Home

User Manual - Jplus Consulting

1. 1860 0 0228 0 2500 1 0 1684 18 13 7 2040 0 0246 02000 Y mesg gi gn 19 14 2220 Topes Y_calc400 8 0 1734 20 15 2400 0 0264 Wen B 0 1752 r 0 1000 _calc 500 21 16 2580 0 0283 rer 0 0 1767 22 17 2760 0 0279 0 0500 S Y calc 600 9 0 1780 23 18 2940 0 0286 0 0000 r Y calc 700 H 0 1791 24 19 3120 0 0278 o 500 1000 1500 2000 2500 3000 3500 4000 3 0 1799 25 20 3300 0 0283 Lerroaren oo or ooroo orre oeoo om 0 1807 26 21 3480 0 0308 01768 04327 0 4456 0 1797 0 0296 01764 04316 0 4453 0 1813 27 22 Figure 43 An overview of the Fit Plots worksheet This worksheet is produced by excel and is completely independent from the ReactLab program This gives the user complete freedom in generating graphs appropriate for their data Its structure is slightly different from the other worksheets and needs a few explanations The default is to present 5 wavelengths spread evenly between minimal and maximal wavelength these wavelengths are produced in row 2 of the worksheet The user can change any of these wavelengths to different values If fewer than 5 wavelengths should be displayed it is sufficient to change some of the wavelengths to values outside the range and Jplus Consulting Pty Ltd 34 ReactLab Kinetics 1 1 Jolus consulting multivariate analytical techn the lines disappear If more than 5 wavelengths should appear in the Figure the user is invited to expand the
2. Help Close F t 0 5 10 15 20 25 ayout Lines Text Color Advanced C1 i T LI I i Auto Actual Size Centered Use manual size and position Left 1 00 Top Width Height 29 68 9 20 98 Orientation Portrait Landscape Rotated Figure 21 Print preview launched from the Graph GUI window SIMULATION Simulation enables the creation of artificial data sets for model evaluation and comparison with real scenarios It is an extremely useful adjunct to the fitting functionality and very informative when used as a what if tool It also allows the easiest route to familiarisation with the ReactLab application Jplus Consulting Pty Ltd 17 ReactLab Kinetics 1 1 Bs multivariate analytical tech Jolus consulting The first step in simulation involves provision and compilation of a model as described earlier page 9 onwards and providing parameter values for the reaction steps However instead of calculating the concentration profiles as a precursor to fitting the model to experimental data these are instead combined with artificial spectra to synthesise a new simulated data set Gaussian curves are used for the artificial spectra The parameters defining these are provided along with a time and wavelength range required for the simulated data in the Sim Excel worksheet shown in Figure 22 A B C D E E G H J K k T wavelength range OO
3. ReactLab ep User Manual Copyright Jplus Consulting Pty Ltd d multivariate analytical technologies Jolus consulting multivariate analytical technolog ReactLab KINETICS Global Analysis and Reaction Modeling for Kinetic Processes USER MANUAL Contents PRS AC Ue PRINT a a ee 1 ABOUT EHIS MAN a E E 3 SYSTEM REQUIREMENTS AND INSTALLATION ccccccccccccsssssssssseseeeeeeeceeeceeeeeeeeeeaeeeeeesseesesees 3 CONTACT INFORMATION AND SUPPORT osssssssssnnneessssssssssssssssssrrerreresesssssssssssssseeeerereeeesssssssse 3 PARTI REFERENCE GUID E ee nen eee eee eee eee ere ee Da eee 4 RO DY CAO Naot cece a a E 4 Sie esu arr E E E 4 STARTING THE MATLAB PROGRAM 7 Progi am OPEra UON ceee an E EE tre an 7 OAC ECC TEC arrn E TT E E O T 7 close Exe FIIO u ene E E EEE T EEE E AEE G E EA A 9 SVC NEW Dl WE 9 MODEL ENTRY AND COMPILATION aa 9 Comple e el ee ea es net de ne 10 RAM TE EIN Re R 11 FIITING THE IO DEE TO DR E 12 Eeer 12 14 RSI 14 EIER NEE 16 MOTO NS un 17 SUIT EL 19 FACTOR TR e E 19 CR E 19 Jplus Consulting Pty Ltd 1 ReactLab Kinetics 1 1 NUMERICAL OPTIONS a een a a mn on 21 FS SHO SEO NS a a a dome 21 dAUITUNG Ee EE 22 ETH 22 D SPE GR A orice da te E 22 AUXILIARY PARAMETER S a E te ec en co 22 NUMERICAL AND OTHER OPTIONS AA 23 HANDLING PROTONATION EQUILIBRIA H OH and Kw 25 MODEL ENTR ES NT CROSS an ana een an at mn os 26 Wie E 27 Example 1 Consecutive
4. and Products See the simple A gt B gt C reaction mechanism Note each reaction step is entered individually ASB and BSC which allows for a one to one correspondence of each reaction step to its parameter value in the Parameter column Parameters values and labels are not required for compilation Figure 6 Entering the ABC model The parameters that can be fitted in this example will be the two forward rate constants A second order step would be entered as Figure 7 Syntax for a 2nd order step allowing a second order rate constant to be fitted If the reaction is reversible with individual forward and reveres rates this is entered as two lines using the following syntax Figure 8 Syntax for a reversible reaction Jplus Consulting Pty Ltd 9 ReactLab Kinetics 1 1 dy Jolus consulting This will allow the individual rates to be fitted independently Note the reverse reaction is actually entered backwards to achieve this If a reaction comprises a rapid effectively instantaneous equilibrium it is entered using the symbol This is typically the case for protonation equilibria L H Figure 9 Using the symbol for a rapid equilibrium In this case the parameter to be fitted is an equilibrium constant an equilibrium constant is always entered as its logarithmic base 10 value This is always entered syntactically as an association constant Kass With the associated product on the right
5. is treated as a special case and if present will enable the automatic incorporation of calculations to account for the autoprotolysis of water In this situation OH will also be added to the participating species list e In this version of ReactLab OH cannot participate in a kinetic step only in the auto equilibrium with H above Thus equilibria can be incorporated into a reaction model in two ways They can be expressed as kinetically observable forward and back reactions each by using gt symbol allowing the individual rates to be potentially fitted Alternatively they can be expressed as equilibria using the symbol where the equilibration is instantaneous at any particular time In this case the equilibrium is defined by its equilibrium constant and the concentrations of the equilibrium species at a particular time are determined using the law of mass action This mode of calculation is particularly suited to equilibria where equilibration is so rapid that it cannot be observed e g protonation equilibria Jplus Consulting Pty Ltd 26 ReactLab Kinetics 1 1 multivariate analytical tect Jolus consulting Part 2 EXAMPLES Example 1 Consecutive Reaction Scheme A gt B 2 gt AtoBtoC xlsx The Experiment The experiment is aimed at the determination of the rate constants for the consecutive reaction scheme ky k2 A a Ba 0 0 Absorption spectra are measured as a function of
6. The residuals as a 3 D plot in the excel format The residuals can be represented in an Excel 3 D plot as demonstrated in Figure 17 They are also displayed in the Jplus GUI as shown in Figure 14 The main purpose of exporting the residuals is to enable the construction of plots that demonstrate the quality of the analysis in a readily publishable format Naturally the user can also apply any additional statistical analysis to the residual matrix The worksheet Fit Plots has been included in the examples and template files to demonstrate the use of Excel functionality for the preparation of plots that compare the measured data points to the fitted curves at a selection of five wavelengths The experienced excel user will be able to expand the number of curves wavelengths with little effort 70 0000 60 0000 Y_meas 400 50 0000 TR REXX ER 9s Y_meas 440 A i Ka A O gt Y_meas 480 TU Y_meas 520 Y_meas 530 30 0000 Y_calc 400 20 0000 Y_calc 440 Y_calc 480 10 0000 LE Y_calc 520 Y_calc 530 10 0000 Figure 18 Plot of the measured data different markers and fitted curves lines in the Fit Plots worksheet Jplus Consulting Pty Ltd 15 ReactLab Kinetics 1 1 Bs JDIUS consulting multivariate analytical technolog Figure 18 shows the default format in the Fit Plots worksheet Markers line styles and colours can be adapted by the user to any preferred format in the usual excel way
7. all others including the buffer components are non absorbing LA ICT m2 H B WH BH oF 2 50E 04 0 00E 00 0 00E 00 1 00E 01 3 00E 01 000E 00 300E 01 000E 00 non abs non abs non abs non abs non abs non abs Figure 64 Definition of the initial concentrations and spectral status of all species Initial Concentrations in Models with Protonation Equilibria The initial concentrations need more careful explanations we need to distinguish between species that are involved in protonation equilibria and those that are not During the progress of the kinetics the protonation equilibria are always updated according to the prevailing relevant concentrations This is particularly the case at the very beginning i e time zero In the above example the species that take part in protonation equilibria are L H B LH BH and OH In order to compute the actual protonation equilibrium position ReactLab needs to know the total concentration of the components and the protonation constants in the example the relevant total component concentrations are L tot L LH 0 25M B tot B BH 0 6M and H tot H LH BH OH 0 4M It does not matter how the species concentrations in the spreadsheet are defined in detail as long as the total concentrations are correct E g the species concentrations in Figure 65 are identical with the ones in Figure 64 The difference is the detailed definition of th
8. d On On P Co MN sch start step WE 10 9 10 start step Sp Gs St an 13 Gaussian 14 Spectra 15 Position 550 1000 20 P E E EE E E ee ee EC RE E RE ET E DEE TE EE 1500 1200 J eee ee EE RE S BEC RE US PS AS PS PS ES RS RE b mn Figure 22 The Sim worksheet showing data simulation parameters It is necessary to provide three parameters for each Gaussian spectrum the position on the wavelength axis the Gaussian peak half width in wavelength units and its height this creates a vector of molar absorptivities for each species in the shape of a Gaussian curve Simply leave the Gaussian parameters blank if it is intended that a species be modelled as colourless or set its height to zero The overall wavelength and time ranges and their resolution are entered in corresponding start step and end fields The resulting absorption spectra are shown in Figure 23 The noise parameter will add an overall percentage of Gaussian noise relative to the maximum overall absorbance of the simulated data set 160 000 140 000 120 000 100 000 80 000 60 000 40 000 20 000 0 000 400 000 450 000 500 000 550 000 600 000 Figure 23 The absorption spectra created by the parameters of Figure 22 Note When a simulation is calculated all pre existing data and results in the worksheet will be overwritten or removed Note the model species list is automatically copied to th
9. 06 1 0E 07 1 0E 08 1 0E 09 1 0E 10 Figure 68 Removing the buffer components from the reaction results in a dramatic slowdown of the second step as the pH drops to about pH 9 Replacing the buffer with one of logKgy 8 lowers the pH and slows down the reaction 1 0E 00 Figure 69 Using a buffer with protonation constant of 8 The ability of allowing the incorporation of protonation equilibria into the kinetics is a unique feature of ReactLab Kinetics It allows the correct modeling of pH changes thus Jplus Consulting Pty Ltd 47 ReactLab Kinetics 1 1 Jolus consulting multivariate analytical technologies removing the necessity of using buffers or if buffers are used allows the computation of the resulting smaller pH changes Jplus Consulting Pty Ltd 48 ReactLab Kinetics 1 1 References Marcel Maeder Yorck Michael Neuhold Practical Data Analysis in Chemistry Elsevier 2007 Kinetics John Ross Igor Schreiber Marcel O Vlad and Adam Arkin Determination of Complex Reaction Mechanisms Analysis of Chemical Biological and Genetic Networks Oxford University Press 2005 Robert W Hay Reaction Mechanisms of Metal Complexes Albion Harwood Pub 2000 H Gutfreund Kinetics for the Life Sciences Cambridge University Press 1995 James H Espenson Chemical Kinetics and Reaction Mechanisms 2nd edition McGraw Hill 1995 S K Scott Oscillations Waves and Chaos in Chemical Kinetics Oxf
