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MetaPlab 1.1 User Guide

1. Figure 17 The same line chart depicted with different data sampling values 1 on the left and 30 on the right IOAN RO A A FO I 10 0 02C 0 02B 0 02CAN R1 A B FI _ __ _ I 10 0 02C 0 02B 0 02BAN R2 A C F2 I 10 0 02C 0 02B 4BN R3 B A A Io I 4 4C N A F4 R4 C A ET aa el Chan A time series Update connrmation Would you like to update the organism with the experiment values stored in memory Refreshing information x 0 250 500 750 The MP graph is successfully refreshed hal Simulation steps eA Views chat poets GO renes No errors found while checking the time series l Submit Figure 18 The update of the MP graph after the closure of the plugin manager windows on the left and the new time series for A on the right 19 Navigator Navigator MP graph visualization dialog Visualization criteria Select visible node types Seled visible edge types a Visualize only selected m Hide all the selected graph nodes graph nodes General node types MP node types OC A m Substance nodes ot y Organism node E 1 Reaction nodes O cl o gt w Frames Flux nodes o D Param
2. 33 2075 B Poly2 223 8820 4 6858 x C 2 2090 B Poly3 4 3747 0 0014 x A C Poly4 0 2607 In the picture below the second interface is depicted after the regression performance the values obtained are identical to that achieved by performing linear regression by Matlab 99 Select a reaction Select only one polynomial for each reaction HL Ar E FEP AE BAI Add gt gt RIAC meee Ra C E RE Oo Renove a Result of regressi Description Save Select one of the regression results Log out lt Back RO 23 8912 7986207972 O 002 1529608733548 7667AC2 0 008607192307 7089043 B C R1 0 259395180983 497 33 21086789541219 B 1 RS 4 374692412851705 0 001520123 722450782 274 C Re 217 12996073 280896 45435078913 25628 C 2 142715 729731311376 R4 0 2853914335232873 Figure 8 Polynomials and coefficients generated by linear regression plugin 7 Work in progress The plugin framework explained ad the beginning of Section 2 makes Meta Plab an extensible software Whoever wants to process MP model data in a specific way can implement a new Java plugin by extending an abstract class contained in the MetaPlab source code New plugins files inserted into the pluginExt folder of the MetaPlab package are automatically loaded when the software starts Our research group is currently developing the following plugins e NeuroSynth generates flux regulation functions and in
3. Select a Workspace Workspace path C Users Caste DocumentsitestRegression1 Workspace selection Select a reaction R1 Reaction selection Polynomials available for reaction R1 Polynomial 1 for reaction R1 passaas 4i Enter a polynomial Polynomial 2 for reaction R1 Substances and Parameters M V1 Polynomial 3 for reaction R1 C 2 M 2 X 2 ora Constant Polynomial Vikc M Cancel Description Polynomyal 4 for reaction R1 Polynomials visualizer Polynomial generator Next gt gt Figure 34 First GUI Generation of parametric polynomials Second interface Performing linear regression The second GUI is composed of three main sections as displayed in Figure 35 By the top most section we can easily select one polynomial among those generated by the first GUI for each reaction We firstly select a reaction from a list and then we use the Add and Remove buttons to select and deselect polynomials Once a specific set of polynomials has been selected we perform the linear regression process in order to compute coefficients that make polynomials fit the time series data of substance parameters and fluxes stored in the MP model Results i e optimized polynomials are showed in the central part of the interface The user can analyze these results and choose if to save them in a file as regression experiments with a suitable description or to discard them performing a new regression
4. Substance A Substance Substance C Substance A R1 Substance Substance C Substance A Substance Substance C Substance R4 Substance Substance C Run Log Gain Plugin Return to Plugin manager Figure 26 Sirius tuners Computing the flux time series If all the tuners and the covering reac tions are correctly inserted then we can compute the flux time series of every reaction by clicking on the Run Log Gain Plugin button see Figure 30 The plugin starts its computation and after few seconds this time depend on the dimension of the problem and on the quantity of data used it returns an information message which announces the end of the computation At this time flux time series are automatically returned to the plugin manager In order to complete our example it is possible to see the results obtained by the Log Gain plugin in Figure 31 Fluxes inferred from substances time series by the Log Gain plugin are almost identical to flux time series generated in Section 3 during the dynamics computation It is always possible to return to the plugin manager by clicking on the button Return to Plugin manager see Figure 32 Log Gain plugin requires that a few conditions related to the Log Gain Principles be satisfied otherwise the software returns warning and error messages The main warning messages are displayed when e the initial value of some fluxes has not been defined into the MP graph In this case
