ORE E dia 202 Defining a New Equation 1 cssssssssseen mmm 203 Defining the Oxygen Binding Equation eeeeeeseeeeeense 204 Defining a New Equation 2 00oococcccnconconononconcnnnnoncanan menm 206 Defining the Equation ssssssssssrerersererrerersrrerrrrererrererrrrernrrerere 207 Fitting th Equation 2 ree dd ende ede des 207 Multiple REQreSSiON cececeee cece cece e eee m emnes nnne 208 GraFit User s Guide Displaying Multidimensional Data eese 209 Reading Values from a Calibration Curve ssssssseen m 211 Choosing an Equation to Fit the Data ccecce 211 Reading Values from the Fitted Curve sssssseeee 213 Fitting Several Data Sets with Some Parameters Common and Some Specific prec 213 Method Used to Share Variables Between Data Sets 214 Example Paired Denaturation Curves s sss 216 Equations Provided ooomonononononanananararannnnononnnornrnrnrncnnnnnnnnnnnnnnnnrarararnrnnananas 219 2 Subsbrates E E NE AE 220 PINO PONG ati 220 Ping pong Li
4. X data column t 0 0000 110 0000 108 6346 1 0000 80 0000 81 4794 2 0000 60 0000 3 0000 45 0000 4 0000 35 0000 5 0000 28 0000 All fitted GraFit equations have only a single y value that corresponds to each x value and so there is no need to specify interpolation limits as in the previous column type When calculating y values it is possible to choose whether to use the fitted values or the explicit initial estimates that were used in the Estimatrix see Chapter 6 This allows the generation of a hypothetical data set which would result from the initial estimate values When no initial estimates were used these options are unavailable as in the figure above as the estimates were generated automatically for the equation used 49 GraFit User s Guide Difference Use this column type to calculate the difference between the experimental and the calculated y values using the fitting model described in a selected workspace item Difference Between Experiment and Fitted y Data 2l x Fitting results Fit number E 110 0000 1 3654 0 0000 1 0000 80 0000 1 4794 2 0000 60 0000 1 1121 3 0000 45 0000 0 8360 4 0000 35 0000 0 6216 5 0000 28 0000 2 2151 Plots of difference versus x or y values are very useful to indicate whether the calculation accurately reflects the variation in the data A good fit is characterized by a random distribution of small difference
5. 1 No Systematic Trend There are many examples of such data and two are displayed below lCleland W W 1967 Adv Enzymol 29 1 32 2Bevington P R 1969 Data Reduction and Error Analysis for the Physical Sciences McGraw Hill 3Duggleby R G 1981 Analytical Biochemistry 110 9 18 4Press W H Teukolsky S A Vetterling W T amp Flannery B P 1992 Numerical Recipes in C Cambridge University Press 5Motulsky H J amp Ransnas L A 1987 FASEB J 1 365 374 6_eatherbarrow R J 1990 TIBS 15 455 458 175 GraFit User s Guide 176 6 A un 2 A rainfall chart 2 O Jn Feb Mr Ay My Jn U Ag Sp Qt My Ec Nil 4 T L An elution profile from a pl purification column O ok LrLtlrrrrtlrrrtlrri LI 5 10 15 D 5 FractionNUntiex Such data are typically presented as bar or column charts or as scatter plots with the data points joined by lines or possibly by a smooth curve As no systematic relationship describes the data they are not suitable for data fitting 2 The Trend is Described by a Known Equation This is the situation where data fitting is most useful In this case based on knowledge of the experiment and the laws that govern it the data are described by a known equation i e y f x Di D P3 we In non mathematical terms the observed data y also known as the dependent variable varies as a function of some experimentally controlled value x th
6. 230 Chapter Error AutoText entry not defined Equations Provided 10 Bound vs Total cece ote as The previous equations require the unbound ligand z e concentration to be known However although the 841 total ligand concentration is always known this is 1j A what you have added the proportion bound and free zj is not always certain This is particularly the case if the y axis is an observation that is not directly related o O D gt Gm 4 t to the bound concentration for example fluorescence is intensity or absorbance Here the equation relates the y axis to the total ligand added t K t Cap K t Cap 4 t Cap 2 Bound vs Total tight binding limit This transformation shows the maximum possible amount bound or change in absorbance etc for a given total amount of ligand added if the binding were infinitely tight Cooperative A generalized equation describing cooperative binding or multiple binding sites of differing affinities is _ L Cap K L Here n is a measure of the cooperativity For normal binding to a single site n should not differ significantly from 1 0 Cooperative with background This is the same as the equation above but includes an unknown background level in the y axis observations i e L Cap m background Ka LD 231 GraFit User s Guide pH These equations are used when the observed value varies wit
7. X3 In this case the analysis is termed multiple non linear regression GraFit allows unlimited independent x variables as well as unlimited numbers of parameters Note however in all cases it is assumed that only the y axis data contain errors Note Multiple regression is sometimes also referred to as global analysis Uses for Multiple Regression Multiple regression is essential when the data to be examined are inherently multidimensional Examples include peak shape analysis of 2D spectra However there are several situations where multidimensional data are collected but are traditionally analyzed by a performing a series of normal two dimensional x y curve fitting Example The progress of an enzyme catalyzed reaction at a fixed concentration of substrate is given by the equation A A 1 e Here A is the extent of reaction at time t A the maximum extent of reaction and k the rate constant at this concentration of substrate The value of k from this equation is related to the kinetic parameters by the equation Veal S max K S In this equation V and K are the parameters that we need to obtain from data fitting The usual way of analyzing these data is to collect a series of progress curves A as a function of t at varying concentrations of substrate For each concentration of substrate the data are fitted to the first equation and a value for k obtained The resulting k value
8. both modify the size of text displayed on screen However changing font size using Table Preferences also changes the size of printed text while View Zoom only affects the on screen appearance Importing and Exporting Data 34 Importing Data To import data into a data table position the data entry position where you want the data values to start and select the Edit Paste From command Select the file that holds the values to import and press the Open button The contents of the file will be inserted into the data table Importing Data as a New Data Table It is also possible to import a file into the GraFit workspace as a new data table item To import a data file in this way use the File Import Data command Chapter Error AutoText entry not defined Data Tables Exporting Data To export data from a data table into a file that can be read by other programs select the range of values to be exported and use the Edit Copy To command Save As L2 x Save in 3 My Documents E 3 e E GraFit Data Storage File name FO Save as type TextFis El _ Cancel Z The Save as type entry determines the format in which to save the exported data GraFit supports a number of data export formats and the available types are listed in this box GraFit supports export as ASCII DIF and CSV formats as standard though additional formats may be available Column Types Columns can hold simple data values or ca
9. 216 if dataset 1 then y al b x return endif if dataset 2 then y a2 b x return endif if dataset 3 then y a3 b x return endif assumes that dataset must be 4 y al b x Example Paired Denaturation Curves This technique of sharing parameters between two or more data sets is not limited to linear equations Any equation may be recast in this manner For example the equation below describes the denaturation of a protein as a function of the concentration of a denaturing solvent15 m D AG exp RE m D AG RT F 1 1 expl In this equation F is the fraction of the protein that is denatured D is the concentration of denaturant e g guanidinium hydrochloride or urea R is the gas constant T is the temperature AG is the stability of the protein and m is a slope factor Finding the difference in stability between two proteins is often more important than determining the absolute stability If the proteins are highly related it can be assumed that the value for m is the same for each but AG differs Using the technique described above it is possible to fit two data sets to a common m value but different AG values In this case the equation to be used can be defined as if dataset 1 then a exp m D G1 8 314 1 else a exp m D G2 8 314 1 endif 1 a 1 a The x variable is the concentration of denaturant D the slope factor is m and the two values of AG a
10. Add Remove button Follow the instructions GraFit User s Guide CHAPTER 3 GraFit Basics Running GraFit The GraFit installation program will add a GraFit entry to the Programs list on your Windows Start menu When you run the GraFit program the main GraFit window will open E GraFit Untitled File Edi View Add Window Help 0 S 5 Sem oo zw s B GOOG B J de z v Ae ali es Workspace toolbar item buttons AB Bi i E ES BL Project window jo7A X SO Ore When initially opened the GraFit workspace is empty GraFit User s Guide The GraFit Workspace A GraFit file can comprise one or more data tables graphs data analyses equation definitions transformation definitions notepads and embedded objects Collectively these items make up the GraFit workspace which can be stored to disk as a single file After adding a number of items to the workspace the appearance of the GraFit window is shown below 3 GraFit Untitled File Edit View Add Table Window Help peas sse oo e 8 uz e Riera aaa J rimes New Roman ie B Z U lle E ls Su E lel ES Results NumberFormat Fonts Indents Settings Constants Estmati Fitting Criteria Estimates General xva Equation Equation alii Microsoft Word D Jo Ala x A Ready Row C To NUM 7 A GraFit workspace with a number of items adde
11. Checking the Limit X range box allows a lower and upper limit to be set on data that will be included in the analyses Y Data Column This entry specifies the column that holds the y data values See the Data Layout section above for further information Error Column If explicit weighting is chosen the error values are read from a separate column which is selected here 71 GraFit User s Guide Results Pane The Results pane holds a summary of the fitting results Linear Fit Iof x Settings Re j j Number Format Fonts Indents KI 4I gt py x column x Data i ij 2 w Y column y Data Ercolumn Number of data points B Ch value 0 4429 Correlation coefficient 0 9707 The Results pane of the Linear Fit tem Parameter Value StdEmor gt 2 7000 0 6429 If more than one set of data is specified in the Settings pane each fit can be viewed by clicking the arrow buttons The File Print and File Print Preview commands show the results in a more stylized manner as illustrated below Linear Fit Bl gt DQ a o Seffings Results X datu cobra Y dta cole Using Print Preview from Nascher of data podats the Linear Fit item Ch value 29 The formatting of these results is controlled from the Number Format Fonts and Indents panes 72 Chapter Error AutoText entry not defined Linear Fit Item Showing the Fitted Results on a Graph A listing of the fitted parameter val
12. Embedding and Linking without using the Clipboard Data objects can also be inserted into a target application directly using an Insert Object command which is often found on the Edit menu Obs Type Cancel Create New Microsoft Graph 97 Chart Microsoft Map Microsoft Photo E ditor 3 0 Photo Microsoft Photo Editor 3 0 Scan Microsoft PowerPoint Presentation Microsoft PowerPoint Slide Microsoft Word Document Microsoft Word Picture zl C Create from File Result Inserts a new Microsoft Word Document object into your document The Insert Object command allows the insertion of OLE objects into a document When the Create New button is selected an empty object of the selected type is inserted as a new embedded OLE item If the Create from File button is chosen it is possible to initialize the embedded item using the contents of an existing file or to create a linked object The Create from File option allows C Create New His creation of an embedded object ile 2 rMpDomerit based on the contents of an existing file If in addition the Link Browse F Link button is checked a linked object will be created rather than an embedded one Embedding and Linking with GraFit 172 GraFit can act as both a container of OLE items that come from other source applications and as the source of OLE items that are inserted into other targets The situations where GraFit can act as
13. High to Low Show Limit eseseee 232 pKa min 0 High to Low Show pKa sseemmIIHHe 233 pKa Double rediere npe ride 233 pKa Double Show Curve 1 ssssseeee meme 233 pKa Double Show Curve 2 sssssssseeeemememenemeenee 233 GraFit User s Guide xiv pKa Double Show Limit 1 0 0 0 cece e eee nara rarornnnnnnnns 233 pKa Double Show Limit 2 rissen iee eee eect m 233 pKa Double Show Limit 3 1 0 0 cece cece eee eee e 233 pKa Double Belli cios Ei et tH Ee vetas fug 233 pKa Double Bell Curve 1 02 ccc cece eee eee teeter nora rnrnnnnnnnns 234 pKa Double Bell Curve 2 sssssssseem mem 234 pKa Do ble Bell Elitr eer ass 234 pKa Single O 234 pKa Single Linearized plOt ooooocococccccnccncococornnnnnnnnnn nono ee eee teen ed 234 pKa Single Show Limit 1 02 0 eect eee eee eee rete ea ea ed 234 pKa Single Show Limit 2 cece eee eee eee eee ee AES 234 pKa Single Show pKa die etr HERE RR ha gees 234 Ria A A A A UH BARRE SETRRER IRSE RASTA 235 Ist Order z 3 A 235 1st order decay curve sssssssssssssseeeeme memes 235 1st order show limit n aieiaa eee erecta MM 235 Tst order Show initial sce itte eet Pe d 235 TIstorder CoffSet 205 urere vr ee D lr t E rie eh c f edel 235 1st order offset decay curve sssssssssseene nennen 235 1st order offset show liMit oo o nncncccnnccn naco nn Henne 236 1st ord
14. at low pH to another at high pH Y 4 UD with the variation depending upon the ionization of J A two groups The pK values of these groups determine a MEN CN the shape of the curve o pKa Double Show Curve 1 This shows the first of the two ionization curves in isolation pKa Double Show Curve 2 This shows the second of the two ionization curves in isolation pKa Double Show Limit 1 Displays the lower limit of the double curve pKa Double Show Limit 2 Displays the middle limit of the double curve pKa Double Show Limit 3 Displays the upper limit of the double curve 10 pKa Double Bell a E Sometimes two ionizations determine the value of the e observed parameter If the first ionization results in 7 al increasing activity and the second destroys activity this results in a bell shaped curve The equation assumes that activity is zero at low and high pH al 4 5 233 GraFit User s Guide pKa Double Bell Curve 1 This display equation is used to display the effect of the first ionization in the bell shaped curve pKa Double Bell Curve 2 This display equation is used to display the effect of the second ionization in the bell shaped curve pKa Double Bell Limit This shows the upper limit of the bell shaped activity profile pKa Single el c X This equation is used when the observed parameter varies from one value at low pH to an
15. bit program that requires Windows 95 or later or Windows NT 4 0 or later It is not compatible with Windows 3 1 or earlier The Help system requires installation of Microsoft Internet Explorer version 3 02 or later Microsoft Internet Explorer version 4 01 is supplied with GraFit and it is recommended that you install this before installing GraFit Hardware The minimum hardware required is a PC with a 66 MHz 486 processor with 8 Mbytes RAM and the recommended configuration is a 100 MHz Pentium with 16 Mbytes RAM or better You need at least 10 Mbytes free space on your hard disk drive and a mouse or compatible pointing device A CD ROM drive is highly recommended and although installation from 372 disks is possible 3Y2 media are not supplied as standard see Installing GraFit for details on obtaining GraFit on 31 disks The CD ROM includes optional tutorial files in the form of screen capture movies these files make use of sound and so to view these you need a PC with a Windows compatible sound system The GraFit Package The GraFit package comprises the following GraFit program CD ROM The GraFit User s Guide this manual Depending upon the GraFit package that was purchased this guide may only be available in electronic form on the CD ROM When GraFit is first run you will be able to register the product This will ensure that you are informed of the latest updates to the program GraFit User s Guide Instal
16. column Y data column When the Source is a data table item it is necessary to select which columns hold the x and y data values to be plotted For all other source types these selections are not available Error column Checking the Error column box allows a quick way of producing an error plot when the Source is a data table item Select the column that holds the error values from the list More extensive error plotting options are available once the graph has been produced see page 139 Chapter Error AutoText entry not defined X Y Scatter Graphs Transform as Check the Transform as box to plot the data after transformation using the selected transformation item All available transformations which must be present in the workspace are listed Transformation of data is only available if the Source is a data table or a non linear fit item See Chapter 10 for more information about plotting transformed data Set Initial Scaling XY Graph Wizard Set Initial Scaling 21 xi X axis TY axis Type E Type Linear gt Autoscale Autoscale C Manual scaling C Manual scaling Eran From To d Ti V axis text r Y axis text Text p Data Text p Data lt Back Cancel The Set Initial Scaling page allows the scale of the x and y axes to be specified By default the scale is set automatically and linear axes are chosen These can be altered as required it is also possibl
17. column type to x n Data which gives the following dialog X n Data Column BEI Independent data set Low X data set tt fl rm r Column type label Label 21 Data Load Default Label use the placeholder 1 where you wish to display the x data set H It is necessary to have one x n Data column for each independent variable in the equation and these must have their X data set entries set to correspond to the X variables number in the equation definition See Chapter 6 for information about using this option when fitting data 37 GraFit User s Guide 38 y Data You may optionally select this column type if the data in the column are used as the y values for data fitting Designating a column to contain y data is not essential for data fitting but can be useful to document the data layout y Data with Associated Value It is common that an equation has two independent x variables Under these circumstances the most usual way of collecting data is to measure a series of y values at varying x for a fixed x2 then to collect a further set of y values at the next x value etc For example the variation of enzyme catalyzed reaction rate might be measured as a function of substrate concentration at a certain fixed inhibitor concentration The measurements are then repeated at the next inhibitor concentration and so on Here the second independent variable x2 in this exam
18. concentrations of a solution The standard curve that is produced can then be used to allow in this example the concentrations present in an unknown solution to be determined by extrapolating values from the curve These processes can be performed using GraFit by the following procedure 1 Fit the data to an equation that describes the observed trend 2 Usethe Table Column Type Calculated Values x Values or Table Column Type Calculated Values y Values commands to read values from the fitted curve The sample data file Standard curve holds the analysis described below Choosing an Equation to Fit the Data In many circumstances the relationship between the x and y data values will be well defined In these cases the data will be fitted by linear or non linear regression in the usual manner However some calibration data show a clear trend of how y varies with x but are not necessarily defined by a well characterized equation 211 GraFit User s Guide 212 For example the data below show the absorbance reading given by varying concentrations of a compound and a straight line fit to the data In theory the plot of absorbance versus concentration should be linear but the data shown above describe a shallow curve While it might be of interest to find out why this effect occurs the only important consideration here is to allow readings to be taken from the calibration curve Quite clearly fitting
19. container target or source are discussed below Chapter 18 Embedding and Linking GraFit as an OLE container There are several places where it is possible to insert OLE items into GraFit GraFit Project Window The main GraFit project window can hold OLE objects which are inserted from the Clipboard using the Edit Paste or Edit Paste Special commands or created anew using the Edit Insert New Object command Objects inserted into the project window are always displayed as icons Activation of these objects will always launch their source application in a separate window Graph Window All graph windows can hold OLE objects which can be inserted from the Clipboard as usual or created anew using the Edit Insert New Object command Objects inserted in a graph window can be moved and sized as required In place editing is available by double clicking on the item The size of the object can be reset using the Edit Reset Original Size command Equation and Transformation Definition Windows These GraFit item windows hold textual comments which can incorporate embedded OLE objects See Chapters 9 and 10 for further details GraFit as an OLE source The contents of a GraFit workspace can be embedded or linked into other applications What is displayed is the contents of a particular graph window although the entire workspace information is copied To embed a GraFit graph into another application first activate the graph to us
20. curve are available 3 4 5 and 6 the illustration is created using order 3 Higher orders give smoother curves Spline curves smooth out variation in the data and do not necessarily pass through the data points These options control the appearance of the line that is drawn joining the points Modifying Graphs Once created graphs can be customized as required This involves selecting the appropriate part of the graph and invoking a specific property sheet by double clicking right clicking or choosing the Edit Properties command 122 Chapter Error AutoText entry not defined X Y Scatter Graphs Selectable Regions of a Graph The illustration below shows the various parts of a graph that can be selected For each a specific property sheet is available that controls the formatting options y axis scale Legend box Main graph region 6 O O pata set 1 m Legend text a a 4 Data curve roperties O prop 2 0 2 4 4 x Data x axis text x axis scale y axis text Main Graph Region The main graph region acts as the parent of the other selectable regions and is always visible the other parts of the graph can optionally be hidden Moving the main graph region will also move all the other child parts of the graph however the child regions can be moved individually to position them This ensures that the whole graph can be moved around the page while maintaining the relative positioning of the const
21. data table For example time values in nanoseconds could be entered into the data table as whole numbers of nanoseconds then a Scaling power of 9 applied Axis Text Regions Axis text properties are controlled in exactly the same way as normal text objects See Chapter 13 for further information Legend Box Region The legend box lists all the data sets currently present within the graph Legend Page Legend Box Properties HE Legend Fil Line Location Order Data set 2 Data set 3 Data set 4 Move Down m Layout n Number of columns 2 Cancel Apply Order The current arrangement of items within the legend box is displayed This order can be changed by selecting an entry and clicking the Move Up or Move Down buttons Layout This section controls the number of columns into which the data entries are arranged 132 Chapter Error AutoText entry not defined X Y Scatter Graphs O Data set 1 0 Data set 2 4 data entries with Number of columns set to 1 the default Lr Data set 3 setting E Data set 4 O Dataset 1 1 Data set 3 4 data entries with Number of I t to 2 Data setH2 Hm Data set 4 EAS RED Fill Page This page sets the fill settings for the legend box Line Page This page specifies the line used to draw the surround of the legend box Location Page This page controls the position of the le
22. default the graph is displayed with a background grid to help position the various items that form part of the graph This grid does not show during print preview and is not printed It can be turned off by the View Grid Lines command which toggles their display Element Outlines By default text elements and OLE objects are displayed with dotted and solid outlines respectively These do not show during print preview or printing and can be hidden by the View Show Outlines command which toggles their display Adding Drawing Objects 104 Various drawing objects can be added to the graph as controlled by the Draw menu or the Drawing toolbar k OOOG als Graph Wizard Text Polygon Ellipse Round Rectangle Rectangle Line Selection tool Selection Tool When the selection tool is selected the mouse pointer displays as an arrow Clicking on a drawing object will select it allowing moving or resizing Clicking on the graph background and dragging will allow selection of a number of items which can also be achieved by clicking on items while holding down the suirr key Chapter Error AutoText entry not defined Graph Item All Other Tools Use of all other drawing tools follows a simple procedure The tool is selected which results in the mouse cursor being shown as a cross Click the left mouse button where you wish the element to be drawn and drag until it is the correct size When the button is released the eleme
23. displays the second of the two phases in isolation Double Exponential with offset This equation is used when a double exponential process decays to a non zero limit value 224 Chapter Error AutoText entry not defined Equations Provided 10 Single Exponential N The equation for a single exponential decay is E e miere y A e i si The observed values decay with time t from an J Tse initial value Ag at t 0 to 0 at t o The rate A constant for the decay is k The half life for the e process T is given by log 2 Kk To display a linearized plot of this equation set the y axis to have a logarithmic scale Single Exponential with offset If the observed values do not decay to 0 but to some defined offset or background value the equation for a single exponential process is y 2 A e offset In this equation offset is the limit of the decay Triple Exponential For a triple exponential decay process the equation is kt k t k t y A e 7 Age Aog e gt Triple Exponential with offset This equation is used when a triple exponential process decays to a non zero limit value IC 50 These equations are used for analyzing radio immuno assays or Dose response curves IC50 0 100 This equation fits inhibition data to a 2 parameter equation where the lower data limit is O and the upper data limit is 100 i e the data are both background and range corrected 100
24. eee eee teeters eee e eed 94 Compiling the Transformation sss emen 94 Notepad Item cocococncncnononononananararararnnnnnnnnnnrornrnrnrncnnnnannnnnnnnnnnrarararnrnnananas 95 Uses of Notepads nic ee eee adela Der RE REUS 95 The Notepad Item Window ssssssssseeemmHH emen 95 Alternatives to the use of Notepad Items ssssssseen 95 Creating GraphS omcnoconororaconnononononorornrnrncncnnnnnnnnnnnnnnrararnrnrnnnnnnanrnrnrnrncanasa 97 How to Create a New Graph 2 0 0 eee eee 97 Available Graph Type Shrii prei iia e i a emen 97 X Y Scatter Graphic tee ere RE EEEE AEn terete 98 Column Ghart aid dans id 99 Bal CNE a di 100 HIST AM ii A a dat 100 KdrChhBicclupmm 103 Overview of Graph Items cece cece cece eee eee eee m eee emen 103 Controlling the Page View sss meme 104 Adding Drawing Objects sssssssssseseee mmm 104 Manipulating Drawing Objects sssssssseeememmmne 105 Selecting Objects citet oe p RR HE Diana TARA IHRER BE TREE ES 105 Moving Objects cep ee E Res e piene Cem x nc ebbe ext 105 Sizing Objeto E e e t OR REEF EA edhe 105 COMMON ACHODS oec a MANI Re E Ue e IDE ERN 107 Grouping Objects etit piti TR ERE RETE ERE RR RR SOR ERRER ES 108 Aligning Objects eee Ree bie iet tet p Ee nbn beu 108 Setting tlie Z Order oes eme e ER HEU RETE Eo E e das 108 Setting the Object Color a
25. enzyme For equation is Visus K S The Hill coefficient n equals 1 if standard kinetic behavior is followed but differs significantly from 1 if the enzyme kinetics are cooperative Allosteric kinetics Hill Linear plot This transformation is used to display the linearized Hill plot where v Vmax v is plotted versus S The slope is n Ky 222 Hale Hale Hale Hale 8 o 64 4 m gee a 7 m4 Y LI BzBn or T 31 T si o 2 4 6 8 tree 10 el m 0 4 m al m a 8 al m E E EBEN is 2 S E N 4 amp A o T T T T o 2 4 6 8 10 Fake S5 ceret I ry d e y 1 F i HreicGine E Som i 2 Sow V s o T T T 31 o 2 4 6 8 40 S amp cerei 2l see a e 7 Hil Gire a 2 o T T T o 2 4 6 Scri Chapter Error AutoText entry not defined Equations Provided Enzyme Kinetics This equation fits the basic Michaelis Menten enzyme kinetics equation V max 19 v gt K 18 In this equation the rate v varies with the concentration of substrate S depending upon the maximal rate Vmax and the Michaelis constant Km 10 Enzyme Kinetics Eadie Hofstee a al Exdebtiseeha This transformation draws the linear Eadie Hofstee s 9 plot for fitted enzyme kinetic data al 2 o T T T Oo 2 4
26. gatblank corresponding entry in the endif current column to be 23 3 greater Derivative The derivative column type fills the column with the calculated derivative order 0 to 5 of a selected source data column The contents of the source column are not affected by this operation Derivative Calculation 2l xi Source data column Derivative order fi y Savitzky Golay smoothing factors Window width E points must be odd number Polynomial order 4 v N B It is assumed that the source data are already sorted IF this is not the case you first need to sort them Calculation of derivatives for a set of data is performed after application of Savitzky Golay smoothing to the source data and so it is necessary to set the Savitzky Golay smoothing factors A full description of Savitzky Golay smoothing is found under the Smooth data processing type Chapter Error AutoText entry not defined Data Tables Series The series column type provides a convenient way of filling a column with a series of equally spaced values for example time series values Data Series 2 xi Start value i Increment jo Cancel Data points jo Smooth This fills the selected column with the result of applying a Savitzky Golay smoothing function to a source data column The contents of the source column are not affected by this operation Savitzky Golay Smoothing HES Source data column Smoothing factors
27. in the residuals can mean that the equation used was inappropriate to describe the data The differences between experimental and calculated values can be calculated using options available in the data table see Chapter 5 The data shown below have been fitted to a single exponential decay and to a double exponential decay and the residuals from each have been plotted Clearly the residuals from the double exponential fit are smaller and more randomly distributed and show that this fit is superior Errors Single Exponential Value Chapter 20 Theory Only the Y Data Contain Errors Only the dependent variable which by convention is always the y variable y is subject to error the other xj is known exactly This requirement should be satisfied by suitable experimental design the x data values often comprise time or concentration values which should be known with precision The Errors are Normally Distributed The errors in the y data values should follow a normal distribution function i e if sufficient replicates were taken they would have a Gaussian spread about the true y value Two common factors that invalidate this assumption are the presence of i systematic errors and i i outliers data points that are wildly inaccurate usually due to operator or machine failure Systematic errors invalidate any data analysis and should be removed by correct experimental design Outliers can be e
28. into ascending or descending order using the Table Sort Column s command after first selecting the columns that you wish to sort Sort Data Index column Cancel v amp mount 1 column s selected Order Ascending C Descending The Index column selection specifies the column on which the sort order is based In addition to this column any of the other columns can be included in the sort by checking the box to the left of the column name Data Table Appearance Colors and Fonts The colors used to display the items in the data table and the font that is used to draw the table are set using the Table Preferences command Number Format The manner in which numbers are formatted for display can be set on a column by column basis The Table Column Format command is used to control the displayed numerical precision This command applies to all columns that fall within the current selection 32 Chapter Error AutoText entry not defined Data Tables Column Format 121 xi Number Format 12 Decimal places Max digits Thousands separator Scientific format IV Use scientific format f Trailing zeros in fraction zd Save As Defaults Restore Defaults al Column Format dialog box or small values Show O s Cancel Specification Decimal places Max digits Thousands separator Scientific format Use scientific format for small v
29. is necessary to have the Adobe Acrobat Reader version 3 or later installed If you do not already have this software installed you can choose to do so by selecting Install Acrobat Reader Chapter Error AutoText entry not defined Installation Installation from Floppy Disks GraFit is shipped as standard on CD ROM and no floppy disk media are provided If you do not have a CD drive on your system it is possible to install GraFit by one of the following routes The program on 3 disks is available from Erithacus Software for a nominal charge that covers media costs plus postage and handling Please contact Erithacus Software for pricing and availability contact details are given in Chapter 1 It is possible to create a set of 3 installation disks if you have access to another computer with a CD drive You will need a number of blank formatted 3 disks To create this disk set double click on the Make Floppy Disk Set file located in the root directory of the GraFit CD Note GraFit on floppy disk only includes the main GraFit program file The CD ROM version also includes electronic documentation and tutorials that are too large for 312 media Uninstalling GraFit GraFit can be removed from your system by the following procedure 1 From the Windows Start menu launch the Control Panel application from the Settings sub menu Double click the Add Remove Programs icon Choose GraFit 4 to uninstall and click the
30. ligand concentration is not zero The equation for this is L Capy L Capo y background Kay L Kay L 2 Site with background Show background This transformation shows the background binding 229 GraFit User s Guide 2 Site with background Show Capacity 1 This transformation shows the capacity of the first binding site This value is on top of the background 2 Site with background Show Capacity total This transformation shows the total binding capacity for ligand on top of the background value 2 Site with background Show Curve 1 This transformation shows the binding curve for the first binding site in isolation 2 Site with background Show Curve 2 This transformation shows the binding curve for the second binding site in isolation Adair 2 sites The Adair equation describes the binding of ligands to multiple sites on a receptor when the dissociation constants for binding of successive ligands are to be individually defined from the data The equation for n sites is B Cap L K a 21 KaKo t L MK Kg K n l L Ka l Kg Kg L Kg Kg Kan In this equation B is the amount bound L the concentration of free ligand Cap the maximum capacity of the system to bind ligand and Kq Kaz etc the successive dissociation constants for ligand Adair 3 sites Use this equation for 3 binding sites Adair 4 sites Use this equation for 4 binding sites