10. 155 0 0101 41315 12923 0 0726 0 0535 16 305 3653 13631 01477 FALSE TRUE FALSE FALSE 06532 0 8885 0 2701 0 6592 0 6425 0 4005 0 2864 o H 0 0833 0 1793 0 0371 0 0808 0 296 0 0393 0 0405 0 163 44856 14744 0 0735 Goen 16 256 3 6043 12248 0147 FALSE TRUE FALSE FALSE 0 7036 0 3082 0 2602 0 7036 0 5436 0 0413 0 0608 o 12 0 0885 0 1663 0 019 0 1814 04477 0 0367 0 1904 0 4062 4 6567 16532 0 0756 0 0633 16 201 3 5483 1 0836 ouer FALSE TRUE FALSE FALSE 0 7535 oam 0 2431 0 7535 0 6646 01233 0 1653 H 13 0 0922 0 1506 0 0044 0 0215 0 521 0 0748 0 2522 0 1975 48835 18197 0 0734 0 0732 16 137 3 4358 0 9731 0 1453 FALSE TRUE FALSE FALSE 0 7855 0 8476 0 4438 0 7855 05395 0 2862 0 3888 o 14 00958 0 1384 0 027 0 2242 0 433 0 0897 0 1351 0 0206 5 1031 19734 0 0841 0 074 16 068 3 4473 0 8719 0 1452 FALSE TRUE FALSE FALSE 0 8154 0 872 0 3045 0 8154 0 4739 0 2667 0 2832 o 15 0 0932 0 1352 0 0364 0 0662 0 27093 01271 0 0516 0 0284 5 3443 21188 0 0871 0 076 15 394 3 4002 0 7304 0 1436 FALSE TRUE FALSE FALSE 0 845 0 8503 0 4526 0 545 0 2527 oam 0 1423 o 16 01023 0 125 0 046 0 0503 04315 0 233 01303 0 237 5 5613 22465 0 0939 0 0772 15 913 3 351 0 7066 0 1435 FALSE TRUE FALSE FALSE 0 8712 0 834 0 4336 0 8712 0 0328 0 4315 0 0448 o m 01043 0 1173 0 0586 0 0436 0 0704 0 3832 0 2304 0 0835 5 8213 23639 00996 0 0773 15 827 3 3037 0 6292 0 1434 FALSE TRUE FALSE FALSE 0 8931 0 8234 0 5308 0 8931 0 1339 0 6148 0 1083 o 18 01064 0 1131 0 0731 0 0263 0 0526 0 4507 0
11. A B C D E F G H J K L M N O wavelength 400 440 480 520 530 Y_meas Y_meas Y_meas Y_meas Y_meas Y cac Y cac Y cac Y cac Y cak 1 time 400 440 480 520 530 400 440 480 520 530 2 Ip 0 0896 2 0090 07738 214366 49 6348 0 5401 0 3398 02020 210850 49 9985 3 01 1 2226 0 4496 59728 249731 46 5428 0 4982 04257 67512 25 7139 48 0247 4 02 06168 1 0808 128666 293000 46 6744 04614 045811 126318 298355 46 2114 5 6 LO OO rd On On E WMH 7 03 0 1967 2 3174 17 7514 33 6171 04 0 0278 0 0218 22 2416 38 1660 1217 05 0 2950 3 2511 266412 39 259 1318 06 1 0839 30304 29 2888 422774 60 0000 14 9 07 0 6152 2 7675 326268 46 1831 15 110 08 14117 1 9870 370269 47 4703 16111 7 09 1 5548 2 7069 41 0960 47 4954 70 0000 50 0000 Ses Figure 19 Section of the Fit Plots worksheet the user can select the wavelengths in the blue cells D2 H2 The worksheet is populated by a selection of five wavelengths covering the complete wavelength range in the blue cells D2 H2 The user can change the wavelengths to any other values the rest is done automatically by excel Invalid wavelengths results in removal of the trace thus if the measurements at only one wavelength are required the remaining four entries are set to an invalid number i e outside the measured range Please note the Fit Plots worksheet is provided by the authors to demonstrate the use of Excel functionality to process and chart data from elsewh
12. Note for such equilibria the individual forward and reverse rates are not fitted In addition leading numbers prefixing a species letter or string will be interpreted as stoichiometry coefficient for the species in question e g 2A gt B Similarly trailing numbers are used to represent multiple species in a particular complex e g ML ML2 ML3 etc Essentially normal chemical reaction equations can be used For further information on the syntax rules see page 26 In all cases a label for each parameter can be provided This allows easier reference to mechanisms with multiple steps These labels and the parameter values themselves are not required prior to compilation see PARAMETER ENTRY below Figure 1 gives an example of annotated rate and equilibrium constants This relatively simple syntax allows accurate models of realistic complexity to be correctly modelled see Examples Important It is necessary for any new entry in the Excel workbook to be properly completed i e by hitting return or pressing the arrow key to take the focus away from the cell in question once the desired value has been assigned otherwise the Incomplete worksheet entry warning will be raised Failing to enter values properly prevents ReactLab from accessing the worksheet cell through the ActiveX interface Compile Model When model entry is complete press the Compile Model button ReactLab reads in the model and translates it into an internal c
13. Reaction Scheme a p_ c AtoBtoC xIsx 27 THE EXPE Enri ee ee da te ne 27 EE 27 AS MIO E 28 COPI g el a eee 28 Initial Concentrations and Definition of Spectra cc eeccccssecccessccceeseceeeseeeeeecesseeeeesees 29 Definition of Initial Guesses for the Rate Constants 30 Beleg 30 d aa a nb ie dns 31 An Interesting Problem and Local Minima 32 Non Negative SPEC A anse TT seen dan Gestes ee en enrimre 33 RSA a 34 Measurements at Only One Wavelength ss 35 Example 2 Enzyme Kinetics E S gt ES Ee E P Enz1 xlsx 35 TO re E E E EER A E E EE E EE E EE EE 36 e ONO E 39 Enzyme substrate interaction as an equilibrium ss 39 Example 3 Second order reaction A B gt C AplusBtoC xisx 41 Rank deficiency KNOWN spectra sise 42 Simulation as a tool for exploring rank deficient data 43 Jplus Consulting Pty Ltd 2 ReactLab Kinetics 1 1 Jolus consulting multivariate analytical techn PUG VAN Par NCCC lS de A 44 Example 4 Kinetics Coupled with Protonation Equilibria Ni ammonia_kinetics xisx 44 Initial Concentrations in Models with Protonation Equilibria ccccceeccseeseeeeseeeneees 45 FS OCS dd does de da ds da a ed soe 49 ABOUT THIS MANUAL This manual is in two parts Part 1 comprises a comprehensive description of the program architecture and functionality and provides a systematic guide to using it Part 2 consists of a serie
14. and certain key cells containing Excel formulas generally in grey used to calculate data ranges for ReactLab It is straightforward to unprotect any sheet using the Excel unprotect command but please be aware that corrupting the layout or formulae will prevent the correct interaction of the Jplus Consulting Pty Ltd 5 ReactLab Kinetics 1 1 Bs Jolus consulting multivariate analytical technoloc spreadsheet with ReactLab One exception is the red coloured Expand tabs on certain worksheets see Figure 1 These provide an increased cell range for complex models if required To activate these tabs first unprotect the sheet and then expand or contract the cell ranges as required Please re protect the sheet afterwards It is up to the user whether to include a password for un protection To get a practical demonstration of ReactLab capabilities quickly refer to the Example workbooks and corresponding descriptions in Part 2 of this manual What follows here is a systematic overview of the whole program When working with new measurements start with an empty workbook template We advise making a copy of Master ReactLab Kinetics Template xls xlsx for this purpose The first step is to populate the Data worksheet with a new measurement matrix Y dimension n_times by n_lam as well as the corresponding wavelength and time vectors see Figure 2 Important when using Excel 1997 2003 compatible workbooks the maximum
15. do the computation of the concentration profiles for the present set of rate constant as well as the corresponding absorption spectra They appear in the GUI Jplus Consulting Pty Ltd 30 ReactLab Kinetics 1 1 Jolus consulting multivariate analytical technologies ReactLab KINETICS About License DBAS Excel filename AtoBtoC xlsx SVD FA L e Graph GUI mol absorbance mol conc 500 600 1000 2000 3000 4000 wavelength nm time sec Li et CONS Gr fea Figure 36 ReactLab GUI after Update absorption spectra concentration profiles and 3D representation of the residuals The Results worksheet will also be updated with the concentration profiles and molar absorption spectra They can be graphed as normal Excel plots Naturally they are the same as in the GUI A B C D E F G H J K L 1 Concentration profiles and spectra 4 5 Conc A B C Spectra A B C 6 60 000 0 001 0 000 0 000 400 000 54 917 18 338 57 425 7 240 000 0 000 0 001 0 000 1400000 SS 6 490 NAN D ODC D ANA Annn Ss 1200 000 EJ 1000 000 11 0 001 800 000 12 re 600 000 ch 13 J 400 000 3 14 9 001 200 000 Ant 15 1 16 0 000 0 000 17 1 200 0000 999 599 999 699 998 99 999 899 000 18 _ 400 000 19 0 000 600 000 20 0009 20 1000 000 2000 000 3000 000 4000 000 DU UU 45 773 329 9251 STT A4TO 21 700 000 51 205 3
16. in fact both computed spectra are incorrect while the fitted rate constant is correct It is equally valid to declare the species A as non absorbing and B as colored Less obvious is the possibility of declaring C as non absorbing with A and B colored In all three modes the rate constant is correct while the spectra are not Option 2 is a better way of breaking the rank deficiency ReactLab allows the possibility of independent determination of any spectrum and declaring this spectrum as known In this example this can be done for any of the three spectra Of course it is also possible to define more than one spectrum as known This is clearly a preferable option How is it done Figure 60 The preferred option to overcome rank deficiency is to independently define any of the three spectra e g C The definition of a known spectrum or spectra is done in the Aux worksheet Fixed Spectra Lambda a B c 400 000 0 000 410 000 0 000 420 000 0 001 430 000 0 006 440 000 0 021 450 000 0 070 460 000 0 204 470 000 0 535 480 000 1 250 490 000 2 608 500 000 4 861 510 000 8 088 520 000 12 019 530 000 15 949 540 000 15 900 550 000 20 000 560 000 18 900 570 000 15 949 560 000 12 019 590 000 8 0868 600 000 4 861 Figure 61 The spectrum of C is defined in the Aux worksheet The wavelengths at which the measurement and the known spectrum were taken have to be identical and the spectrum supplied is in
17. involved in a process and the autoprotolysis of water should not be implemented automatically an easy option is to call it P or anything but H Jplus Consulting Pty Ltd 25 ReactLab Kinetics 1 1 MODEL ENTRY SYNTAX RULES e Akinetic reaction step is indicated by the symbol gt e g A B gt C e The parameter associated with gt is a rate constant 1 or SE order e Reversible kinetic steps slow equilibria are expressed over two lines i e A B gt C C gt A B In this case both forward and reverse rate constants are independently defined and can be fitted e Arapid instantaneous equilibrium is indicated by e The parameter associated with is an equilibrium constant K This can be fitted but the microscopic forward and reverse rates are not accessible e The parameter when is used for an equilibrium is log10 of the association equilibrium constant logK Note this means it can be negative or positive depending on whether the equilibrium constant itself is less or greater than 1 e Each equilibrium can only have one product e No two equilibria can have the same product e Reactants and products within a particular step are combined using the symbol e Species names can be single or multiple characters e The stoichiometries of species in a particular step are indicated by an integer to the left of the species name no integer is assumed to mean a stoichiometry of 1 e The species name H
18. will be either fixed kept constant LJ or fitted optimised M by ticking the appropriate tick box Reaction re Reactants me Products Label ee Figure 11 Parameter value entry alongside the model in the Main sheet The initial concentration of each species in the model must be entered below their name and the spectral status of each assigned colored non abs or known using the corresponding drop down box Figure 12 Species list initial concentrations and setting spectral status Defining a species as colored means it is predicted to have a spectrum contributing to the measurement i e it absorbs in the wavelength range covered by the measurement Colored spectra will be calculated and optimised during the analysis A non abs species will be fixed as colourless meaning the species is invisible in the measurement all molar extinction coefficients are zero Selecting known allows an existing spectrum to be supplied for a species For example this may be for a reagent or product whose spectrum can be measured independently or for a species whose spectrum is known from other work It must be pasted under the corresponding species name in the Aux sheet prior to an Update or Fit otherwise an error will be raised It is essential it is in a compatible format to the experimental or simulated data with the same number of wavelengths and in correct molar extinction units f