5. Substance A v Select a regulator Substance A elect a reaction Ro v Add regulato 1 ETETE regulator Add reaction Delete reaction i Run Log Gain Plugin Return to Plugin manager Log gain tool Log gain regulators Offset parameters Select a reaction RO Select a substance Substance A Select a regulator Substance A x Select a reaction RO Add regulator Delete regulator Add reaction Delete reaction Run Log Gain Plugin Return to Plugin manager Log gain tool Log gain regulators Offset parameters Select a reaction Ro ks Select a substance Substance A Select a regulator Substance A v Select a reaction RO Delete regulator Add reaction Delete reaction RO Substance A Run Log Gain Plugin Return to Plugin manager Figure 25 Adding tuners to reactions i a reaction tuner entry is selected ii the Add regulator button is clicked iii the couple is inserted into the list on the right side 26 Log gain tool Log gain regulators Offset parameters Select a reaction RE Selecta substance Substance A Selecta regulator Substance C Select a reaction rR t lt s s s sCS Add regulator Delete regulator Add reaction Delete reaction RO
6. The window is divided in two parts in the left side there is a table where we can directly add edit or delete each value of the parameter time series while in the right side it is depicted a chart of time series Under the table there are some buttons that enable to perform some automatic operations that can help the user when he she has to manage a time series having many values For example MetaPlab gives the possibility to import data from files or to export loaded values to filet In order to model a noisy function we need to generate random data MetaPlab provides a generator of random values which can be started by clicking on the button having a small chart as icon The generation window is depicted in the right side of Figure 21 It enables to generate random values By now MetaPlab considers only text files which have each value in a single row without the addition of other characters 2l N time senes Chart N time series VNelelinlejehe m eaea EE Number of values 1 000 Minimum value Maximum value o 15 Random values Gaussian normally distributed values 250 500 750 Simulation steps Replace the time series with these new values Add new values to the head of the time series v Visualize chart lines 3 R Refresh Visualize chart points
7. 1 plugin manager Local MP plugins Available plugins Plugin description Chart Plugin This tool computes flux time series IHTML Plugin from substance and parameter time u series by using the Log Gain ory lux Discovery Log Gain Theo Simulation Plugin 2 Run Online MP plugins r Figure 23 Launching the Log gain plugin in the left side we assign a set of tuners to each reaction while in the right side we set up the set of reactions which satisfies the covering property of the phenomenon under investigations Assigning tuners to reactions Let we suppose to want to assign the substance A to the reaction RO in the left part of the plugin interface We select entry RO from the upper drop down list and the entry Substance A from the lower list and then we click on the Add regulator button After these steps the entry RO A is added to the list panel below Figure 25 24 Log gain tool Log gain regulators Offset parameters Select a reaction Selecta substance Substance A Selecta regulator Substance A Select a reaction Ro O Z Add regulator Delete Delete regulator Add reaction Delete reaction _ Run Log Gain Plugin Return to Plugin manager Figure 24 The main graphical interface of the Log gain plugin graphically shows how the plugin GUI is updated after each step By follow ing the same steps we add tuners to every reaction Figure 26 shows in
8. MP store the third concerns with the processing of these data by means of computational units called MP plugins and finally the fourth arranges a set of vistas which support the MP systems analysis The new extensible data processing layer makes MetaPlab a proper virtual laboratory wherein MP plugins act as virtual tools for processing MP systems 6 MP Graph Input and Data Structure Visualization MP store vaya Data Processing MP plugins Output k utput MP Plugin Output GUls li l Name Molana By D 4 Values Output Parameters RegFunc Values a Output i am i zj Output i Tepatogy dec overy loai Ganet Pr ogy arrears mai Output Figure 3 The MetaPlab framework Some plugins are distributed along with the MetaPlab main package while further plugins or update versions can be downloaded from the plugins page of the MetaPlab website http mplab sci univr it plugins Plugins php The downloading procedure consists of selecting the Download link for a spe cific plugin and then choosing a suitable directory where storing the archive The uncompressed plugin file has finally to be copied into the pluginsExt di rectory of the MetaPlab package in order to be automatically loaded at the Start up 2 2 MetaPlab input GUI Figure 4 shows the input GUI of MetaPla