31. lim A Multiplication m x Multiply m by x Division a b52 Divide a by b52 Exponentiation 23 N Calculate 23 E Assignment yum UA Assign y to be twice the value of x Logical Operators Symbol Operation Example gt Is greater than k 7 lt Is less than x value conl a Is greater than or equal to test gt 23 87 lt Is less than or equal to rate lt maxrate Is equal to i76 0 Note The symbol is used for both assignment and as a logical operator Which action is taken depends on the context Logical operators allow a comparison to be made The result of the comparison is either O if FALSE or 1 if TRUE To see how these operators work consider a graph of the form y x lt test 1 3 Here x is the x axis and test is a constant that has the value 2 This function is plotted below Chapter Error AutoText entry not defined Equation Item These comparisons can be used to introduce a discontinuity into a curve and though they will seldom be used in equations are extremely useful for displaying limits etc to annotate a graph An alternative method to obtain discontinuities is to usethe if then endif constructs described below Note To obtain a sharp discontinuity it is necessary to create the curve with Resolution set to High see page 120 Numbers can be entered directly into the equation definitions and can include exponents e g 27 87e 12 Functions A large number of functions
32. limited only by available memory The data are grouped into columns and the contents of one or more columns can be used for data fitting or graph plotting 24 Chapter Error AutoText entry not defined Data Tables Within a column each individual cell holds a data value that may be one of three different types Data Type Description Numbers Numbers are the most common data form that will be entered into GraFit They are used to plot x y scatter plots and for data fitting by regression analysis Very small or large numbers can be entered in exponential format for example 1e7 is equal to 10000000 and 1e 23 represents 10 23 Note The representation of numbers particularly the symbol used for the decimal point differs from country to country By default GraFit uses the country specific settings selected for your Windows installation using the Control Panel application Regional Settings However you can override these from the View Options dialog box Number Format page Text Text entries can be used for annotation and are also used to provide the text for the category axes of charts Text values are treated as missing data during data fitting Missing Data Experimental data often contain certain values that are not available perhaps because that particular experimental sample was the one that fell on the floor GraFit allows you to insert missing values by leaving the data entry blank All the graphing and data fitt
33. line from the Y Ticks page Y axis Tick settings X axis selector X Y graphs can have multiple x axes and the scale settings for each are set individually Set the x axis number from this box when first created only a single x axis will be available Axis extent By default the Entire graph size box is checked which ensures that the axis is drawn over the whole graph width Unchecking this box allows the axis to be drawn over just a portion of the graph which can be useful when multiple axes are present Enter the Start and End values as percentages of the whole graph width The Axis break symbol setting controls whether a break mark is drawn at the end of the axis This setting is used when drawing split axis scales see Chapter 15 for more information about multiple axes Y Ticks Page The Y Ticks page controls the tick settings on the y axis in the same way as the X Ticks page controls the tick settings on the x axis see page 125 Y Scale Page The Y Scale page controls the scale settings for the y axis in the same ways as the X Scale page controls scale settings on the x axis see page 127 Location Page This sets the location of the graph within the graph page 129 GraFit User s Guide Axis Scale Regions 130 The axis scale region controls the display and formatting of the scale numbers Scale Page Axis Scale Properties Scale Font Location Scientific format Power format Trailing
34. s Guide Parameters Column HE Sample Equation AAA A ee The column display differs from normal in that the name of the parameter remains displayed on the left with the value on the right When a new parameter value is entered from the keyboard the parameter name remains but the revised value is displayed in the table Constants Entry The Constants Entry column type allows the values of any constants associated with an equation to be entered in the data table This option works in the same way as the Parameters Entry option described above but shows the constants associated with the selected equation Calculated Values The column types under this submenu allow the x or y values to be calculated using the results from a data fitting item 46 Chapter Error AutoText entry not defined Data Tables x Values Use this column type to calculate theoretical x values corresponding to user entered y values according to the fitting model described in a selected workspace item Calculated X Values 21x Fitting results Fit Single bal Cancel Use hited values se mtialestimates Fit number Y data column y Interpolate between X limits From Ho Io 0 0000 110 0000 1 0000 80 0000 2 0000 60 0000 3 0000 45 0000 4 0000 35 0000 5 0000 28 0000 The fitting item that holds the results is chosen in the dialog box It is possible to use either the results fr
35. same data table as the raw data it is also possible to create the analysis in a separate data table Using separate data tables can be preferable if you wish to keep the raw data separate from any analysis Data Fitting The column types under this submenu allow the results from data fitting to be displayed in a column or entry of parameter constants values associated with an equation This lets the results be viewed but more importantly allows the values to be used for subsequent analyses For example the results of one set of data fitting might provide the source data for subsequent fits 43 GraFit User s Guide 44 Results This column type lists the results from data fitting Data Fitting Results 121 xi Fit Parameters Cancel Initial viRate Display Parameter value C Std error value v Value name E 0 0000 110 0000 Initial 108 6346 1 0000 80 0000 Rate 0 2876 EN 2 0000 60 0000 4 3 0000 45 0000 5 4 0000 35 0000 E 5 0000 28 0000 lt Es After the fit to be displayed is selected the parameters available are listed Some or all of these can be included by clicking in the check box to the left of the parameter name If more than one set of data were analyzed in the selected fit the results for each fit are given It is possible to display either the fitted parameter value or the fitted standard error value as chosen in the Display settings I
36. selected object that can be moved in any direction only in a horizontal direction or only in a vertical direction respectively The cursor is over a selected object that can be moved in any direction and the CTRL key is down This means that dragging the element s will result in creation of a copy of the selection Polygon objects only The cursor is over one of the lines of the polygon and the crRL key is down Under these circumstances left clicking will add an additional control point to the polygon Polygon objects only The cursor is over one of the control points of the polygon and the crRL key is down Under these circumstances left clicking will delete this control point from the polygon Text objects only The cursor is over the text object which is currently open for editing Grouping Objects Drawing objects can be grouped in order to ensure that they can be moved as one To group objects select those required and choose the Object Group command Objects that have been grouped can have their grouping removed using the Object Ungroup command Aligning Objects Selected objects can be aligned by selecting those required and choosing the appropriate Object Align command Objects are aligned relative to the last object that was selected Setting the Z Order Objects are drawn on the graph page in a defined order with the uppermost item overlaying ones beneath This z order can be changed for a selec
37. sssssssseeem m 7 Uninstalling Gra ita 2e eot t omes daba 7 GraFit BaSiCS ococococonnnnonononenanananarararnrnnnnnnnnnnrnnnrnrnrncnnnnnnnnnnnnnnnnnnrararararnnananas 9 Runtiing Grablt c acres tte vedere use pru rene de dunce vate dd da 9 The Grafit Workspace ei didas 10 GraFilIterms ordeo oe aedis ie Ve re eti eet erred aed abba 11 Managing tems z ue ied ib 11 Item Representation sss enemies 11 Editing the Item NaMe danari e aa eem memes 12 Changing the Item Co victor tdt 12 Item specific Commands ssssssssssseeeem memes 13 Printing the Item Contents sss nemen 13 Page Settihg Sirin ren riter A EYE e eta 14 Stock Items hentia tec etr vore ore corp OC RD ee ce an SFO ER RE 14 Grafit Templates Ae cde eee dde ada dy 15 ACCESSING Help eR ERR ELI 15 Working with Files ooomcocococncnonononononorncncncanannnnonnnannnnrararnrnennnnnnnnrnrnrnrncnnass 17 GraFit Workspace Files sss mme memes 17 Opening an Existing File ssessssssseen eene 17 Saving a Elle uu co rad 18 Loading and Saving Individual Items oooococococccccononnnnnnnncnncnnnnnnnnos 18 Creating a New File sss emnes 18 Importing Data Files sss memes 18 GraFit Template Files ienicnissi ire a rea r mmm memes 19 GraFit User s Guide vi Template Directories oocooocncciocicocococonononnnncnnncncnennno mmm 19 Data TableS oocococococnonononononananananarararnrnnn
38. than the smoothed ones Subset Data that are imported from other applications or obtained from an instrumental source such as a spectrometer often have more data values than are necessary to define the experimental curve For example the data obtained from a spectrometer may contain more than a thousand points fitting so many points would be extremely time consuming and would not necessarily give a better fitted value than if say thirty points spread over the data range were analyzed The Subset type fills the column with a subset of the data values present in one of the other columns and provides a convenient means of reducing the number of data values for analysis Create Column Subset 2 xi Source data column Column 3 Retain 1 point in every E Select the source data column and enter a value in the Retain 1 point in every field For example choosing to retain one data point in every 10 of a data set that has 200 data values would fill the column with point 1 11 21 giving 20 data points in this column The contents of the source data column are not affected by this operation Locking a Data Column 54 It is possible to lock a data column to prevent any further modifications being made to the values that are present To lock one or more columns e Move the data entry point to the column that you wish to lock or select a range of values encompassing the columns that you wish to lock e Choose the T
39. that give different weighting to one or more data values A full description of weighting is found in Chapter 20 Linear Regression of Transformed Data A familiar method of analyzing non linear data graphically is to rearrange the data to a linear form find the best line through the points and so derive the parameter values This is illustrated in the following example Enzyme kinetic data are described by a hyperbolic equation of the form _ Ax B x This can be linearized by plotting 1 y versus 1 x as 1 1B 1 eee A y xA A The ease of linear regression analysis makes it tempting to use in order to fit data that have been rearranged in this way However the results that are obtained are not statistically optimal This is because the regression calculations make assumptions about the error distribution that are not usually valid after transformation The distortion of the experimental errors by the above transformation is easily demonstrated in the following graphs 179 GraFit User s Guide IU F TU 8 O 2 4 6 8 10 Substrate T T T T I T 1 1 ll 1 ll 1 l 1 j O 1 2 3 4 5 1 Substrate Enzyme kinetics plot The error is present only in the Rate y axis measurement Errors are simple i e all data points have the same error Double reciprocal Lineweaver Burk plot of the data above Note the large distortion of the error bars resulting from this plot Here the error invo
40. the Non linear Fit data layout type x 2 from y header x vi iy See Chapter 6 for more details about the Non linear Fit window It is also possible to have a separate set of x data for each y data corresponding to the Non linear Fit data layout type 2 from y header x i y rzi ye Case 2 The equation has several independent variables When an equation has several independent variables it is necessary to have the x X2 Xn y data in separate columns This corresponds to the Non linear Fit data layout type x n from table stri In order to distinguish the various data types it is essential that all the x data columns are set to x n Data with the n value representing the order of the x variable found in the equation definition See Chapter 5 for further details on column types 183 GraFit User s Guide Data Fitting Apart from the considerations above fitting data that have multiple independent variables is no different from fitting standard equations A sample set of data that has been fitted in this way can be found in the Examples data subdirectory and is named Multiple rate Plotting Results from Multiple Regression 184 The data that form the basis for multiple regression have three or more dimensions To represent such data would strictly speaking require a multidimensional plot which is not available However the usual representation for such data is to plot multiple curves represen
41. the data to a straight line is not suitable Under these circumstances the best recourse is to fit the data to an arbitrary equation that allows a smooth curve to be drawn through the data As there is no theoretical basis for the equation any calculated parameter values will have no physical significance The choice of equation will depend upon the shape of the data and it is possible that more that one equation would prove suitable In the case shown above it might be appropriate to use a polynomial or any equation that can produce a gentle curve Below is shown the results of fitting the data to a second order polynomial y 2 a bx 4 cx using a Linear Fit item and to a first order rate equation by non linear regression The latter equation has no possible theoretical justification but has a suitable mathematical form to allow a smooth curve to run through the data Chapter 21 Worked Data Fitting Examples Reading Values from the Fitted Curve Either of the fitted curves shown above will allow the concentration values that correspond to a series of measured absorbance values to be read from the curve This is performed by entering the unknown absorbance values into a data column then generated the calculated values in a separate column using the Table Column Type Calculated Values x Values command Calculated X Values 12 1x Fitting results 2nd order po ly nomial se hited vales se mitia est
42. zeros in fraction m Number format r Test Decimal places zi Alignment Right y Max digits 10 Thousands separator Omit O s bs Orientation E Format string m Values Scaling power jo E al Cancel Number format These settings determine the way that the numbers are displayed Setting Description Decimal places Max digits Thousands separator Scientific format Enter the number of decimal places to display Note that trailing zeros will be removed if the Trailing zeros in fraction setting is Omit 0 s Enter the maximum number of digits to be used The displayed values will be rounded to ensure that only the requested precision is displayed Check this option to separate groups of digits by a separator Typically digits are grouped into threes and separated by a comma However the grouping and the separator used depend on values set by in the View Options command Number Format pane available from the main GraFit workspace window Check this option to display numbers using scientific format For example 1 234e 003 rather than 1234 Chapter Error AutoText entry not defined X Y Scatter Graphs Setting Description Power format Check this option to display numbers using a power representation For example 1 234 x 10 rather than 1234 Trailing zeros This controls the way that trailing zeros are displayed in a in fraction fr
43. 171 172 173 Color toolbar 109 Column charts 97 99 157 164 column constant 51 Column types A B 39 A B 39 201 A B 39 A B 39 A B 36 Calculated Function 50 209 Column Summary 40 Constants Entry 46 Derivative 52 Difference 50 199 F Test 41 General 37 Information 45 Mean 39 No Data Points 40 Parameter Entry 45 Results 44 209 Series 53 Smooth 53 Standard Deviation 40 247 GraFit User s Guide Standard Error of the Mean 40 Subset 54 x Data 37 x Values 47 211 213 x n Data 37 y Data 38 y Data with Associated Value 38 215 y Values 49 211 Column Types 35 Columns Copying and pasting 28 Deleting 31 Selecting 28 Comment statements 85 Constants 59 79 144 Context Help 15 Cooperative binding 231 CSV format 35 Cursor shapes 24 107 Cut and paste 169 Data Association 152 Copying 28 Deleting 30 Export 35 Fitting several data sets simultaneously 213 Import 34 Import Export 34 Inserting values 31 Layout 57 71 Missing 25 Numbers 25 Overlaying 147 Pasting 28 Rescaling 50 Selecting 27 Smoothing 53 Sorting 32 Text 25 Types 24 Data entry position 26 248 Data fitting Basics 175 Multiple Non linear Regression 182 Data function 51 Data table 23 Appearance 32 Locking columns 54 Degrees of freedom 185 Denaturation Curves 216 Derivative 52 DIF format 35 Difference calculation 36 Directories 17 1
44. 6 RasfSibstrat 15 5 Enzyme Kinetics Lineweaver Burk p AS This transformation draws the linear Lineweaver Burk AS plot for fitted enzyme kinetic data o 4 Or T T T 1 o 2 4 6 VERE IS Enzyme Kinetics show Km Displays the Michaelis constant Km For best results set the curve resolution to High when using this transformation Enzyme Kinetics show Vmax Displays the limiting rate Vaz Koa Epl Enzyme Kinetics show Vmax over Km Displays the linear portion at the beginning of the graph where Substrate lt lt Km 223 GraFit User s Guide Kinetics contaminating S Occasionally the reagents etc used in an enzyme assay will contain traces of contaminating substrate Therefore the rate will vary with added substrate S as Vik S add S con p K a S41 S con In this equation S on is the concentration of contaminating substrate Exponential This page contains equations for calculating the rate constants of various exponential decay processes 10 Double Exponential a If two decay processes occur simultaneously the E e Dey observed values decay with time following the double E exponential decay equation 2 k t k t 7 Y A e Age O gt Oo 1 2 3 5 Here the two processes have separate A and k values Double Exponential phase 1 This displays the first of the two phases in isolation Double Exponential phase 2 This
45. 63 72 Print Preview command 13 63 67 68 72 197 Save As command 19 Save command 18 Store Stock Item command 14 18 File Menu Open command 196 Files Index Creating new 18 Importing Data 18 Opening 17 Saving 18 Template 19 Filters Import Export 19 Fitting criteria 61 62 Font selection 65 67 Font settings 73 95 113 114 Footers 14 Formatting numbers 32 64 130 Functions 83 G Global analysis 181 GraFit Installing 6 Running 9 Technical Support 3 Templates 15 Uninstalling 7 GraFit Items 11 GraFit Workspace 10 17 Graph Axis associations 145 X ticks 125 Graph menu Add Data command 144 199 New Graph command 97 Graph types 97 Graphs Z ordering 108 Graphs 103 Aligning objects 108 Creating 97 Duplicating objects 105 Grouping objects 108 Selecting objects 105 Sizing objects 105 Text objects 106 Graphs Colors 109 249 GraFit User s Guide Graphs Text 109 Graphs Default text properties 110 Graphs Fill properties 111 Graphs Line properties 111 Graphs Rotation properties 112 Graphs Object locations 112 Graphs Arrow properties 113 Graphs Font properties 113 Graphs Legend 115 Graphs Error plots 116 Graphs Transformations 117 Graphs Tick styles 118 Graphs Data point styles 118 Graphs Plotting equations 119 Graphs Curve resolution 121 Graphs Join styles 121 Graphs Selectable regi
46. 9 Dose response Curves 225 Double exponential decay 224 Drag and drop 11 Draw menu 104 Results Listing command 64 73 198 Edit menu 11 Clear command 11 30 31 Copy command 28 29 35 170 171 173 Edit Current Cell command 24 Font command 76 Hide Object command 124 152 Insert New Object command 76 173 Insert Object command 172 Paste command 28 29 34 170 171 172 173 Paste From command 18 34 Paste Special command 172 173 Properties command 109 110 122 151 152 153 Rename command 12 Select All command 173 Editing item names 12 Embedding objects 169 Enzyme Inhibition Competitive 221 Mixed 221 Non competitive 222 Enzyme kinetics 239 Enzyme Kinetics Ping Pong 220 Ternary Complex 220 Equation definition 75 80 81 Equation definition syntax 78 Equation menu Compile command 75 88 Equations 219 Compiling 88 Defining 203 Error Messages 88 Functions 83 Multi line Definitions 84 Multiple Regression 182 Temporary variables 84 Erithacus Software Contacting 2 Error bars 139 Error Messages 88 94 Errors 179 185 186 187 188 190 Estimates Interactive 60 Estimatrix 49 59 60 61 196 Exponential decay 225 243 F F test 41 193 File menu 11 Add Stock Item command 14 18 196 199 219 Import Data command 18 34 New command 15 19 20 237 Open command 17 203 Page Setup command 14 104 Print command 13
47. A T Oo 2 4 6 8 10 1st order show limit This displays the limiting value A 1st order show initial The initial part of the full curve approximately the first 10 is linear with the slope being k A This transformation shows the initial linear portion 10 1st order offset ah RA If the observed y value has a background or offset at e ans cal time t 0 due to experimental constraints for E Sel limi example a starting absorbance may not be zero the Edgard equation becomes AAA A A 1 e offset Aou oe AE Tine 1st order offset decay curve This display equation plots the rate equation as an exponential decay Use it with Decay Curve Offset transformed data 235 GraFit User s Guide 1st order offset show limit This displays the limiting value for the equation containing an offset 1st order offset show offset Use this transformation to show the offset value 1st order rate versus S To find enzyme kinetics parameters it is often necessary to carry out a series of first order rate reactions at different substrate concentrations The rate constant versus S is then analyzed using the Michaelis Menten equation Using this 3D equation allows these procedures to be combined giving A sadi e em y 1st order rate versus S offset Amount This equation is the same as that above but also includes an unknown backgroun
48. Chapter 20 Check the Robust box to add robust weighting to the fit Data Table The data to be fitted must reside in a separate data table item within the GraFit workspace Select the table that holds the data from this drop down list 56 Data Layout Chapter Error AutoText entry not defined Non linear Fit Item The data layout specifies how the data are arranged for data fitting The default layout as shown in the figure above is that the x and y data columns are to be selected individually This is used to fit a single x y data set It is also possible to specify that multiple data sets are present which will result in several sets of results being generated The available options for a standard equation having a single independent variable are given below Layout Lx Iu 1 s ins ye Meaning A single data set is present and the columns holding the x and y data values are specified individually from the X data column and Y data column entries The x and y data columns do not need to be in any particular order within the data table Multiple data sets are present although all data sets have common x data values The x and y data columns are consecutive in the data table The location of the x column is set from the X data column entry the location of the final y column is set from the Last Y data column entry The number of data sets present is determined automatically Multiple data sets are present and the
49. EE IE E E E Itang Ir Free Parameter Value Std Error Capacity 98 1190 0 4356 Plot Kd value 18694 0 2628 zl 421 NONI Screen Size To ensure compatibility with the majority of systems the standard templates are formatted so that they display correctly when GraFit is run as a maximized window at a screen resolution of 800 x 600 Using Your Own Templates In general we recommend that you build your own templates for common data fitting situations The advantages of building your own templates are summarized as follows e Specific data analyses can be created e Graphs can incorporate user specific features such as corporate logos or the name of the user 238 Chapter Error AutoText entry not defined Standard Templates e Graphs can be customized to use specific fonts and or styles Users with color printers may wish to incorporate color into their graphs those with monochrome printers will probably wish to create graphs in black and white e Users with high resolution displays can make best use of the available screen resolution when laying out the various windows Description of the Standard Templates Enzyme Kinetics This template analyzes enzyme kinetic data to the basic Michaelis Menten enzyme kinetics equation V S max K S A graph is made of the fitted data together with an inset Lineweaver Burk plot as shown below
50. For example copying a graph might place an image of the graph on the Clipboard Pasting would then insert this picture as distinct from inserting the information required to draw the graph Source Application arget Applicatio Standard cut and paste inserts an image representing the source object into the target application This image is simply a picture and contains no information about the underlying data in the source application 169 GraFit User s Guide Embedded Objects Embedded objects hold both a display representation and the underlying data A copy of the current state of the source object is created and is passed to the target application This means that subsequent changes within the source application do not affect the newly pasted object In turn although the embedded object can be edited any changes are not reflected in the original source document Because a complete copy of the source data is placed in the target application files containing embedded objects can be large Source Application a Target Application MEE Embedding places a copy of the internal data into the target application as well as an image representing the source Linked Objects Linked objects also copy a representation of the original data but do not copy the data itself to the target Instead the target application maintains a link to the origina
51. GraFit User s Guide 3 GraFit Enzyme Kinetics olx Fie Edit View Add Draw Object Text Graph Window Help Oe 64 a oc sl jes MS g h NDOOG als 1 5 5 Aral y fi2 B Z U i E S Substrate Rate a3 19 1 0000 3 0000 a enome 2 0000 4 0000 7 3 0000 5 0000 E 00 5 000 z ue 4 0000 6 0000 E Graph 6 3000 6 0000 1 Substrate _ T T T T T 7 0000 0 2 E 6 Substrate Lineweaver Burk Parameter Value Std Error Vmax 9 5250 Km 2 5114 o Norrlinear Fit i3 Notes 1 Enter substrate rate data into the data table left 2 Watch BA moOBOBEBEBGNEOOONCDOOOOOOGOOSGEUSUSNHNE Ote Ready Erithacus Software GraFit User s Guide Version 4 0 O Erithacus Software Limited 1989 1998 Program and Manual Designed and Written by Robin J Leatherbarrow GraFit User s Guide Copyright Copyright O Erithacus Software Limited 1989 1998 All rights reserved Portions of the software described in this document copyright O Microsoft Corporation 1985 1998 All rights reserved Information in this document is subject to change without notice and does not represent a commitment on the part of Erithacus Software Limited The software is furnished under a license agreement and the software may be used or copied only in accordance with the terms of the agreement The purchaser may make one copy of the software for backup purposes No part of this publication may be rep
52. J 1981 Methods in Enymology 74 481 508 226 Chapter Error AutoText entry not defined Equations Provided Note Estimating starting values is difficult when there are 4 unknown parameters The method used within this definition works most of the time but can give occasional poor fits Under such circumstances enter initial estimates explicitly in the non linear fit window The curve displays inhibition with increasing dose It is also possible to use the same equation for increasing response with dose In this case the y range is a negative value and the Background is the maximum response IC50 full 4 param show background This displays the calculated background value IC50 full 4 param show IC50 This displays the calculated background value IC50 full 4 param show limit This displays the limiting value of the data Ligand Binding This page contains various equations describing the binding of ligands to surfaces receptors enzymes etc 10 1 Site a This is the simplest form of binding equation The e pS equation is Sal vane 1f ShowGpndty _ L Cap z Bond Ky L o T T T T Oo 2 4 6 8 10 Here y is either the amount bound or is some factor Fee proportional to it e g radioactivity absorbance etc or the number of moles bound per mole of receptor The capacity for binding ligand Cap is either an amount bound in terms of moles of ligand or a stoichi
53. Kg is A A Wimax PAJIB 4 6 a 10 K Ky Kp A K B A B is 3 7 7 Ternary Lineweaver Burk Eom og y Generates a Lineweaver Burk plot for the fitted data 2 2 E Pi d P d Le 14 JP m B o caba T T T o 4 6 3 10 VA 220 Chapter Error AutoText entry not defined Equations Provided Enzyme Inhibition Competitive Inhibition In this multidimensional equation rate is monitored versus substrate and inhibitor The equation for competitive inhibition is SITE o Kon S K 1 I K m Competitive Eadie Hofstee Use this to display the Eadie Hofstee plot Hale Competitive Lineweaver Burk Displays the Lineweaver Burk plot Mixed Inhibition In this most general inhibition equation rate is monitored versus substrate and inhibitor using the equation Vinax LS af p t zs K K No inhibition The normal Michaelis Menten enzyme kinetics equation 221 GraFit User s Guide Non competitive Inhibition In this multidimensional equation rate is monitored versus substrate and inhibitor The equation for non competitive inhibition is db 1 1 K K S Va 5 Non competitive Eadie Hofstee Use this to display the Eadie Hofstee plot Non competitive Lineweaver Burk Displays the Lineweaver Burk plot Enzyme Kinetics Allosteric kinetics Hill The Hill equation describes enzyme kinetics for an allosteric
54. Mask curve option 119 Mean 39 193 Michaelis Menten Equation 223 Multiple axes 147 156 Multiple Regression 208 Advantages 182 Disadvantages 182 Plotting results 184 Uses 181 Multiple x variables 57 79 NMR Titration Curve 195 Non linear fitting 55 Non linear regression 190 Non linear regression Basics 178 Notepad item 95 Number formatting 32 64 72 130 O Object embedding and linking 169 Object menu Align command 108 Bring to Front command 108 Group command 108 Move Back command 109 Move Forward command 108 Send to Back command 108 Ungroup command 108 OLE objects 77 96 103 104 169 Outliers 187 191 251 GraFit User s Guide P Page Settings 14 Paired Data Sets 213 Parameters 79 PDF files 6 Ping Pong Kinetics 220 pKa determination 232 Polynomial regression Basics 178 Print preview 13 Printer Changing 14 Printing 13 Random numbers 51 Rate equations 235 Reduced chi squared 185 Regression analysis 185 Assumptions 186 Basics 177 Linear 187 Non linear 190 Requirements see Hardware Requirements Residual plots 186 192 Residuals 193 199 Residuals plot 92 Results 63 72 Robust weighting 56 187 190 202 Rotation of objects 112 row constant 51 Rows Selecting 28 S Savitzky Golay smoothing 52 53 Scaling power 131 Screen resolution 238 252 SetBlank function 51 52 Special menu Options command 33
55. Mask curves Check this option to ensure that any curves on the graph are not drawn immediately adjacent to the data points Enter Curve Parameters Equation items only XY Graph Wizard Enter Curve Parameters 2 xi r Parameters C Read from table Golan y Direct entry Parameter Value A PO When plotting theoretical curves this page allows the parameter values that describe the curve to be entered Read from table When this option is selected the parameter values are read from the data table item and column that are selected Any column in the data table can be selected 119 GraFit User s Guide but it is most convenient to use a column that has been specifically created to facilitate parameter entry see page 45 Direct Entry When this option is selected the parameter values are entered directly into the grid Enter Curve Constants Equation items only If the equation definition uses constants their values are entered into this page The operation of this page is analogous to that of the Enter Curve Parameters page described above Select Fitting Curve Style 120 Fitting and equation items only XY Graph Wizard Select Fitting Curve Style 21x m Fitting curve X limits check box for autolimit Width Iv Start p Style Line X M End E Color ml Black Resolution Medium h lt Back Cancel Fitting curve Choose
56. Spline curves 122 Split axes 148 Splitter box 23 Standard Curve 211 Standard deviation 40 193 Standard Error of the Mean 40 Status Bar 55 69 75 90 Stock Items 14 Symbol syntax 78 Symbols font 245 Syntax Symbol names 78 T Table menu Column Format command 26 32 Column Properties command 36 Column Width command 24 Delete command 31 Insert command 31 Lock Column command 54 Preferences command 32 36 Row Height command 24 Size Column to Fit command 24 Sort Column s command 32 Technical Support See GraFit Technical Support Template files 17 19 Templates 15 20 237 Standard 237 Temporary variables 84 Text settings 131 Theory 185 Transformation menu Compile command 89 94 Transformations 89 117 137 138 Compiling 94 Curves 92 Data points 91 Defining 93 Error Messages 94 U Uninstalling GraFit 7 V ValidData function 51 52 View menu Grid Lines command 104 Options command 17 18 19 64 130 Show Outlines command 104 Zoom command 34 Visibility Graph objects 124 Index Ww Weighting 56 70 179 187 188 189 Checking 199 Determining weighting type 192 Explicit 204 Window menu Icon command 12 X X Variables 78 X Y Scatter Graph 98 115 XY graph wizard 115 134 135 136 144 253
57. Window width E points must be odd number Polynomial order 4 v N B It is assumed that the source data are already sorted IF this is not the case you first need to sort them Savitzky Golay smoothing is probably the most effective means of smoothing a set of data in such a way that noise is removed without too much loss of resolution as happens with simple moving window averaging In this smoothing procedure the underlying function is approximated by a polynomial fit applied to a window of points around each data value The degree of smoothing is therefore controlled by the window width and by the order of the polynomial applied The lower the order of the polynomial or the greater the window width the smoother the result but at the expensive of losing resolution For a polynomial order of 4 best results are obtained when the window width is between 1 and 2 times the full width at half of maximum of the desired features in the data An excellent discussion of the effects of various smoothing parameters can be found in Press W H Teukolsky S A Vetterling W T amp Flannery B P 1992 Numerical Recipes in C Cambridge University Press 53 GraFit User s Guide Warning Smoothing of data should always be undertaken with care Although smoothing can improve the appearance of a set of data this improvement is cosmetic only If you are fitting data it is almost always preferable to fit to the raw data values rather