19. 0 0 1655 29351 39688 651 15 1979 19 7863 23 5102 31 7939 616791 997356 114 3296 98 3348 591455 294745 121017 10 5489 7 1014 20 28 0 10957 13527 5 8879 90356 18 8596 223213 229085 345937 62 1817 98 8041 116 2494 96 3781 606232 27 4526 135617 685369 6 4765 21 30 0 0 0489 0 3691 2 3194 10 7622 18 3408 23 7825 25 0552 34 1976 62 1121 98 8873 115 5622 94 6436 58 5848 25 2014 10 4014 7 7211 4 2308 22 32 0 01671 06183 4 7588 12 8071 18 9329 26 4856 27 2482 357658 628145 98 0260 117 1880 95 9674 58 6548 25 6205 103668 4 7063 3 9755 3 23 34 0 2 07062 0 360087 3 964587 1124502 23 56678 28 19963 26 20512 36 9319 62 03042 95 5299 13 364 96 166 56 0675 24 5558 6 46556 3 73272 3 772289 BR ASAE ma MIRAA AM APA m mme si AA mms AR mm ma minn mannm m mmmn Figure 2 Key parameters in Data sheet The dimensions in grey are calculated automatically from the data range pasted into the worksheet Once the data is in place the workbook can be saved under a suitable name Important prior to ReactLab Version 1 1 Build 03 the newly populated workbook must be saved first and re loaded into the ReactLab program even if previously opened by it in order for the new data to be recognised by the application Jplus Consulting Pty Ltd 6 ReactLab Kinetics 1 1 Jolus consulting tivariate analytical In later versions ReactLab can be synchronised with new data in the linked workbook by pressing the Sync New Data button in the Main GUI STARTI
20. 01 0 0007 0 0012 8 420 0 0006 0 0008 00008 0 0001 0 0002 0 0008 0 0003 gt 600 0 0002 0 0007 0 0002 0 0006 0 0012 0 0004 0 0004 10 780 0 0012 0 0002 00005 0 0003 0 0007 0 0017 0 0003 11 960 0 0014 0 0004 0 0002 0 0005 0 0004 0 0003 0 0004 12 1140 0 0002 0 0003 0 0001 0 0001 0 0004 0 0005 0 0028 13 1320 0 0016 0 0007 0 0006 0 0007 0 0009 0 0014 0 0003 Figure 42 a section of the Residuals worksheet More informative than the residuals themselves are plots of measured and fitted curves at one or several wavelengths They are produced in the Fit Plots worksheet see Figure 43 for the present example A B C D E F G H J K L M N 7 2 wavelength 400 500 600 700 800 3 4 5 Y_meas Y_meas Y_meas Y_meas Y_meas Y cac Y cac Y cac Y calc Y calc 6 1 time 400 500 600 700 800 400 500 600 700 800 T 2 60 00535 0 0535 0 0202 0 0665 0 0197 00531 0 0537 0 0202 0 0665 0 0195 8 3 7 240 00330 00440 00812 0 2086 0 0647 00332 0 0433 0 0811 0 2087 0 0645 9 4 420 0 0227 0 0470 0 1359 0 2947 0 0944 00233 0 0478 0 1358 0 2943 0 0946 10 5 P 600 0 01686 D NEO4 N 4234 D 3469 D 1146 ANNANN N NEQE N 12377 D2465 0 1154 11 6 780 0 0166 0 5000 9 0 1303 1217 960 0 0194 04500 O Y_meas400 3 0 1413 138 1140 0 0189 o Agen L o Y meassoo 6 0 1495 149 1320 0 0220 4 0 1560 15 10 7 1500 0 0219 93 A Y_meas600 6 01610 16 11 1680 0 0239 9 3000 x Y_meas700 9 0 1651 17 12
21. 1 0 6 0 6 0 6 0 6 0 4 0 4 aa e fie Figure 32 The Compile Model button in the ReactLab GUI The compiler recognizes A B and C as the complete set of the species These are introduced as labels in row 33 of the Main worksheet and also in the appropriate ranges of the Results and Sim worksheets more on them later Dn species Dn aux Dat Figure 33 The list of species is automatically introduced Note the entries n_ species number of species and n_par which is equal to the number of reactions are automatically updated Initial Concentrations and Definition of Spectra After the compilation the list of species is established and subsequently the initial concentration for all of them need to be defined in our case the initial concentration of A Alo 001M all other concentrations are zero Note that these are the concentrations at time 0 not at the time of the measurement of the first spectrum Further the spectral properties of the species have to be defined The property of each species spectrum can be chosen from three options e colored which means that its spectrum is unknown and will be calculated e non abs which means the species does not absorb in the wavelength region e known which means its molar absorption spectrum has been determined independently and should be fixed during the fitting This feature will be discussed later In our example all three species ar
22. 35585 830 610 22 2940 000 0 000 0 001 0 000 720 000 47 549 315 192 711 897 23 3120 000 0 000 0 001 0 000 740 000 40 761 271688 622769 24 3300 000 0 000 0 001 0 000 760 000 34 020 215 602 550 097 25 3430 000 0 000 0 001 0 000 780 000 21 995 159 224 485 146 26 800 000 13 910 108 955 418 576 97 Figure 37 Concentration profiles and absorption spectra in the Results worksheet Fitting Obviously the fits are not perfect with these starting guesses for the rate constants but they are also not hopelessly wrong Thus we can hit the Fit button in the ReactLab GUI The progress of the fitting can be observed in the GUI and in the spreadsheet either on the Main or the Results page In Figure 38 we show the final GUI Jplus Consulting Pty Ltd 31 ReactLab Kinetics 1 1 Bs multivariate analytical techno NG j Jplus consulti ReactLab KINETICS About License e Excel filename AtoBtoC xlsx Load Excel File convergence Close Excel File Compile Model log sqsum Simulate Ka YI ke m DI x iteration spectra spl juil ei je ien Graph GUI Restore Options mol absorbance Nm E CH CH mol conc Jal co 500 600 700 1000 2000 3000 4000 wavelength nm time sec Figure 38 The ReactLab GUI after the fitting random distribution of residuals and best fit spectra The top left panel shows the progress of the fitting via a graph o
23. 3595 0 2288 6 0607 2 4694 01002 0 0782 15 736 3 2556 0 5605 0 1434 FALSE TRUE FALSE FALSE 0306 0 8122 0568 0 906 0 2239 0 7271 0 1216 o 13 01087 0103 0 0873 0 0736 0 0402 0 3766 0 3051 0 3004 6 2994 25711 01005 0 0848 15 641 3 2042 0 4985 0 1433 FALSE TRUE FALSE FALSE 0 9256 0 7761 0 6745 0 9256 0 0865 0 5578 0 2101 o 20 01098 0 0345 0 0861 0 1735 0 0231 0 2262 0 1838 0 2552 65354 26602 ome 0 0852 15 542 34519 0 453 0 1433 FALSE TRUE FALSE FALSE 0 3351 0 8033 0 5064 0 3351 0 0371 0 3276 0 1425 o a1 01087 0 083 01002 0 08 0 0036 0 0302 0 0752 0 2678 61644 27421 01127 0 0853 15 441 3103 0 4031 0 1403 FALSE TRUE FALSE FALSE 0 9333 0 7401 0 7066 0 9339 0 0248 0 1136 0 0338 o 22 0 124 0 0804 0 101 0 0103 0 0035 0 0242 0 0258 0 3044 6 9965 2 8194 0 1247 0 0856 15 333 3 0505 0 3777 0 1406 FALSE TRUE FALSE FALSE 0 9573 0 7474 0 6674 0 9573 0 0659 0 0053 0 0806 o 23 0 158 0 0768 0 0398 0 0583 0 0014 0 01 0 0027 0 0627 7 2283 2 8871 0 1381 0 0883 15 23 3 0002 0 3503 0 1406 FALSE TRUE FALSE FALSE 0 3688 0 7536 0 6441 0 9688 0 0302 0 0263 0 0222 o 24 0 1156 0 0748 0 0351 0 1938 7 4638 2 9456 01535 0 0304 15 19 293501 0 3228 0 1383 FALSE TRUE FALSE FALSE 0 9847 0 7125 0 8508 0 9847 25 0 1142 0 0683 0 0362 0 0478 7 6866 23978 0 1793 0 0306 15 003 2 9004 02853 0 1366 FALSE FALSE FALSE FALSE 0 722 0 7152 0 7353 0 9722 26 0 1161 0 0656 0 1101 0 1053 7 314 3 0501 0 1881 0 0306 14 83 2852 0 2516 0 1364 FALSE FALSE FALSE FALSE 0 9885 0 7417 0 6404 0 9
24. 878 0 1104 0 1444 0 1834 022 10 780 nuer 0 0527 0 1113 0 1223 0 0858 0 0754 0 0892 0 1150 0 1452 0 1816 02244 027 11 960 0 0194 0 0429 0 0818 0 0955 0 0840 0 0879 0 1113 0 1418 0 1745 0 2161 0 2620 930 12 1140 0 0189 0 0381 0 0669 0 0833 0 0876 0 1024 0 1327 0 1640 0 2037 02449 02897 oan 13 units 1320 0 0220 0 0369 0 0605 0 0791 0 0929 0 1129 0 1462 0 1854 0 2251 0 2702 O3160 0 35 14 time sec 1500 0 0219 0 0366 0 0590 0 0766 0 0964 0 1248 0 1593 0 2000 0 2464 0 2903 0 3366 939 15 wavelength nm 1680 00239 0 0357 0 0545 0 0792 0 1025 0 1338 0 1703 0 2171 0 2630 03093 03558 939 16 absorbance 1860 00228 0 0385 0 0566 0 0820 0 1083 0 1422 0 1825 0 2290 0 2762 03261 03685 gar 17 2040 00246 0 0405 0 0601 0 0834 0 1104 0 1502 0 1912 0 2387 0 2885 03365 0 3837 p42 18 2220 00275 opp 0 0610 0 0863 0 1180 0 1559 0 1979 0 2478 0 2979 0 3466 03926 0 493 19 2400 00264 0 0393 0 0615 0 0878 0 1193 0 1609 0 2072 0 2565 0 3062 03584 04024 0 44 20 2580 0 0283 0 0423 0 0635 0 0918 0 1244 0 1639 0 213 0 2611 0 3147 03655 o4089 0 44 21 2760 00279 0043 0 0632 0 0924 0 1250 0 1676 0 2152 0 2671 0 3194 0 3714 04149 045 22 2940 00286 0 0444 0 0642 0 0912 0 1285 0 1689 0 2185 0 2692 0 3231 03743 04194 0 45 23 3120 00278 0 0442 0 0664 0 0943 0 1305 0 1718 0 2182 0 2753 0 3299 03817 0 4246 045 24 3300 0 0283 0 0452 0 0683 0 0935 0 1310 0 1755 0 2253 0 2789 0 3307 0 3832 04294 0 46 25 3480 00308 0 0472 0 0682 0 0972 0 1329 0 1768 0 2257 0 2790 0 3350 03857 04327 046 26 Fi
25. 885 at 0 1153 0 0562 0 1038 0 0205 81263 3 0977 0 2072 0 0306 14 772 2 7972 0 2265 0135 FALSE FALSE FALSE FALSE 0 9621 0 6999 0 7086 0 3821 28 0153 0 0503 0 11 0 0658 8 3356 3 1445 0 2203 0 0312 14 654 27478 0 2042 0 1345 FALSE FALSE FALSE FALSE 0 9816 0 6904 0 6837 0 9816 23 0165 0 0505 0 111 0 0073 85453 3 1862 0 2344 0 0318 14535 2 6966 0 1939 01339 FALSE FALSE FALSE FALSE 0 9921 0 6867 0 7353 0 5921 30 01174 0 0452 01124 0 0345 3 7544 3 2266 0 2434 0 0921 14 414 26421 0 1815 0 1322 FALSE FALSE FALSE FALSE 1 06326 0 683 1 31 0 1167 0 0437 0 1038 0 0107 8 3565 3 2622 0 2638 0 0944 14 283 25871 0 1746 0 129 FALSE FALSE FALSE FALSE 0 9937 0 6668 0 7573 0 9937 Figure 26 Overview of the SVD worksheet NUMERICAL OPTIONS A number of numerical and measurement options may be pre set in the Main worksheet See page 23 for details Restore Options This button will restore the program default options if they have been adjusted previously by a user For details see page 23 Jplus Consulting Pty Ltd 21 ReactLab Kinetics 1 1 Jolus consulting multivariate analytical QUITTING REACTLAB Quit This will ask for confirmation before both closing the Excel workbook and then ReactLab FIXED SPECTRA In addition to the option to define species as colourless the known spectrum feature allows predetermined spectra to be assigned to model species prior to model fitting During the fitting the fixed spectra are not adj
26. 93 48 7995 46 0089 36 6879 44 0634 59 9039 68 6107 56 6486 3 3 6 0 1 0271 0 1014 0 3306 0 0556 0 5018 52058 6 1884 140991 33 2743 54 0335 66 0430 58 0049 44 5697 413691 50 1369 55 9416 45 9654 2 10 8 0 0 4095 19669 1 1834 3 0446 2 4113 4 3396 8 4271 17 9098 39 3377 66 9020 793379 699702 49 8702 382390 43 9089 45 3820 37 461 2 11 10 0 1 4671 0 6301 1 7560 18865 3 5667 6 6004 39 0219 226674 43 9263 73 8244 90 6669 771459 52 7308 38 1122 35 5084 36 5715 30 2791 1 12 12 0 0 4293 07926 3 2061 2 2137 4 4142 5 1040 10 7733 22 4010 50 211 616694 98 5508 684 8090 56 1699 36 3065 319094 321527 25 5870 1 13 units 14 0 04959 0 1982 1 3256 3 3660 6 3623 60502 13 8612 26 4207 54 4045 87 0963 105 0878 90 4830 59 4564 34 9040 27 6299 25 6125 18 7896 1 14 Time s 16 0 42869 18685 0 5616 35710 686208 10 1727 119293 27 6795 55 7592 922073 10 8327 90 5447 59 5105 32 3819 24 1564 216661 16 7238 15 Wavelength nm 18 0 33675 0 5912 1 3014 4 1352 876d 127934 155020 26 6209 57 4871 95 712 113 4559 96 1567 59 6228 32 9595 20 0250 17 0676 13 4799 16 Absorbance 20 0 1 4061 0 8280 42366 92853 100221 121913 16 2681 290346 59 2528 969482 12 7537 98 3503 605466 314804 18 8774 13221 105381 17 22 0 3 7249 15453 1 7961 5 1894 110295 165392 18 9317 311418 59 4089 97 4316 112 9048 97 7160 60 4692 326986 15 9251 12 7975 10 3050 18 24 0 10534 2 3023 45531 85450 13 7311 16 4374 217329 32 4445 60 851 99 5173 117 3668 100 1622 58 3708 301578 13 8345 105247 7 0010 13 26
27. Chemists A Comprehensive Guide 2nd edition Wiley VCH 2001 Jplus Consulting Pty Ltd 50 ReactLab Kinetics 1 1
28. K log K Parameters KH gt gt gt gt Figure 63 The complete reaction scheme in ReactLab notation Note the logK parameter for the buffer is actually the same is the buffer pKa This is because the buffer pK is defined in terms of the acid dissociation constant of the buffer Since ReactLab requires association constants only and logK logKgiss PKaiss is numerically equal to the logK and therefore the parameter required This applies to all protonation constants in the example for the protonation of L to form LH Also note we define the rate constants for the back reaction as a function of the fitted forward rate constant and independently known equilibrium constants these are stored as auxiliary parameters The entry in cell for km is F7 101K7 which refers to ky and logKm In theory these values could also be fitted but with the present data set they are not defined and thus need to be kept fixed The two rate constants for the forward reaction km and kw are fitted The protonation constant for L is taken from ammonia and the equilibrium constants logKy and logKmw gt are taken from the first two interactions between ammonia and Ni II The protonation constant of the buffer and the rate constants are fictional After compilation of the model the initial concentrations of all species have to be defined as well as their spectral status In the example only the metal containing species are colored