9. depicted in the left part of Figure 6 In order to edit the initial concentration of each Substance node we use the window depicted in the right part of figure 6 which is visualized by clicking the Edit time series button his second window has some commands which enable to edit and plot time series of concentration values In our case we only need to update the initial concentrations by the values given at the beginning of this section The position of each Substance node can be changed dragging and dropping the related graphical elements obtaining the graph of Figure 7a In order to complete the stoichiometry of the system now we need to add five Reaction nodes which represent the five rewriting rules defined at the beginning of this section To do this we need to click on the button of the side bar having a black circle as icon and to pass again to the insertion mode In the same way we add five flux nodes and two gate nodes by clicking respectively on the buttons of the side bar having a red rectangle or a green triangle as icon We finally exit from the insertion mode as usual and we drag nodes to positions showed in Figure 7b Now let we edit the data collected in each new node by the two windows displayed in Figure 8 They can be opened as usual by double clicking on a node or selecting a node by a single click and then starting the editing procedure by pressing the F2 button of the keyboard The first interface enables to modify
10. process Saved experiments are stored in a text file called exp txt in the workspace and they immediately appear in the third part below of the interface On the left side of this section exper iment descriptions are listed The user can select them visualize the related polynomials by clicking the gt gt button and send them to the MP model one for each reaction as regulation functions 36 a Linear Regression step 2 selection of polynomials araom Select a reaction R1 Select only one polynomial for each reaction R2 M Xp Polynomial 1 for reaction R1 R3 C 3 M C 2 M 3 X 1 M Add gt gt R4 X 2 X C 2 C Polynomial 2 for reaction R1 M v1 Remove Polynomial 3 for reaction R1 C 2 M 2 X 2 Polynomial 4 for reaction R1 Result of regression Regression results Description Select one of the regression results Reg ress ion resu Its selectio n Reg1 Reg2 lt lt Back Log out Figure 35 Second GUI Linear regression 6 3 Managing linear regression workspace Before executing the plugin some notes have to be emphasized This pro gram is organized along two interfaces and the user can switch between them In these interfaces there are some indirect operations of creating and or delet ing text files and creating folders so the user has not to directly manipulate the workspace folder where he she is working Otherwise there could be a wrong execution of the plugin When
11. properties and appearance of a gate node while the second In order to visualize the window please use the same procedure described to edit the Organism node 2 An important feature of this window is the possibility to change the gate orientation 11 one permits to update the data of a Flux node 3 2 Drawing edges After having updated the properties of each node by the Sirius data pre sented at the beginning of this section we can start to create the edges required to complete the MP graph definition The creation of dependence edges is automatic when we enter an evolution formula for a flux node Each new edge is initially displayed by a straight line but its appearance can be changed by adding some control points and by dragging them to different positions of the drawing area as displayed in Figure 10 We can add or remove a control point to an edge by clicking with the right button on the edge that we want to modify Bent edges if Figure 9a have been created by using control points Now it is time to complete our model by adding reaction edges and reg ulation edges The creation of an edge is easy to be perform in MetaPlab In Figure 11 it is depicted a magnification of some MP nodes where we can distinguish some small rectangular areas These areas are called ports If we want to create a new edge we have to place the mouse pointer over the port of its source node click on it when the mouse pointer changes its shap
12. select the node by a single click and then start the editing procedure by pressing the F2 button of the keyboard Organism fe ge e mei preli lleje Wodel constants Identificator Edit constant Name inertia stant No errors found while checking user inputs E Inertia 100 0 none Figure 5 The windows employed to edit the Organism node content on the left and the list of the model constants on the right When we begin to edit the node a window is visualized as in the left part of Figure 5 and we can change the default values by typing new values as This procedure is general and can be used in the following to edit the data of each type of node Aime seres step Value Chart A time series P Substance A properties dialog i 0 0000000 Simulation steps i Cancel g Submit Figure 6 The windows to edit the Substance node content on the left and the time series of concentration values on the right shown in the left side of Figure 6 In the window each text box is associated to a small check box visualized on its right side This check box can be selected in order to force the visualization of the data into the MP graph In the center part of the window the