58. a 125 X Ticks Pa je cetur t Rt ER ELE MARRE E RERUM Ra aasa 125 KS Cale Page ete doin te eee rade ie nl dte enit n 127 Y Ticks Page t PME EE ude LEE ORE ete eot A 129 X Scale Page oce eoe e e cerei toe depen tuts 129 Location Page ten e b Reid 129 Axis Scale REGIONS 2 t P e Ehe eu FR ERROR nap EEN 130 Seale Page tui tnit seti no Eti I E ERE ERR EE egens 130 AXIS Text Reglons te E RR ERE Arata 132 l 6gend Box Region ee Rt oreet Mid E ed 132 Legend Page x ooa t eee thee O a 132 Eill PAGE x tren I eee A pE Mis A 133 Lirie Page add Ue RM ear rine 133 Location Page oe lide v e ers 133 Data Curve Properties nn ieaie a A mme 134 Data Points Page picada A 134 Join Points Pagers ine a ti DAR ERE RE Er 135 Fitted Curve Page ore e ec ple E ORE REN RAN 136 Data SOURCE PAE escocia te RE ERE ERRORES TER Arana 137 Data Source Page sette teer rese ete a nian ba pre ua n 138 Error Bars Page tt rU reeves ERR r 139 Axis Association Page oer oe as 142 Equation Page dept en RO ERE RE ERR Eh 143 ix GraFit User s Guide Parameters Page rs ral CREE RNV ES 143 Constants Page iustis A PE SERER ARAS ERA NR ret TR Eo aaa alea enters 144 Legend Text Regiotis mitico iO HX ERR UE E LER HER RR ERR NER HEU RE RR 144 Adding Extra Data to the Graph ssssssssssseeeee memes 144 Set Axis Associations Page sss eene 145 Using Multiple Graph Axes oomonocorocococnonononononororacanannnannnnan
59. able Lock Column command or click the al button on the toolbar Repeat these actions to unlock the column s CHAPTER 6 Non linear Fit Item Overview of Non linear Fitting A non linear fit item is used to control data fitting by non linear regression This item specifies the data source and equation to use and also presents the results of the data fitting The item is created from the main GraFit window using the Add Non linear Fit command The non linear fit window itself contains a tabbed dialog box with several panes that are used to specify how the fit is calculated Each of these panes is discussed below Data fitting involves making appropriate selections in the Settings pane and possibly one or more of the other panes as described below then selecting the Calculate Fit Data command After fitting the data the results can viewed from the Results pane Differences from Linear Fitting Non linear regression allows much more general equations to be used for analyzing data The biggest practical difference however is that non linear regression requires starting estimates of the unknown parameter values linear regression needs no such estimates Status Bar Indicators When a fitting item is selected the status bar shows the current fitting status indicating whether the item is Fitted or Not Fitted In addition the status bar shows when a calculation is in progress Whenever any calculation is being processed the cal
60. action Some examples of different formatting are shown below all have Decimal places set to 4 and Max digits set to 10 Effect Settings Effect Settings 0 01 1e 2 0 005 Omit 0 s 56 3 Omit 0 s scientific format 0 0 0 0100 10 0 0050 Show 0 s 5x 10 Omit 0 s power format 0 0000 0 Text These settings control the text display Setting Description Alignment The scale text can be aligned to the left right or centrally Orientation Select the orientation of the text The following orientations are available ol 21 4 Format string Check this option to embed the numeric value within a text string The number is substituted for any occurrences of 1 within the entered text Values The Scaling power setting allows a scaling factor to be applied to the numbers Before display the scale numbers are multiplied by 10 raised to the power of the value entered The power must be a whole number and may be positive or negative For example an entry of 4 would cause the value of 40 000 to be displayed as 4 An entry of 3 would cause the value 0 002 to be displayed as 2 0 002 x 10 2 2 A scaling power of 0 results in the actual value being displayed 10 1 Scaling power entries are very useful when dealing with large or small data values By scaling the displayed numbers it is possible to produce graphs that are correctly 131 GraFit User s Guide scaled but to enter conventionally ranged values into the
61. additional weighting that is applied to a data set It acts to reject data points that are very much in error and so removes the occasional rogue data point or outlier that may be present in a data set A complete description of the background to robust weighting can be found in Chapter 20 To show the detrimental effects of outliers on curve fitting and see how robust weighting eliminates these effects an analysis has been created which can be found in the file Robust weighting The data being have a linear relationship but are fitted using a linear equation defined as a non linear equation in order to make use of the robust weighting option that is available for non linear fitting Note It is not possible to use a linear fitting item when using robust weighting The graph obtained by plotting the data with the best fit lines obtained with and without robust weighting is shown below Chapter 21 Worked Data Fitting Examples As is apparent without robust weighting selected the presence of the outlier biases the fit considerably This is because the large sum of squares residual from this point has a disproportionate effect on the regression analysis However using robust weighting eliminates the outlier and the regression line is drawn through the majority of the data points Defining a New Equation 1 There are very few examples found in the literature where both raw data and calculated values are included However
62. aeree Deer rm SE DRE E 167 Embedding and Linking leeeeeeeeeie eese einen nena nana nnn nnn 169 What is Embedding and Linking ssssssssse emm 169 Original Cut and Paste Model sssssssseeems 169 Embedded Objects sssssssssssssseeee emen 170 Linked Objects ia otto rt ee bares 170 Using Embedding and Linking ssssnm nano tena ee teen ed 170 Comparison of Data Transfer TypOS oocccccncnicoconncnconnnnnnnnnnancncnnnos 171 Embedding and Linking without using the Clipboard 172 Embedding and Linking with GraFit ssssssssennm eee es 172 GraFit as an OLE container sss 173 GraFit s an OLE SO FC iiini ite te p RR EE EA ERROR REA HEN 173 Contents Data Fitting Basics cococococnnnnnnnnnonenananannarararnrnnnnnnnnnnnnrnrnrnrncnnnnanannnnnnnanens 175 When Is Data Fitting Appropriate ssssssssesesem mH 175 TYPES Of Data eei Utd A eee 175 Regression Analysis 5 v arate edu p iE e ees vod vae eset esa 177 Practical Considerations cece eee eee eee mme 177 Types of Regression Analysis ccececeee eee e seen ee eee nmm 178 Linear Regression cis ee bene ee ba Sets 178 Polynomial Regression iena ra ee eee eee eee eee ence memes 178 Non linear Regression sessssssssse memes 178 Additional Considerations for Non linear Regression 178 Weighting Scheme
63. alues Trailing zeros in fraction Save As Defaults Restore Defaults Meaning Enter the number of decimal places to be displayed for numbers Note To ensure that all decimal places are displayed set Trailing zeros in fraction to Show 0 s Enter the maximum number of digits to use when displaying numbers Check this box to include a grouping separator The symbol used for this separator and the number of digits in the group are set for the View Options command on the main GraFit window Check this box to display the values using scientific format e g 2 435e003 instead of 2435 000 Check this box to ensure that small values which would otherwise be displayed as 0 0000 are shown in scientific format e g 2 0987e 008 Chooses the way that trailing zeros are displayed in the formatted numbers It is possible to show the 0 characters to omit them or to replace them with spaces Stores the current settings as the default for future GraFit sessions Restores the current GraFit formatting defaults to the selected columns 33 GraFit User s Guide Magnification The magnification of the data table text can be adjusted to allow more or less values to be visible Magnification is controlled by the View Zoom command or by using the zoom control on the Standard toolbar D c E SQ tael wo o x Zoom control Changing the magnification and altering the font size Table Preferences command
64. ameters Constants Definition Description Michaelis Menten Equation Fits data to the Michaelis Menten equation where the rate is plotted as a function of the concentration of substrate ks Eo LS v O The General pane of a 5 the Equation item Initial estimates are provilied by use of linear fitting using the Scatchard rearrangement The description is optional but adding a text description of your equation definitions is strongly recommended As illustrated in the figure above the descriptive text allows rich formatting options with multiple font types styles sizes and colors allowed It is also possible as shown above to include any OLE object in the text In this particular example a Microsoft Equation 3 0 object has been embedded within the text Note The Microsoft Equation editor which comes with Microsoft Word is not provided with GraFit Changing Font Styles To alter the style of a selected region of text use the Edit Font command Inserting OLE Objects To insert an OLE object into the description text position the cursor where you wish the object to be placed and select the Edit Insert New Object command 76 Chapter Error AutoText entry not defined Equation Item Obie Type Create New Microsoft Equation 3 0 Microsoft Excel Chart Microsoft Excel Worksheet Microsoft Graph 97 Chart Microsoft Map Microsoft Photo E ditor 3 0 Photo Microsoft Photo Editor 3 0 Scan T Display As Ico
65. ao leet 179 Linear Regression of Transformed Data ssssssssseeee 179 Information Obtained from Data Fitting sssssssssemH 180 Multiple Regression eie e x ers Ath dete e Oe cene 181 Uses for Multiple Regression sss 181 Advantages of Multiple Regression sssssssn m 182 Disadvantages of Multiple Regression ooocococccccocnnnnnnnoncncnccnnnnnano 182 Defining Equations neto n eR a D De dia e nh eee te 182 Fitting Data by Multiple Non linear Regression sss 182 Data Fittirig pieces te eo t CELER EHE saree HS ERLEREETRRTRRORURATESERTERR RIA 184 Plotting Results from Multiple Regression seeseseese 184 Ta E III CIE 185 Regression Analysis revertere rede eerte LA aetate i E 185 Assumptions in Regression Analysis ooooococococccoconnnnnnnnnncncnanononorarnnnnnnns 186 l inear Regressloncz s ose ede Ert ut Pe et ceeded Cs 187 Weighting deep EUROS ERGEBNIS 188 Weighting Types 5i iiie ti ita RE POR RES 189 Non linear Regression cece eee cece e eee emnes eres 190 Standard Errors of the Calculated Parameters ssssssss 190 Robust Weighting ici toe ere aer resp oce a e rere eee 190 Determining the Most Appropriate Weighting oocccccccococnnnnnnnnnnncnnnnnnano 192 Plot of Residual Errors ccceeceeeee eee eee nett eens 193 Testing Goodness of Fit F Te St eee ee cece memes 193 Mean and Standard Deviation
66. ar Pe Druid 79 DefihitlonPaliez tira cioe teft ced one tine Pia QUE ama Pri a adi 80 Equation Definition Syntax oococcccccococococncononnnnnnnnnncnnnnronornrnrnnnnnnn 81 Multi line Equation Definitions ssssssssee mmm 84 Use of Temporary Variables ssssssssssse mmm 84 Gonditional Statemients cie edet ee t t E OG RE EE RE REA 84 Comtnents ucc da DOCERE EC ELA DHT EP C EA e rd 85 LOOPING Statements 3 core e tt ete RERO E DH ines pil 85 vii GraFit User s Guide Goto Statement m iones resa piae lebe ee pe Re HR ENA 85 Estimates Parier SiG dd cia 86 The Need for Starting Estimates sesssssssemm 86 Method Used to Obtain Initial Estimates ssssseeeeee 86 The zEstimates Pane eie at te De et ELE ede s 87 Compiling the Equation ccccceee cece eee e eee Hmmm 88 Transformation Item oooncnononononononanacanananannonananannnararararnrnnanananrnrnrnrnrncanasa 89 Overview of Transformation DefinitiONS oooococccnccicicocococonononnnnnnnnnnnnnns 89 Status Bar Indicators uie p RE TREE RU 90 GeneraliParne teen He 90 Data Points Pane tee RERO RIED EE UHR ERRORI ERAT iaa ted 91 Data Transformation Definitions ssssssseen eens 91 Axis Name Settings nere rr ete esee Ree erm peter e nd 92 CURVE PAN Gi nc sss IA tE LAS ates 92 Transformed Curve Definition cccece eee e eee eee eee mmm 93 Fonts and Indents Panes ccecece
67. are As a rough guide the standard error should not be greater than about 1096 of the parameter value if you are to have confidence in the calculated parameters High standard errors will be obtained if the data are of poor quality or if the data do not allow accurate estimation of one or more of the parameters Robust Weighting 190 One of the assumptions of regression analysis is that all the data points have a normal error distribution However a common feature of actual experimental data is the presence of one or two observations that are well outside the error range of the other observations The stray data points are usually due to mistakes by the experimentalist incorrect addition of reagents inaccurate keying in of data etc and are termed outliers If these points are included in the analysis they will 7 Marquart D W 1963 J Soc Ind Appl Math 11 431 41 The Marquart method is sometimes also referred to as the Marquart Levenburg method It is perhaps best explained in reference 2 8 Bevington P R 1969 Data Reduction and Error Analysis for the Physical Sciences McGraw Hill Book Company Chapter 20 Theory disproportionately affect the results since the square of the residuals for these points will dominate the fit It is possible to edit the data manually to remove such points but it is preferable to eliminate them in a less subjective manner Robust methods achieve this by applying an additional weighting fa
68. are provided for use in equation definitions Function Returns abs x Absolute value of x i e if x 0 returns x otherwise returns x acos x Cos of x alog x Antilogarithm to base 10 of x asin x Sin of x atan x Tan of x cos x Cosine of x exp x e frac x The fractional part of x The fractional part of 13 387 is 0 387 int x The integer part of x The integer part of 13 387 is 13 log x The logarithm to base 10 of x ln x The natural logarithm of x sin x Sine of x sqr x The square of x x sqrt x The square root of x 4x tan x Tangent of x The expression within the brackets may be of arbitrary complexity for example exp k sqrt j 1 All the geometric functions sin cos etc use radians as their units The following predefined constants are also available 83 GraFit User s Guide Constant Value _pi_ x 3 1415926536 ce e 2 7182818285 rnd A random number between 0 0 and 1 0 _grnd_ A random number with Gaussian error distribution The number has a zero mean and unit variance Multi line Equation Definitions In its simplest form as described earlier the equation definition is a single line that calculates the y value For example if the equation to be used was y ax b then the equation definition might be written as Here a and b have been declared to be the symbols that represent the parameters x has been declared to be the symbol tha
69. are saved in one of the following Ways Select the item in the Project window then issue the File Store Stock Item command From the open item window select the File Store Stock Item command By default items should be saved in the item store directory or a subdirectory off this The location of the item store directory is specified using the View Options command Loading Items Stored items can be loaded using the File Add Stock Item command Creating a New File To reset the GraFit workspace Click on the File New toolbar item Ej Note This command is different to the File New menu command which loads a new file based on a template Importing Data Files Data can be imported into GraFit to create a new data table item that holds the imported data To create this item select the File Import Data command from the main GraFit window Any file for which a filter is available can be imported into GraFit see the following section on I mport Export Filters It is also possible to paste data from a file directly into an open data table To do this use the Edit Paste From command of the data table item Chapter Error AutoText entry not defined Working with Files Import Export Filters In order to perform conversions between GraFit and other data types GraFit uses installable import export filter files Several standard filter types are supplied by default with GraFit and other filters may be a
70. ata with separate numeric x and y values whereas a Column Chart has data values that associated with named categories 97 GraFit User s Guide L2 x Beate Cancel Select Graph Type Gallery X Y Scatter Column Chart Bar Chart Graph Histogram Select the basic graph type from the gallery Specific styling is then applied using the graph creation wizard which is launched when you click the Create button After selecting the type of graph to create clicking the Create button will result in a specific graph creation wizard that allows the graph to be customized A description of the kind of graphs that can be created for each type is given below and more detailed information is found in the following chapters X Y Scatter Graph X Y Scatter Graphs have numeric ranges on both x and y axes Some of the types of graph that can be created are illustrated below y Data 0 2 4 6 8 10 12 x Data This graph shows data points joined by a smooth Bezier curve 14 16 6 4 o Q o 1 o 2 4 03 c 7 o S o2 c e 2 01 o 7 0 02040608 1 1 Substrate 0 T T T T T 0 2 4 6 Substrate This graph shows data and a fitted curve inset is a linear transformation of the data Chapter Error AutoText entry not defined Creating Graphs 100 A E 124 140 TB o ZEE J 9 4 7 o L 05 s i EE 3s p 120 3 20 7 L 100 0 0 M usc qu
71. ated In the figure shown above the graph has a single x and y axis and so no modification is needed 145 GraFit User s Guide 146 CHAPTER 15 Using Multiple Graph Axes When to Use Multiple Axis Scaling Graphs created using GraFit can optionally have several different x and or y axes which are independently scaled Overlaying Data that have Different Scales Multiple axes are useful when data need to be overlayed but have quite different numerical ranges For example in the plot below there are two separate y axes but a common x axis Two different data sets are plotted each associated with different y scales Data associated Bl with 2nd y scale m Data associated with 2nd y scale 1st y scale XY scatter graphs can have as many different x or y axes as you require bar charts and column charts allow unlimited numeric axes the x and y axes respectively for these plots 147 GraFit User s Guide Split Axes Split axes are used when it is necessary to show some region s of a data set at a different scale to the remainder The example drawn below has a single split x axis GraFit uses multiple axes to construct the splits and permits any number of splits on both x and y axes X Axis split rr oa gimp rim ZZ I m eee H m MANN Creating and Managing Multiple Axes By default GraFit graphs have just a single x and y axis Any additional axes must be added t
72. ately for each item in the workspace Page Setup EES Paper Size 44 210 x 297 mm Source Auto Sheet Feeder bd Drientation Margins inches Portrait Left fr Right fr Top fro Bottom fr Header fo 3 Eooter 0 552 C Landscape Header text J amp F 84 gt eT Footer text Pase gt Fonts Cancel Printer A header and footer are printed at the top and bottom of the page respectively The header and footer text can contain special strings such as the file name or the time that the item was printed These special strings are specified by clicking on the gt button To omit the header and or footer from the output leave the entries for the Header text and or Footer text blank The font used to display the header and footer text can be selected by clicking on the Header Fonts button Changing the Printer To change the printer from the default click on the Printer button Stock Items 14 Individual GraFit items can be stored for future reuse by selecting an item and using the File Store Stock Item command They are reloaded using the File Add Stock Item command Storing and loading of items is especially useful for saving and restoring equation definitions but can be used for any GraFit item See Chapter 4 for more information about the location of item files Chapter Error AutoText entry not defined GraFit Basics GraFit Templates Workspace files can
73. ations having multiple independent variables is achieved in the same way as the definition of normal two dimensional x y equations but the equations have more that one x variable Fitting Data by Multiple Non linear Regression For a normal data set that contains x y data these data must be present in the data table with the x data and the y data in separate columns When multiple independent variables are involved there are special considerations as to how the data should be arranged Case 1 The equation has only two independent variables In many circumstances there will be just two independent variables in an equation In these circumstances it is common to collect one set of 54 y data at a particular x value then the next set of 1 y data at a different x2 value etc In Chapter 19 Data Fitting Basics the case of the example described above this would entail collecting A versus t at one particular S then another set of A versus t at the next S and so on When this arrangement of data is present it is convenient to enter the x y data into the data table and to associate the x value with the y data column For example the data can be entered as shown below Data PI ES y 3 0000 y3 3 0000 4 0000 5 0000 6 0000 7 0000 8 0000 9 0000 10 0000 Note that the y data each have an associated x value For this particular data set all the y data are associated with the same x data which corresponds to
74. aw the transformed curve which in the example above gives the linear Lineweaver Burk plot it is necessary to have an appropriate equation definition For the example that we are using the transformed equation is Dopo Kw 1 V ASK LE KLE What is being plotted is 1 v the y axis versus 1 S the x axis To show this line we therefore need an equation that is defined as E 1 k Eo Kanal Here x and y are the transformed data The transformed curve definition uses the X name and Y name entries which correspond to x and y in the above equation The syntax used for this definition is as described for equations see Chapter 9 and can occupy more than one line if required ld y x 93 GraFit User s Guide Fonts and Indents Panes These panes control the way that the results are formatted The contents of these panes are common to several different item windows and are described in Chapter 7 Compiling the Transformation 94 To compile the equation choose the Transformation Compile command Compilation translates your definition into an internal form that can be executed rapidly During compilation the definition is comprehensively checked to ensure that the correct syntax has been used If an error is detected a message box will be displayed informing you of the mistake after pressing the OK button to continue the cursor will be placed at the most likely place of error GraFit Missing A A
75. be To specify additionally the size of the negative lobe click the button and select the column that holds the value of this error If you select the same column as selected for the positive error this will result in symmetrical error bars Hint If you want to create a single sided error bar that has just a negative lobe ensure your column of error values are all negative and select these as your positive errors the net effect is to draw the error bar in a negative direction Chapter Error AutoText entry not defined X Y Scatter Graphs Some examples of error bar types are shown below No error bars Absolute error bars on Proportional error bars on the y axis the y axis Absolute error bars on Explicit error bars on the Explicit error bars on the the x axis proportional y axis only the positive y axis the positive and errors on y lobe is shown negative lobes each use the same error column Y Error bars This section is used to specify the type of errors present on the y axis The settings are analogous to those described above for x error bars 141 GraFit User s Guide Axis Association Page Fitted Data Properties M 1 Scale O to 7 oO 2 Scale O to 10 The Axis Association page allows the data to be associated with the various axes that are present see Chapter 15 for information on multiple axes XY graphs can contain many different x and y ax
76. be arranged contiguously in the data table and multiple y data sets can be present The location of the X data column and the Last Y data column are selected and from the program can work out how many data sets are present All the y data sets need to be in columns that are of the type y Data with Associated Value This option is only available if there are two independent variables As with the previous layout the second x variable is obtained from the column type header The difference is in the arrangement of data columns For this layout pairs of x y data columns are arranged contiguously in the data table and a separate set of x data values are used for each y data set All the x data columns hold values corresponding to the first independent variable as defined in the equation values for the second independent variable are obtained from the type header The First X data column and the Last Y data column are selected and from this the program can work out how many data sets are present This layout is available whenever there is more one independent variable and is the only layout type when three or more independent variables are present When using this layout the program determines which column is associated with which independent variable by examining information present in the column type headers of the data table The column types of the various independent data sets x axes need to be set to x n Data with
77. be created by adding a number of items as described above Alternatively it is possible to load a pre built workspace from a template using the File New command See Chapter 4 for more information about using templates Accessing Help GraFit includes a complete on line help system to guide you through learning the product To view the help topics e From the Help menu select the Contents command To obtain specific help on the function of a menu item toolbar command or window item e Click on the Context Help toolbar button and then on the item for which further information is required To obtain specific help within a dialog box e Click on the Context Help button 3X in the top right of the dialog box and then on one of the items in the dialog box Column Format 2x Number Format Decimal places J4 Save As Defaults Max digits 12 3 Restore Defaults I Thousands separator Scientific format Check this option to display small numbers that would otherwise be displayed as 0 000 using scientific format This E is useful to ensure that small number values can still be read while other values are formatted normally Context sensitive help gives specific information on each item within the dialog box 15 GraFit User s Guide 16 CHAPTER 4 Working with Files GraFit Workspace Files The GraFit workspace consists of all the items displayed in the main GraFit window data tables gra
78. bjects have more complex color settings than can be made using the Color toolbar For these it is possible to select other color options from the object Edit Properties dialog Setting Default Colors The default fill line and text colors for new graph objects can be specified by altering the color when no object is selected The new default colors will be used next time an object is added Setting Text Properties Text properties are specified by commands found on the Text menu or alternatively on the Formatting Style toolbar Formatting x i e arial sf HB z u Ml Ail P ab amp qe 109 GraFit User s Guide The font size style alignment and orientation of the text can be specified from this toolbar Further text properties are also available from the Edit Properties dialog including superscript and subscript settings If a text object is selected by clicking on it changing text properties will alter the appearance of the entire object For example if a text item is selected and the color set to red then all the object text will become red Finer control of text settings is possible for editable text by double clicking on the text item then selecting just a portion of the text The Edit Properties command or the Formatting Style toolbar buttons will then apply only to the selected text Graph lel ES To alter just a of text Double click to edit the text object Select the part to cha
79. by having a numeric range on the x axis and named categories on the y axis and have the same range of styles available as column charts Some of the types of chart that can be created are illustrated below Comparison of values using a bar A Low High bar chart chart Histogram 100 Histograms have numeric ranges on both x and y axes but the x axis represents value ranges and the y axis shows the number of occurrences within the range Some histogram styles are shown below Note Despite the similar appearance a histogram is fundamentally different to a column chart Chapter Error AutoText entry not defined Creating Graphs V mt ga y A distribution of data AA Im Lu EAS A O0 E EAN Comparison of two distributions 101 GraFit User s Guide 102 CHAPTER 13 Graph Item Overview of Graph Items Graph items display a page of information that can hold one or more graphs and may also display results or contain OLE objects This item window is created from the main GraFit window using the Add Graph command The appearance of a blank graph item window at 5096 magnification in landscape orientation is shown below 103 GraFit User s Guide Controlling the Page View The orientation of the printed page is controlled using the File Page Setup command The magnification is set from the View menu or using the Zoom selection on the toolbar Grid Lines By
80. cept that legend text cannot be displayed rotated See Chapter 13 for further information on text formatting Note The overall width of the data legend depends on the size of the individual legend text elements Each of these can be individually sized using the mouse Adding Extra Data to the Graph 144 Additional data sets fitted results or equations can be added to the graph by selecting the main graph region then choosing the Graph Add Data command This re invokes the XY Graph Wizard to allow further data to be added Most of pages are equivalent to those described earlier for creating new graphs although those pages that control initial scaling are not relevant and so are not displayed Chapter Error AutoText entry not defined X Y Scatter Graphs Set Axis Associations Page When graphs are first created they have a single x and y axis with which the selected data sets are associated However after creation it is possible that a graph may have additional axes and so the axis association needs to be specified when adding data This results in an additional Axis Associations page being added to the Wizard XY Graph Wizard Set Axis Associations 2l xi m Associations X axis Y axis Select AX W 1 Scale 0 to 100 Select All Y reser This is equivalent to the Axis Association parameters page described on page 142 Check the boxes of the axes with which your data should be associ
81. ces press the Finish button to add the new axis Splitting an Existing Axis Choosing to split an existing axis from the Axis Manager will give the following page Axis Manager Split Settings ont EEEEEERNENN Split position L 50 Split value jo lt Back Cancel The axis to be split should be selected from the list available The initial split position can be set using the slider control By default the axis is split in the middle i e at 50 Use the slide to set this to an appropriate position The axis is 150 Chapter Error AutoText entry not defined Using Multiple Axes split so that the scale for two new axes is set as below using the Split value to set the end of the first scale and the start of the second Original Axis Start Finish AH A Split Axis Start Split value Finish After entering a suitable Split value click the Finish button to create the new axis Removing an Axis If you elect to remove an axis using the Axis Manager you will be presented with a list of all axes that can be deleted Axis Manager Remove x Axis x Axis to remove Scale Start Scale Finish Data Sets 1 5e 010 1 9e 006 1 2 3e 006 0 00705 1 Any data or curves associated with a deleted axis will become reassociated with the default first axis Double click on the data symbol to modify the associations lt Back Cancel Choose the axis to remove then click the Finish button to delet
82. ck v Line z D 167 GraFit User s Guide The Select Bar Style page allows the histogram bar representation to be chosen Click the Finish button to create the chart 168 CHAPTER 18 Embedding and Linking What is Embedding and Linking Embedding and linking are two related ways that information from one application can be incorporated into a different program Also known as Object Linking and Embedding OLE it provides a uniform mechanism for Windows programs to cooperate and to share information Most Windows applications allow information to be copied between programs using the Clipboard For example a picture could be copied from one application and pasted into a second The problem with simple cut and paste is that the second application often has no idea what information is being transferred In non OLE applications this often means that once the information is copied it is impossible to make any subsequent changes to the image OLE gets around this by allowing two cooperating applications to pass information between themselves in such a way that editing is still possible even after pasting into an application that has no knowledge about the information transferred Both embedding and linking are extensions of the standard Clipboard cut and paste mechanism Original Cut and Paste Model The original use of the Clipboard was to pass a representation of the object being copied
83. clicking in the row selection region allows whole rows to be selected Copying and Pasting Data Selected regions of the data table are copied to the Clipboard using the Edit Copy command and pasted using Edit Paste Data may also be pasted to and from other applications in the same way Copying and Pasting Regions of the Data Table 1 Select the region of data that you wish to copy Choose the Edit menu and select Copy 2 3 Move the data entry position to where the data is to be copied 4 Choose Edit Paste The data will be inserted at the data entry position Copying and Pasting Columns Entire columns of data can also be copied and pasted Pasting into the data table when a column is selected results in the pasted values being placed in a new column in front of the selected column 28 1 Chapter Error AutoText entry not defined Data Tables Select the column s of data that you wish to copy Data Choose the Edit menu and select Copy Select the column in front of which the data are to be inserted Data Al ES Choose Edit Paste When pasting into a fully selected column you have the option to overwrite the selected data or to insert the new data in front of the selection the overwrite option is only available if the number of columns available to paste is the same size as in the selected region Paste Columns 21 x C Overwrite selected columns Cancel The data are
84. could be significant Entering the data as O to 1 femtoseconds may be more appropriate Types of Regression Analysis Regression acts to minimize the sum of the squares deviations of the experimental values from values calculated using some theoretical equation However the mechanics of the calculations are different for linear and non linear equations Linear Regression Linear regression is a technique that should be familiar to most scientists It is the mathematical equivalent of using a ruler to draw the best line through a series of data points to obtain values for the slope and intercept of this line The calculations needed to perform linear regression are relatively simple and are even found on many scientific calculators Polynomial Regression Polynomial regression is an extension of linear regression where the equation is y a bx o t d 4t ex Non linear Regression Non linear regression allows data to be fitted in the more general case to any equation where the y data value can be described as a function of the x data and a series of parameters i e y f x Pz D P3 an As a result it is applicable to many more situations than linear regression and is more generally useful for analyzing experimental data The only drawback to non linear regression is that the calculations are too complex perform using a calculator and require a computer program such as GraFit Additional Considerations for Non li