29. K7 to the cell where the value is stored A aia Parameters EL 1 423E 01 1 712E 02 KR ml Figure 62 the initial concentration of the reactant B is defined as a fittable auxiliary parameter As mentioned kinetics is not a good analytical tool and this is indicated by the large standard deviation of some 10 of the parameter values which should be B 5 0 15 Example 4 Kinetics Coupled with Protonation Equilibria Ni_ammonia_kinetics xlsx The full power of ReactLab KINETICS is demonstrated using a complex mechanism of coordination chemistry It is the stepwise reversible formation of the complexes ML and ML from a mono dentate ligand L e g ammonia and the metal M e g Ni the complication arises from the fact that in aqueous solution the ligand is also involved in protonation equilibria To make things more interesting a limited amount of buffer has been added to the solution The complete reaction mechanism is shown in the set of chemical equations below NI reacts with ammonia to form more complexes up to ML For the purpose of this example we restrain the model to the formation of only ML and MLy It would be straightforward to expand it to a more complex reaction scheme M L ML ML Eat ML L gt ML NL2 L Ht logKyy 5 LH logK px B H BH The translation into the ReactLab notation is straightforward Jplus Consulting Pty Ltd 44 ReactLab Kinetics 1 1 Parameters Auxiliary k
30. NG THE MATLAB PROGRAM When ReactLab is launched it also requires the Matlab MCR to initialise This can take a while and is very much dependant on computer performance after which the ReactLab GUI appears as in Figure 3 K a BB ReactLab KINETICS se x About DAN Excel filename Load Excel File 0 0 2 04 0 6 0 8 1 0 0 2 04 0 6 0 8 1 0 O02 04 O06 08 1 0 O02 04 06 08 1 ETE Figure 3 Matlab GUI control panel at startup This GUI provides the main control interface for the program with a series of pushbuttons on the right hand side for key functions These provide all the ReactLab program commands and their operation is described over the following pages Note depending on the workbook status e g whether a data or model are present some of these functions may be disabled In addition an About menu item at the top left provide details of the ReactLab version and licensing information Program Operation Load Excel File Press Load Excel File in the ReactLab GUI to select and link to an Excel Workbook This will launch a new instance of Excel and load the requested workbook independent of any other open Excel workbooks Only ReactLab KINETICS workbook templates can be loaded Important Excel is launched as an ActiveX server in an independent process linked to ReactLab which communicates with it through its Microsoft component object model COM inter
31. R 3 T Uu W x Y S AA AB AC AD AE AF AG AH A Ad Ak TI al T 4m AN 40 AF 1 2 LU bar ZS bar Vt_bar EFA_f EFA_b C_Wwin C_norm A bor 3 0 0187 0 312 0 361 0 0132 16 452 o o o 0 0032 0 0005 0 0044 0 4627 1 7365 H o o 16 452 4415 2 8053 01539 FALSE FALSE FALSE FALSE 0 1589 0 9312 0 3521 0 1583 omg 0 0453 0 1018 o 4 0 0303 0 2927 0 3066 0 0443 0 4 4115 o o 0 01 0 0225 0 0277 0 0857 2 3772 omer o o 16 443 42124 25817 01539 FALSE FALSE FALSE FALSE 0 2631 1 0 2786 0 2631 0103 0 0654 0 0644 o 5 0 0403 0 2663 0 2553 0 0177 o 0 2 8053 o 0 0382 0 0725 0 0887 0 1241 2 8142 0 3347 0 0428 H 16 441 40619 2 3447 01538 FALSE TRUE FALSE FALSE 0 3485 0 9639 0 1443 0 3485 0 3234 0 1953 0 1752 o 6 0 0492 0 2505 0 2032 0 0012 o o 0 0 1533 00921 0 1741 O218 0 1535 3 1586 0 5062 0 0619 0 0355 16428 33531 2 1127 0 1537 FALSE TRUE FALSE FALSE 0 4131 0 9485 0 0422 0 4191 0 6777 0 4264 0 3243 o il 0 0589 0 2334 01608 0 0303 0157 0 2949 0 3536 0 1348 3 4546 0 7077 00635 0 0368 16 403 3 8626 18984 01537 FALSE TRUE FALSE FALSE 05018 0 9255 0 1245 0 5018 4471 0 7319 0 5702 o 8 0 0656 0 2153 0 1218 0 2237 01924 0 3523 0 4173 0 1206 3 7155 0 9058 0 0635 0 05 16 381 3786 17015 0 1532 FALSE TRUE FALSE FALSE 05584 08787 0 5059 0 5564 14632 0 899 0 7333 o 3 0 0726 0 2018 0 0874 0 063 01877 02887 0 3425 0 0427 3 9536 11067 00668 0 0563 16 547 3 7193 15258 0 1483 FALSE TRUE FALSE FALSE 0618 0 8983 0 2549 0 618 12456 0 7316 0 5304 o 10 00774 0 1873 0 0636 0 0073 02006 01668 0
32. ain worksheet which is the principle sheet of the workbook requiring user interaction The various fields in this sheet will be described later on in this document Fal PE EA EE Ni_ammonia_kinetics xlsx Mic File Home Insert Page Layout Formulas Data Review View Add Ins Acrobat En cut n 2 w Zi Arial 1122 A A IS gt c Wrap Text General h E Normal 2 EE A ii g 2 tional F Normal 2 6 aste H I Uv He ES S oe SS Merge amp Centery 9 lt 0 Conditional Format Norma Format Painter 2 SS S R 00 7 Formatting as Table Clipboard Font P Alignment 4 Number u66 fe AE D B e D E F G H I dy Model Editor Auxiliary Label Fit Parameters k log K Reaction Type nou v v v v yaaa z TW AY Ay Ty yy TY TT 27 T 28 or 00008 23 n CG Se 0 0005 30 au par 2 3 Species om tc m wv B ih BH o 35 Spectrum non abs non abs mon abs non abs nonabs non abs 36 37 38 Numerical calculation options 39 s 42 000E 4 901 DOE 2 45 100E 06 si 000E C 46 00E 03 7 J EH 48 C ms _ 49 50 51 52 53 54 55 data 1 0 000E 00 E C 56 57 ct al Figure 1 The Main worksheet illustrating a fairly complex reaction model in coordination chemistry Important The workbooks provided have certain areas of each sheet protected These areas include data entry headings generally in yellow
33. all species using a logarithmic y axis and the right panel displays the details for the first 100 msec It is instructive to inspect the right hand panel of Figure 56 This early period of the reaction is the so called pre steady state phase during which time the enzyme bound intermediates build up to their comparatively stable steady state levels During this phase it is possible to monitor the enzyme bound intermediate concentration changes When combined with clever experimental design it has proved possible to elucidate quite complex microscopic enzyme mechanisms by the analysis of such intermediate transients This approach using a variety of rapid reaction techniques led to the emergence of the field of pre steady state or transient kinetics This subject is too complex to discuss in detail here and the user is referred to a number of classic textbooks on enzyme kinetics see References Nonetheless ReactLab provides all the necessary means of simulating and analyzing both pre steady state and steady state kinetic data Note that all these enzyme kinetics computations are using the stiff solver k Example 3 Second order reaction B gt C AplusBtoC xlsx The third example appears to be almost trivially simple a second order reaction between A and B to form the product C We will use this example to introduce the concept of rank deficiency the fact that in this example it is not possible to determine all three absorption spect
34. an be chosen in one of the options in the lower part of the Main sheet spectra linear reg Figure 41 the tick box to impose non negative spectra Using that option the wrong solution is excluded and from any reasonable initial guesses the correct solution is found Molar absorptivities are of course always positive and it is possible to select this option for any fitting problem Computations can be more robust but usually the difference is not noticeable Additionally calculated negative spectra can be indicative of a problem Nevertheless it is possible to perform ESR or CD titration and these spectra of course can be negative Jplus Consulting Pty Ltd 33 ReactLab Kinetics 1 1 Bs Jolus consulting multivariate analytical technologies Residuals Judging the quality of the fit by comparing the sum over the squares of the residuals ssq or better their standard deviation with an expected value which might be based on the known performance of the spectrophotometer is possible but visual examination of fitted and measured curves is more satisfactory and might reveal potential problems with a particular model ReactLab computes the matrix of residuals and stores them in the Residuals worksheet see the section R on page 14 for more background information A B C D E F G H 2 2 4 5 400 420 440 460 480 500 520 6 60 0 0004 0 0005 0 0001 0 0004 0 0002 0 0002 0 0005 7 240 0 0002 00007 0 0001 0 0010 0 00
35. at can re start the catalytic cycle It is instructive to use a reasonable set of parameters and observe the resulting concentration profiles To do that we can use the Simulation option available in ReactLab Simulation First the reaction model has to be defined compiled and rate constants need to be defined as well Reaction arameters Reactants N Products Labe Parameters Fit v Type klog K SE kH Lungen FAE SE o k ja e e Figure 46 The model and parameters for the Michaelis Menton mechanism In order to compute the concentration profiles a few additional parameters have to be defined they include the initial concentrations for all species and the time vector defining when the concentrations need to be computed Note that the concentration of the enzyme is significantly lower than the concentration of the substrate init 1 00E 00 1 006 04 0 00E 00 0 00E 00_ non abs non abs Figure 47 The initial concentrations for all species and their spectral status Simulation also includes the computation of a measurement based on simulated molar absorption spectra The simulator computes spectra as Gaussian curves defined by position width and maximum it also demands a wavelength vector at which absorption data are taken Jplus Consulting Pty Ltd 36 ReactLab Kinetics 1 1 multivariate analytical technologies Jolus consulting sum step end SE WS _ Spectra oS Ee
36. dard Matlab installed and is supplied as part of the installation package All raw data model entry and results output are organised in Excel Workbooks which are launched from and dynamically linked to the ReactLab application It is therefore necessary for Excel to be installed on the same computer as ReactLab The use of Excel provides a familiar spreadsheet format for all experimental and analysis data and results and allows the independent application of Excel tools and features for further processing and graphical presentation It also provides the interface for entering reaction models and all fit related parameters and numerical analysis options When a workbook is saved it contains all information and settings associated with the current analysis session as well as the numerical data and results This allows any number of data analyses with different model scenarios and parameter settings to be developed and saved in a self contained format These workbooks can be further analysed by ReactLab as required or reviewed independently just using Excel The program requires Excel analysis workbooks to retain a strict format as is provided in the examples and templates The process of analysing a data set using the program involves launching ReactLab and loading a workbook pre populated with measurement data Note the workbook can be saved or reloaded at any time and will re synchronise with ReactLab program according to the
37. do it A less trivial but more controversial use of the auxiliary parameters feature would be to fit the initial concentration of a reactant While the application of kinetics as an analytical tool is neither common nor robust it is certainly a possibility see the section on Auxiliary Parameters on page 44 There are numerous other possibilities to use the auxiliary parameters feature NUMERICAL AND OTHER OPTIONS A range of numerical calculation and other options are provided in the Main sheet that can be adjusted There are also a number of software flags Numerical calculation options Numerical Integration Equil Speciation Non linear reg Spectra linear reg Stiff Solver Init marpar O00E 06 WO Oo O Rel tal 000E Max iter 5 000E 01 Sas OETA El its Measurement options Miscellaneous Delta Tzero 0 000E 00 1 400E 04 1 000E 00 Sree Figure 28 The array of option definitions Numerical Several of the numerical options and are included for completeness rather than intended for routine customer use Numerical Integration e Stiff solver This is switches the numerical integration routine used during the calculation of concentration profiles during update or fitting It is relevant when very large differences in rates of change occur in concentration profiles Particularly with Jplus Consulting Pty Ltd 23 ReactLab Kinetics 1 1 dy Jolus consulting multistep reactions with fast second