13. the program has been launched the user has to select a workspace The folder selected can be there because referring to another graph in this case a warning or an error message can appear In the first case the user can still work in the folder while in the second case the user must select another folder Two cases can be found in the workspace e the number of the reactions of the loaded graph is lower than the text files present in the folder and the file called exp tzt is not present e the number of the reactions is greater than the number of the text files with the name of the reactions and there is a file named exp tzt In this second case if the user is positive that the exp tzt file is relevant for his her estimations there are two possibilities to avoid execution errors 37 1 manually create an empty text file with the name of the missing reac tion s 2 cut and paste the ezp tzt file outside the workspace launch the ap plication for adding new polynomials to the missing reaction s close the application paste the previous exp tzt file in the current workspace and finally execute the plugin In order not to modify the workspace content the user can open a new empty folder and work there in this case the plugin creates all the files needed 6 4 Generating Sirius regulation functions The plugin has been initially tested on Sirius model introduced in Section 3 Other variants have been tested by intro
14. two different ports the first one on the left must be used to define output rules while the other one is for input rules has to correct them before launching any plugint When the model is finally completed and correct we can save it 4 Simulating and plotting an MP system be havior After generating a new MP graph and obtaining the correctness confirmation from the MetaPlab checker many processing tools can be run We start explaining a plugin for computing the MP model dynamics and then a second tool which enables the user to plot and analyze dynamics charts Please remember that when we edit a model we can always come back to its previous versions by using the undo redo support given by MetaPlab aaisa ael pe e ee eiee Multiplicity E No errors found while checking user inputs Figure 12 The window which permits to change the multiplicity value of a reaction edge 14 MP graph check dialog Pe some errors found in the MP graph E Return Q Hide errors details 1 Ais not connected with a Reaction node 2 B is not connected wit i h a Reactio d 3 C is not connected with a Reaction node LiL gt av 4 RO rule is not valid jav ea 5 RO is not associated with a Flux node Q 6 R1 rule is not valid oe O C gt 1 is not associated with a Flux node O C gt 8 R2 rule is not valid oe 9 R is not associate
15. Add new values to the tail of the time series Cancel Submit No errors found while checking the time series Cancel Submit Figure 21 The windows to set the time series of the noise Parameter node or Gaussian distributed values By now we set the window as displayed in the picture and then we click on the Submit button After having started the generator the time series updates its content and the parameter node is ready to be used We edit the flux functions as specified at the beginning of this subsection The final model is depicted in Figure 20 We finally compute the dynamics of the model as explained in the pre vious subsection and we compare it to the one previously obtained without the noisy signal Figure 22 displays the charts of the two test cases obtained by the simulation of 500 steps of the two models 5 Log gain plugin By using mathematical models we can examine systems that we are unable to observe and understand directly In the last years different approaches for constructing models of biological phenomena starting from experimental data have emerged Their goal is to give a view of the phenomena under investigation at different organization levels and to test their responses to different inputs The core of each procedure that generates these models is the identification of some parameters that make models consistent with observed data MP systems pr
16. Chart Plugin HTML Plugin Online MP plugins o an 100 200 i 300 E 400 a 500 W 600 E 700 ga 800 j 900 Fi 1 000 Z Time oles B moles C moles X axis label Time Line chart Phase chart Options Y axis label Values X range values Restore defaults C From LJ To ry n Create Update chart B grams C4 t LIV Chart points Figure 15 The procedure to display the simulation values of an MP model 17 Me taPlab LO chart pidgin irae Fil MetaPlab simulation Sirius creativus 0 100 200 300 400 500 600 700 800 900 1 000 1 100 A moles amp Y Line chart Phase chart Options X axis series A moles w Y axis series B moles v v Visualize chart lines Create Update chart Visualize chart points Figure 16 A phase chart of the substance A and B of the Sirius model Now we try to improve the readability of the MP graph by adding some frames and labels The MetaPlab input GUI offers also the possibility to hide a part of the MP graph without deleting its nodes as depicted in Fig ure 19 a useful feature for managing complex graphs This operation can be performed by a window which can be launched by clicking on the button of the side bar having a pair of binoculars as icon or by selecting the ri