85. ctor varying for example from 1 0 for points that have low residuals to O for extreme outliers effectively eliminating such points GraFit employs optional robust weighting using the algorithm of Mosteller amp Tukey as implemented by Duggleby19 An additional bisquare weight b is incorporated into the analysis and is calculated as ua if u lt 1 b j 0 if lu gt 1 i Here with z being the residual weighted by the a priori weight and N the number of observations E Zi Y Isl N Including robust weighting will result in improved estimates for the parameters in the presence of outliers This is however gained at the expense of more calculation which will slow down the fitting procedure The effect of using robust weighting is seen in the graph below O Fock Fast Vir Vagjira7 F hnst Vitra ae 9 Mosteller F amp Tukey J W 1977 Data Analysis and Regression Addison Wesley Reading MA USA pp 353 65 10 Duggleby R G 1981 Analytical Biochemistry 110 9 18 191 GraFit User s Guide The data which contain a single outlier have been fitted to a straight line with and without robust weighting enabled When robust weighting is omitted the presence of this outlier markedly affects the calculated results With robust weighting selected however the rogue data point is rejected and the calculated line now correctly follows the main trend Determining the Mo
86. ctories the user file has precedence To create a new workspace file based on one of these templates select the one to use and click OK 21 GraFit User s Guide 22 CHAPTER 5 Data Tables The Data Table Item To add a new empty data table to the GraFit workspace e Click the data icon on the Workspace toolbar zl or select the Add Data Table command The parts of the data table window are shown in the following illustration Column selection region Column resize region Type indicator row Column heading Data entry position Row selection region Splitter box Position row 1 column 1 in the above figure is marked by a dark outline this is the current data entry position Data entries are edited in situ by typing in the new entry When the entry is complete pressing RETURN TAB Or a cursor key or clicking the mouse on a different position in the data table will accept the data and move 23 GraFit User s Guide the data entry position To edit the value at the current data entry position select the Edit Edit Current Cell command or press F2 The following table describes the elements in a data table Certain sub regions are distinguished by the mouse cursor changing shape when it is over them Element Data table Column selection region Column resize region Row selection region Row resize region Split table horizontally Split table vertically Description The data va
87. culation pane shows the message Calc o unc B l 4 x ummmmmmmmmum EMEIRN IEEEEEEEENEENENENHN G Ready Fitted NUM 4 Fitting status pane Calculation pane 55 GraFit User s Guide Settings Pane The Settings pane is used to specify the main details of the fit Non linear Fit olx Results Number Format Fonts Indents Constants Estimatrix Fitting Criteria Equation Enzyme Kinetics Weighting Simple y I Robust Data table Data y The Settings pane of the Data layout 6 Non linear Fit item X data column Substrate ha Substrate Limit x range to Y data column Rate v ISITGTIGO UTI Equation Choose the equation to use for the data analysis The equation must exist as a separate item within the main GraFit window See Chapter 9 for information about equation items Weighting All types of regression analysis require information about the error distribution in your data The reason for this is explained fully in Chapter 20 but briefly it is necessary to specify whether the inaccuracies are likely to be the same for each data point Simple weighting are proportional to the value of the y data points Proportional weighting or have been individually estimated Explicit weighting The default Simple weighting is often the most appropriate setting Robust weighting is additional weighting that provides a way of removing outliers see
88. d In this example one each of the following items has been added a data table a graph window a non linear fitting item a linear fitting item an equation definition a notepad a transformation definition and an embedded Microsoft Word 10 Chapter Error AutoText entry not defined GraFit Basics document All the added items are stored inside the same GraFit workspace and can be saved and loaded from disk using the File menu commands If you run a second copy of GraFit you can copy items between workspaces by drag and drop or by using the commands on the Edit menu to copy and paste items via the Windows Clipboard Each item in the workspace is represented by an icon in the project window GraFit Items GraFit items are initially created in a new window that residues within the main GraFit window and are identified by the presence of an icon in the project window Closing an item window does not delete the item it simply makes the window invisible This allows you to keep open only those items that you are currently working on Managing Items Adding New Items To add a new item to the workspace Use the Add menu or click on the item buttons in the workspace toolbar Switching Between Items To switch between items e Click on the window to activate or click on the icon that represents this item in the project window Removing Items To delete an item from the workspace Select the icon that represents the it
89. d value A A 1 exp Yes background K S 236 CHAPTER 23 Standard Templates Data fitting templates provide a quick way of analyzing data and plotting graphs In general you are recommended to construct your own specific templates that are best suited to the data you wish to analyze However GraFit comes with a few standard templates that can be used for common data fitting situations About the Standard Templates All the standard data fitting templates are defined so that as the data values are entered the results are calculated and data plotted in the background Accessing Templates To access one of the data fitting templates select the File New command Choose the template from the list shown New 124 x General Enzyme Kinetics IC 50 Ligand Binding Linear Regression Single Exponential Apply 237 GraFit User s Guide Template Layout All the standard templates are formatted so that the data are entered into a data table that is on the left of the screen and the fitted data and results are updated in the graph on the right This graph is plotted as the data are being typed into the program Y GraFit Untitled of x File Edit View Add Table Window Help JD EIS gs 5 e e poo e 3 212 e BN S666 obi ak a c t t er rn 10 gt EEFILIEEEIEER EE Single site Ligand Binding iv IB
90. d whenever one or more data values in the source columns change A B The column holds the result of subtracting values from the second column from those in the first A B The column holds the sum of adding values in the first and second columns AIB The column holds the result of dividing values in the first column by those in the second A B The column holds the product of values in the first and second columns Statistics The column types under this submenu allow the result of various statistical procedures to be displayed in the column Mean Calculate Mean KE Data columns Value 2 Value 3 J Column 4 D column s selected Each row entry in the column is set to be the calculated mean of the corresponding values from the columns selected in the above dialog 39 GraFit User s Guide 40 The calculated values are updated whenever one or more values within the selected columns is modified No Data Points Each row entry in the column is set to be the number of data values N present in the corresponding rows from the selected columns This will be less than the total number of selected columns if missing data values are present Standard Deviation Each row entry in the column is set to be the calculated standard deviation of the corresponding values from the columns selected in the above dialog Standard deviation o is defined as c 0 2 Standard Error of the Mean Each row entry in
91. data sets have different x data values Pairs of x y data columns are present consecutively in the data table The location of the first x column is set from the First X data column entry the location of the final y column is set from the Last Y data column entry The number of data sets present is determined automatically Equations with Multiple Independent Variables Equations that have multiple independent variables x axes need to access multiple x data columns They therefore have a different set of data layout options Layout Meaning x 2 from y header x vi Ey This option is only available if there are two independent variables In these circumstances it is often the case that a series of y data values are collected at a fixed value of the second x variable For example the progress of a reaction might be collected with time at a number of different reagent concentrations The first x variable would be time the second would be reagent concentration Within the data table it is possible to associate a value with an entire column when this layout is selected the associated value is taken as the second x variable The associated value is set by setting the column type to y Data with Associated 57 GraFit User s Guide Layout x 2 from y header sd x n from table X Data Column Meaning Value and entering a numeric x value as appropriate See Chapter 5 for further details The x and y data need to
92. diting X Y graphs and Chapter 14 should be consulted for further information Select Data Source Page Histogram Wizard Select Data Source 2 xi Legend text Source Values column _ Numbers column hmc F Start position Do Increment i You can use the Graph Add Data command to add more data sets to the plot Eo The Select Data Source page allows you to choose the source and type of data to plot Legend text The data set plotted is associated with an entry in the data legend The entry shows the symbol used to represent the data and a descriptive text The initial text used to describe the entry can be entered into this field 165 GraFit User s Guide Source Graphs are plotted using data that are present in one of the items found in the GraFit workspace The Source selection lists all items that contain suitable data for plotting and one of these must be selected Values column Select which column holds the data values whose distribution is to be plotted Numbers column Check this box if a second column is present that holds a count of the number of items an item in the Values column is present If unchecked that it is assumed that each entry in the Values column is represented once only if checked then the column that holds the number of entries must be selected Start position Enter the starting position for the histogram grouping The histogram records the number of occurrences of data
93. e independent variable and one or more parameters pj Pz P3 etc The exact form of the equation depends on the experiment and the conditions that are used it might be a simple linear equation y ax b or a more complex function In either case the purpose of data fitting is find values for the parameters in this equation that best describe the data For a simple linear equation as shown above this is done by linear regression In general however a more complex equation will apply Such data are fitted by non linear regression Chapter 19 Data Fitting Basics GraFit allows non linear equations of arbitrary complexity to be used for data fitting 3 A Systematic But Uncharacterized Trend is Present Occasionally data may be collected that show a distinct trend but no known equation describes this relationship For example an empirically determined calibration curve may collected If the physical basis for the shape of the data is not well defined the appropriate equation is unknown In such situations it can be useful to fit the data to a general purpose equation such as a polynomial This will allow values to be extrapolated from the standard curve although any parameter values that are obtained will not have physical meaning The use of data fitting for this purpose is illustrated in Chapter 21 Regression Analysis Regression analysis finds the best fit line or curve through a series of data This is considered to be th
94. e the analysis shown below fits an exponential decay to a single exponential equation kt y Ae In addition it fits the data to an equation that has an additional background parameter y Ae background A sample set of data fitted to each of these equations is shown below 41 GraFit User s Guide 42 gt gt gt gt gt gt Using the F test it is possible to test whether the data are fitted significantly better by the presence of the extra parameter Chapter Error AutoText entry not defined Data Tables Fitting results 1 if Fitting results 2 Fi Single Offset Data Amount 0 0000 110 0000 Analysis 1 0000 80 0000 Fit Single 2 0000 60 0000 Single Exponential Decay 3 0000 45 0000 Number of parameters 2 0000 4 0000 35 0000 5 0000 28 0000 Analysis 2 Fit Single Exponential Decay Offset Single Offset Number of parameters 3 0000 Number of data points Chi value 1 Chi value 2 F statistic Probability The results show that the probability that the two fits are equally appropriate is 0 0016 or 1 696 which is low This indicates that we can have reasonable confidence in the merit of including the extra parameter generally we require this value to be 596 but may prefer a value 196 to be sure Note Although the F test results have been shown incorporated into the
95. e then choose the Edit Select All command to ensure that all graph items are selected Note Itis extremely important to use the Select All command as no OLE information is copied unless all items are selected When all objects are selected the Edit Copy command is replaced by Edit Copy All Next choose the Edit Copy All command Insert the information into an OLE compliant application using Edit Paste or Edit Paste Special as appropriate to the application in question 173 GraFit User s Guide 174 CHAPTER 19 Data Fitting Basics This chapter describes some of the basic principles behind data fitting A more complete description of the theory is given in Chapter 20 and additional information can be found in several reviews 1 6 Within GraFit data are fitted using the Non linear Fit or Linear Fit item windows which are described in Chapters 6 and 8 respectively When Is Data Fitting Appropriate Data fitting is the mathematical analysis of a data set in order to analyze trends in the data values This will usually involve linear or non linear regression analysis of these data values in order to define a set of parameter values that best characterize the relationship between the data points and an underlying theoretical model While many types of data can be usefully presented in graphical form not all such data are suitable for data fitting Types of Data In general data can be divided into three groups
96. e SHIFT or CTRL keys while dragging the handle It is possible to combine these effects by holding down both keys together Key Effect on dragging shift The aspect ratio of the object is maintained during resizing ctrl The object remains maintains its current center position during resizing Resizing Text Objects Text objects have slightly different resizing behavior to other graph objects Text objects always wrap their text to fit so the height of a text object is determined by its width the text it contains and the current formatting Resizing a text object will therefore change the text wrapping 106 Common Actions Chapter Error AutoText entry not defined Graph Item The following actions are common to many of the objects that are found on the graph Action Left click SHIFT left click Right click Left click drag CTRL left click drag SHIFT left click drag ALT left click drag Double left click Effect The object under the cursor is selected and any selected objects are deselected If the cursor is not over a drawing object then any selection is removed The object under the cursor is added to the current selection An object specific context menu is displayed The selected object s are moved Dragging can be stopped by right clicking or by pressing the ESCAPE key The selected object s are duplicated and a copy of these of these is moved to the new location Thi
97. e checked If you do not want the program to calculate initial estimates simply leave the box unchecked Defining How to Rearrange the Data Points For our current equation the rearranged plot that we require is of v S against v i e y x versus y The X Data and Y Data entries are used to define the data points for such a plot note that the stored data points in the data table are of course unaffected For this equation the definitions are ydata and ydata xdata respectively The symbols xdata and ydata are predefined by the program to represent the x and y data points 87 GraFit User s Guide These definitions allow the program to perform the rearranged plot and any valid single line expression can be used The grid at the bottom of this page is used to define how we obtain our initial estimates from linear regression on the rearranged plot Shown in the previous figure is the definition of Keat as intercept gradient Eo and Kpn as 1 gradient Use the scroll bar to bring any further parameters into view The symbols intercept and gradient are predefined and represent the intercept and gradient of the rearranged linear plot Other predefined symbol names may also be used when defining initial estimates of your variables The symbol min will give the value of the minimum y data point and max the value of the maximum y data point The corresponding minimum and maximum x data points are minx and maxx respect
98. e entered 159 GraFit User s Guide Select Tick Styles Chart Wizard Select Tick Styles The Select Tick Styles page allows rapid selection of some of the more common axis tick styles More extensive tick style choices can be made once the graph has been created 160 Chapter Error AutoText entry not defined Column and Bar Charts Select Bar Style Chart Wizard Select Bar Style 0 Sa El E POE HON Z aa dea mi m E Black Beckoroung The Select Bar Style page allows the chart bar representation to be chosen 161 GraFit User s Guide Select Data Point Style XY Graph Wizard Select Data Point Style Jada x x e gt lt BEDE It is possible to use data points to represent the values if required By default no data point style is selected 162 Chapter Error AutoText entry not defined Column and Bar Charts Select Join Style XY Graph Wizard Select Join Style It is possible to draw lines that join the points if required By default no lines are drawn Click the Finish button to create the chart 163 GraFit User s Guide 164 CHAPTER 17 Histograms The Histogram Wizard Chapter 12 described the basics of creating graphs Selection of Histogram produces the Histogram Wizard to assist with the procedure all settings can be adjusted later if required The process of editing histograms is broadly similar to e
99. e esee d cot or sed paper eo ho eoo PEERS D PETAT ERR Geha tri TAE Eod t 68 Linea Fit Itemaren rines 69 Overview of Linear FittiNQ o ococococccococnnnoncncnnnonororornnnn mmm 69 Status Bar Indicators ovde rt ita ador 69 Settings PE Por egre ele es HaT Lp Ve CET Ve Ee eE 70 Equation i oie E PRA tee RETE E cee a 70 Weightltig rea ta a a ptg 70 Data table tner omer neer ITEM 70 Data Lali ic 71 XData Colutnf sunt td CERERI CEPE RS LE E 71 Y Data Col rnn reme ve Dec mo c o eee oe P eC 71 Error Columns chews va er Poen finas 71 Results PAN Ein tas IEA aL SOEUR Ta An ARE RAT seamed andas 72 Fonts and Indents Panes 00cocccconcccnnnco nano nee hene aee naaa e nna 73 Equation TteM cononononononononanananannnnononannnnnarararnrnnnnnnnnnnnnrnrnrncnnananannnnnnnnnanans 75 Overview of Equation Definitions cece eect eect eee ee 75 Status Bar INdiCatorS ococcconcconnnannnonnna memes enhn nenne nnn 75 General Pare aseo Nerei miran thea dunt ten dieti eina tt ciel di maus da EE 76 Changing Font Styles sssssssssssssssssneme mm eee e emnes 76 Inserting OLE Objects su eor e i t ER EROR ptos 76 Editinig OLE Ob ects oe Re pe eae 77 X Variables Pane e paene Ut awe 77 Naming Rules erc tee A ele eed einen ur let cs 78 Number of X Variables iecit eaa TER SR XR LP i ata e RAE Raid 78 Parameters Pare n sio e EDAD RR TARERRE MISERE MO SR had IBRO RENE EARS RAS 79 Constants Pare i ete bet O sedat e E Prage Be
100. e it from the graph Any data or curves that are associated with the deleted axis become reassociated with the default first axis You can modify axis associations by editing the properties associated with the data set To do so select the data symbol found in the data legend and choose the Edit Properties command or double click on the data symbol 151 GraFit User s Guide Working with Multiple Axes Axis Text and Axis Scale Text Each axis has a separate text legend that can be positioned and edited as required and a separate scale text that can also be formatted as required Data curve properties Acetonitrile Absorbance y axis 4 6 8 10 12 text 2 Fraction Number axis scale 1 1 y axis scale 2 y axis text 1 Visibility of Axis Text and Axis Scale Text There are often cases where it is not necessary to show a separate axis text and or axis scale text for each axis The various items can be hidden by selecting the item then choosing the Edit Hide Object command Objects can also be hidden and unhidden from the General page of the graph properties double click on the main graph area or choose the Edit Properties command when the main graph is selected Data Association 152 Any data that is added to a graph can be associated with one or all axes When using multiple axes to display data that have distinct ranges it is usual to associate each data set with one
101. e one that minimizes the sums of the squares deviations of the experimental data points from the theoretical curve GraFit uses regression to allow the analysis of experimental data Practical Considerations The Errors are in the y Data It is the convention to assume that the x data values represent the independent variable and the y data values represent the dependent variable i e the x data are what is varied in the experiment for example time concentration etc and the y data are the experimentally observed values L y axis O x axis The vertical distance the gray lines in the above diagram between the data point and the curve or line is that which is minimized by normal regression analysis i e it is assumed that all errors are present in the y data An important aspect of experimental design is to ensure that the x data are as accurate as possible so that this assumption is valid 177 GraFit User s Guide The Data Values Have A Suitable Numerical Range A consequence of computer calculation is that rounding errors can occur particularly if very large or very small numbers are used This is because computers only store decimal numbers with a limited numerical precision Although this should not affect most calculations it is advisable to scale any set of very large or very small values prior to performing calculations For example if a series of time values were entered as 0 to 10 15 seconds the rounding errors
102. e parameters and constants if any entered as on the earlier panes Chapter Error AutoText entry not defined Equation Item Enzyme Kinetics GE x Estimates Fonts General X Variables Parameters Constants Y name E Equation definition v kcat Eo S Km 5 The Definition pane of the Equation item Hu Symbols X variables Parameters Constants 5 kcat Eo Km All equation definitions that are used within GraFit must have the functional form y f x i e it must be possible to describe the variation of y as some defined function of x The information on this pane describes the required equation in symbolic form At the top of the pane is an entry for Y name which allows the y axis to be given a Symbol name using the rules described earlier Equation Definition Syntax The equation definition is built up from the symbols representing parameters and constants if any with whatever arithmetic operators and mathematical functions are required For the example shown in this Chapter we have used the following equation K MESES K 15 In the Equation definition entry this becomes v kcat Eo S Km S The syntax used is similar to that of a programming language and uses the rules described below 81 GraFit User s Guide 82 Arithmetic Operators Symbol Operation Example Explanation T Addition x y Add x and y Subtraction lim off Subtract off from
103. e to adjust the scale settings later The text used for the x and y axis can also be entered 117 GraFit User s Guide Select Tick Styles XY Graph Wizard Select Tick Styles 12 1x m Style DIO DE lt Back Cancel The Select Tick Styles page allows rapid selection of some of the more common axis tick styles More extensive tick style choices can be made once the graph has been created Select Data Point Style not equation items XY Graph Wizard Select Data Point Style 12 1x m Style r Appearance El Al vj el e M Pen jose Holaa fe 3 BE olal None Iv Fill Size Medium 2 Mask curves lt Back Cancel The Select Data Point Style page allows the data point representation to be chosen 118 Chapter Error AutoText entry not defined X Y Scatter Graphs Size Data points are scaled relative to the overall graph width and so the absolute size will depend upon the graph dimensions Choose a size that represents your data appropriately with more data you should use smaller data points If very many points are present it can be more effective to set the Style as None and to join the data points with lines next page Pen Check this box to draw an outline around the data point The size and color of the outline can be specified Fill Check this box to fill the point with the solid color selected If Fill is not checked the data points will be transparent
104. ed in degrees which is measured in a counter clockwise direction The rotation can be set as an absolute figure or relative to the current rotation Location Properties Rectangle Properties 21x Fil Line Rotation Location Position From left From top fo 333 Relative to Margin y Size Width 2 521 i Heart v Maintain aspect ratio Cancel Breil The location of the selected object is set from the Location page This allows the object position to be specified exactly relative to the current margin or to the edge of the page 112 Chapter Error AutoText entry not defined Graph Item Arrows Properties Line Properties 21 xi Line Arrows Rotation Location M Arrows Ends e J End size Medium hz End width Normal y Cancel Apply Objects that can have lines with terminating ends allow the end type to be specified via the Arrows page Choose from a variety of arrow styles for each end of the line together with the end size and width The arrowhead color is set to be the same as the line color Font Properties Text Properties 2i x Font Paragraph Rotation Location Font Font style Size me Regular fi 2 E Arial Black Baltic Italic und ap Arial Black Central Europear T Arial Black Cyrillic ip Arial Black Greek IT Arial Black Turkish Ip Arial Black Western x Bold Bold Italic Effec
105. ed the various buggy beta versions with great tolerance and many useful additions have been due to him My thanks also go to Walter Ward for his help and sound advice Steve Clarke has made a large number of valuable suggestions and am very grateful to Ron Duggleby for his comments and encouragement Plaudits also to Alessandro Aliverti lan Auld Bogdan Bogdanov Bjarke Ebert John Gebler Florence Guye Douglas Kell and Karsten Olsen for many recommendations and suggestions As usual Marcella has been long suffering in her support without which this version would still be in development April 1998 London ROBIN J LEATHERBARROW Version 3 Many of the improvements in this version are due to the excellent suggestions that have come from various GraFit users My thanks to all who contributed particularly to Pietro Belfiore John Gebler Douglas Kell Steve Matthews and David Tew for many valuable recommendations and to Martin Reddington Walter Ward Tim Wells and Marcella for their continued advice Version 2 My thanks to the many people who have given advice for improving the program In particular am grateful to Bjarke Ebert Bernard Mangold Sanjoy Ray Martin Reddington Walter Ward and Tim Wells for many constructive suggestions Once again this program and manual would not have been possible without the help and encouragement of Marcella Version 1 In the preparation of this program I have benefited from encouragement a
106. ee the effect of changing the indent settings use the File Print Preview command 68 CHAPTER 8 Linear Fit Item Overview of Linear Fitting A linear fit item is used to control data fitting by linear regression This item specifies the data source and equation to use and also presents the results of the data fitting The item is created from the main GraFit window using the Add Linear Fit command The linear fit window itself contains a tabbed dialog box with several panes that are used to specify how the fit is calculated Each of these panes is discussed below Data fitting involves making appropriate selections in the Settings pane and possibly one or more of the other panes as described below then selecting the Calculate Fit Data command After fitting the data the results can viewed from the Results pane Status Bar Indicators When a fitting item is selected the status bar shows the current fitting status indicating whether the item is currently Fitted or Not Fitted n addition the status bar shows when a calculation is in progress Whenever any calculation is being processed the calculation pane shows the message Calc uu a a gt TA SRO a 0 HET Ready Fitted NUM 4 Fitting status pane Calculation pane 69 GraFit User s Guide Settings Pane The Settings pane is used to specify the main details of the fit Linear Fit A x Settings Results Number Format F
107. eful symbol that is specific to the data transformation definition is ycalc This returns the y value that is calculated from the fitted parameters Therefore to generate a residuals plot define the transformed y data as ydata ycalc Axis Name Settings When first creating a transformed plot the text used to name the x and y axes is taken from the Default X name for graph and Default Y name for graph entries The following special entries can be used Entry Effect 1 All occurrences of this are replaced by the name of the untransformed x data column oo N All occurrences of this are replaced by the name of the untransformed y data column Curve Pane The Curve pane describes how fitted curves are transformed for plotting If the Transform curve box is unchecked no curve transformation is used Otherwise the remainder of the window describes the transformed curve definition 92 Chapter Error AutoText entry not defined Transformation Item Lineweaver Burk of x General Data Points Fonts Indents Y Transform curve X name s Y name Transformed curve definition y l kcat Eo S Km kcat Eo The Curve pane of the Transformation item Symbols Parameters Constants kcat Eo Km In the sample shown above the curve transformation displays a line through the transformed data points making use of the fitted parameter values Transformed Curve Definition To dr
108. em in the project window and choose the Edit Clear command Item Representation When an item window is closed the contents of the item still remain present in the GraFit workspace file The item window can be reopened by double clicking on the icon The icon that represents the item is shaded so that it indicates the current state of the item as shown below 11 GraFit User s Guide 12 1 GraFit item open The icon is drawn normally Linear Fit open GraFit item closed The icon is drawn as a ghosted image which is Linear Fit lighter than normal closed w Embedded object open for editing The object icon is shown Embedded Overdrawn with hatched lines item open HE Embedded object closed The icon is drawn ghosted Embedded item closed y a Linked item closed Switch between item windows to edit their contents Information about using each of the GraFit item types is found in Chapters 5 13 Linked object closed A shortcut overlay 2 is added to the icon Editing the Item Name Items are referred to by the name shown in the project window so it is useful to change this from the default to something more meaningful To edit the item name select the icon in the project window and choose the Edit Rename command Type in the new name Item names can contain any characters but must be different from any other item name in the workspace Changing the Item Icon The icon tha
109. entries CTRL DOWN It is often convenient to press RETURN Or DOWN between entering data points Moving the data entry position using the mouse To move the data entry position using the mouse move the mouse pointer to the position you require and click the left mouse button Chapter Error AutoText entry not defined Data Tables Selecting Regions of the Data Table Selecting Part of the Data Table To select a portion of the data table drag the mouse over the required region Alternatively hold down the sHiFT key and use the cursor keys to extend the selection The selected region is displayed inverted as shown below Data OF x Substrate Selected region 0 2500 0 5000 1 0000 Clicking the mouse within the row selection area results in the entire row being selected To make a more extensive selection Click on the start position Use the scroll bars to move the window as necessary e Hold down the suirt key then click on the end position for the selection Discontinuous selection e Hold down the crRL key and click the required entries 27 GraFit User s Guide Selecting Entire Columns Whole columns of data are selected by clicking on the column selection region The selected column is displayed inverted Data PII ES Substrate Column selection region Drag the mouse along the column selection region to extend the selection In a similar fashion
110. er offset show offset o ooonccccncconnncnnncn emen 236 1st order rate versus S c sss menn 236 1st order rate versus S offset ncns 236 Standard TemplateS momccoconocaroconnnnononononorornrnrnnnnnnnnnnnananannnnrararararnnnnananas 237 About the Standard Templates sssssssssseee meme 237 Accessing Templates ssssssssssseeemem mene 237 Template Layout mte p ans 238 Using Your Own Templates ssssssse mener 238 Description of the Standard Templates rnern 239 Enzyme Kihetlcs vio tia e ed Eee en 239 foul EE 240 Ligand Binding rire tier het REFERRED AE ARAARA EN 241 Linear Regression eese es 242 Single Exponential ceci nd te me ER REM EN SERA pee Eu PR UR 243 GraFit Symbols Font ueseieieieieiese seen enean hehehe nhanh nana na na na na nnn 245 Grafit Symbols Font pt ER e ER e RR ee exei 245 DO qu 247 CHAPTER 1 Introduction Welcome GraFit version 4 for Microsoft Windows combines presentation quality scientific graphs with comprehensive data fitting The result is a powerful package that is easy to use produces stunning output and can also fulfil the needs for quantitative data analysis Data can be fitted using various types of theoretical models and your own equations can easily be added to those supplied with the program Comprehensive graph plotting facilities allow you to display y
111. eree eget 109 Setting Text Properties sssssssssssseee nemen 109 General Object Properties ssessssssssssnn ees 110 viii Contents Fill Properties ie e apodaca ai Pri den 111 Line Properties es s ter eR D LE ORE FREUE AERE R I 111 Rotation Properties iner e e e repe PO EE ees 112 Location Properties ee tt ER PERSE Fedra nasa 112 Arfows PFopertl6s eeepc te o ets ema qu eg Ee n RATER AR 113 Font Properties oe pre e ERE REX ED ER POR ERR X ERR ER de 113 Paragraph Properties oe atlas 114 X Y Scatter GraphS omococococnonononononoroaracacanannnnnnonannnnnararnrnnnnnnnnnnrnrnrnrncanasa 115 THE XY Graph Wizard oi esent esten ae DR er ia Pat De cete 115 Select Data Source Page ssssessssssssssesen menn 115 Set Initial Scala ede eds 117 Select MTS Ye c ero a ose ero in enr ve e 118 Select Data Point Style sssssssssssssssee eene 118 Enter Curve Parameters ooocccccccnnnncnnnnnnnnnana narran ana na sonar an rnarananas 119 Enter Curve Constant sssssssresserrrrrrssrnrnrrrreserrurrrresrenenoreeue 120 Select Fitting Curve Style ocooococccncncncncccnonononornnnnnnnn eene 120 Select oin Style ier ve e eta v e el rs 121 Modifying Graphses o Ios 122 Selectable Regions of a Graph ooocccccccncncnonoconnnnnnnnnnnnnnononnnnnnnnnnns 123 Main Grapli ReglOn Er et p iia alae in 123 General Page ek X EUER RU Mi MR RE 124 Fill Pagem ia DT 125 liti Page eroe toee o