38. e Sim worksheet at compilation time Initial concentrations of species for simulation must be entered in the Main sheet in Jplus Consulting Pty Ltd 18 ReactLab Kinetics 1 1 the usual place Note however the spectra settings in the Main sheet colored known etc are ignored during simulation Simulate Selecting Simulate will now create a synthetic dataset and populate the Data and Results worksheets with the results of the simulation Data created by simulation can now be analysed in the same way as experimental data using the fitting procedures already described above This allows different model scenarios to be tested as candidate mechanisms in particular providing a means of testing for the resolvability of the data model combinations Simulation also provides an invaluable general educational tool for learning and understanding the behaviour of kinetic processes For example it provides an easy route to investigating the importance and use of known spectra in the determination of complex models since the Gaussian spectra used in the simulation and which now appear in the Results sheet can be simply cut and paste to the Aux sheet for experimentation FACTOR ANALYSIS Factor analysis is provided as an additional tool that can be used to estimate the number of coloured components in the data set thereby providing insight into reaction complexity The two principl
39. e colored Jplus Consulting Pty Ltd 29 ReactLab Kinetics 1 1 Jolus consulting multivariate analytical techn 1 00E 03 0 00E 00 0 00E 00 Spectrum Figure 34 Initial concentrations and spectral properties are defined Definition of Initial Guesses for the Rate Constants The fitting of the rate constants is a non linear process it has to be started from a set of initial guesses Naturally the better these initial guesses are the faster and more reliably the best parameters can be computed They are allowed to be significantly wrong but if they are completely wrong the algorithm will collapse Where the borders between significantly and completely wrong are is not well defined no general rules can be given as they strongly depend on data set and reaction model However there are specific rules that can be given in the example often convergence is better if the guess for the fast rate constant is too high and the guess for the slow constant too low Reaction Parameters Reactants Type Products Label k log K D ki 1 000E 02 po oc k 1000E04 F EL Figure 35 Input of initial guesses for parameters The rate or equilibrium constants can be labeled e g k and ka but this information is not relevant for any computation The tick boxes indicated whether a parameter is be fitted or left fixed at the entered values Update Hitting the Update button in the ReactLab GUI will
40. e algorithms used are singular value decomposition SVD and in conjunction with the results of this evolving factor analysis EFA The critical difference between this and the model fitting functionality is that these analyses are model free and do not yield reaction mechanism or rate constant information SVD is an incredibly useful algorithm mathematically decomposing a matrix Y into three matrices such that Y U S V Put very simply these matrices comprise the eigenvectors and eigenvalues of the original data matrix These define the data in terms of the linearly independent components along with their significance This correlates with the underlying chemical complexity by a defining the minimum number of species required in a reaction model and b the maximum no of independent coloured species in the model The user is referred to the references on page 49 for further information SVD This opens a new GUI window which graphically displays a reduced subset of the singular value decomposition of the data matrix Figure 24 Jplus Consulting Pty Ltd 19 ReactLab Kinetics 1 1 Jolus consulting multivariate analytical Singular Values 6 1486 3 3244 1 959 0 11193 0 096935 0 091979 0 088047 0 083091 0 079804 OO OO 4 OO P wn zz Basis Vectors Reduce to first 4 Save all from EFA window wavelength Figure 24 The SVD GUI The graphs display the selected number of kine
41. e buffer Jplus Consulting Pty Ltd 45 ReactLab Kinetics 1 1 Jolus consulting multivariate analytical techr components and the proton but the total concentrations are the same This is a very useful property as it does not require the user to compute the actual initial concentration for all these species the definition of the total concentrations is sufficient Species m L m m2 H B WH BH on init 4 00E 04 0 00E 00 0 00E 00 4 00E 01 0 00E 00 0 00E 00 oppen Cd Spectrum non abs non abs non abs non abs nonabs non abs Figure 65 identical initial concentrations as in Figure 64 Remember also that the hydroxide ion OH is introduced automatically if protons H are part of the species list This has been explained on page 25 The initial concentration of all species that are not taking part in protonation equilibria need to be defined correctly i e as they are at time zero And to reiterate the actual initial concentration L of the ligand will not be 0 25 M as a fraction of the total amount of ligand will be protonated the exact concentrations of L and LH are determined by ReactLab Figure 1 File Edit View Insert Tools Desktop Window Help O6G48 k A88O0e4 8 08 an Figure 66 The measurement The measurement is a series of 41 spectra measured between 0 and 0 2 sec the wavelength range is 500 to 700nm in 10nm intervals The fitting from arbitrary but reasonab
42. el worksheet and the concentration and spectra matrices in the Results worksheet Any Excel graphs linked to these data ranges will be updated accordingly Figure 16 The implementation of such graphs is entirely at the discretion of the user and these can of course be created and manipulated entirely independently of ReactLab A B E D E E G H J K E M N O Concentration profiles and spectra A B C Spectra A B C 0 1 0000 0 0000 0 0000 400 0 5401 0 0938 1 3060 0 1 0 9047 0 09468 0 0005 410 0 5246 0 1205 6 3608 0 2 0 6185 0 1797 0 0019 420 05570 0 3605 21 4157 0 3 0 7405 0 2555 0 0040 430 0 5296 0 3056 49 9357 10 0 4 0 6699 0 3232 0 0069 440 0 3398 0 8245 83 4019 e 8 037 Ola NO mS wr a Le Q 5 bi 1 2000 0 1 160 0000 13 ane 2 140 0000 14 e 1 120 0000 16 0 8000 4 0 2 17 5 100 0000 kad etic 0 6000 t 80 0000 21 0 4000 10 6 20 0000 28 2 2 0 1104 0 7693 0 1203 29 2 3 0 0999 0 7721 0 1280 30 2 4 0 0904 0 7739 0 1357 31 2 5 0 0818 0 7748 0 1435 32 2 6 0 0740 0 7748 0 1512 Figure 16 Results worksheet showing user defined graphs of the concentration profiles and spectra These along with the data are constantly updated during fitting Update Update provides a useful precursor to fitting It allows checking of a model and the starting parameters without actually executing a fit which attempts to iteratively optimise the parameters The intermediate concentratio
43. ere in the workbook in this specific case for presenting residual plots It is not necessary for ReactLab analysis functionality and can be deleted from all workbooks if it is not required Graph GUI This will launch a standalone GUI Figure which allows close inspection of individual fitted spectra and reaction profiles either together or individually The real data can be superimposed on the best fit curves along with separate residual plots A slider control is available for easily scanning through the individual traces Modes for auto scaling are available as well as the option to plot the y axis logarithmically This can be useful for visualising intermediates occurring at very low concentrations The best fit concentration profiles and intermediate spectra can also be displayed here Again a toolbar provides access to plot zooming Jplus Consulting Pty Ltd 16 ReactLab Kinetics 1 1 Jolus consulting multivariate analytical technologies Figure 20 Example displays in the Graph GUI window Right clicking within the display area will open a context sensitive menu allowing the current graph to be pasted to the Windows clipboard for direct transfer to other applications such as Microsoft Word It is also possible to print any plot from this GUI and a print preview facility is provided to align and size the output graph E StyleSheet default Save Asu Zoom Overview v Print Refresh
44. f the sum of squares The result of the fit includes the concentration profiles and molar absorption spectra as shown in Figure 38 and also in the Results worksheet More important are usually the fitted rate constants and estimates for their standard deviations they appear in the Main worksheet Additional statistical information is the sum of squares and the standard deviation of the residuals all shown in Figure 39 cui Pe baie Type Parameters k log K Fit W D kd 2 996E 03 1 005E 05 Fe Er es Gc k2 9951E 04 4887606 K Es Ss Se SSS 7 e Ss eee EE Ki Oo WE Wi Ee ae on Ee sees Oo WE WO Ss ae WE a WE WO Fees ei WEE EES ne RS or 00010 Figure 39 Results of the fit rate constants with estimates for the standard deviation also the sum of the squares ssq and standard deviation of the residuals or An Interesting Problem and Local Minima There is a well known problem with this particular reaction scheme without additional knowledge it is impossible to distinguish the above result from another one where the two rate constants are swapped see Figure 40 Depending on the initial guesses for the rate constants one or the other solution results Which one is the correct one Jplus Consulting Pty Ltd 32 ReactLab Kinetics 1 1 Bs Jolus consulting multivariate analytical tech This specific case has similarities wi
45. f these modes provides a number of supplementary options or constraints When data are present in the workbook they are also displayed in a separate figure window e B Figure 1 MED o em wg wm File Edit View Insert Tools Desktop Window Help i E IRAN DR QD en 100 400 Figure 5 3D Data display Jplus Consulting Pty Ltd 8 ReactLab Kinetics 1 1 Jolus consulting multivariate analytical techn Close Excel File This will on confirmation close the current workbook and link prior to opening another If any changes have been made to the workbook the user must first switch focus to the workbook where he she will be prompted as to whether the changes to the workbook need to be saved Sync New Data Press this to synchronise new or edited data in a workbook with ReactLab without having to save and re load it this was required prior to version 1 1 Build03 The new or modified data will be displayed in the ReactLab Figure window MODEL ENTRY AND COMPILATION Before proceeding to analyse data or simulate new data it is necessary to enter a reaction model and compile it In addition to the data and results all model information is placed in the Excel Workbook The reaction scheme is entered in the model entry area of the Main worksheet see Figure 6 The species names and reaction types using drop down list options are added to the list in the fields headed Reactants Reaction Type
46. face The launch of Excel and ActiveX server linkage is initiated by the Matlab program Linking to an already open workbook in Excel is NOT supported If a workbook is prepared for analysis following the steps above it should first be saved and re opened from the running ReactLab application Note all Excel functionality is available to manipulate the Jplus Consulting Pty Ltd 7 ReactLab Kinetics 1 1 multivariate analytical techr Jolus consulting workbook as normal while it is linked to ReactLab To duplicate the following displays try loading the ABC xlsx sample in the Examples folder When a workbook is first loaded depending on its contents various displays of data or fitted results will be created in the Matlab GUI We will use the example workbook ABC xIsx to illustrate ReactLab features This workbook contains a simulation of an ADSBOC reaction scheme The data produced have then been fitted to that model for illustrative purposes Note the graphics are restored to reflect the result as in Figure 4 J ReactLan KINETICS sg 7 Figure 4 The ReactLab GUI display reflects the Workbook content when it is loaded This shows the data residuals fitted concentration profiles and spectra for the reaction modeled in the workbook ABC xlsx The toolbar offers zooming and rotating tools for the plots These are inbuilt Matlab features Right clicking on a graph while in any o
47. gure 30 The data arranged in the Data worksheet The time vector is stored in the column of cells C6 C25 the vector of wavelengths in the row of cells D5 X5 the matrix of data in the array D6 X25 The number of times and wavelengths are computed by Excel and stored in the cells B5 and B6 The Model The next step is to define the reaction mechanism or the model This is done in the Main worksheet Reaction Products Reactants Figure 31 Definition of the model There are two reaction steps the first is the reaction ASB and the second is the reaction B C Note that there are only 2 options for the Reaction Type gt or The gt stands for a normal reaction step the for an instantaneous equilibrium e g a protonation equilibrium We will introduce this feature later in Example 4 Kinetics Coupled with Protonation Equilibria Ni_ammonia_kinetics xlsx Compilation The next step is to Compile the model Compilation is the translation of the reaction model into the code required by the numerical computation software that calculates the concentration profiles of all reacting species as a function of the reaction time Compilation is initiated by pressing the Compile Model button in the ReactLab GUI Figure 32 Jplus Consulting Pty Ltd 28 ReactLab Kinetics 1 1 Jolus consulting multivariate analytical tech Jplus gui DASHI x MM_AtoBtol xlsx