17. EN e X 1 2 n is the set of substances the types of molecules e R r1 72 m is the set of reactions over X that is pairs in arrow notation of type a 8 with a b strings over the alphabet X V vj vo Uk is the set of parameters such as pressure tem perature volume pH equipped by a set hy N R v EV of parameter evolution functions Q is the set of states that is the functions q XUV R from substances and parameters to real numbers We denote by qx the re striction of q to substances and by qy its restriction to parameters b y r R is a set of flux maps where the function pp Q R states the amount moles which is consumed produced in the state q for every occurrence of a reactant product of r We set by U q y q r R the flux vector at state q v is a natural number which specifies the number of molecules of a conventional mole of M as its population unit u is a function which assigns to each x E X the mass u x of a mole of x with respect to some measure unit T is the temporal interval between two consecutive observation steps qo E Q is the initial state N Q is the dynamics of the system given by 6 0 qo and Si Dix Ax UAG x v Sli 1 y h i lw eV where A is the stoichiometric matrix of R over X and x are the usual matrix product and vector sum Cyclin synthetization and degradation _ Mitotic oscilla
18. In the following we introduce a few basic concepts related to linear regression models and then we show how they have been applied in our tool 6 1 Short preliminaries about linear regression model In regression analysis often the variable of interest depends on more than just one other variable Let us consider the general case it depends on a set of k independent variables and let use describe the k multiple regression model The regression model of a dependent variable Y on a set of k independent variables X with i 1 n is given by the following equation Y po Pint 62X2 OkXk 2 where 6o is said the intercept of the regression model and each coefficient 6 t 1 n represents the slope of the curve Y with respect to the variable X Notice that the independent variables of equation 2 may represent even non linear functions If we consider a set of n numerical observations for each of the independent variables then the equation 2 can be rewritten in the following manner Y gine Oe OAE T ly 2 ang 3 31 MetaPlab simulation Sirius creativus o 5 o 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1 000 Time FO F1 F2 F3 F4 MetaPlab simulation Sirius creativus i 100 150 200 250 300 350 400 460 500 550 600 650 700 750 800 850 900 950 1 000 ime 0 50 FO F1 F2 F3 F4 Figure 31 Fluxes obtained by Log gain plugin top an
19. Linear regression plug in em ploys two graphical user interfaces GUIs The first one appears as soon as the tool is launched and it enables the user to generate parametric polyno mials The second interface is displayed when the generation of polynomials is finished and it enable to compute the polynomial coefficients by linear regression Let s we start explaining the first GUI displayed in Figure 34 By clicking on the topmost button we firstly select a workspace directory where the plug in will automatically store files generated for the current MP model Then we select a reaction of the MP model e g R1 in Figure 34 and we start to generate one or more parametric polynomials which will be employed in the following regression stage Each polynomial is a linear combination of substance and parameter variables representing respectively 34 lin synthetization and degradation _ ee eee E JeESCTIIDIIOIL ite Ori T T 4 j MetaPlab 1 1 plugin manager Local MP plugins Available plugins Plugin description Chart Plugin This tool computes flux regulation HTML Plugin funtions from substance time series Flux Discovery Log Gain and flux time series by a classical regression method eur Linear regression Simulation Plugin 2 a Online MP plugins Figure 33 Calling the Plugin manager by clicking on the highlighted button in the MetaPlab toolbar Available plug