112. ertainties need be known and if we assume that all the data points have the same inherent errors the equations simplify to give 2 3 X TE Nd Xx pet N y E DA Yn AN DA S Xs 188 Chapter 20 Theory This assumption that the errors are constant is often made for example in the simple linear regression calculations performed by pocket calculators Although often true this assumption is not always valid In many experiments the uncertainty varies with the magnitude of the y value such that the percentage error is constant To account for the different types of error distribution we introduce a weighting factor which is related to 1 0 and is used to multiply all elements of the above matrices Weighting Types The following types of error distribution are easily accounted for and can be selected for use in the GraFit program within the Linear Fit or Non linear Fit item windows Constant error The standard error c is the same for each data point and therefore a weighting factor of 1 is used Simple weighting This type of error is often given by instrumental variations for example a gauge may be read to an accuracy of 0 1 units etc Statistical error For statistical variation where o varies in proportion to y the weighting factor is 1 y This type of error distribution is uncommon but is found in systems where the main errors arise from sampling for example counting low number
113. es and the data can be associated with one the minimum or many different axis scales Check the boxes of all axes that you wish to be associated with this data set 142 Chapter Error AutoText entry not defined X Y Scatter Graphs Equation Page equation data only Curve Properties 12 1x Fitted Curve Equation Parameters Constants Axis Association Equation definition Equation Enzyme Kinetics x JJ This page selects the equation that describes the curve to be plotted All equation items present in the GraFit workspace are listed Parameters Page equation data only Curve Properties 12 1x Fitted Curve Equation Parameters Constants Axis Association Parameters z 3 C Read from table y x 143 GraFit User s Guide This page is equivalent to the Curve Parameters page of the XY Graph Wizard see page 119 for further information Constants Page equation data only Curve Properties 12 1x Fitted Curve Equation Parameters Constants Axis Association r Constants Read from table y Constant x Ja This page is equivalent to the Curve Constants page of the XY Graph Wizard see page 120 for further information This page is present even for equations that do not define any constants as is the case for the figure above Legend Text Regions Legend text properties are controlled in the same way as normal text objects ex
114. ffset value 1 Site with background Scatchard Use this transformation to display Scatchard plots for binding data containing a background value 1 Site with background Show background This transformation shows the background value 1 Site with background Show Capacity This transformation shows the capacity 228 Chapter Error AutoText entry not defined Equations Provided 1 Site with background Show Kd This transformation shows the dissociation constant K For best results set the curve resolution to High when using this transformation 2 Site e i a A Often there is more than one type of site involved in 2 4 binding the ligand This equation describes the case of 3 two sites characterized by individual Ky and Capacity 2 LigrulBrury 25165 values The equation is LI Capg LJ Capo me um a m A ue 4 Kay HEY Kay L 2 Site Show Capacity total This transformation shows the total binding capacity for ligand 2 Site Show Capacity 1 This transformation shows the capacity of the first binding site 2 Site Show Curve 1 This transformation shows the binding curve for the first binding site in isolation 2 Site Show Curve 2 This transformation shows the binding curve for the second binding site in isolation 2 Site with background This equation describes the situation where two independent binding sites are present but the y value at zero
115. finition but it is rare to find equations that involve more than four or five parameters Constants Pane The Constants pane is used to define constants in the equation definition Constants are used to allow the entry of a value into an equation definition that is 79 GraFit User s Guide fixed in any single experiment but varies from experiment to experiment The presence of constants is optional but when present an equation definition can include any number of constants When constants are included in an equation used for non linear regression their values are entered into the non linear fit item window as described in Chapter 6 Enzyme Kinetics A x Estimates Fonts Indents General X Variables Parameters Constants Definition _ Symbol Description A Eo Initial enzyme concentration The Constants pane of the Equation item Delete Row Insert Row The organization of the Constants pane is very similar to that of the X Variables pane and the definition of Symbol and Description names is performed in an analogous manner see the X Variables Pane section above The number of rows of information that are entered into the grid defines the number of parameters in the equation If no constants are required as will be the case for many equations this page should be left blank Definition Pane 80 The definition pane describes the functional form of the equation using the Symbol names of the x variables th
116. gend box within the graph page 133 GraFit User s Guide Data Curve Properties Data Points Page Fitted Data Properties xx 0 3123 s Of Of we Medium y This page is equivalent to the Data Point Style page of the XY Graph Wizard See page 118 for further information 134 Chapter Error AutoText entry not defined X Y Scatter Graphs Join Points Page Fitted Data Properties This page is equivalent to the Join Style page of the XY Graph Wizard See page 121 for further information 135 GraFit User s Guide Fitted Curve Page fitted data and equations only Fitted Data Properties This page is equivalent to the Fitting Curve Style page of the XY Graph Wizard See page 120 for further information 136 Chapter Error AutoText entry not defined X Y Scatter Graphs Data Source Page fitted data only Fitted Data Properties Select the data fitting item to be plotted from the Results selection which lists all the available linear and non linear fits in the GraFit workspace Fitting items can hold several fits and the Fit number can be chosen The first fit is fit 1 which in most cases will be the only fit present Check the Transform as box if you wish to display the data points and fitted curve transformed as defined in the selected transformation All the transformations present in the workspace are listed See Chapter 10 for information abou
117. gram depending upon the value of a parameter constant or independent variable if extra 1 then return al b x endif if extra 2 then return a2 b x endif if extra 3 then return a3 b x endif return a4 b x Comments Comments can be added to annotate the equation definitions Anything after an apostrophe is a comment as is anything after a semi colon Looping Statements The or statement has the following syntax for varname startValue to endValue statements for varname startValue to endValue step stepValu statements Goto Statement Another statement that will be familiar to programmers is the goto statement In GraFit equations this is implemented in the following manner labelName statements goto labelName 85 GraFit User s Guide labelName can be any valid name using the same rules as apply to the names for symbol names The label may come before or after the goto statement Note Indiscriminate use of goto could result in an infinite loop Estimates Pane 86 The Need for Starting Estimates Non linear regression works by taking initial estimates for the best fit parameter values and by an iterative process calculates successively better values until the best fit values are reached It is therefore necessary to provide the program with suitable starting estimates which should generally be of the same order of magnitude as the actual ones If an equation defin
118. h pH They usually involve the determination of one or more pK values from the experimental data pKa min 0 This equation is used when the observed parameter varies with pH from 0 at low pH to a limiting value at high pH Examples include various enzymatic activities The equation is Y _ Limit 104 10 PHP 41 pKa min 0 Linearized Plot Displays the line for the linearized titration curve The linearized equation is y amp 4 Limit H pKa min 0 Show Limit This displays the limit value of the y axis at high pH pKa min 0 Show pKa This transformation is used to represent the position of the pK on the curve where there is a single ionization and the starting value is O For best results set the curve resolution to High pKa min 0 High to Low This equation is used when the observed parameter varies with pH from a limiting value at low pH to O at high pH pKa min 0 High to Low Show Limit This displays the limit value of the y axis at low pH 232 Chapter Error AutoText entry not defined Equations Provided pKa min 0 High to Low Show pKa This transformation is used to represent the position of the pK on the above curve For best results set the curve resolution to High a UnbBep s pKa Double pups This equation is used when the observed parameter j M iun varies from one value
119. he slope and intercept to be found from which it is possible to calculate Kk as Chapter Error AutoText entry not defined Equation Item intercept gradient Eg and K as 1 gradient It must be stressed that this approach does not provide strictly correct values for koat and K this is why we wish to use non linear regression in the first place Further information can be found in Chapter 19 The values provided are suitable however to use as initial estimates for the non linear regression analysis It is instructive to compare the initial estimates provided by this method with the final values produced by the non linear regression analysis As they are demonstrably different this illustrates the danger of using linear regression of a linearized function for analyzing data The Estimates Pane Enzyme Kinetics olx General x Variables Parameters Constants Definition Estimates Fonts Indents IV Estimate from linear transform r Data transforms f data ydata X data a Y data pdatazsdata 00000000000 r Parameter estimates from transform f intercept gradient Parameter Definition d kcat t intercept aradient Eo Michaelis Constant 1 gradient The Estimates pane of the Equation item To specify that initial estimates are provided for an equation the Estimate from linear transform box should b
120. he program are installed into the Group Item Store directory and can be accessed using the File Add Stock Item command Equations are grouped into separate sub directories which appear as different pages on the Add Item dialog box Add Item Lx General 2 Substrates Enzyme Inhibition Enzyme Kinetics Exponential IC 50 Ligand Binding pH Rate IC50 full 4 param IC50 full 4 param show background IC50 full 4 param show IC50 T IC50 full 4 param show limit GK Cancel Apply Equation and transformation definitions are distinguished by the nature of their icons The following sections describe the contents of these various pages 219 GraFit User s Guide 2 Substrates The definitions on this page are designed to analyze enzyme kinetic data involving two substrates Ping pong Use this equation where a ping pong mechanism applies The equation relating the rate of reaction v to the concentration of substrates A and B and the constants Ky and Kg is 2 Vmax l AJIB K A K B A B 12 Ping pong Lineweaver Burk zh MA i Bas Generates a Lineweaver Burk plot for the fitted data eos E gt A BL Q4 E cel eu A o T Oo 2 4 VA 10 Ternary B J i BS Use this equation where a ternary complex is formed i The equation relating the rate of reaction v to the B concentration of substrates A and B and the 7 B 05 constants K Ka and
121. his is defined as below Y ed V Here v is the number of degrees of freedom which is given byv 2 N n 1 Nis the number of data points and n is the number of variables in the equation Regression analysis is the mathematical equivalent of finding the best line by eye it has the advantage however of being non subjective It is also possible to fit the best curve through the data by non linear regression This has no manual equivalent because humans are very poor at judging accurate curvature but is equally simple mathematically using computational methods 185 GraFit User s Guide Assumptions in Regression Analysis 186 Regression analysis is probably the most powerful method to analyze data However such analysis involves several assumptions about the function chosen and the error structure of the data These assumptions are listed below The Correct Equation is used This assumption is often overlooked but should be borne in mind when using any data analysis technique It is important to be aware that deviations from ideality are often caused by use of an inappropriate equation Graphical methods provide a useful means to see whether the chosen model equation is appropriate This is because use of an inappropriate equation often results in systematic deviations from the curve which is easy to see in a graph Residual plots of Ay versus x are useful to assess whether the equation is appropriate Systematic deviations
122. imates Fit number fi Y data column Unknown Absorbances Estimated from polynomial Estimated from non linear fit Interpolate between X limits From 1 0 To 200 Fitting Several Data Sets with Some Parameters Common and Some Specific To illustrate imagine that you have collected two linear data sets and that you already know that for this experiment the slope is the same for each although the intercepts are different Using GraFit it is possible to fit these two data sets to find the best slope that is common to each and the two intercept values that are specific to the two data sets Indeed it is possible to fit two or more data sets to any of the normal equations that GraFit can use and to share one or several parameters between the data sets The example below shows how this is done for the paired linear data Two raw data sets are illustrated below these data are in the example file Paired linear regression Fitting these two data sets individually results in similar but not identical values for the slope This is shown in the figure below 213 GraFit User s Guide IS If the data sets are known to have the same slope this can be incorporated into the data fitting as follows Method Used to Share Variables Between Data Sets 214 Sharing variables between data sets involves using an equation with a second independent x variable which is defined in such a way that that this
123. ineweaver Burk transformation is used to produce a double reciprocal plot ofthe data The transformation is associated with the The General pane of Michaelis Menten enzyme kinetics equation The transformation is the Transformation i item v 5 PAGAN Kon En The description is optional but adding a text description of your transformation definitions is strongly recommended As illustrated in the figure above the descriptive text allows rich formatting options with multiple font types styles sizes and colors allowed It is also possible as shown above to include any OLE object in the text In this particular example a Microsoft Equation 3 0 object has been embedded within the text Chapter Error AutoText entry not defined Transformation Item Data Points Pane The Data Points pane describes how data points are transformed for plotting If the Transform data points box is unchecked no data point transformation is used Otherwise the remainder of the window describes how the data are to be rearranged when this transformation is applied Lineweaver Burk olx General Curve Fonts Indents Y Transform data points m Transformed x data r Transformed y data Definition f xdata ydata Definition f xdata vdata 1 xdata 1 ydata fa l The Data Points pane Default X name for graph Default Y name for graph of the Transformation item fi ES fi 32 m Symbols Parameters Cons
124. ing elements of the program will recognize such points and omit them from the analysis The representation of these different data types is illustrated in the following diagram Data 2 OF E Text 1 2345 Text Label 5 431 A Another label Number Missing value 25 GraFit User s Guide Forcing Text Entry GraFit displays text items as they are entered but formats numbers dependent upon the current column formatting Table Column Format command To force numbers to be treated as a text item enter them with a preceding symbol for example 2 34 Forcing text entry can be useful if a number is used as one of the entries in the category axis of a chart Note Numbers forced to act as text are not available as data items and will be treated as missing items during data fitting Moving the Data Entry Position 26 When you have entered your data value you will need to move to the next data entry position by pressing TAB RETURN Or DOWN after entering the value The following keys control movement of the data entry position within the data table To Press Move the entry point to the right TAB Or RIGHT Move the entry point to the left SHIFT TAB Or LEFT Move the entry point up UP Move the entry point down DOWN Or RETURN Move to the first column of a row CTRL LEFT Move to the last column that contains data entries CTRL RIGHT Move to the first row of a column CTRL UP Move to the last row that contains data
125. iption p p po2 Parameters Symbol Description K K1 K1 value K3 K2 K2 value K3 K3 K3 value Ka K4 K4 value Y name Sat Definition 12 Sat 100 Kl p 2 K1 K2 p p 3 K1 K2 K3 p p p 4 K1 K2 K3 K4 p p p p 4 1 Kl p K1 K2 p p K1 K2 K3 p p p K1 K2 K3 K4 p p p p The appearance of the equation definition item after entering this definition and changing the name of the item is shown below 12 As this definition is for demonstration purposes only it is defined in this way as this is the nearest form to that of the equation given Although the definition would function in this form it is rather inefficient to write it like this and a better approach would be to enter the mathematically simpler Sat 100 K1 p 1 K2 p 2 K3 p 3 K4 p 4 4 1 K1 p 1 K2 p 1 K3 p 1 K4 p Chapter 21 Worked Data Fitting Examples Oxygen binding To fit these data add a new non linear fitting item using the Add Non linear fit command then complete the Settings page as below ff Non linear Fit Explicit user defined y T irj pas 0 0 0 sj Error Note the use of Explicit weighting which requires the selection of the column that holds the error values The results of the analysis are as follows 205 GraFit User s Guide NV VY For comparison the results quoted by Roughton et a are given below Parameter Standa
126. irectories that have special significance when storing template files These are the user and group template directories the location of which is specified from the View Options command Directories tab 19 GraFit User s Guide 20 Click on the button to change a directory setting By having two separate locations for templates it is possible to keep user specific files separate from general templates that are used by a group of users It can be useful as illustrated above to maintain a group directory on a network server Files in a template directory appear on the General tab of the File New dialog box Any subdirectories have special significance and result in additional tabs on this dialog clicking on the tab accesses the files in these subdirectories Note that empty subdirectories do not appear Chapter Error AutoText entry not defined Working with Files 31 User Templates 3 Subdirectory 3 Subdirectory 2 3 Subdirectory 3 General Subdirectory Subdirectory 2 Subdirectory 3 E E Template File Template File Template File 2 Cancel al The files displayed on this dialog box are the sum of those present in the user and the group template directories The specific location of any individual file can be found by right clicking on the icon and choosing the Properties command In the event that a file with the same name is found in both the user and group dire
127. is definition Function Description Data x y Returns the data value present within the data table at column X TOW y ValidData x y Returns TRUE if a valid number is present in the data table at column x row y and FALSE otherwise SetBlank If this statement is encountered the current cell is set to be blank and the calculation skips to the next row column Returns the number of the current column This value is most useful in conjunction with the pata function row Returns the number of the current row This value is most useful in conjunction with the pata function rnd Returns a random number between 0 and 1 grnd Returns a random number that falls within a Gaussian distribution that has a zero mean and unit variance 51 GraFit User s Guide 52 The following examples show how calculated functions might be specified and used Process Result field Description Background data 1 row 0 234 Subtracts the value 0 234 from subtraction the values in column 1 Log log data 2 row Takes the logarithm to base calculation 10 of the values in column 2 Complex data 1 row 1 34 For each row in column 1 rescaling data 2nrow J data3 dg multiplies this value by 1 34 then subtracts the data in column 2 which has been divided by the value in column 3 row 2 Multiple line if validdata 1 row then For each valid data entry in statement P oca data l row 23 3 column 1 sets the
128. ition alone is provided the program cannot know what initial estimates are appropriate In this event when the equation is used the program will ask you to enter initial estimates before fitting the data To relieve users the inconvenience of estimating parameter values GraFit provides a means of generating these estimates automatically It should be noted that the method used is not foolproof and requires familiarity with manipulating equations It does however make data fitting simpler and can be over ridden if the estimates provided are inappropriate In addition equations can be defined without provision for automatic initial estimation Method Used to Obtain Initial Estimates The method used is based on performing linear regression on rearranged data It is often possible to rearrange data in such a way that a linear plot is obtained with the parameter values being related to the gradient and intercept As linear regression needs no initial estimates this can be used to estimate these parameter values providing the program knows the following 1 The rearrangement that is needed 2 How the parameter values relate to the gradient and intercept This process is illustrated using the previous example where the equation is Ky SI Eo Kn S We can rearrange this to a linear form by plotting v S against v v kKj4 Eg v S K K m m This is the so called Eadie Hofstee equation Plotting v S against v and allows t
129. ituent parts 123 GraFit User s Guide Note The x and y axis scales have a particular relationship with the main graph as it is usual to ensure that their numbers line up with the scale marks For this reason by default it is only possible to move the x axis scale in a vertical direction and the y axis scale in a horizontal direction This effect can be overridden by holding down the ALT key when moving the axis scale texts General Page 124 XY Graph Properties HES General Fill Line X Ticks A Scale Y Ticks Y Scale Location r Graph frame Drawing options M Top Iv Left Draw frame and axes Gi 3 over data points v Bottom M Right m Visibility MX axis text IY axis text Ix Axis Scale IY Axis Scale W Data Legend Box Apply Cancel Graph frame Check the various boxes to draw a line on the various edges of the graph Drawing options Check this box to specify that the graph frame axes and tick marks should be drawn after the data points which will result in these items lying on top of the data points By default XY graphs have this option unchecked and column graphs have it checked Visibility The components of the graph are listed here and their visibility can be set by checking the appropriate box Individual items on the graph can also be hidden selecting the Edit Hide Object command Chapter Error AutoText entry not defined X Y Scatte
130. ively These values can be of benefit if you need to obtain rough estimates of limits where the limiting value can be approximated by the maximum recorded value It is also possible to enter numeric values directly as estimates In some situations rough numerical values provide suitable estimates without recourse to the more complex methods described above Compiling the Equation 88 To compile the equation choose the Equation Compile command Compilation translates your definition into an internal form that can be executed rapidly During compilation the definition is comprehensively checked to ensure that the correct syntax has been used If an error is detected a message box will be displayed informing you of the mistake after pressing the OK button to continue the cursor will be placed at the most likely place of error GraFit Missing N An Error Message Box To obtain further information on the specific error click the Help button or press the F1 key Once the equation has been correctly compiled it can be used for data fitting and or graph plotting CHAPTER 10 Transformation Item Overview of Transformation Definitions Transformation definitions are used in order to allow data and curves to be displayed on a graph after application of a user defined transformation For example one use of a transformation definition would be to allow a double reciprocal plot to be displayed Transformations describe meth
131. l sets of results being generated The available options for a standard equation having a single independent variable are given below Layout Meaning A single data set is present and the columns holding the x and y data values are specified individually from the X data column and Y data column entries The x and y data columns do not need to be in any particular order within the data table x Yai vei Multiple data sets are present although all data sets have common x data values The x and y data columns are consecutive in the data table The location of the x column is set from the X data column entry the location of the final y column is set from the Last Y data column entry The number of data sets present is determined automatically ES Multiple data sets are present and the data sets have different x data values Pairs of x y data columns are present consecutively in the data table The location of the first x column is set from the First X data column entry the location of the final y column is set from the Last Y data column entry The number of data sets present is determined automatically X Data Column This entry specifies the column that holds the x data values See the Data Layout section above for further information Limiting X Data Range It can sometimes be useful to restrict data fitting to a subset of the values in the columns For example it can be useful to fit just the initial portion of a data set
132. l source file Changes to this source data file result in the information copied to the target application also changing In addition if the linked object is edited from within the target this will change the original document Because linking must always involve files it is only possible to create a link after the information in the source application has been saved to disk Source Application Target Application a Linking does not copy the original data but allows the target application to maintain links to the original source file Changes to the source result in the target application being updated Using Embedding and Linking Windows applications that are able to employ OLE use the convention that Edit Copy from the source program will place the necessary information on the Clipboard and Edit Paste from the target application will embed an object 170 Chapter 18 Embedding and Linking Therefore it is the standard that embedding is used by default To link to an object the same Edit Copy command is used in the source program but depending upon the target application the object is inserted with the Edit Paste Link or Edit Paste Special command The OLE object can be activated by double clicking on its representation within the target or by accessing the object menu which resides on the Edit menu and is often also available by right clicking on the object Comparison of Data Tran
133. le independent x variable In equations with multiple independent variables the observed value y varies as a function of more than one variable condition For example the rate of an enzyme reaction may vary as a function of both substrate and inhibitor concentrations In this case there are two independent x variables In principle it is possible to have any number of independent variables although in practice it is rare to fit data where more than two independent variables are present Parameters Pane The Parameters pane is used to define the parameter values in the equation definition The parameter values are the unknowns in the equation and non linear regression allows data to be fitted in order to find optimal values for these parameters Enzyme Kinetics olx Estimates Fonts Indents General X Variables Parameters Constants Definition Symbol scription l Michaelis Constant The Parameters pane of the Equation item Delete Row Insert Row The organization of the Parameters pane is very similar to that of the X Variables pane and the definition of Symbol and Description names is performed in an analogous manner see the X Variables Pane section above The number of rows of information that are entered into the grid defines the number of parameters in the equation At least one parameter must be defined There is no formal limit to the number of parameters allowed in a GraFit equation de
134. liminated by use of robust techniques as will be described later in this chapter The Correct Weighting is used An explanation of what weighting of data in regression analysis is why it is incorporated into all such analysis including the subjective regression performed by drawing the best line using a ruler and how the appropriate weighting can be determined are described later Linear Regression The simplest case for regression analysis is when the equation is linear For the linear equation y a t bx x is defined as xl O i 1 Z Iho a e i In this equation o is the standard deviation of the data point The best fit to this equation will yield parameter values for a and b that produce the minimum possible value of x2 This is equivalent to saying that the first derivative of y with respect to a and b is equal to zero 187 GraFit User s Guide Q VE 7 1 2 a y ayi y a bx x Cy a ix 0 E A cpu m syi y a ix X 25 y a br 0 If we rearrange these equations it is possible to solve for a and b exactly to give values for these parameters that minimize y2 This is shown in the equations below Ez Los PME mos 1 i Nd ie x ELE 1 qum A l L no ze Weighting This analysis presupposes that we know the standard deviation of for each data point In general we will not have such information available However only relative unc
135. linear It is possible to fit these data by defining a new specific equation The required definitions are as follows 14 Toney M D amp Kirsch J F 1989 Science 243 1485 1488 208 Chapter 21 Worked Data Fitting Examples Equation Name Multilinear kinetics X Variables Symbol Description pK pKa pKa value Vol Vol Molecular volume Parameter Symbol Description B Beta Beta V V V C C Constant Definition beta pKa V Vol C The results obtained from fitting these data are Variable Value Standard Error P 0 39 0 05 V 0 055 0 005 C 0 7 0 5 Displaying Multidimensional Data Displaying data sets that have more than one x axis can be difficult One solution is to remove all but one dimension from a plot For example in the above data a plot of logk V Vol versus pK will result in a linear graph with a slope p and intercept c We can create the logk V Vol data using the data manipulation abilities of GraFit the result for V is obtained from the curve fitting The first step assuming that the data have already been fitted is to allow the calculated V value to be accessed This can be done by creating a data column that displays the fitting results To do this select a blank column and choose the Table Column Type Data Fitting Results command and select the appropriate Non linear Fit item The second step is to select the next blank column and choose the Table Column Type Data Processi
136. ling GraFit CD ROM Installation Insert the GraFit CD ROM into your CD drive The Welcome screen will load automatically Note Some systems are configured so that automatic running of CD ROM software is disabled If your system is set up in this way the Welcome screen can be displayed by selecting the Run command from the Windows Start menu and entering the command D VCDRUN where D is the drive letter of your CD ROM Microsoft Internet Explorer GraFit uses a new HTML help system that will become a standard feature in the next generation of Windows To use this help system it is necessary to have Microsoft Internet Explorer version 3 02 or later installed on your computer If you do not already have this software installed select the Install Internet Explorer 4 option and follow the instructions Note The installation of Internet Explorer will update some of the system files on your computer If you are running Windows NT this will require Administrator privileges Please consult your computer administrator if your account does not allow you to do this GraFit Select the Install GraFit option to install GraFit onto your computer The installation program will copy the files to your hard disk and place an entry for the GraFit program on the Start button under the Programs entry Adobe Acrobat Reader The GraFit CD ROM includes this user manual saved in Adobe Portable Document Format PDF If you wish to read this file it
137. ll items that contain suitable data for plotting and one of these must be selected Category axis Select which column holds the category names that are to be plotted Upper data The Upper Data selection is used to choose the data column that holds the values to be associated with the selected categories Error column Checking the Error column box allows a quick way of producing an error plot Select the column that holds the error values from the list More extensive error plotting options are available once the graph has been produced Lower data Check the Lower data box to generate a High Low chart where the entries have both an upper and lower value If this box is unchecked a standard chart will be produced if checked then it is necessary to choose the column that holds the lower data values for the High Low chart Lower error column When the Error column and Lower data boxes are both checked the error values for the lower data are selected from this box Chapter Error AutoText entry not defined Column and Bar Charts Set Initial Scaling Chart Wizard Set Initial Scaling aam Categories fey poo The Set Initial Scaling page allows the scale of the data axis to be specified By default the scale is set automatically and a linear data axis is chosen These can be altered as required it is also possible to adjust the scale settings later The text used for the data and category axes can also b
138. lues themselves are listed in the data table Click the mouse on a value to move the data entry position drag the mouse to select larger regions of the data table Newly entered data is placed at the data entry position which can be moved using the cursor keys or by clicking the mouse on a different part of the data table Click and drag the mouse on the column numbers to select entire columns of data Click and drag the edges of a column to resize it Click and drag the mouse on the row numbers to select entire rows of data within the data table Click and drag the edges of a row to resize it Drag the splitter box on the horizontal scroll bar to divide the data table window in two The two halves can be independently scrolled allowing distance regions of the table to be viewed simultaneously Drag the splitter box on the vertical scroll bar to divide the data table window in two The two halves can be independently scrolled allowing distance regions of the table to be viewed simultaneously Resizing Rows and Columns Cursor np de lb The row height and column width can be set using the Table Row Height and Table Column Width commands respectively or by using the mouse to drag the edges of the rows or columns within the row or column selection region Columns can be sized to fit their contents using the Table Size Column to Fit command Data Types The number of data points that can be entered is