48. ific convergence limit for a true minimum or if the fit is not converging when a pre set iteration maximum is reached see NUMERICAL AND OTHER OPTIONS on page 21 Jplus Consulting Pty Ltd 12 ReactLab Kinetics 1 1 EI Jolus consulting multivariate analytical technologies ReactLab KINETICS MIE Excel filename ABC xlsx Load Excel File convergence residual Close Excel File Sync new data Compile Model Simulate iteration spectra log sqsum m ad I i i bi mol absorbance Restore Options 500 wavelength nm time sec Figure 14 ReactLab GUI following fit convergence Note random residual surface Statistical output includes standard deviations for each fitted parameter including auxiliary parameters as well as the sum of squares ssq and the standard deviation for the residuals o Figure 15 Model Editor Reaction arameter Reactants E E eecht Fit v Type k log K 02E 7 518E 03 GrE 02 3 548E 03 THT Ty TT D D D D TT or EE WE 2568 1558 Species A B J c Spectrum Figure 15 Main worksheet following fit convergence Note optimised parameters and errors and the final ssq Jplus Consulting Pty Ltd 13 ReactLab Kinetics 1 1 Jolus consulting multivariate analytical techno During iterations the intermediate and final best fit results are also updated numerically in the Main Exc
49. il or associated parameters Jplus Consulting Pty Ltd 20 ReactLab Kinetics 1 1 Jolus consulting multivariate analytical technologies J EFA_cuI EFA Settings Max N ev from SYD N comp lt N_ev Threshold log EFA Save all to Excel absorptivity Ze n gt gt on So in on E concentration Figure 25 The EFA GUI Max N_ev represents the number of singular values and corresponding eigenvectors selected in the SVD GUI This represents the maximum possible number of components that can be modelled with EFA In fact only significant species should be included in this calculation and any noise vectors in the group excluded This can be adjusted in the N comp edit box The Threshold parameter is adjustable to reject baseline noise so that the C_ window display reflects as accurately as possible the emergence and disappearance thresholds of the independent species over the reaction time course An option to Save all to Excel is provided here An SVD worksheet is created if it doesn t exist already and the current SVD U S and V matrices truncated to N_ev vectors and singular values and the EFA results are all saved here see Figure 26 for an overview for an example of this worksheet If a pre existing SVD EFA worksheet exists the user is prompted whether or not to overwrite a previous output A B D E F G H 1 J K L M N o P a
50. le initial guesses for the two forward rate constants is straightforward and results in ky 1012 9 and kw 2 501 2 which is correct It is interesting to analyze the concentration profiles in Figure 67 the complex species behave as expected with some equilibrium reached that includes a small amount of free metal some ML complex and mostly ML In spite of the excess of ligand the reaction does not go to completion because of the relatively low pH The right hand panel displays the concentrations of all species on a logarithmic concentration axis The figure indicates that the initial pH is about 9 1 and drops to about 8 9 This small pH change is the result of the added buffer Jplus Consulting Pty Ltd 46 ReactLab Kinetics 1 1 A Jolus consulting multivariate analytical technologies 1 0E 00 1 0E 01 0 00 0 0 gt 1 0E 02 A 1 0E 03 1 0E 04 1 0E 05 1 0E 06 1 0E 07 1 0E 08 1 0E 09 1 0E 10 Figure 67 The calculated concentration profiles for the complexes and using logarithmic concentration axis which shows that the pH hovers around 9 The modeling power of ReactLab is demonstrated below removing the buffer from the reaction does not affect the initial part of the reaction as the pH and free L are similar but due to complexation the pH drops to pH 8 and this results in slower reaction and a different equilibrium position 1 0E 00 1 0E 01 0 80 1 0E 02 1 0E 03 1 0E 04 1 0E 05 1 0E
51. molar absorption units Fitting now results again in the correct rate constant and additionally in the correct absorption spectra for all components Simulation as a tool for exploring rank deficient data The second order reaction we just investigated is an almost trivially simple example The question remains how is this trick of setting certain species to non absorbing applied to more complex mechanisms Jplus Consulting Pty Ltd 43 ReactLab Kinetics 1 1 Jolus consulting multivariate analytical tech It is often not straightforward to figure out what the rank of the data matrix is or how many spectra can be calculated This is where the simulation capabilities of ReactLab are incredibly useful to experiment with alternative mechanisms and combinations of colored and non abs species and see what can and cannot be successfully analysed Auxiliary Parameters The initial species concentrations are important in second order reactions and it is theoretically possible to fit initial concentrations for one of the reactants This is not a robust method for concentration determination and there are not many applications but we use this example to demonstrate the use of the auxiliary parameters a powerful option in ReactLab In order to fit the initial concentration of B we define it as an auxiliary parameter as indicated in Figure 62 The entry in the original cell for this concentration is the reference
52. most recent operation A selection of example workbooks accompanies the program in an Excel template subfolder they are described in detail in Part 2 of this document Note this manual describes the kinetic implementation of Jplus global analysis ReactLab Kinetics A separate manual describes operation of the complementary equilibrium titration analysis application ReactLab Equilibria EXCEL TEMPLATES To inspect an Excel ReactLab KINETICS workbook load it directly into Excel or via the Load Excel button in the ReactLab GUI The workbook is pre formatted containing several worksheets which provide spreadsheet formatted data and results as well as purpose designed model and parameter entry interfaces Jplus Consulting Pty Ltd 4 ReactLab Kinetics 1 1 Jolus consulting multivariate analytical technologies Template Worksheets e Main The principle model and parameter entry interface e Data Location for experimental or simulated data e Results Location for fitted or simulated concentration profiles and spectra e Sim Simulation parameter entry interface e Aux Used for managing known spectra e SVD Dynamically created sheet for storing SVD or EFA analysis results e About Sheet with contact information and the workbook format version The format of these sheets is important as ReactLab depends on everything being in particular locations Figure 1 illustrates the organisation and model entry fields in the M
53. n and absorbance matrices are calculated according to the current model and current parameter values The results of these calculations along with the residuals are shown graphically and will indicate whether the model and initial parameter values are remotely consistent with the current data or indeed have been entered incorrectly If the discrepancy between measured and calculated data is excessive it is improbable that a fit will converge Experiment with different initial guesses until the results of an update are more reasonable Residuals At the end of the fitting procedure or after an update the residual matrix is copied into the Residuals worksheet A very brief description of the residuals how they are defined and calculated is given below According to Beer Lambert s law the data matrix D can be decomposed into the product of a concentration matrix C and a matrix A of molar absorptivities However due to experimental noise the decomposition is not perfect and the difference makes up the matrix R of residuals D CxA R Jplus Consulting Pty Ltd 14 ReactLab Kinetics 1 1 Jolus consulting multivariate analytical technologies The matrix D is the one stored in the Data worksheet the matrices C and A are stored in the Results worksheet The residuals are computed as D CA and are stored at the end of the fitting or an update in the Residuals worksheet 5 n rf Figure 17
54. n to be defined specifically as an equilibrium Note the logK value is entered in this case the value 1 0 which corresponds to the previous specification of k 1 k 1 10 Krs k E S ES 2 E P Jplus Consulting Pty Ltd 39 ReactLab Kinetics 1 1 Jolus consulting multivariate analytical technologies Figure 53 The model with an instantaneous equilibrium for the interaction of the enzyme with the substrate followed by a slow release of the product The concentration profiles for the mechanism based on an instantaneous equilibrium are similar but not identical to the ones resulting from the mechanism with specified forward and back reactions for the enzyme substrate interaction Figure 54 The transition from zeroth order behavior at the end of the reaction is sharper for the fast interaction of E with S 50 000 100 000 150 000 200 000 100 000 150 000 200 000 Figure 54 Concentration profiles for the mechanism shown in Figure 46 to the left and for mechanism shown in Figure 53 to the right It is interesting to further investigate the detailed concentration profiles in more realistic enzymatic reactions taking advantage of the simulation capabilities of ReactLab k k E S ES 2 gt EP OE P 1 3 This extended mechanism involves the reversible reaction of the enzyme and substrate to form an intermediate ES complex In the key catalytic step defined by kz the substrate is transformed in this example i
55. ncentration profiles of Figure 50 Stiff solver Another note on that example the set of differential equations for the Michaelis Menton mechanism create a so called stiff problem The default numerical integration routine in ReactLab is a Al order Runge Kutta algorithm It is a very good and simple algorithm but it cannot deal with stiff problems You are welcome to try but be patient Ticking the stiff solver option results in quick calculation Numerical Integration Stiff Solver Figure 52 Tick box to choose the stiff solver in the Main worksheet Unfortunately it is not trivial to predict whether a particular reaction mechanism requires a stiff solver A rule of thumb is when rate and or concentrations are very different a stiff solver might be preferable A more practical option is to change to the stiff solver if nothing happens using the standard solver ReactLab issues a warning if computation times appear to be excessive and suggests to switch to the stiff solver Why should we not use a stiff solver in all instances The Runge Kutta algorithm is superior for most problems Enzyme substrate interaction as an equilibrium The Michaelis Menton mechanism in its original form assumed that the interaction between the enzyme and the substrate is an essentially instantaneous equilibria or in other words the rate constants k and k are much larger the dissociation reaction k ReactLab allows this interactio
56. ned before the enzyme concentration is much smaller than the initial substrate concentration Thus the ES complex concentration is _ d ES A i always very low As a consequence the derivative TE is always small as well Setting this derivative to zero allows simplification of the integration of the differential equations that are defined by the Michaelis Menten mechanism The straightforward availability of numerical integration routines circumvents such procedures making life easier but also better as the steady state approximation is not always correct It is interesting to observe the concentration profiles of the substrate and product they change almost linearly for a significant length of time which is an indication of a zero order mechanism in this steady state phase see Figure 50 The turnover of substrate to product is limited by the availability of enzyme Figure 51 shows a logarithmic plot of the concentration profiles which now includes also the concentrations of the free and complexed enzyme They are much smaller than the concentration of substrate and product The derivative with respect to time is consequently also very small Note these concentration profiles were generated with a much finer time vector points are calculated in 0 1 sec intervals Jplus Consulting Pty Ltd 38 ReactLab Kinetics 1 1 0 000 a 100 000 150 000 200 000 250 000 1 E 01 1 E 02 1 E 06 Figure 51 Logarithmic plot of the co
57. nts and temperature This equilibrium is included when modeling reactions involving protonation equilibria to correctly deal with H and therefore pH See below for more details Status Flags e data comp fit Not for user adjustment These flags are assigned and used by Excel and ReactLab to allow synchronization of a workbook when it is loaded HANDLING PROTONATION EQUILIBRIA H OH and Kw In some cases reaction models in aqueous solution may include protonation equilibria In such instances the autoprotolysis of water has to be taken into account This is done automatically by ReactLab if any of the components in the system is identified as H which is interpreted as a proton This is one of the very few rules about the names of components or species in ReactLab As a consequence of the presence of protons it is assumed that the reaction is performed in aqueous solution and the equilibrium H OH lt gt H O is internally added to the present model Further the hydroxide OH will be added automatically to the list of species The ionic product Ky is represented as Kw H 0H The unionized water is omitted from the expression as its concentration is essentially constant The value of Kw is then 1 00x10 M for pure water at room temperature If measurements are taken at a different temperature solvent or ionic strength the correct value for logK is stored in cell 155 of the Main worksheet If protons are
58. number of wavelengths permitted is 253 due to the column number restriction in this version of Excel For Excel 2007 ReactLab can in principle handle gt 17000 wavelengths the program currently resolves 3 letter column headings 26 combinations Note therefore that saving an xlsx workbook in xls format can lead to truncation of large data sets The time vector occupies the left hand column C6 C7 etc and the wavelength vector the top row D5 E5 etc The data are placed in an n times x n_lam array for each corresponding time and wavelength coordinate Please note that several fields in the workbook are automatically populated by Excel formulas For example the count of the number of wavelengths and number of times at the top left B5 and B6 of Figure 2 are evaluated by Excel from the number of time and wavelength entries These field formulas must not be altered They are protected using Excel cell protection features by default 4 B G D E GE G H J K Le M N Oo P Q R 5 d 1 3 4 5 n_times 51 400 410 0 420 430 0 440 450 0 460 470 0 480 490 0 500 510 0 520 530 0 540 590 0 560 T 6 n lam 21 0 0 0 6262 0 0301 0 1166 0 92956 0 1574 0 2754 0 5235 0 6574 1 4898 13308 0 0146 5 7396 201166 48 4607 82 5046 1011303 84 0066 4 Ti 2 0 2 1388 1 4001 0 56693 13036 0 8404 29336 19870 59026 14 0732 220574 26 7167 30 0805 313275 45 8531 714366 815644 67 8065 4 3 4 0 2 6199 1 2448 05292 02709 1 0988 1 1613 4 6678 35410 25 7626 4299
59. oefficient form necessary for its subsequent numerical calculations of the concentration profiles of all participating species It also extracts all the intermediate species names and lists them in a row in the Main Excel worksheet to allow initial concentrations to be inserted below see Figure 12 Species headings are also written to the Sim and Results worksheets Any previous results are also cleared at this point Certain key values are calculated automatically by Excel and are required by ReactLab namely the number of reactions specified in the model for which there is a rate or equilibrium constant field n_par the number of individual chemical species in the mechanism n_species and the number of auxiliary parameters n_aux_par Do not overwrite the formulae in these cells they are protected in the templates supplied Jplus Consulting Pty Ltd 10 ReactLab Kinetics 1 1 Figure 10 Model information automatically generated by Excel Auxiliary parameters are an advanced feature which can be ignored during program familiarisation PARAMETER ENTRY Prior to fitting numerical parameter estimates or known values should be entered in the appropriate fields Figure 11 Rates constants are entered as absolute values but for equilibrium constants the parameter value must be expressed as its log e g 3 for Ka 10 M This is numerically more stable for the fitting routine The user must decide whether parameters
60. or further information see FIXED SPECTRA on page 22 Jplus Consulting Pty Ltd 11 ReactLab Kinetics 1 1 Jolus consulting multivariate analytical technologies Model Editor bb Reaction Doka Oia Parameters Type k logK gt gt KR M x m x E C a a m m a a x D m x a m x Figure 13 Main sheet overall model entry area ready for fitting Having completed these steps the Main worksheet will look like the example in Figure 13 and is now fully prepared for model fitting FITTING THE MODEL TO DATA Fit Selecting Fit initiates the data fitting algorithm which proceeds to attempt to minimise the residual square sum or ssq which is a measure of the difference between the real data and that predicted by the current model and prevailing parameters It does this by iteratively refining the free parameters of the model using an adaptation of a Marquardt Levenberg algorithm and adjusting the colored spectra according to a least squares criterion The details of the Marquardt Levenberg algorithm are described in the reference material Fitting progress can be monitored graphically in the ReactLab GUI which displays both intermediate concentration profiles and spectra as well as the 3D residual surface of the whole dataset Figure 14 The log of the ssq is also displayed as a function of the number of iterations which indicates progress of the algorithm Iterations stop according to spec
61. ord Oxford Chemistry Press 1994 Ralph G Wilkins Kinetics and Mechanisms of Reactions of Transition Metal Complexes VCH 1991 A Fersht Enzyme Structure and Mechanism Freeman 1985 S W Benson The Foundations of Chemical Kinetics McGraw Hill New York 1960 Equilibria Arthur Martell Robert Hancock Metal Complexes in Aqueous Solutions Modern Inorganic Chemistry Springer 1996 Arthur Martell Ramunas J Motekaitis The Determination and Use of Stability Constants 2nd Edition Wiley 1992 Juergen Polster Heinrich Lachmann Spectrometric Titrations Analysis of Chemical Equilibria VCH 1989 Kenneth A Connors Binding Constants The Measurement of Molecular Complex Stability Wiley 1987 M T Beck Nagypal The Chemistry of Complex Equilibria Van Nostrand Reinhold London 1970 Fitting Philip R Bevington D Keith Robinson Data Reduction and Error Analysis 3rd edition McGrawHill New York 2002 Meloun Milan Jiri Militky and Michele Forina Chemometrics for Analytical Chemistry Vol I II Ellis Horwood 1994 Peter Gans Data Fitting in the Chemical Sciences by the Method of Least Squares Wiley 1992 William H Press Brian P Flannery Saul A Teukolsky and William T Vetterling Numerical Recipes in C The Art of Scientific Computing 2 edition Cambridge 1996 Jplus Consulting Pty Ltd 49 ReactLab Kinetics 1 1 Jolus consulting multivariate analytical technologies E Joseph Billo Excel for
62. order interactions The standard solver is a qn order Runga Kutta which is usually reliable and fast but under stiff conditions can slow down significantly If the numerical integration takes too long ReactLab issues a warning and suggest a switch the stiff solver If you suspect you are facing a stiff problem select the Stiff solver option or indeed select it by default prior to saving the workbook Abs tol Rel tol Do not adjust Used to determine tolerances in the numerical integration calculations Equilibrium Speciation Conv tol Max Iter Do not adjust Used for speciation calculations by Newton Raphson algorithm Not relevant for models with no rapid equilibria Non linear regression Init marpar Initial value for the Marquardt parameter used to determine the nonlinear regression algorithm strategy If there is serious divergence from the beginning it is worth trying to start with a Marquardt parameter Num diff Accuracy term used in the numerical partial differentiation of the parameters in the non linear regression algorithm Do not adjust Conv limit Reduction in ssq accepted to define convergence Default value 1e or 01 Max iter Maximum number of iterations before exiting non linear regression Default is 50 but can be reduced or increased if preferred Note exit of a fit at this limit means convergence is not valid Spectral linear Regression Non neg Switches the normal linear regression algorithm used for spect
63. ra for A B and C AIR EG First we simulate data with the following parameters Jplus Consulting Pty Ltd 41 ReactLab Kinetics 1 1 Bs Jolus consulting multivariate anal Simulation 400 o 600 end Reaction Parameters kK log K pi A B C Position 450 500 550 Height 10 5 20 Width so 90 70 Reactants Products Label Figure 57 Parameters used to generate data for a second order reaction A B_ gt c Figure 58 The data generated by the parameters given in Figure 57 Trying to update or to fit the data and calculate the spectra of intermediates in the normal way results in a rank deficiency error and nonsensical spectra There are several options to overcome this issue Rank deficiency known spectra At this stage it might be difficult to define the condition of Rank Deficiency suffice it to say that the data matrix can be composed of only two spectra and that it is impossible to fit all three spectra for the species A B and C essentially there are an infinite number of solutions Option 1 is to declare one of the species to be non absorbing e g species B Spectrum Figure 59 To overcome rank deficiency the species B is declared non absorbing Jplus Consulting Pty Ltd 42 ReactLab Kinetics 1 1 Bs Jpolus consulting multivariate analytical te The fit is perfect but of course the computed spectra are not correct
64. rreversibly to the product P still bound to the enzyme in an EP complex This complex is in equilibrium with the released product and the enzyme Using the values of Figure 55 the concentration profiles of Figure 56 are computed Reaction Parameters Reactants Products Type Figure 55 Rate constants used for mechanism above Jplus Consulting Pty Ltd 40 ReactLab Kinetics 1 1 Jolus consulting multivariate analytical tech It is noteworthy that for this hypothetical enzyme the catalytic step defined by k is responsible for driving the reaction forwards by the specific mechanism of catalytic action The direct step S gt P would be much slower in the absence of the enzyme The concentration profiles for a simulation of this model are shown in Figure 56 The profiles are represented in the normal mode in the first panel using a logarithmic concentration axis reveals the concentration profiles of all minor species in the middle panel and the right hand panel shows the details of the first 100 msec 0 012 1 E 02 ge WEE gg CS Q 40 000 60 000 80 000 100 00 0 000 0 020 0 040 0 060 0 080 0 100 0 010 1 E 03 1 03 1 E 04 1 04 0 006 1 E 05 0 004 Ee Erza 0 002 ie 1 E 07 0 000 0 000 20 000 40 000 60 000 80 000 100 000 1 08 Figure 56 Concentration profiles for the extended mechanism left panel shows essentially the profiles for substrate and product the middle panel reveals the concentration of
65. rum calculation to an algorithm that enforces non negativity from Anderson C A http www models kvl dk source This can be very useful for monopolar data such as absorbance or fluorescence but not for bipolar measurements such as circular dichroism Measurement Delta Tzero This is particularly important for measurements made using rapid reaction instruments such as stopped flow where the true time zero does not correspond exactly to the apparent zero time measurement due to instrument dead time This means reactant spectra appear to have lower amplitude than they should since the reaction has proceeded during the dead time but could not be measured If this value is known empirically it can be inserted here ve only The data time vector Jplus Consulting Pty Ltd 24 ReactLab Kinetics 1 1 Jolus consulting multivariate analytical techr will be adjusted during the calculation so that whilst the time vector in the spreadsheet data will remain starting at zero the calculated concentration profiles and therefore the reactant spectra will take this into account e Cell Path cm Pathlength of the cell in which the data is measured This is used to allow calculation of correct molar absorption spectra Miscellaneous e logKw This is an advanced feature and allows adjustment of the log of the ionic product of water Kw 1 00x10 M if required LogKw is 14 for pure water at room temperature but changes with mixed solve