139. lved in the high data points of the transformed plot is much greater than in the low data points this is simply a consequence of the reciprocal transformation Linear regression unless suitable compensation is made for the distorted errors is therefore not an appropriate way to analyze the data and the original data should be fitted to the appropriate non linear equation Information Obtained from Data Fitting 180 Data fitting provides the following information regarding the experimental data that are analyzed 1 2 The values of the parameters in the equation used that best describe the data These parameters may include for example rate constants inhibition constants etc whose values need to be determined The accuracy of these calculated parameters From this information it is possible to judge how well the data fit the experimental model equation that was used In most cases however it is the numerical values of the parameters that are important and whose values are required from the analysis Chapter 19 Data Fitting Basics Multiple Regression The most common form of non linear equation that is analyzed by GraFit is of the form y f x where the right hand side of this expression may contain one or several parameters Such an equation has one dependent y and one independent variable x In addition GraFit can be used to analyze equations with more than one independent variable i e y foa Xz
140. menus are present a vertical bar is used to separate the sub menus For example the Windows Control Panel application is started from the desktop Start Settings Control Panel command Important information that should be noted is written in italics and separated from other text by horizontal rules as here Contacting Erithacus Software Address Erithacus Software Limited PO Box 35 Staines Middlesex TW18 2TG UK Chapter Error AutoText entry not defined Introduction Technical Support At Erithacus we are working hard to provide you with intuitive technical products However if you find yourself with a technical question that you cannot resolve please contact our technical support department Registered users can obtain technical support from one of the following sources Fax 44 0 1784 442005 Email support erithacus com e Internet http www erithacus com Note Always quote your serial number and the product version which are shown on the About screen Help About GraFit command Internet Our web site can be found at http www erithacus com and here you will find latest information about our software products In addition we post technical notes tips and answers to common problems Tip Be sure to check out http www erithacus com to download the latest fixes and updates GraFit User s Guide CHAPTER 2 Installation System Requirements Software GraFit version 4 is a fully 32
141. more convenient to use pK values where pK log K The variation of the ratio of A and AH is given by the Henderson Hasselbalch equation A pH pK logi HA The chemical shift observed for the nucleus varies between that measured at the extreme acid range 5 and that at the extreme alkaline range 5 depending on the ratio of A T HA The data obtained are chemical shift values in units of ppm or parts per million at various pH readings These values need to be fitted to a single ionization curve 195 GraFit User s Guide 196 where the start and end chemical shift values and the pK are the unknown parameters Fitting the Data The example data are in the file pH Titration which can be opened using the File Open command Two columns are present in the data table pH and Chemical Shift No other workspace items are present Load the Equation The first action to take is to load the correct equation Use the File Add Stock Item command select the pH tab and choose the pKa Single equation definition item Add a Non linear Fit Item to the Workspace Use the Add Non linear Fit command to add a non linear fit item to the GraFit workspace Fill out the Non linear Fit Item Settings Complete the Settings page as shown below Non linear Fit olx Results Number Format Fonts Indents Settings Constants Estimatrix Fitting Criteria Equation pka Single Weighting Si
142. mple Robust Data table Data y Data layout E y data column pH pH Limit x range ta Y data column Chemical Shift y Errar column lnc El Set up Initial Estimates The pKa Single equation is one for which initial estimates for the parameter values are difficult to provide automatically Therefore it is necessary to enter these initial estimates explicitly For equations that require initial estimates it is essential to set these from the Estimatrix page Click on the Estimatrix tab then on the Interactive Estimator button Chapter 21 Worked Data Fitting Examples Non linear Fit Bl x Results Number Format Fonts Indents Settings Constants Estimatrix Fitting Criteria la Estimates from metry Interactive Estimator Stc Interactive Estimator 27 xi Cancel Graph scale A min NN Xmax 19 04 Y min 7 8502 Y max e7558 4 5 6 7 8 3 Auto Scale puru Status OK Chemical Shift Enter values into the Estimated value grid as you move the entry position the new values will be used to create a theoretical curve red on the plot As described in Chapter 20 the starting estimates for non linear regression should be reasonably close to the true values but it is not necessary to be too exact The program then iterates to find successively better values until a satisfactory fit is found When you are satisfied with your estimated values click OK to retu
143. n Microsoft PowerPoint Presentation Y C Create from File Result Inserts a new Microsoft Equation 3 0 object into your document Choose the object type to create then click OK Editing OLE Objects An inserted OLE object can be edited by double clicking on the object of by choosing the appropriate menu command from the Edit menu X Variables Pane The X Variables pane is used to define the names of the independent x variables that are used in the equation All equations must have at least one independent variable and can include more than one Enzyme Kinetics Ox Estimates Fonts Indents Parameters Constants Definition The X Variables pane of the Equation item nse how 77 GraFit User s Guide 78 Naming Rules All name definitions for use in an equation definition are entered into a grid that has space for a Symbol and a Description entry All names must have a Symbol entry but the Description field is optional Description Entry If a Description entry is made GraFit will use this long name whenever it refers to the name for example when listing results If no Description entry is present GraFit will use the Symbol entry Description entries can incorporate any characters including spaces and punctuation characters that are illegal in Symbol entries Symbol Entry The symbol entry is the name used in the equation Definition page Symbol names must obey a number of r
144. n addition the name of the parameter can optionally be displayed next to the data value by checking the Value name option Chapter Error AutoText entry not defined Data Tables Information This column type lists information about a data fitting item Fit r Fitting information Cancel x data column name VY data column name Error data column name w Number of data points VICh value W Correlation coefficient Data V Display value name 0 0000 110 0000 X column Time 1 0000 80 0000 Y column Amount 2 0000 60 0000 data 6 0000 3 0000 45 0000 Chi 293 3333 4 0000 35 0000 Corr coeff 0 9688 5 0000 28 0000 After the fit to be displayed is selected the available information items are listed Some or all of these can be included by clicking in the check box to the left of the parameter name If more than one set of data were analyzed in the selected fit the information for each fit is given The name of the information type can optionally be displayed next to the data value by checking the Display value name option Parameter Entry The Parameter Entry column type gives a convenient way of entering parameter values for a particular equation into a column Certain graph plotting options allow these values to be used when displaying graphs The equation to use is selected after which it is possible to enter values into the column 45 GraFit User
145. n Error Message Box To obtain further information on the specific error click the Help button or press the F1 key Once the transformation has been correctly compiled it can be used for graph plotting CHAPTER 11 Notepad Item Uses of Notepad The notepad provides a text editor window where information can be stored in the GraFit workspace Uses include making notes about the data the analysis of the results and writing brief documentation on how to use a particular data file or template The notepad item is created from the main GraFit window using the Add Notepad command The Notepad Item Window EE Notes iO x Hello These notes are stored in the GraFit workspace Notes can include text with MULTIPLE fo nts styles Sie and colors They can also include embedded objects such as the The Notepad item Microsoft Paint picture added below window The font styles are set from the formatting toolbar or using selections from the Font menu Notepad windows automatically wrap their contents so that the line width is equal to the width of the window Alternatives to the use of Notepad Items The notepad item provides a simple text editor that has many of the capabilities of the Windows WordPad application However it does not provide the wealth of features present in a dedicated word processing application such as Microsoft 95 GraFit User s Guide Word It is however possible to harness the power of a
146. n be used just like any other Windows font The various symbols are associated with the characters as shown in the following table A B CI DIE FG H1 J K L M N OP OJLD A VIOoJ O X xX w e La 94 10 0 ajb ci d e fig h i ji k l minjo p 8 A v9 9 X XI 4 0 0 S T JU V W xX Y Z 1 2 3 4 1 5 EJ ug A MEBI NS 31 sexes Note The GraFit symbols font does not contain any hinting information to assist reproduction on low resolution displays For this reason it will not display well on screen although it will print correctly 245 GraFit User s Guide 246 Index _grnd_ function 51 84 _rnd_ function 51 84 A Adair Equation 230 Add menu 11 Data Table command 23 Equation command 75 204 Graph command 97 103 198 200 Insert New Object command 173 Linear Fit command 69 Non linear fit command 205 Non linear Fit command 55 196 Notepad command 95 Transformation command 89 Adobe Acrobat 6 Allosteric Data 203 Allosteric Kinetics 222 Arithmetic operators 82 Arrows 113 ASCII format 35 Axis manager 148 150 151 Axis offset 126 Axis scaling 153 Bar charts 100 157 164 Bezier curves 122 Cc Calculate menu Fit Data command 55 69 Calculated values 46 Calibration Curve 211 Chart Wizard 157 Chi squared 185 187 Clipboard Windows 28 169 170
147. n be set to hold the results of various calculations or data manipulations For example a column can hold the difference between the values in two other data columns The results of these calculations are automatically updated when the source data change allowing powerful processing of the underlying data 35 GraFit User s Guide 36 Example setting up a difference calculation As an illustration we will show how to set up the following data table in which the third data column holds the difference between the values in the first and second columns Type area of 1 0000 column 3 0 1000 The column type of the third column needs to be set by moving the data entry position to somewhere within this column and choosing the Table Column Type Column Combinations A B command Alternatively the Column Type submenu can be accessed by double clicking in the type area of the column For this column type setting the following dialog is displayed Calculate A B 121 xi Data column 4 Data column B Value 2 Difference Difference Choosing Value 1 as the first column and Value 2 as the second gives the result above The values that are displayed in this column cannot be overwritten or edited and are updated whenever the values in the source columns changes The text color of the calculated values can be adjusted using the Table Preferences command but is typically shown a different color than the editable text in order
148. name so that you can identify it in the current example it has been set to Differences To create a graph of the residuals on a new graph page select the Add Graph command and create an X Y Scatter Graph Create this graph using the data table as the source the Chemical Shift for the x data and the Differences column for the y data XY Graph Wizard Select Data Source Data set 1 Data te All fits C Single fit Differences Elect to join the points with a straight line as below Chapter 21 Worked Data Fitting Examples Join points Ipe EHNMENNNNNN Width fos pt Style Line v Coot mmo z coe The resulting graph is shown below As is clear from the shape of this plot see the discussions in Chapter 20 it was probably correct to use simple weighting with these data Ay versus x plots are easily made by plotting pH against the Differences To make Ay y versus y plots it is possible to create a new column to hold the result of dividing the Differences column by the original y data column Chemical Shift This can be created after data fitting by setting the Table Column Type of one of the next available columns to Column Combinations A B 201 GraFit User s Guide Calculate A B 21 xi Data column 4 Data column B pH Chemical Shift Differences Column 4 Using Robust Weighting 202 Robust weighting is
149. nd advice from many sources My thanks to all my friends and colleagues who have given help and advice including all the members past and present of the Biological Chemistry section Dept of Chemistry Imperial College of Science Technology and Medicine London U K especially Alan Russell Tim Wells Alan Fersht and Sanjoy Ray am particularly indebted to my wife Marcella who proofread the manual and put up with the ups and downs associated with program development Contents Introduction cocococncnnnonononononnnananarnrnrnrnnnnnnnnnnrnrnrnrncncnnnnnnnnnnnnnnrnrarnrarnranananas 1 Welcome A a A ue d adco e ace det eue dee e 1 Key Features of Grafit zi eO gs le ae Med Ss 1 About this Guide 22 de rp a tam el ede E beg eu tea 2 Notational Conventions sssssssssersrrerersererrrrtrersrrerirsrrerurrererrerene 2 Contacting Erithacus Software sssssssssssssssssssennmn enne nene 2 Pep rcsec EE UN 2 T chnical SuppOLFt esee cheer Ree aaa 3 A chi baie ee Pau Raata tenner ie enn Molla autnes 3 Installation cocococncnnnononononanananananarannnnonnnnnnnnrnrnrn caca nana nn nnnnnnnnnnnrararararanananas 5 System Requirements tetro PR Pe LEO Ere P PE Rte 5 The GraEit Package odore t eser iet pev re per terree es 5 Iistalling GEaFIE gessie eona eaa eet HL Net Ea RF ER rua OE RR TERR ERE EA iu 6 CD ROM Installation cocino patea ratonera a EAE RU ER EUR 6 Installation from Floppy Disks
150. near Regression The more complex nature of the non linear regression calculations does require some further considerations compared with linear regression 178 Chapter 19 Data Fitting Basics Equation to Use Non linear regression can employ a vast range of different equations It is therefore necessary to select an equation that is appropriate to the particular experimental situation before fitting the data Initial Estimates The mathematical method used to perform non linear regression acts to take starting estimates for the parameters in the equation and optimize them during the calculations As described in Chapter 9 GraFit provides a mechanism for providing these initial estimates automatically for some equations but in principle it is necessary to give the calculations some rough estimates prior to data fitting Convergence Criteria Unlike linear regression non linear regression does not provide an exact solution but by an iterative process calculates successively better parameter values until a suitable tolerance is reached The criteria for defining this tolerance are determined by the program and can be specified when using GraFit Weighting Scheme Both linear and non linear regression analyses incorporate assumptions about the accuracy of the data points Normally they assume that all data points are equally accurate and so carry equal weighting in the analysis It is also possible to use other weighting schemes
151. neweaver Burk ooooococccncncncnnconnnncnnnnnnnanonoronenonanons 220 TernaEy sicci ren ere rRRExEA E oia 220 Ternary Lineweaver Burk sssssssssseee memes 220 Enzyme 1M MIDitlOn rara 221 Competitive Inhibition ssssssee memes 221 Competitive Eadie Hofstee ssssssssssseseeeenes 221 Competitive Lineweaver Burk ssssssssseemms 221 Mixed InhIbIEIORn iuc eret eren ter e ever ere bi Po resi ed b ne u 221 WiexIujelle alor more 221 Non competitive Inhibition sessssssse eee eae e eee nes 222 Non competitive Eadie Hofstee esasen ereere 222 Non competitive Lineweaver Burk ssessssmm m 222 Enzyme KInetlCs iocis e repe cte tiara ele bd 222 Allosteric kinetics Hill ooo onn ncccn cnc naco nana nano Hem 222 Allosteric kinetics Hill Linear plot esseseeen anna 222 Enzyme KIDetlcs escort perire ia 223 Enzyme Kinetics Eadie Hofstee sssssssssseeennn 223 Enzyme Kinetics Lineweaver Burk ssssseen 223 Enzyme Kinetics show Km ssssssssseee meme 223 Enzyme Kinetics show Vmax sesssssseseeem meme 223 Enzyme Kinetics show Vmax over Km ssssss enm 223 Kinetics contaminating S eect eee mmm 224 Exponential viii Ibl e bre eie tad per EDI beate oles lira 224 Double Expornientlal err ene tune rre R ER ER cannes 224 Double Exponential phase 1 sssssssssses mmm 224 Double Exp
152. ng Calculated Function command to set up a calculation The following calculated function allows the column to be filled with the logk V Vol entries 209 GraFit User s Guide Calculated Function pKa Mol Volume Data fitting results DLog Rate V Vol Note the use of the data function to access data present in the data table The appearance of the data table that uses this calculated function is shown below E Data TES PASA A A ASA AA ES Mol Volume Log Rate Data fitting results Log Rate V Vol 10 6000 42 1000 40 0000 1 6021 Beta 0 3934 10 6000 80 9000 1 3000 0 1139 V 0 0549 10 5000 79 8000 0 2700 0 5685 Constant 0 6977 10 6000 98 7000 0 0090 2 0458 10 0000 74 6000 0 0840 1 0757 715000 0 0780 1 1079 23 2000 21 0000 1 3222 64 4000 0 2570 0 5901 70 5000 0 0108 1 9666 71 6000 0 0073 2 1367 51 1000 0 0500 1 3010 B m 3 m EN Ka c 7 EIA a The result plotting logk V Vol versus pK and using a transformation definition to display the appropriate line through the data is shown below 210 Chapter 21 Worked Data Fitting Examples IN Reading Values from a Calibration Curve A calibration curve records the variation of an observed value when an experimental condition is altered in a defined manner For example an instrumental reading may be measured for various known
153. nge Use the Edit Properties command or the Formatting toolbar Setting Default Text Properties The default font properties for new text objects can be specified by altering a property for example changing the font size when no object is selected The new defaults will be used next time a text object is added General Object Properties 110 Selecting the Edit Properties command or double clicking on a graph object shows the object properties dialog box This dialog box contains a number of pages some which are common to many objects and some which are specific to the object selected The common property pages are shown below specific property pages discussed later Chapter Error AutoText entry not defined Graph Item Fill Properties Rectangle Properties Check the Fill box to fill the object with the selected color If this box is unchecked the object will be transparent Line Properties Rectangle Properties The Line page sets the width style and color of the line It is possible to set the Style to No line if you do not wish a line to be drawn 111 GraFit User s Guide Rotation Properties Rectangle Properties 12 1x Fill Line Rotation Location Type C Absolute Rotation Degrees jo VA Current rotation is 0 0 degrees Cancel El Objects can be rotated and their rotation is specified from the Rotation page Rotation is enter
154. ning Chi change This setting is optional and is activated by checking the Chi change box When selected fitting will terminate when the change in the y value is less than the percentage value entered providing the minimum number of iterations has been reached Minimum iterations GraFit will always perform the specified number of iterations Maximum iterations Fitting will terminate when the specified number of iterations has been reached irrespective of whether the designated change in y has taken place The maximum iterations limit serves to guard against the possibility that the calculations will never reach a minimum and so forces control to return to the program eventually The settings can be stored as the defaults by clicking the Store settings as defaults button GraFit will remember these defaults next time the program starts 62 Chapter Error AutoText entry not defined Non linear Fit Item Results Pane The Results pane holds a summary of the fitting results Non linear Fit OP x Constants Estimatrix Fitting Criteria Number Format Fonts Indents K KICI x column Substrate Y column Rate Err calum Number of data points B Reduced ch value 0 0193 The Results pane of the Faena Viae Sims 7 NOBSUREOINOEORS If more than one set of data is specified in the Settings pane each fit can be viewed by clicking the arrow buttons The File Print and File Print Preview commands
155. nnnnnnn ananas cncnnnnnnnnnnnnnnnnrnrararnrnnananas 23 The Data Fable Mem ys eee at a oie AAA ae Vis 23 D ta y eS ds tdci 24 Forcing Text Entry oo ede e D ee e x Ee 26 Moving the Data Entry Position ssssssssssseeee memes 26 Selecting Regions of the Data Table ooooooocccccccccnccicocononononononnnnannnnnnnnnos 27 Selecting Part of the Data Table eee c etree eee eee eee eae 27 Selecting Entire Columns sss emnes 28 Copying and Pasting Data sisie ei u enemies 28 Copying and Pasting Regions of the Data Table ssssssss 28 Copying and Pasting Columns ssssssssee eem 28 REMOVING Data ederet Pret adi bat 30 Clearing a Region of Data ssssssssssseee nemen 30 Deleting a Region of Data cece eee memes 31 Inserting Values into the Table sssssssssseee meme 31 Sorting Datar tee tee VE Vint E EE RR at ea ieee ead 32 Data Table Appearance irvinenn a a E EA AE ORARE eene eee 32 Colors and FONTS cr dl Rr tddi akan Ede Rs 32 N mber FoFrnat x taa id 32 Magnifica fon 34 Importing and Exporting Data ococcccccicocococococononnnnnnnnnncncnnnororornrnrnnnnnnn 34 Importing Data orte ent deed e ex redit erar 34 Importing Data as a New Data Table ssssseeeene 34 Exporting Data tr eire rer dedu os 35 Column Types eie verre eter sitos serrer Eta dee oper tae Seeds aay 35 General Column Type ssssssssseen mnm nemen 37 Data Types a teens vai n
156. nnnnnrararararanananas 147 When to Use Multiple Axis Scaling ssseemmHHRHH 147 Overlaying Data that have Different Scales sssssssssss 147 Split AXES tasca 148 Creating and Managing Multiple AX8S ooooocccccccccnococonnnnnnnnnnnnnnannnnnnnns 148 Running the Axis Manager sssssssseeee meme 148 Adding a NEW AXIS 2 ere eg A ERR S ERN SERRA 149 Splitting m Existing AXIS ie o GO RR REIR ERES 150 Removing am AX S sorre esti ete P t e FE RR ERROR EAR MEET REL e Rete pen 151 Working with Multiple Axes sss mmm 152 Axis Text and Axis Scale Text 152 Data Associate ce ren hae HE eR RUE EH 152 Axis Scaling and Sizing sssssssssssseee emen 153 Column and Bar Charts coconococococonncnononononorornrncncanananannnnnnnnnnnrararararnrnnananas 157 The CharE Wizard ease rer a 157 Select Data Source Page sss emen 157 Set Initial Scala OR EAD eR 159 Select Tick Styles ote Oe en DO Re e e c ERE MR 160 Select Bar Style 2 oe ctc t E RENE EE RERUM MEA E ERR stos 161 Select Data Point Style sss enne 162 Select Join Style ior t e E HUE E ER LEE RE dies 163 Hist ogra MS s 165 The Histogram Wizard die SESS HERR das 165 Select Data Source Pag sssssssssseseee enemies 165 Set Initial Scalig ia ei et ege is Sa CR 166 Select Tick Styles A 167 Select Bar Style oce e v ee deg uit
157. nt is drawn using the current fill line and font settings these can be specified see later Creating graphs using the graph wizard will be discussed in the next chapter Manipulating Drawing Objects Selecting Objects To select an object move the mouse pointer over it and left click Text Object 1 ET Text C ject2 Text Object 1 A A S IN AAA EA AAA EEEE 02228280224 Re O A S Click to Selected select Object Moving Objects To move an object or group of objects select the objects required and then drag them to where you wish them to be placed Duplicating Objects If the cTRL key is held down while dragging an object a duplicate of the object will be moved to the new location Sizing Objects To resize an object first select it and then drag one of the resizing handles that are drawn in the corners of the object Solid resizing handles are drawn on objects that can be resized hollow handles are found on objects that do not permit resizing 105 GraFit User s Guide j B This selected object has hollow resizing handles and cannot be resized This selected object has solid resizing handles that permit resizing Graph olx AIN PPE nee N EE 001 TONS ON ee ere a A TN EN ITE E i NE il Drag one of the EE i i t resizing handles to T de c i i alter the size of a Y i i i graph object p 4 pem Az The resizing action can be modified by holding down th
158. nt on both axes XY type Effect h Cross Error bars are drawn for the x and y axes separately V4 Diagonal 1 A single error bar is drawn which extends diagonally to show the x and y error extents w Diagonal 2 A single error bar is drawn which extends diagonally to show the x and y error extents 139 GraFit User s Guide 140 The Source data entry must be completed if Explicit errors are specified for either x or y errors Select the data table that is used for the explicit errors from the list given X error bars This section is used to specify the type of errors present on the x axis Error type Effect None No error bars are drawn This is the default setting Absolute The size of the error bar is the same for each data point of the data set this size is entered into the field to the right of this button Proportional The size of the error bar depends upon the magnitude of the data point the size is expressed as a percentage of the data point value and is entered into the field to the right of this button Explicit The size of the error for each data point is specified individually The error values must be stored in a data table which is specified in the General section and the size of the positive and negative parts of the error bar is set separately The data column that holds the positive error values is selected from the list marked If only this option is chosen the error bar just has a single lo
159. o the graph using the Axis Manager which allows axes to be created or deleted and simplifies generation of split or multiple axes Running the Axis Manager To activate the Axis Manager select the graph to modify and choose the Graph Axis Manager command This will launch the Axis Manager Wizard 148 Chapter Error AutoText entry not defined Using Multiple Axes Axis Manager Choose An Option IHETITGVE pans Six options are available on the initial page Add a new x axis Add a new y axis Split an existing x axis Split an existing y axis Remove x axis Remove y axis If only a single axis is present the Remove axis options will not be available as a minimum of one axis must exist Select one of the options and click the Next button Adding a New Axis Choosing to add a new axis will give the following page 149 GraFit User s Guide Axis Manager Add y Axis m Initial tick style alamaa r Text location Axis offset 3 E Offset 0 PF J TEXT ae A number of initial tick styles and axis text locations can be chosen and in addition it is possible to specify that the new axis is created offset from the main graph All new axes have associated axis and scale text which needs to be positioned as appropriate In addition the new axis ticks are set and scaled independently of any tick settings already present on the graph When you have made your initial choi
160. ods for rearranging data and equations that can be applied during graph drawing without the need to create a separate set of rearranged data A An example of a transformed double reciprocal plot The transformation definition defines the way that the data points and the fitted curve are rearranged The transformation item is created from the main GraFit window using the Add Transformation command The transformation window itself contains a tabbed dialog box with several panes that are used to define the transformation After defining the transformation it must be compiled using the Transformation Compile command before it can be used Each of the panes in this item window is discussed below 89 90 GraFit User s Guide Status Bar Indicators When an equation definition item is selected the status bar shows whether the equation is Compiled or Not Compiled ud A o o lA OOOO OOOO OOOO Ote Compiled NUM 7 Ready Compilation status pane General Pane All transformations are associated with an equation definition item which must also be present in the GraFit workspace See Chapter 9 for more information about defining equations The general pane also allows a description of the transformation to be entered Lineweaver Burk OP x General Data Points Curve Fonts Indents Associated equation Enzyme Kinetics y Description Lineweaver Burk Transfomation The L
161. om the data fitting or the parameter values used as the initial estimate values starting values only when carrying out the calculations Values are calculated for x values that correspond to the y values present in the selected Y data column entry A potential problem with calculating x values for a given y value is that some equations will have multiple solutions For example consider the curve shown below 47 GraFit User s Guide 48 O 1 2 3 4 x At y 6 the value of x read from the curve is 3 4 but at y 3 5 there are three x values 0 55 1 52 and 2 9 Clearly whether the curve is single or multiple valued in x depends upon the equation in use and the value of y that is used To overcome this complication it is necessary to specify limits to the x values between which the data are to be calculated The Interpolate between X limits entries in the above dialog control the range between which the values are tested For example in the plot above the solution x 1 52 at y 3 5 would be correctly found by setting interpolation limits between x 1 and x 2 Chapter Error AutoText entry not defined Data Tables y Values Use this column type to calculate theoretical y values corresponding to user entered x values using the fitting model described in a selected workspace item Calculated Y Values 2 lx Eitting results OK Fit Single m sefitedvalues Weeinitial estimates Fit number p
162. ometric quantity in terms of moles of ligand per mole receptor depending upon the definition of y The dissociation constant of ligand from the receptor is Kg The concentration of free ligand L is the x data axis 227 GraFit User s Guide 1 Site Scatchard Plot The Scatchard plot is the usual way to linearize binding data This display equation takes the Cap and K values calculated by fitting to a single site binding curve and draws the line for the Scatchard plot Use this display curve with the Scatchard data transformation bouna rree 1 Site Show Capacity This transformation shows the capacity on the plot 77 1 Site Show Kd 1 site 10 amp 4 H SadadHa Se a 2 o T T T T Oo 2 4 6 ts 10 Bau This transformation shows the dissociation constant K For best results set the curve resolution to High when using this transformation 1 Site with background Often binding experiments have an inherent background y value This value can usually be determined separately by control experiments However such controls sometimes do not accurately reflect the real experiment and it can be preferable to treat this background as a separate parameter to be obtained from the data fitting The equation is _ IL Cap K IL bound background Here the parameters are the same as for the single site ligand binding except for the inclusion of a background or o
163. onential phase 2 ssssssssssee mmm 224 Double Exponential with offset lssssssssssssse nm 224 Single Exponential lt 2 icc canieiscamscwes rk eto peer Ene a ree rk d RE SV ETUR VEA 225 Single Exponential with OffSet oooooooocccccccccnicocononoconononnnnnnancnnnnns 225 Triple Exponentlal ci tre eR tr A RARE SERERE ERU 225 Triple Exponential with OffSet ooonocococccccocncncnnncncncnnnononorornrannnnnn 225 ej LUI 225 IC50 0 10096 iion ita tart tte delta ied ta eed dared plies 225 1650 0 100 show 1C50 vis cechivtaniecieectedcipimeieetriemapayianteteerens 226 xii Contents IC50 background corrected sssssssssee emm 226 IC50 background corrected show IC50 s sss 226 IC50 background corrected show limit eene 226 ESO FUMA param ada da od EE 226 1C50 full 4 param show background cocococccccccncnnnnnnnoncncnccnnnnnnos 227 1C50 full 4 param show 1C50 eect eet eee es 227 1C50 full 4 param show limit esses 227 Ligand Blind ta IRE es 227 Mec E 227 1 Site Scatchard Plot sss emen 228 lSite Show Capacity 3 erre ee ae eere eere e 228 1 Site Show Kd 1 site csse 228 1 Site with DACKQrOUNA ce ceecc eect eee eect ee tee mmm mene 228 1 Site with background SCatChArd cccceseceee ee eeteeeeeee eee eeeneed 228 1 Site with background Show background usse 228 1 Site with backgr
164. ons 123 Graphs Main graph region 123 Graphs Visibility 124 Graphs Grid settings 127 Graphs X scale 127 Graphs 250 Y ticks 129 Graphs Y scale 129 Graphs Location 129 Graphs Axis scale 130 Graphs Axis text 132 Graphs Legend box 132 Graphs Data curve properties 134 Graphs Error plots 139 Graphs Axis association 142 Graphs Legend box 144 Graphs Adding data 144 Graphs Multiple axes 147 Graphs Split axes 148 Graphs Multiple axes 156 Graphs Legend 158 Graphs Error plots 158 Graphs Error plots 158 Graphs Scaling 159 Graphs Tick styles 160 Graphs Chart bar style 161 Graphs Data point style 162 Graphs Join style 163 Graphs Legend 165 Graphs Error plots 166 Graphs Tick styles 167 Graphs Histogram bar style 167 Hardware Requirements 5 Headers 14 Help commands 15 Help menu Contents command 15 Hill Plot 222 Histogram 100 165 168 Histogram Wizard 165 1C50 equations 225 240 Icon Changing 12 Indents 65 68 73 Initial estimates 60 Initial Estimates 86 196 Installation 6 Floppy 7 Internet 3 Internet Explorer 5 6 Items Loading and Saving 18 L Ligand binding 241 Ligand binding equations 227 Limiting x data range 59 71 Linear fitting 55 69 Linear regression 187 242 Index Basics 178 Linking objects 169 Logarithmic scaling 128 Logical operators 82 Marquart algorithm 190
165. ontrol the way the information is displayed when printing Fonts Pane The Fonts pane selects the fonts to use when displaying the contents of the item window Non linear Fit GE x Settings Constants Estimatrix Fitting Criteria Results Number Format Indents ltem Normal text ed Font Font style Size Times New Roman ma ao UES New id Roman T Times New Roman MT Extra B Tp Transistor Bold Y Trebuchet MS Central Europee Bold Italic Y Trebuchet MS Turkish T Y The Fonts pane of the Non linear Fit item Trebuchet MS Western TypoUpright BT Turkish y y Sample This pane behaves in the same way as a standard Windows font selection dialog The fonts to use can be set for a variety of different text elements specified by the 67 GraFit User s Guide Item selection To see the effect of changing the font settings use the File Print Preview command Indents Pane The Indents pane controls the organization of information for printing Non linear Fit Settings Constants Estimatrix Results Number Format Fonts Headings L Jnfarmatian Loremiprum More information Dolorsit amot fi Gub lovelinfarmation Conroctoctueradipircing i i lit red diam nonummy Fesults Parameter Value Std Errar 10 456 1 890 The Indents pane of the E Non linear Fit item m Indent sizes Each of the different indent levels can be individually set To s
166. onts Indents Equation y a bx Linear Regression v Weighting Simple rl Data table Data m e p c da X data column xData mw Limit x range to ans Yoon a Equation Choose the equation to use for the data analysis All the available equations are linear and are of the form given below y a bx cx di The default linear regression equation is y a bx Weighting All types of regression analysis require information about the error distribution in your data The reason for this is explained fully in Chapter 20 but briefly it is necessary to specify whether the inaccuracies are likely to be the same for each data point Simple weighting are proportional to the value of the y data points Proportional weighting or have been individually estimated Explicit weighting The default Simple weighting is often the most appropriate setting Data Table The data to be fitted must be in a separate data table item within the GraFit workspace Select the table that holds the data from this drop down list 70 Chapter Error AutoText entry not defined Linear Fit Item Data Layout The data layout specifies how the data are arranged for data fitting The default layout as shown in the figure above is that the x and y data columns are to be selected individually This is used to fit a single x y data set It is also possible to specify that multiple data sets are present which will result in severa
167. options available in the data table see Chapter 5 Testing Goodness of Fit F Test There are situations where it is necessary to know whether a set of data is fitted better by one particular equation or another The F test is a statistical way of judging the goodness of fit by two different equations This test compares the y values obtained from the two fits and the degrees of freedom in each and calculates the probability that the fits are equally good The F statistic is calculated from the equation below z Gi z2 QG Xa lv F A low probability value indicates that one of the two equations that giving the lower y fits the data significantly better To be significant the probability should be lower than 0 1 and preferably lower than 0 05 To perform the F test use the column type options available in the data table see Chapter 5 Mean and Standard Deviation For a full description of means and standard deviations see any text on statistics for example that by Bevington8 A brief description follows The mean value of a set of data points is defined as H N i Here u is the mean of the parent distribution and x is the mean of our experimental sample The uncertainty or standard deviation of the data points c is estimated from the data as follows 1 Y ORmsSs ard The uncertainty of the mean Syw is given by the equation 193 GraFit User s Guide All the above equations assume that the uncer
168. os E 8 08 Bai T ox qq s 9 8 r 80 2 J i 5 0 6 F z o f ES J 602 ge 40 4 ge s ni E J i Q U 40 207 i i E 0 2 d 0 LA pmp rr Aro 0 0 Y 0 0 109 107 10 105 10 102107 0 20 40 Inhibitor Fraction This graph shows a semi log plot with This graph shows a single graph having a split axis scale multiple axis scales 100 o 0 6 1 31 J o Exponential F AR AR g q SI 10 4 79 Decay LE a S 6 7 M 04 AE UN S e T A Bo ee A S 4 E o Ayo o e 5 2 o EET T J gt g 1 seo 10 j 0 LL au b ou b a d ul l TT a aay TT 0 2 4 6 8 10 0 2 4 6 Time Time This graph shows offset axes and This graph shows multiple data sets fitted error bars simulatiously to an equation with two independent variables Column Chart Column Charts are categorized by having a numeric range on the y axis and named categories on the x axis Some of the types of chart that can be created are illustrated below gt gt lt _ gt gt _ gt gt gt e u u O OKA See _ gt gt HS Sl Simple comparison of a set of Summed area plot parameter values 99 GraFit User s Guide A Low High column chart A chart with different y axis scales for the two data sets plotted Bar Chart Bar Charts are categorized
169. other at high pH with the variation depending upon the ionization of a group The pK value of this group determines the inflection point of the curve The equation is i 5 6 7 8 9 10 _ Lim Lim 1099 H E In this equation Lim and Lim are the limits of the titration curve at low and high pH pKa Single Linearized plot Displays the line for the linearized titration curve pKa Single Show Limit 1 Displays the limiting y value at one extreme of pH pKa Single Show Limit 2 Displays the limiting y value at the other extreme of pH pKa Single Show pKa This transformation is used to represent the position of the pK on the general ionization curve For best results set the curve resolution to High 234 Chapter Error AutoText entry not defined Equations Provided Rate This set of equations fits data describing a first order rate equation 10 7 1st order IM MENU The equation for a process where the observed value e increases with time is E Ei DES RS a peta A A l e 2l J Iritid Re Here A is the amount of A at time t A is the j d AE Am A maximum amount of A formed and k is the rate dee constant that describes the process 101 1st order decay curve Diane This transformation converts the data into an E exponential decay curve To linearize the curve E 5 display the y axis with a logarithmic scale a1 T AA
170. ound Show Capacity sssesseseess 228 1 Site with background Show Kd ssess mmn 229 VEI PME MI 229 2 Site Show Capacity total mmn 229 2 Site Show Capacity 1 0 0 eect memes 229 2 Site Show Curve Divehi vanea E EE nme nennen nnn 229 2 Site Show Curve 2 ssssssssesee enm nennen nee nnn 229 2 Site with background sssssssssseene mmm nmm 229 2 Site with background Show background sss 229 2 Site with background Show Capacity 1 sss 230 2 Site with background Show Capacity total sssss 230 2 Site with background Show Curve 1 sseseeem eae 230 2 Site with background Show Curve 2 sss 230 Adair 2 5sites 3 rete te bere t two ceni cr vire o Re d Qe ara d 230 dal 3 SItes s saved dutem bre esc gato n neret areis p ol 230 Adair ASES ov redes e re v pee eat a at AR Ca 230 BOUNCIVS Total et HL 231 Bound vs Total tight binding limit esce 231 Cooperative inci id A ek a ved dba 231 Cooperative with background sssse nmn 231 PH se tero Pe a ees tea E arre diete ree sedeat ee 232 pKa Min Q iic ree eer e rx YE Far D RA Fe 232 pKa min 0 Linearized Plot ssssssee m mmn 232 pKa min 0 Show Limit esssseeen mmm 232 pKa min 0 Show pKa cssssssssseeem mmm nnn 232 pKa min 0 High to Low ssssssseee mmm 232 pKa min 0
171. ouping separator The symbol used for this separator and the number of digits in the group are set for the View Options command on the main GraFit window Chapter Error AutoText entry not defined Non linear Fit Item Specification Scientific format Use scientific format for small values Trailing zeros in fraction Meaning Check this box to display the values using scientific format e g 2 435e003 instead of 2435 000 Check this box to ensure that small values which would otherwise be displayed as 0 0000 are shown in scientific format e g 2 0987e 008 Chooses the way that trailing zeros are displayed in the formatted numbers It is possible to show the 0 characters to omit them or to replace them with spaces Fonts and Indents Panes These panes control the way that the results are formatted The contents of these panes are common to several different item windows and are described in Chapter 7 65 GraFit User s Guide 66 CHAPTER 7 Formatting Item Windows Formatting Options Several GraFit Item windows are built from a tabbed dialog box that allows various settings to be entered The Linear Fit Non linear Fit Equation and Transformation definition items are all built in this way In each case the settings in the window can be displayed using the File Print Preview command and printed by the File Print command Each of these item windows includes a Fonts and an Indents pane that c
172. our data on screen and edit the graphs interactively Key Features of GraFit GraFit provides the experimental scientist with a tool for visualization and analysis of their data For the occasional user GraFit can be configured to perform routine analyses with minimal intervention in many cases it is possible just to enter the data and allow GraFit to calculate the results and plot the graphs in the background Advanced users can utilize the full power of GraFit for analyzing complex equations and may create custom fitting templates for routine data processing GraFit User s Guide About this Guide This manual describes how you can use GraFit to examine your data and to plot graphs We recommend that you read the manual fully and try out some of the examples described Notational Conventions The following notational conventions are used throughout this manual Convention SMALL CAPITALS Monospace Bold Meaning Small capitals indicate keys to be pressed For instance A indicates press the A key If more than one key needs to be pressed this is written as for instance SHIFT END which would mean hold down the Shift key and then press the End key Monospace type indicates text that should be entered on the computer keyboard For example to obtain a directory of drive A when in DOS you would enter DIR A RETURN Bold text is used for menu item commands e g the Edit menu Where cascading
173. phs etc The contents of the workspace are stored together in a GraFit workspace file which has the GFF extension In addition to the contents of the workspace the current window sizes and positions are also stored in the workspace file Opening an Existing File Choose the File Open command to open an existing GraFit workspace file This will bring up the Open dialog box as shown below pen J GraFit Data Storage Sample GraFit workspace file File name Sample GraFit workspace file Files of type Grarit Workspace Files y Cancel 3 User Data Y User Template The buttons marked User Data and User Template allow you to change directory rapidly to the default data and user template directories respectively The locations of these special directories are chosen from the View Options menu By default GraFit workspace files are listed but you can elect to display and open GraFit template files by changing the Files of type selection 17 GraFit User s Guide 18 Saving a File GraFit workspace files are saved using the File Save or File Save As commands The contents of the workspace are saved along with the current window positions and order When the file is reloaded these positions and order are restored Loading and Saving Individual Items Saving Items The GraFit workspace comprises a number of individual items such as data tables graphs and analyses These individual items
174. ple is the inhibitor concentration is the same for an entire set of x y substrate rate data pairs Under these circumstances it simplifies the data entry to associate a single x value with a whole column of different y values This is done by specifying the column type as y Data with Associated Value This command is also available from the Data toolbar EN Y Data Column with Associated x n Value 21 xi Associated values 2t fl Cancel r Column type label Label 2 2 Load Default Label Use the following placeholders where you wish to display the x n data value s X2 42 3 x 3 4 x14 X5 x The x data value is entered in the above dialog and is normally displayed in the column type area Data columns that have associated values are used when fitting to equations with two independent variables See Chapter 6 for information about using this option when fitting data Up to four values can be associated with a data column allowing x2 x3 x4 and xs values to be stored if required for equations having up to five independent x variables Chapter Error AutoText entry not defined Data Tables Column Combinations These column types allow the values within the designated column to be the result of an arithmetic combination of two other columns In each case the number of calculated entries depends upon the number of values in two selected columns and the values are update
175. pplications such as Word by embedding documents into the GraFit workspace For example a Word document can be embedded as an OLE item within the main GraFit window as described in Chapter 18 If you have access to OLE compatible editors such as Word incorporating notes in this manner can be a more suitable alternative to using a notepad item 96 CHAPTER 12 Creating Graphs How to Create a New Graph To create a new graph first add a graph item window to the workspace using the Add Graph command You will then be given a choice of graph type to create from the Select Graph Type dialog below The resulting graph will be created using the default size If you want a graph of a specific size press the Cancel button which will result in a blank graph page Then use the Graph tool S to add the graph at a specific location and size Adding Graphs to an Existing Graph Item It is possible to create as many graphs as required on each graph item page To add an additional graph to an existing graph item window either select the Graph New Graph command which will create a graph of a default size or click the Graph tool and drag to position the new graph where you wish it to be placed Available Graph Types Although GraFit can create a large variety of different graphs the initial choice when making a new graph is between four fundamental graph types These differ in the data that they use for example X Y Scatter Graphs hold d
176. r 21 Worked Data Fitting Examples IL EEG m sib Rm m Ss e E A C o m E lt rE E m HE E EP A m To use this transformation load it using the File Add Stock Item command then click on the graph and select the Graph Add Data command The data source is the Non linear fit item and the Transform As box should be checked to allow the pKa Single Show pKa transformation to be selected Checking the Weighting It is often useful when performing an experiment for the first time to estimate the type of weighting that should be used It must be stressed that for these checks to be meaningful a large number of data points should be available and the equation describing the data must be well established As was described in Chapter 20 plots of residual error Ay versus y or Ay y versus y give characteristic patterns for the common simple and proportional error distributions We will produce these plots for the data that have been fitted above Drawing Residual Plots We will plot the residual plot Ay versus y To make this plot we need a column of data containing the Ay values This can be created after data fitting by setting the Table Column Type of one of the columns to Calculated Values Difference 199 GraFit User s Guide 200 Difference Between Experiment and Fitted y Data Select the Non linear fit that was generated above and click OK It is advisable to set the column
177. r Graphs Fill Page The fill style applies to the graph background Line Page The line style applies to the frame drawn around the graph as set on the General page It does not apply to the color of the tick marks which are set on the appropriate tick page X Ticks Page XY Graph Properties 12 1x General Fill Line XTicks x Scale Y Ticks Y Scale Location axis selector Tick marks X axis Y Width jas pt agiram Eo um Black open Ft b Major grid Lower Outside y Width jos pt X axis for Style No line Size Medium Color a Black A Minor grid Width jas pt Axis offset Style Nie e Distance from frame Color mm Black Close Apply X axis selector X Y graphs can have multiple x axes and the tick settings for each are set individually Set the x axis number from this box when first created only a single x axis will be available Tick settings Ticks can be drawn on the inside outside both sides or neither side of the Upper graph edge the Lower graph edge or on the X axis itself assuming the scale settings are such that this lies in the center of the graph The tick sizes can be set to small medium or large which are scaled relative to the overall graph width or to specific where the exact tick size is entered into the edit field 125 GraFit User s Guide 126 Left Lower ticks o
178. rd value Error KI 0 0961 0 0049 K3 0 1040 0 0293 K3 0 3352 0 1018 K4 0 9263 0 0648 It should be borne in mind that Roughton et al performed their regression analysis without the aid of personal computers or even pocket calculators Defining a New Equation 2 206 The hybridization of RNA and cDNA molecules is used to provide information about the genome organization and complexity of an organism This hybridization can be described by the equation E TS Y e7 0 693 Rot d D i l Here d D is the fractional hybridization at any given value of Rot moles second L of nucleotides of RNA B is a background value P is the proportion of the total cDNA hybridized to the ith component and Rot 5 is the Rot value at which 50 of the cDNA of the th component is hybridized In practice the data obtained may be fitted assuming three binding components giving a total of seven independent Chapter 21 Worked Data Fitting Examples variables Green et al 13 have presented a sample of such data these can be found in the file DNA hybidization Defining the Equation The equation can be defined as follows X Variables Symbol Description Rot Rot Rot value Parameter Symbol Description B B Background Pi P1 Proportion Component 1 Rot 5 1 R1 Rot 0 5 1 Pj P2 Proportion Component 2 P3 P3 Proportion Component 3 Roto s 3 R3 Rot 0 5 8 Y name Sat Definition Sat B P1 1 exp 0 693 Rot R1 Fi
179. re G1 and G2 The temperature is T and should be defined as a constant The dataset column x5 must hold the value 1 0 if the x and y columns 15 Jandu S K Ray S R Brooks L amp Leatherbarrow R J 1990 Biochemistry 29 6265 6269 Chapter 21 Worked Data Fitting Examples are from the first data set and 2 0 if they are from the second Clearly this can be extended to further data sets if required The value a in the above definition is a temporary value used to simplify the calculation The figure below shows the guanidinium hydrochloride unfolding of a native protein and of a mutant variant of this protein The mutation has caused the protein to become less stable making it unfold at lower concentrations of denaturant The solid lines indicate the fitted curves using the above equation The difference in stability can therefore be determined 1 2 1 0 0 3 O 6 O 4 0 2 Gan HCI 217 GraFit User s Guide 218 CHAPTER 22 Equations Provided GraFit comes with a large number of equations provided These equations may be edited to see how they have been defined and further equations can be added This chapter briefly describes the equations that come with the program It does not attempt to discuss the detailed background of each equation as it is assumed that the user of a specific equation will be familiar with this The equations and transformations that come with t
180. rn these as the starting estimates on the Estimatrix page Fit the Data To fit the data choose the Calculate Fit Data command The results are then calculated and can be displayed using the File Print Preview command or viewed from the Results page 197 GraFit User s Guide 198 Graph the Fit To plot a graph of the fitted data add a new graph to the workspace using the Add Graph command Elect to create an X Y Scatter Graph then use the newly created non linear fit item as the source of the data XY Graph Wizard Select Data Source zix Legend text Data set 1 Source i Non linear Fit All fits C Singe ft P 4 A dete column Y date column Error column D E Transform as app 7i You can use the Graph Add Data command to add more data sets to the plot lt Back Cancel Show the Results on the Graph It is often a good idea to display the data fitting results on the graph To do this select the Draw Results Listing command and elect to display the results of your non linear fit item Results Listing ES Results source Non linear Fit Cancel Fit number The Final Result For these data the final result is shown below Here the results listing has been added to the graph and in addition the pK value has been indicated visually using the pKa Single Show pKa transformation It is clear in this instance that the fitted curve describes the data well Chapte
181. roduced transmitted stored in a retrieval system or translated into any language in any form or by any means including photocopying and recording for any purpose other than the purchaser s personal use without the written permission of Erithacus Software Limited Erithacus Software Limited PO Box 35 Staines Middlesex TW18 2TG UK VERSION 4 Last revision October 1998 Trademarks GraFit is a trademark of Erithacus Software Limited Microsoft Windows NT are trademarks or registered trademarks of Microsoft Corporation Other brands and products are trademarks or registered trademarks of their respective holders and should be noted as such Citing GraFit in Publications When citing GraFit simply treat this software publication as you would a book For example Leatherbarrow R J 1998 GraFit Version 4 0 Erithacus Software Ltd Staines U K Version 4 is dedicated to Catherine right and Emma new features that have been added since version 3 was released GraFit User s Guide Acknowledgements Version 4 Well it took rather longer than anticipated but version 4 has finally appeared The changes from version 3 are far more substantial than a single version number increment may lead one to believe and represent a radical overhaul to the program There are many people to thank for their encouragement and assistance and would like to mention some of those who have contributed most Paul Edwards has suffer
182. s iv position E M Draw Y axis and ticks 127 GraFit User s Guide 128 Scale Type Select linear or logarithmic scaling LLL LL T Graph with linear x axis scale The same graph with a logarithmic x axis scale Scale Start If the box is checked this value is set automatically from the graph data Uncheck the box to specify the starting value of the x axis left edge Scale Finish If the box is checked this value is set automatically from the graph data Uncheck the box to specify the finishing value of the x axis right edge Scale major increment If the box is checked this value is set automatically from the graph data Uncheck the box to specify the major increment value The major increment value controls how often scale numbers and major ticks are drawn Scale minor increment If the box is checked this value is set automatically from the graph data Uncheck the box to specify the minor increment value The minor increment value controls how often major ticks are drawn Chapter Error AutoText entry not defined X Y Scatter Graphs Scale y axis position If the box is checked this value is set automatically from the graph data Uncheck the box to specify the axis position which should lie in between the Start and Finish values The y axis position has been set so that it appears between the Start and Finish values If required tick marks can be drawn on the y axis
183. s of radioactive disintegrations Proportional error For many experiments the percentage error is constant In this case o is proportional to y leading to a weighting factor of 1 y A typical example of such errors might be when for instance a measuring instrument is accurate to 2 of the delivered volume and the so error is proportional to the recorded value Individually determined error All the above cases make assumptions about the error of each measurement However if sufficient replicates of each data point are available or a complex error function is applicable it is possible to calculate o for each point and use these values explicitly This method can also be used if you know that certain values are less accurate than others for example if they were measured in a different way as again only relative o values need be given In practice the use of simple weighting or proportional weighting is most often appropriate If the errors are small the weighting function chosen has only a small effect on the calculated values We will see later how it is possible to estimate which type of error function best describes a set of data If any data values are 189 GraFit User s Guide close to 0 it is not appropriate to use proportional weighting and simple weighting should be selected Non linear Regression For an equation that is not a linear function the determination of best fit parameters becomes slightly more diffic
184. s procedure can be stopped by right clicking or by pressing the ESCAPE key The selected object s are moved but the movement is constrained to a purely horizontal or vertical direction depending upon the initial direction of the drag Certain objects are normally constrained in their locations For example graph scale text is normally only allowed to be moved normal to the axis orientation Holding down the ALT key removes such constraints and allows arbitrary positioning For most objects this displays the object Properties dialog The exceptions are text objects for which this results in editing of the text and OLE objects for which this results in executing the default object action normally opening the item for editing The shape of the mouse cursor gives information about the current action or about which actions are available Cursor shape Meaning N Standard cursor This cursor is shown when the selection tool is chosen and the cursor is not over a selected object A drawing tool other than the selection cursor has been chosen Left click where you wish the object to be positioned then drag until it is the desired size Y The cursor is over a resizing handle which can be dragged to alter the shape of the element There are several different resizing cursors depending upon which edge of the object is to be resized 107 GraFit User s Guide Cursor shape ES B B 1 Meaning The cursor is over a
185. s are then fitted to the second equation to find V nax and K A better solution is to recast the equation as a three dimensional one where the progress of the reaction varies with t and S which are the two independent variables The equation is obtained by combining the previous ones 181 GraFit User s Guide A eA 17 eo s This allows Vmax and Km to be determined directly from the raw data which has two x variables t and S A sample set of data that has been fitted in this way can be found in the Examples data subdirectory and is named Multiple rate Advantages of Multiple Regression 182 Use of multiple regression simplifies the analysis as the curve fitting need only be carried out once In the above example the value of A is fixed for the entire experiment and only found once for the multidimensional equation However if the data are analyzed by several applications of the first equation the A value would be determined several times Disadvantages of Multiple Regression The disadvantages of multiple regression are as follows e Conceptual It is often difficult to visualize the problem in more than two dimensions e Finding initial estimates This is sometimes difficult for the same reasons Difficulty of display The current version of GraFit does not support three dimensional plotting the display of four dimensional data is even more problematic Defining Equations Definition of equ
186. s between the raw and fitted data Data Processing The column types under this submenu allow various types of processing to be performed to generate data values for the column Calculated Function The calculated function column type fills the selected column with the results of a user defined function This column type can be used to perform sophisticated processing of data including background subtraction calculation of logarithmic values and complex rescaling The calculated function dialog box is shown below 50 Chapter Error AutoText entry not defined Data Tables Calculated Function L2 x m Number of Rows CR DK e jo i Cancel From column Time z Result m Update after changes to these columns Time Amount Column 3 0 column s selected The Number of Rows of data to be calculated can be a defined number or can be set to be the same as the number of entries in one of the other columns The function definition is entered into the Result field and uses the same syntax as is used for equation definitions see Chapter 9 By default the text entered into this field is used to calculate a result without the need for an explicit assignment statement However the name Result is predefined so that it is possible to assign values using a Result statement In addition to the standard arithmetic functions sin cos etc the following can be included within th
187. selector section which allows each different axis to be selected After choosing the axis to modify alter the tick settings as required 155 GraFit User s Guide 156 CHAPTER 16 Column and Bar Charts The Chart Wizard Chapter 12 described the basics of creating graphs Selection of Column Chart or Bar Chart produces the Chart Wizard to assist with the setup all settings can be adjusted later if required Column and bar charts differ only in their orientation and so the same process is carried out for each The process of editing charts is broadly similar to editing X Y graphs and Chapter 14 should be consulted for further information Select Data Source Page Chart Wizard Select Data Source 12 1x Legend text Source Category axis m Upper data a Error column y Lower data OS lower eran column oO y You can use the Graph Add Data command to add more data sets to the plot Bact Cancel The Select Data Source page allows you to choose the source and type of data to plot 157 GraFit User s Guide 158 Legend text The data set plotted is associated with an entry in the data legend The entry shows the symbol used to represent the data and a descriptive text The initial text used to describe the entry can be entered into this field Source Graphs are plotted using data that are present in one of the items found in the GraFit workspace The Source selection lists a
188. sfer Types The following table compares the various ways that data can be transferred between applications via the Clipboard How to paste information in this format Non OLE Clipboard transfer For non OLE applications Edit Paste For OLE applications Edit Paste Special and select a non OLE format Embedding For OLE applications Edit Paste Linking For OLE applications Edit Paste Link or Edit Paste Special and choose to paste as a link Advantages Compact data format Allows information to be edited after pasting Pasted information is stored within the target document Allows information to be edited after pasting Since data are kept within the source file this allows efficient use of space when several documents may wish to link to the same object Disadvantages No editing allowed after pasting No link maintained with the source document Documents containing embedded objects tend to be large Linked information is kept in a separate file which may become lost 171 GraFit User s Guide Note The default action for a Windows application that supports OLE is to embed information whenever possible if the Edit Paste command is used As described in the table above embedding is not always the most appropriate way of sharing the information and linking is frequently more desirable for which you need to select the Edit Paste Special command
189. show the results in a more stylized manner as illustrated below Non linear Fit iO xi al ojala Close Seftings Resul s rea Subaru Using Print Preview from pM the Non linear Fit item Number of dam po sts 63 GraFit User s Guide The formatting of these results is controlled from the Number Format Fonts and Indents panes Showing the Fitted Results on a Graph A listing of the fitted parameter values can be displayed in a graph item window by selecting the Draw Results Listing command from the graph window See Chapter Error AutoText entry not defined for further information Number Format Pane The numeric result values are displayed formatted as is specified on this pane LE ICE stimatrix Fitting Criteria Fonts Indents Non linear Fit Settings Results Decimal places 4 4 Max digits 12 3 Thousands separator Scientific format M Use scientific format for small values Trailing zeros in fraction Show O s Meaning Specification The Number Format pane of the Non linear Fit item Decimal places Max digits Thousands separator 64 Enter the number of decimal places to be displayed for numbers in the results listing Note To ensure that all decimal places are displayed set Trailing zeros in fraction to Show 0 s Enter the maximum number of digits to use when displaying numbers in the results listing Check this box to include a gr
190. specific axis For split axes it is usual to associate all data sets with each axis The data association for an axis is set from the Axis Association Page found by double clicking on the appropriate Data Curve Properties region of the data legend see figure above Further information about modifying data properties is found in Chapter 14 Chapter Error AutoText entry not defined Using Multiple Axes Axis Scaling and Sizing Each of the multiple axes has separate scaling size and tick settings These are modified from the Scale or Ticks pages of the graph properties To access these select the graph and choose the Edit Properties command or double click on the main graph region For more detailed information about setting these properties see Chapter 14 Scaling XY Graph Properties 2 x General Fil Line X Ticks X Scale Y Ticks Y Scale Location Scale check box for autoscale Y axis selector Type Linear Yat ENE Start 5 Anis extent v Entire graph size Iv Finish fi 10 Start Major End 100 M increment 1 Evis Break None Minor 0 symbal iv increment i a il Drawing options aus p M position z I Draw X axis and ticks Use the Axis selector to choose which axis is to be scaled then set the scale as appropriate Sizing The Axis extent settings on the page shown above control the proportion of the graph over which the current axis ex
191. st Appropriate Weighting 192 For most experimental data the error is commonly either independent of the value of the observation simple or constant errors or is proportional to the y data value proportional errors Simple errors may be caused by instrumental uncertainties for instance a machine reading may be only accurate to some intrinsic error independent of the magnitude of the reading Providing sufficient data points have been sampled it is possible to determine the correct weighting by examination of the residual error the experimental minus the calculated value A plot of the residuals versus the observed value Ay versus y is diagnostic of the type of error involved For simple errors by definition the residual is independent of y as is seen in the plot a If the errors are of a proportional nature the residual plot will be as plot c A plot of the relative residual Ay y versus y results in the profiles b and d for simple and proportional errors respectively and confirms the error distribution Chapter 20 Theory Plot of Residual Errors Above is shown the type of residuals plots obtained when the error is constant or proportional in nature It must be stressed that visualization of clear cut plots of this kind depends upon having many data values to define the curves The dotted lines on the plots show the envelope within which all points are expected to be found Residuals can be calculated using
192. t defining transformation items 137 GraFit User s Guide Data Source Page raw data only Data Properties Select the Data table item that holds the data together with the columns that hold the x and y data Check the Transform as box if you wish to display the data points transformed as defined in the selected transformation All the transformations present in the workspace are listed See Chapter 10 for information about defining transformation items 138 Chapter Error AutoText entry not defined X Y Scatter Graphs Error Bars Page Fitted Data Properties BEI Data Paints Join Paints Fitted Curve DataSource Error Bars Axis Association General Style lest T Bar Too Line width rm XY type f s Color O Black Source data Y mx error bars None C Absolute C Proportional 10 C Explicit la r Y error bars None Absolute C Proportional C Explicit Apply General This section defines the general types to use for the error bars including the width and color of the pen used to draw them The Style choice is only available after error bars are selected in one of the X error bars or Y error bars sections Style Effect ER Line The error bars are drawn as simple lines E T Bar The ends of the bars are delimited with a T bar The XY type option is only available if error bars are prese