66. s P Position 400 500 500 500 Height 1 o fo E _ Width 50 1 1 10 II Figure 48 Simulation parameters in the Sim worksheet it is self explanatory A measurement is created with a user defined amount of white noise its standard deviation is defined as a function of the maximal absorption reading of the complete measurement The measurement can be seen in a ReactLab window or in the Data worksheet in Excel ee oO 15 O D 2 145 O Wa O D 600 100 500 150 200 a wavelength nm time sec Figure 49 The measurement Jplus Consulting Pty Ltd 37 ReactLab Kinetics 1 1 Jolus consulting multivariate analytical technolo A B E D E F G H J K L M N 1 Concentration profiles and spectra 4 5 Cone S E SE P Spectra S E SE P 6 0 000 1 000 0 000 0 000 0 000 400 000 1 000 0 000 0 000 0 125 H 10 000 0 917 0 000 0 000 0 083 410 000 0 895 0 000 0 000 0 212 8 20 000 0 836 0 000 0 000 0 164 420 000 0 642 0 000 0 000 0 339 3 30 000 NFSG Annn ANAN D 294 430 000 136 O00 NANNA NKI EEE EEE D 10 1 200 2 500 e 1 500 0 600 21 0 400 0 500 0 000 24 0 200 7 0 000 27 e 28 0 000 50 000 100 000 150 000 200 000 400 000 450 000 500 000 550 000 600 000 Figure 50 Concentration profiles and molar absorption spectra for the data simulated and displayed in Figure 49 The steady state approximation As mentio
67. s of worked examples demonstrating specific examples of analysis using pre prepared workbooks All these are provided in the Excel examples folder in the application installation package They can also be downloaded independently from the web site Note when they are installed in the default program files directory they are automatically assigned read only Status but can of course be copied or re saved to a suitable working directory SYSTEM REQUIREMENTS AND INSTALLATION Please refer to the System Requirements and Installation Guide available on our website and included with the ReactLab download CONTACT INFORMATION AND SUPPORT support jplusconsulting com www jplusconsulting com Jplus Consulting Pty Ltd 8 Windsor Road East Fremantle WA 6158 Australia ABN 83 135 664 603 Jplus Consulting Pty Ltd 3 ReactLab Kinetics 1 1 Jolus consulting multivariate analytical tech PART 1 REFERENCE GUIDE INTRODUCTION ReactLab KINETICS provides global analysis for fitting chemical reaction schemes and their parameters to multivariate spectroscopic data It also offers extensive reaction modeling and data simulation capabilities The program including all algorithms and the GUI frontend has been developed in Matlab and compiled to produce the final deployable application It requires the Matlab Component Runtime MCR to be installed on the same computer This allows the program to run on computers without stan
68. spreadsheet accordingly or to simply copy paste the extra values into a different range of the worksheet and graph them appropriately As this worksheet is produced by excel and not by ReactLab it is not as general as the other worksheets The user might have to change a few cells or ranges of cells to produce the desired outcome Of course the graphics of the Figures can be changed in the usual way colors markers labels legends can be changed in the usual way using the tools provided by excel Measurements at Only One Wavelength Traditionally kinetics was performed most commonly by measuring the absorption of the reacting solution at one particular wavelength Choosing a good wavelength was important a problem fortunately not relevant today were diode array detectors are very regularly used Here we demonstrate that ReactLab is perfectly able to analyse such one wavelength data sets choosing the wavelength 520nm as a non ideal choice 1000 1500 2000 2500 3000 3500 4000 Figure 44 The same reaction but only measured at 520 nm Figure 44 displays the measurement indicating that the first step is probably only poorly defined The result of the fit confirms the suspicion with standard deviations for the two rate constants which are considerably larger than the ones based on the analysis of the complete data set at several wavelengths The two outputs are compared in Figure 45 for the single wavelength fit the fitted values are sub
69. stantially off the correct values of k 0 003 and k 0 001 but they are just outside the one standard deviation Reaction Reactants Products Label ee Fit v Type k log K A WA 6 vo 2 996E 03 1 005E 05 M B RA C TG 9 951E 04 4 887E 06 Parameters k log K vu 3781E 03 6 767E 04 Reactants Tna Products Label Type gt a Ce B A C k2 9238E 04 4 518E 05 Figure 45 The fitted parameters and their standard deviations for the fit at 520 nm on the left and at 400 800nm on the right A k Example 2 Enzyme Kinetics E S z ES _ 2 Ap Enz1 xisx Ky The microscopic functionality of enzymes is usually very complex and virtually impossible to investigate using traditional steady state measurements This is because under conditions of excess substrate enzyme bound intermediates initially build up to steady state levels at which point they do not significantly change until the substrate is depleted There is Jplus Consulting Pty Ltd 35 ReactLab Kinetics 1 1 Bs multivariate analytical techn Jolus consulting therefore no dynamic information about these intermediates during this steady state phase Nevertheless steady state enzyme kinetics can often be quantitatively described by the Michaelis Menton mechanism k Agape a E P Ky The substrate S reacts reversibly with the enzyme E to from the ES complex which in turn decomposes to release the product P and the free enzyme th
70. th so called local minima but it is also significantly different Non linear fitting usually cannot guarantee that the global minimum of the sum of squares is found the result depends on the initial guesses However in data fitting of reasonably complex models local minima that are not obviously wrong are rather rare Parameters k log K 9 952E 04 4 894E 06 Excel filename AtoBtoC xlsx 2 994E 03 1 003E 05 convergence residual log sqsum B 0 0010 seg 0 0004 o 2 40 6 8 40 4000 gg 500 em 700 Di spectra x 10 concn ti g 1000 T 06 Equil Speciation ee z S E 04 Convtol 1 000645 3 Max iter E 1000 0 2 CES E 0 400 500 600 700 800 D 1000 2000 3000 4000 wavelength nm time sec Figure 40 The other minimum swapped rate constants and different concentration profiles and spectra identical sum of squares In this particular example the resulting spectrum for the intermediate B is partially negative and thus this solution can be discarded However it is important to know that the wrong solution is not always identifiable by a negative spectrum If nothing is known about the spectra the two solutions are indistinguishable Note that absorption spectra have to be positive ESR or CD spectra don t have such a restriction Non Negative Spectra An interesting solution for the above problem is using an algorithm that only allows non negative spectra This option c
71. the execution of the any Excel cell formula defining relationships between them Thus an auxiliary parameter can be set up to define the ratio of two conventional rates for example see Figure 27 This can be achieved by expressing the dependent rate value in cell F8 as a formula which calculates the ratio of the primary rate in cell F7 to an auxiliary parameter in cell K7 Because the ratio is defined as an auxiliary parameter it can be fitted as well as the primary rate if required Note that the target of the calculation the parameter value in F7 must be defined as a fixed parameter otherwise it too will be optimised rather than being a value derived from other parameters Jplus Consulting Pty Ltd 22 ReactLab Kinetics 1 1 Jolus consulting A E E D E aia Taa G H J K L M i Reactants daii Products Label RE Type kK log K Sa as Auxilia Label d Fit v Parameters ola IO IO gt fw m S 5 1 1002E 0017518E03 Y B WA ve Leo 3 548803 M Figure 27 Entering a simple auxiliary parameter example This example demonstrates the approach to using an auxiliary parameter but in this case could be done more trivially by directly defining the second rate as a fixed ratio of the first explicitly without involving the auxiliary parameter feature but if the relationship is more complex and it is necessary to allow the relationship to be optimised the auxiliary parameter mechanism can
72. tic and spectral basis vectors of the decomposition essentially the eigenvectors of Y which reside in the columns of U and rows of V and lists the corresponding singular values from the diagonal matrix S The number of significant singular values equivalent to the number of principle eigenvectors n_ev over the noise background is equal to the number of linearly independent coloured components in the system The corresponding eigenvectors whilst not representing real spectra or kinetic profiles represent the set of linearly independent vectors from which all the data can be re composed by linear re combination The number selected here is used to determine a reduced decomposition to save in the Excel worksheet Saving of SVD and complimentary EFA results is done from the EFA GUI below EFA This opens a GUI window providing basic model free evolving factor analysis of the current data Figure 25 Evolving Factor Analysis provides a model free approach to predicting concentration profiles and spectra of coloured components in the data It results in some indication of spectral shapes and the evolution of independent species during the measurement which can offer useful insight into appropriate reaction models for fitting For example compare the concentration profiles and spectra in Figure 25 with the fitted equivalents in Figure 14 Note however that whilst the shapes are similar EFA does not provide any quantitative reaction mechanism deta
73. time starting soon after dissolution of component A and introducing the solution into the spectrophotometer In the example the first spectrum is measured at time 60 s and then subsequent spectra are acquired in 180 s intervals for a total of close to one hour Spectra are acquired in the wavelength range 400 to 800 nm in 20 nm intervals The data set is represented in Figure 29 Figure 1 E 5 x File DS HS AAV 08 08 4000 400 Figure 29 The measurement spectra measured as a function of time The Data The data required for analysis by ReactLab consists of the following A series of spectra recorded as a function of time the vector of times at which the spectra were measured and a vector of wavelengths at which absorption measurements were taken The three parts of the complete data set are transferred into a copy of the ReactLab Excel spreadsheet template supplied Jplus Consulting Pty Ltd 27 ReactLab Kinetics 1 1 Jolus consulting multivariate analytical technologies D B re D E F G H l J K L M N o 1 CE 3 4 5 n_times 20 400 420 0 440 460 0 480 500 0 520 540 0 560 580 0 600 620 e In lam 21 60 0 0535 0 3081 0 7488 0 7476 0 3091 0 0535 0 0064 0 0034 0 0064 00120 00202 ons 7 240 0 0330 0 1816 0 4405 0 4431 0 1893 0 0440 0 0192 0 0242 0 0373 00557 0 0812 om 8 420 0 0227 0 1113 0 2641 0 2696 0 1277 0 0470 0 0426 0 0554 0 0753 0 1013 04359 os 9 600 00188 0 0742 0 1663 0 1736 0 0993 0 0591 0 0666 0 0
74. usted The benefits of using fixed spectra are significant and discussed in the context of worked examples in Part 2 When a model is compiled a corresponding species list is created in the Aux worksheet Known spectra should be cut and pasted under the appropriate species name That species should be selected as known in the Main worksheet Note Fixed spectra must be provided in units of molar absorptivity i e the fictional absorption spectrum of a 1M solution measured in a 1cm pathlength cuvette The easiest way to experiment with this feature is to simulate data to a particular model and copy and paste the simulated spectra from the Result sheet to the Aux sheet species columns These then correspond to the spectra from which the simulated data set was calculated and can be selected as known for species during experimental fitting AUXILIARY PARAMETERS The Auxiliary parameter feature is unique to ReactLab and depends on the parallel execution available through the independent Excel process Auxiliary parameters are treated like normal reaction parameters during fitting but can be used to define arbitrary relationships between virtually any of the workbook data or conventional parameters involved in the fitting calculations The feature works using Excel formulas and depends on the fact that at key points of each fit iteration parameters are written out and read back from Excel but not before

User Manual - Jplus Consulting

Contents

Download Pdf Manuals

Related Search

Related Contents