193. t represents an item may also be changed This can be useful to allow similar items to be visually distinguished To change the icon select it and choose the Window Icon command For each item type there are a number of alternative images that can be used In addition it is possible to use an icon image that resides in any executable or DLL file on your computer Chapter Error AutoText entry not defined GraFit Basics Item specific Commands Although some commands apply to all GraFit items many are item specific For example the Fit Data command applies to the Linear fit and Non linear fit items but not to the Data table or Graph items Commands that are not available are shown grayed In addition each item window has one or more specific menus that are only present when this window is selected For example only graph items have Graph and Object menus Printing the Item Contents The contents of any item window can be printed using the File Print command and the printing previewed using the File Print Preview command Data Biel x Print preview 1 0000 2 0000 4 0000 3 0000 3 0000 4 0000 5 0000 5 0000 4 0000 6 0000 6 0000 7 0000 6 0000 8 0000 7 0000 9 0000 6 0000 10 0000 13 GraFit User s Guide Page Settings The File Page Setup command allows the paper size and orientation to be specified and the margin sizes to be entered These settings are stored separ
194. t represents the x data and y the symbol that represents the y data Note that the multiplication between a and x needs the explicit inclusion of the multiplication operator The equation definition can also be defined over several lines in order to simplify a complicated definition This allows the calculation to be broken up into several steps Use of Temporary Variables Temporary variables can be used to hold intermediate calculation results and simplify definitions For example the following definition uses three temporary variables a b and c 1 Kd total Capacity total Capacity b sqrt sqr b 4 a c The remaining symbols Kd total Capacity are defined in the equation editor as parameters or constants Values are assigned to the temporary variable using the assignment operator after which they may be used in expressions as normal Use of temporary variables makes the above definition more easily read and speeds up the calculation as the value for b need only be calculated once Each line of the definition is separated from the next by pressing the RETURN key Conditional Statements The values that are evaluated can be controlled using the i statement This takes the form if condition then statements 84 Chapter Error AutoText entry not defined Equation Item or alternatively if condition then statements For example it is possible to return different values to the pro
195. t to limit this grid search to a sensible number of combinations for example if 10 parameters were present and 10 steps were selected for each this would involve 10 values to be tested clearly an unrealistic number When data fitting starts each permutation is tested and the combination that gives the best fit lowest y value is used as the starting estimates for non linear regression If both automatic and manual estimates are present each is tested and the best of the two is used as the starting estimates for regression Interactive Estimator Finding suitable initial estimates can be a laborious task and to simplify things GraFit provides an interactive visual tool that is accessed by pressing the Interactive Estimator button The Interactive Estimator dialog is shown below 60 Chapter Error AutoText entry not defined Non linear Fit Item Interactive Estimator 12 1x Cancel d r Graph scale X min Rate X max Y min 12 68 652 The Interactive Y max f Estimator dialog Auto Scale ho Q P un e Substrate Status OK A simple graph of the data selected on the Settings pane is shown The graph is automatically scaled by default although the scale can be altered if desired To see the curve generated by a particular set of parameter values type in values into the Estimates value column of the grid When you move the data entry position the graph will be updated
196. tainties of all the data points are equal If they are not for reasons described earlier we must use equations that incorporate weighting For example calculation of the mean becomes a ID LY aro 194 CHAPTER 21 Worked Data Fitting Examples This chapter provides some further examples of data fitting to help acquaint you with the program The examples are presented so that they can be worked through in a step by step manner The data files that are used can be found in the Examples sub directory of your data directory Don t worry if the examples do not seem relevant to the type of data that you need to analyze the same principles are involved in all data fitting This chapter assumes that you are familiar with the basic functioning of the program and if not you may like to consult the earlier chapters Using One of the Equations Provided We will fit the data obtained from an NMR titration curve to obtain the pK of an ionizable group Background The position of a peak in the NMR spectrum the chemical shift position resulting from a magnetic nucleus that is part of a titratable group depends upon the equilibrium between the two ionized forms For example in the following equilibrium A Ht AH Nuclei close to the ionizable group A will have chemical shift values that depend on the ratio of A and AH By definition the acid dissociation constant K is given by A IH Ka A It is usually
197. tants kcat Eo Km In the sample shown above the data transformation involves plotting the reciprocals of the x and y data Data Transformation Definitions Two transformation definitions need to be entered one each for the transformed x and y data Use the edit fields to enter the transformation definitions The rules for these transformation definitions are the same as described in Chapter 9 for equation definitions although the definition is limited to a single line and only the right hand side of the Definition equation is entered The definition can be of arbitrary complexity and can include mathematical functions parameter names etc The pre defined symbols xdata and ydata represent the original x and y data values respectively The symbol xdata2 can be used to access any data values associated with the y data column y Data with Associated Value column type see the discussion of column types in Chapter 5 In the example illustrated above we wish to take reciprocals of these data the definitions are therefore 1 xdata and 1 ydata Any algebraic expression may be entered for example xdata ydata sqrt xdata 91 GraFit User s Guide is a perfectly valid transformation definition It is permissible to access the values of parameters and constants in the equation if desired The symbol names of these are listed at the bottom of the Data Points pane Generating Residuals Plots A very us
198. te wie cto 37 Column Combinations sssssssssee menm 39 Statistics suo er Eure Tei ront Vr rer E ERN EE Tes 39 Data FIEEIngi ecrire RERUM rep dtm se t d xo 43 Calc lated Vallies ccc ves ee 46 Data Processing aerei a eee 50 Locking a Data Column ias areia etter nes 54 Non linear Fit Item 0 cccceeeeeeeeee ee ee sees esse ease ee ee un ee eee eee essen esses na nana 55 Overview of Non linear Fitting csse emen 55 Status Bar INdiCators ce eens 55 Settings PANG tisk E DE 56 Equation Absentee dl rd 56 Weighting ysr iinn r aE a E EE ML 56 Data Mali A e dex uni deeper ATE 56 Data Lay OUt x a A a Cue ee A EA 57 X Data CONAM depre vt as 58 Y DatacColumini e 59 Error Colum itid rere eerie i geste Dee erar REEE 59 Contents Constants Panes ascii a T RR EET EL AREE RE LX T E RE ERRARE PARET MBA Tanit 59 Estirriatrbe Pane su e tutte RU A ee o a AA Da E eT T T ah 59 Interactive Estimator vere det ry V er E E e Pe Peces PY acd 60 Fitting Criteria Peas edu ep ai eA Ee eet e Voy vae i teet eee 61 Fitting Criteria Re Ep RR EM Pis Eee a 62 Resu lts Pane cix Du A eL a E P eC t Pisa ate 63 Number Format Pa senii ap a e AE A A Ea Ta I 64 Fonts and indents PANES cia on EE RECETA ERR TIAS ATTIE 65 Formatting Item Windows oomomonononononananarararannnnnnnnnnnrnrnrnrncnnananannnnananncananas 67 Formatting Options cot ru s atv te ee oe rer resur de 67 Fonts Pane usada ile c dang 67 indents Pan
199. ted object by using commands found on the Object menu 108 Command Bring to Front Send to Back Move Forward Meaning The selected object is brought to the front of all objects on the graph The selected object is placed underneath all objects on the graph This may result in the object becoming obscured by others on the page The selected object is moved one place forward in the z order Chapter Error AutoText entry not defined Graph Item Command Meaning Move Back The selected object is moved one place back in the z order Setting the Object Color The fill pen and text colors of an object are specified separately and can be set using the Object menu A quicker and more convenient way to set these colors is using the Color toolbar located by default at the bottom of the graph window e2A x INDOBHDONENENENBNDODOEHNJDUUDIDUUDOUDEUEEtESHIWSI Otbh The color settings right side are applied to fill pen or text depending on the selection made at the left of the toolbar Color Meaning selection ij Fill color is specified 4 Pen color is specified A Text color is specified The Xx toolbar item is used to specify that no color should be used For example making this selection for the fill color of an object results in the object being drawn transparently The Other button is used to make more specific color selections than are available from the toolbar Note Some objects notably graph o
200. tends When using multiple axes to show data of with different numerical ranges it is normal to have the axis set to occupy the Entire graph size However in some circumstances it can be useful to limit the axis to a small region For example this can be a good way to overlay residuals as illustrated below 153 GraFit User s Guide 154 LO a E m In this graph there are two y axis scales the first which holds the normal fitted data and the second that is used to plot the residual error The first y scale is set to occupy from 0 to 70 of the graph size the second is set from 70 to 100 Setting the Split Position Split axes are created by using axis extents less than the full graph size and by including a suitable Axis break symbol In order to modify the split position along the axis it is necessary to change the Start and or End position of the Axis extent This must be done for each axis concerned Tick Settings Each axis has full control over where and how often ticks are drawn For this reason when a new axis is created it often the case that the initial tick settings overlap existing settings from existing axes If this is the case it is necessary to modify the tick settings for one or more axis in order to obtain a suitable appearance Chapter Error AutoText entry not defined Using Multiple Axes XY Graph Properties The Ticks page also includes an Axis
201. the n value representing the order of the x variable found in the equation definition See Chapter 5 for further details on column types The position of the y data column is selected from the Y data column entry This entry specifies the column that holds the x data values See the Data Layout section above for further information 58 Chapter Error AutoText entry not defined Non linear Fit Item Limiting X Data Range It can sometimes be useful to restrict data fitting to a subset of the values in the columns For example it can be useful to fit just the initial portion of a data set Checking the Limit X range box allows a lower and upper limit to be set on data that will be included in the analyses Y Data Column This entry specifies the column that holds the y data values See the Data Layout section above for further information Error Column If explicit weighting is chosen the error values are read from a separate column which is selected here Constants Pane Some equations are defined to include Constants the values of which are passed to the equation when fitting data If the selected equation includes Constants values these are entered into the grid found on this pane For equations that lack Constants this pane is empty Estimatrix Pane Non linear regression analysis requires approximate starting estimates for the parameter values These starting values are then improved upon by iteration until
202. the best fit curve is calculated Some equations provide a means of generating estimates automatically for other equations it is always necessary to enter explicit estimates see Chapter 9 For the former case this pane allows supplementary estimates to be entered for the latter it is essential to enter initial estimates into the grid found on this pane 59 GraFit User s Guide Non linear Fit GE x Results NumberFormat Fonts Indents Settings Constants Estimatrix Fitting Criteria v Estimates from matrix Interactive Estimator Parameter Stat End Steps The Estimatrix pane of the Non linear Fit item For equations that automatically provide estimates the Estimates from matrix box needs to be checked in order to allow supplementary estimates to be entered into the grid If automatic estimation is not available then this box is always checked The grid is used for entry of estimates which can be done in one of two ways 1 Just the Start value is specified In this case the value entered is taken as the initial estimate for this parameter 2 Values are entered under the Start End and Steps columns In this case a range of estimates total number Steps is generated between the Start and End values inclusive It is possible to enter just a Start value for some parameters and a range for others Whenever a range of values is involved a matrix of permutations is tested It is importan
203. the column is set to be the calculated standard error of the mean for the corresponding values from the columns selected in the above dialog SEM o is defined as o 0 Hu JN Column Summary The entries in the column give a summary of the values present within a single selected column Chapter Error AutoText entry not defined Data Tables Column Summary Statistics 2l x Source data column Value 2 2 2000 Source 3 5000 4 5000 1 1000 Data points 6 2000 5 6000 0 6000 Minimum 4 5000 3 6000 1 0000 Maximum 4 0000 3 9000 0 1000 Range Total Mean Median variance n Variance n 1 Std dev n Std dev n 1 This summary gives the number of data points minimum and maximum data values the data range sum mean median variance calculated for a divisor of n and of n 1 and standard deviation calculated for a divisor of n and of n 1 F Test The entries in the column show the results of performing an F test comparing the goodness of fit of two fitting analyses that use different equations A fuller description of this test is found in the theory section Chapter 20 but briefly the F test evaluates whether one fit is significantly better than another This test can be used to ascertain whether it is realistic to use an equation with additional parameters over a simpler version or whether one equation fits a data set significantly better than does a second For exampl
204. the paper by Roughton et al 1955 11 is notable because the raw data are presented with a set of calculated results Also the equation to be fitted is somewhat complex Because of this these data provide a good test for a data analysis package The Roughton paper examines the binding of oxygen to sheep hemoglobin as a function of the pressure of oxygen Hemoglobin has four non equivalent sites and the binding is described by the equation Kyp 2KK p 3K K K p 4K K K K p 4 1 K p K K p KK K p KK K K p Saturation x 10096 In this equation p is the pressure of oxygen and K to K are the equilibrium constants for the binding of four successive moles of oxygen per mole of hemoglobin The data are in the file Hemoglobin saturation Read this file in using the File Open command An interesting feature of these data is that some data points were 11 Roughton F J W Otis A B amp Lyster R L J 1955 Proc Roy Soc London Ser B 144 29 54 203 GraFit User s Guide 204 collected with greater accuracy than others To account for this it is necessary to use Explicit weighting Defining the Oxygen Binding Equation To define this equation we need to create a new definition in our workspace using the Add Equation command See Chapter 9 for a complete description of defining equations Definition of the new equation requires that we make appropriate entries in this item window X Variables Symbol Descr
205. the width line style and color of the curve that represents the fit X limits By default the fitted curve is drawn over the entire range of the x axis Some equations however are undefined over certain ranges for example at x 0 When the Start or End box is checked GraFit will set the limit automatically but by unchecking these boxes it is possible to define the range over which the curve should be displayed Chapter Error AutoText entry not defined X Y Scatter Graphs Resolution Fitted curves are calculated for a range of values between the Start and End limits The Resolution entry controls how many points are used in this range High resolution uses more points which takes longer and uses more memory In general use the medium resolution unless the curve has a sharp discontinuity e g when plotting a step function Under such circumstances use the high resolution setting Select Join Style not equation items XY Graph Wizard Select Join Style None ha WIGS jiga Solar Type Chooses the type of join to use Effect Join Type None 121 GraFit User s Guide Effect Join Type J Wf Width Style and Color Line Bezier Three degrees of curvature are available slight medium and strong The illustration shows a medium curve Bezier curves give smooth lines between the points and always pass each data point Spline Four orders of spline
206. then pasted into the table 29 GraFit User s Guide Data Removing Data Clearing a Region of Data The Edit Clear command or the DEL key can be used to clear the currently selected data or columns 1 Select the data value s or columns or rows to be cleared olx 30 Chapter Error AutoText entry not defined Data Tables 2 Choose Edit Clear or press DEL Data olx Data in the selected region are cleared leaving a gap in the table Deleting a Region of Data Select the data value s or columns or rows to be cleared Choose Table Delete command When deleting a range of cells the data values are moved up so that no gap appears in the table When deleting a column the remaining columns to the right of the selection are moved along to fill the gap Inserting Values into the Table Values are inserted into the data table using one of the Table Insert commands Command Action Table Insert Cells Inserts blank cells in place of the current selection Cells are moved down to accommodate the new entries Table Insert Column Inserts blank columns in place of the current selection Columns are moved to the right to accommodate the new entries Table Insert Row Inserts blank rows in place of the current selection Rows are moved down to accommodate the new entries 31 GraFit User s Guide Sorting Data The data in one or more columns can be sorted
207. ting the raw data as collected on the same graph This is particularly simple for the situation noted as Case 1 above Choosing to create a graph to display the non linear fit will automatically generate a suitable plot In the case of the sample data set the fitted curve is shown below A A CHAPTER 20 Theory To make best use of GraFit it is helpful to know some of the theory behind regression analysis Chapter 19 provided a general overview this section describes more of the theoretical background Regression Analysis Regression analysis is a technique used to calculate the best fit line or curve through a data set by minimizing the deviation of the data from the curve Mathematically it finds values for various unknown parameters in an equation for example the slope and intercept of a straight line that produce the smallest possible sum of the squares deviations of the experimental values from the calculated ones This quantity that is minimized is denoted by the symbol y chi squared The value of y includes the variance of the data point the variance of data point is cj so that data points that have greater errors contribute less to the analysis It is calculated as ex O i Ay is the difference between the experimental and calculated y data values the subscript is used to indicate the ith data value A further useful statistic is x or the reduced chi squared T
208. to distinguish it The dialog settings for the calculated values can be altered by repeating the command or by choosing the Table Column Properties command which corresponds to the E toolbar command Chapter Error AutoText entry not defined Data Tables To reset the column type to the default non calculated settings choose Table Column Type General Note Even though columns that hold calculated values do not allow these values to be edited it is always possible to modify the column name entry General Column Type By default all columns are set to be of General type and hold general data values that can be edited normally Data Types The column types under this submenu are used to designate that the column holds a certain type of data which may have associated additional values The entries in the column are editable but the data held in the column may have special significance for data fitting x Data You may optionally select this column type if the data in the column are used as the x values for data fitting Designating a column to contain x data is not essential for data fitting but can be useful to document the data layout x n Data When fitting an equation that has more than one independent x variable one way to hold the data is to have n separate columns for the different x values During the data fitting GraFit needs to know which column holds which x data set This is done by setting the
209. to show the curve generated by the current set of values These estimates should be such that the calculated curve falls close to the data values J ust how accurate these parameter estimates need to be depends upon the equation in use and the data present However it is usually only necessary to produce a curve that roughly follows the data as shown above for the subsequent data fitting to find the best fit values When acceptable parameters have been found pressing OK will return these values into the Start column of the Estimatrix pane Fitting Criteria Pane As described in Chapter 20 non linear regression calculates best fit parameters by a series of iterations that produce successively more accurate results It is up to the program to decide at what point the values are deemed acceptable and at which point the calculations stop The criteria used to decide this are set from the Fitting Criteria pane It is likely that for most situations you will not need to change the default values on this page 61 GraFit User s Guide Non linear Fit olx Results Number Format Fonts Settings Constants Estimatrix Iv Ch change fi pa Minimum iterations Maximum iterations 20 zi The Fitting Criteria pane of the Non linear Fit item Store settings as defaults Restore GraFit defaults Fitting Criteria GraFit uses three separate criteria to decide when the calculations are acceptable Criterion Mea
210. ts r Sample Underline I Strikeout Color CE Tem AaBbYyZz Superscipt Subscipt a Cancel Apply 113 GraFit User s Guide The Font page sets the font to use together with the style size and various effects including superscript and subscript options Paragraph Properties Text Properties This page sets the formatting for the selected paragraph s or text 114 CHAPTER 14 X Y Scatter Graphs The XY Graph Wizard Chapter 12 described the basics of creating graphs Selection of an X Y Scatter Graph produces the XY Graph Wizard to assist with the procedure all settings can be adjusted later if required Select Data Source Page XY Graph Wizard Select Data Source 12 1x Legend text Source date column vodata column 7 Error column A Transform as z You can use the Graph 4dd Data command to add more data sets to the plot Bact Cancel The Select Data Source page allows you to choose the source and type of the data to plot Legend text The data set plotted is associated with an entry in the data legend The entry shows the symbol used to represent the data and a descriptive text The initial text used to describe the entry is entered into this field This text field can also contain two special entries that allow the data set number or the fit number to be inserted into the data legend 115 GraFit User s Guide 116 So
211. tting the Equation P2 1 exp 0 693 Rot R2 P3 1 exp 0 693 Rot R3 The following initial estimates are appropriate to analyze the data B 0 05 P4 0 3 P gt 0 3 Roto 5 2 40 0 P4 0 3 Rot 5 3 600 0 It is interesting to note that when Green et al published their results in 1982 using an Apple II computer and employing a Patternsearch algorithm they reported that these data were fitted in approximately two hours of calculation Compare this to the amount of time taken by GraFit using a modern PC which should fit the data in a couple of seconds The calculated result is displayed below 13 Green S Field J K Green C D amp Beynon R J 1982 Nucleic Acids Research 10 1411 1421 207 GraFit User s Guide M FII AL OL AOL LL LL LL H M EN EA E Multiple Regression Multiple regression is used when the observed data values depend on more than one dependent x value As an example of this we will examine the data listed by Toney Kirsch14 These data consist of observations of the rate constant of a reaction k as a function of the pK of the group involved in the reaction and the molecular volume of this group Vol The data are described by the equation logk B K V Vol c Here f V and c are unknowns in the equation which is a multiple linear equation having two independent variables The data presented in the paper are in the file Multiple
212. ues can be displayed in a graph item window by selecting the Draw Results Listing command from the graph window See Chapter Error AutoText entry not defined for further information Fonts and Indents Panes These panes control the way that the results are formatted The contents of these panes are common to several different item windows and are described in Chapter 7 73 GraFit User s Guide 74 CHAPTER 9 Equation Item Overview of Equation Definitions Equation definitions are used for non linear fitting see Chapter 6 for more information about non linear fitting items The item is created from the main GraFit window using the Add Equation command The equation window itself contains a tabbed dialog box with several panes that are used to define the equation After defining the equation it must be compiled using the Equation Compile command before it can be used Each of the panes in this item window is discussed below Status Bar Indicators When an equation definition item is selected the status bar shows whether the equation is Compiled or Not Compiled SE USAGES im A cts o Ie Zia HUOUEDOBSONEBNENBUDESNIDUIDOUOLDLDLCDLE C E E E E BN Cher Ready Compiled NUM 4 Compilation status pane 75 GraFit User s Guide General Pane The general pane allows a description of the equation to be entered Enzyme Kinetics Ox Estimates Fonts Indents General X Variables Par
213. ules in a similar way to variable names within a computer program e The name must begin with a letter and contain only letters and numbers In particular a symbol name cannot contain the space character The following names are legal symbols Fred k on x23 The following names however are invalid 2nd starts with a number k off contains a space test 2 contains a minus sign ten contains a punctuation character e No distinction is made between upper and lower case characters within a symbol definition Therefore the symbol names grafit GraFit GRAFIT and gRA IT are all considered identical We recommend using meaningful names wherever possible when defining symbol names Using Final to represent the final concentration of a substance rather than z will make understanding your definitions far easier for others as well as yourself In addition it is often useful to add a full descriptive name Number of X Variables After entering an x variable definition the data entry grid will show a blank entry position immediately below the defined variable If you enter a second definition in this location a further blank entry position will appear The number of rows of information that are entered into the grid therefore defines the number of x variables in the equation Chapter Error AutoText entry not defined Equation Item When to use Multiple X Variables Most equations are of the form y f x and so have just a sing
214. ult although the principles discussed above still apply The difficulty arises because it is not possible to derive an exact analytical expression for minimizing x2 It is possible however to take initial estimates for the best fit parameter values and to improve on them by a series of iterative calculations until values are obtained that approach the minimum y value Apart from this mathematical inconvenience non linear regression functions in the same way as linear regression We still need to know the weighting that has to be applied to the data and the calculations still aim to minimize y The advantage is that non linear regression may be used to analyze any function that may be written y f x i e the y data value is dependent upon some arbitrary single valued function of the x data value GraFit performs non linear regression using the method of Marquart using a numerical second order method to calculate partial differentials In this way it is possible to incorporate equations of arbitrary form For an excellent explanation of regression analysis the reader is referred to the text by Bevington8 Standard Errors of the Calculated Parameters As well as giving the best fit values for the parameters regression analysis can provide estimates of the standard error of each parameter GraFit calculates these errors by the matrix inversion method These estimated standard errors are useful to show how accurate the calculated parameters
215. urce Item Type Entry Linear non linear Fit Equation Data table 961 Replaced by the fit Replaced by the data Replaced by the data number number number 962 Replaced by the data not applicable not applicable number A data legend showing the symbol and descriptive Q Data set 1 text Source Graphs are plotted using data that are present in one of the items found in the GraFit workspace The Source selection lists all items that contain suitable data for plotting and one of these must be selected GraFit graphs can plot three different types of plot on an X Y graph depending on the source selected Item Type Effect Data When raw data are plotted the data table item is selected and the x and y columns are selected for display The data points can optionally be joined with lines or curves If the data have been fitted to an equation it is usually better to select the data fitting item as this will also show the fitted curve Equation To plot a theoretical curve select the equation item for the curve you want Linear Fit Selecting a data fitting item linear or non linear fit results in il Noni i the data being plotted together with the fitted curve This is oninear FR usually the way of plotting data fitting results Data fitting items may contain multiple fits so when a data fitting item is selected you have the option of displaying a single fit and selecting which you require or of plotting all fits X data
216. utside Left Lower ticks inside Left Lower ticks both sides Axis offset The axis offset controls the distance that the axis scale is drawn from the frame If the offset is O the scale is drawn immediately adjacent to the central graph frame increasing offset results in the scale being removed from the frame as shown below No offset x axis offset x and y axes both offset If more than one x axis is present it can be useful to set each to have a different axis offset This allows the two scales to be differentiated Tick marks These settings control the width and color of the pen used to draw the tick marks Chapter Error AutoText entry not defined X Y Scatter Graphs Major grid Minor grid These settings control the display of grid lines drawn across the axis at intervals determined by the Major increment and Minor increment settings Scale Page pu you N ef w LI LI No grid x axis with major grid x axis with major grid solid lines solid lines and minor grid dotted X Scale Page XY Graph Properties xj General Fill Line x Ticks X Scale Y Ticks Y Scale Location r Scale check box for autoscale gt axis selector Tune gi xe ox IV Start E Axis extent v Entire graph size M Finish 10 Start p E j At 100 7 p Maior 3 End 00 y increment Avis Great None z Minor Symbol v increment r Drawing options Y axi
217. vailable from certain instrument manufacturers or from Erithacus Software These filter files are installed into GraFit from the View Options dialog box Data Filters tab Please contact Erithacus Software if you have special requirements for a specific filter file GraFit Template Files Template files are pre made workspace files that are used to speed up use of common procedures Template files differ from workspace files in the following ways e They are represented by a different icon e Double clicking on a template file opens a copy of the file rather than the file itself Templates stored in the user or group template directories can be rapidly accessed using the File New command Creating a Template File To store a workspace as a template file select the File Save As command and save as type GraFit Template Files If you wish to access this template using the File New command ensure that the file is saved into your user or group template directory see the following section on Template Directories To help with this the Save As dialog box contains a command button that will jump immediately to your user template directory Creating a File Based on a Template The File New command creates an untitled file based on a selected template This command in described in the following section Chapter 23 describes the standard templates that come pre defined with GraFit Template Directories There are two d
218. value acts as a switch to decide which parameters apply to the data value For the simple example described above the independent variables are x and dataset parameters al and a2 are the two intercepts and b is the common slope The equation is then defined as if dataset 1 then y al b x return endif y a2 b x How does this work When data from the first data set are accessed the value of dataset is 1 and the equation returns al b x When data from the second data set are accessed the value of dataset is 2 and the equation returns a2 b x Therefore the value of a1 is determined in effect from only the first set of data and a2 from the second However the slope b is applicable to all the data The graph below shows these data fitted to a common slope in this manner Chapter 21 Worked Data Fitting Examples The dataset setting is set using the Table Column Type Data Types y Data with Associated Value command resulting in the appearance shown Data L Of x 1 0000 3 8814 6 7743 2 0000 5 3815 8 5039 3 0000 8 1534 11 2915 4 0000 10 3019 14 1558 5 0000 12 0741 14 5182 6 0000 13 0814 17 0320 7 0000 15 7954 18 5855 8 0000 17 4193 21 0429 9 0000 19 4161 22 9451 10 0000 22 0809 245048 Py It is simple to extend this approach to many data sets The equation to find the best slope through four data sets and a separate intercept for each is 215 GraFit User s Guide
219. values within a specified data range This range is defined as having an origin at the Start position value and the group size is set by the Increment value Increment Enter the histogram increment value as defined above Set Initial Scaling Histogram Wizard Set Initial Scaling 21 xi mX axis Y axis Type E Type Linear gt Autoscale Autoscale C Manual scaling C Manual scaling Eran D From 0 TIG feo To 00 X axis text Y axis text Text Data Text Number lt Back Cancel The Set Initial Scaling page allows the scale of the data axis to be specified By default the scale is set automatically and linear axes are chosen These can be 166 Chapter Error AutoText entry not defined Histograms altered as required it is also possible to adjust the scale settings later The text used for the x and y axes can also be entered Select Tick Styles Chart Wizard Select Tick Styles L21x r Style DIO LIE I lt Back Cancel The Select Tick Styles page allows rapid selection of some of the more common axis tick styles More extensive tick style choices can be made once the graph has been created Select Bar Style Histogram Wizard Select Bar Style 2 x m Fill style Type E am ad El El Bar type HAT B Ol E Fill colors Iv Fore SS Lime a el El M Bak we y Outline style Width jos pt Style Color Bl Bla

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