20. MetaPlab 1 1 User Guide Vincenzo Manca Alberto Castellini Giuditta Franco Luca Marchetti Roberto Pagliarini Verona University Computer Science Department Strada Le Grazie 15 37134 Verona Italy vincenzo manca alberto castellini giuditta franco luca marchetti roberto pagliarini univr it February 26 2009 Abstract Metabolic P systems shortly MP systems are a special class of de terministic P systems introduced for modeling biological metabolism MetaPlab is a software written in Java which provides a plug in based architecture of tools for i defining MP systems ii computing their dynamics tii inferring MP systems having the same behavior of an observed metabolic system In this document we will present a step by step guide of the main functionalities of MetaPlab A quick introduction to MP systems and MP graphs Metabolic P systems 2 3 4 7 8 9 11 12 13 16 17 18 21 22 19 20 23 24 MP systems for short are a special class of P systems introduced to model quantitative aspects of biological systems while avoiding the use of complex systems of differential equations Differently from classical P sys tems typically based on non deterministic evolution strategies MP systems dynamics is computed by means of a discrete deterministic evolution strategy called Equational Metabolic Algorithm EMA l Using MP systems it has been possible to provide models of several famous biochemical processe
21. Reaction nodes black circles they represent reactions Input gates triangles with an edge at a vertex they are connected to reaction nodes which specify rules that do not respect the Lavoisier Principle 17 because they introduce new matter into the model Output gates triangles with an edge at a basis they are connected to reaction nodes which specify rules that consume matter Flux nodes rounded corner boxes they represent fluxes of matter transformed by reaction nodes Each reaction node is connected to one and only one flux node containing the evolution function which regulates the reaction flux at each step Parameter nodes rectangle boxes they represent parameters Each parameter evolution can be defined by means of an evolution formula or a time series Reaction edges arrows they connect Substance nodes to Reaction nodes specifying reactants and products of each reaction Regulation edges dashed arrows they connect Flux nodes to Re action nodes in order to represent the regulation of each rule Dependence edges dashed arrows they connect Substance nodes or Parameter nodes to Parameter nodes or to Flux nodes whose evolu tion formula refers to them In Figure 1 is depicted the MP graph obtained by modelling by MP systems the Golbeter s differential model of mitotic oscillations 15 17 MetaPlab a brief introduction MetaPlab 6 is a Java software which intends to as
22. ane Computing WMC 2008 LNCS 2988 pages 180 189 Springer 2004 A Goldbeter A minimal cascade model for the mitotic oscillator in volving cyclin and cdc2 kinase PNAS 88 20 9107 9111 1991 V Manca MP systems approaches to biochemical dynamics Biological rhythms and oscillations In Membrane Computing WMC 2006 LNCS 4961 8699 Springer 2006 V Manca Metabolic P systems for Biochemical Dynamics Progress in Natural Science 17 4 384 391 2007 V Manca Discrete Simulation of Biochemical Dynamics In DNA 13 LNCS 4848 pages 231 235 Springer 2008 V Manca The metabolic algorithm for P systems Principles and Ap plications Theoretical Computer Science 404 142 157 2008 42 20 21 22 23 24 25 26 27 28 V Manca Log gain Principles for Metabolic P Systems In Natural Computing Series Springer 2008 In print V Manca Fundamentals of metabolic P systems In G Paun G Rozen berg and A Salomaa editors Handbook of Membrane Computing chap ter 16 Oxford University Press 2009 To appear V Manca Metabolic P dynamics In G Paun G Rozenberg and A Salomaa editors Handbook of Membrane Computing chapter 17 Oxford University Press 2009 To appear V Manca and L Bianco Biological networks in metabolic P systems BioSystems 91 3 489 498 2008 V Manca and L Marchetti XML Representation of Metabolic P sys tems Accepted to the IEEE Congress on Evolut
23. b with some magnifications of the most important sections The input GUI is displayed when MetaPlab is launched by clicking on the MetaPlab jar file or on one of the batch files called MetaPlab windows xxxM or MetaPlab linux macOS xxxM that en able to allocate specific amounts of memory to the software The input GUI 7 Weta Te ab aon inpu DULIGUN Home mare tl Ricerca MetaPlab builds MetaPlabed O GPLedist models Loticav olterra imps 5 Lotka Volterra wane 025 EA i E Aal Drawing area Side bar Eile o Em View MetaPran l D Complete view E New Ctri N undo Ctrl Z Zoom in Ctrl Piu QB Error checking Ctrl C Open Ctrl 0 Redo Ctrl Q Zoom out Ctrl Meno Plugin manager k save Ctrl S Delete Zoom 1 1 Ctrl 1 be Correct a Save as Ctri Maiusc S 8 Graph visualization Ctri V my Put selected nodes to front cor gt Print FM Put selected nodes to back Ctri 8 2 Simple guide fi 5 Export gt To image Graph grid tri G 4 License C Page format E K Graph rulers Slm Qui A Lock the graph Ctrl L Figure 4 MetaPlab input GUI is divided into three different areas which includes menus a top toolbar a side bar and a central drawing area where MP graph can be depicted At the bottom o
24. d with a Flux node Fill MP graph check dialog AS P 19 errors ASA Figure 13 The checking of the model s correctness by MetaPlab KR tre MP graph is correct Ebe 4 1 Dynamics computation plugin In order to process MP models we employ plugin tools performing various tasks We launch the plugin manager by clicking on the rightmost button of the top toolbar highlighted in Figure 14 or by using the related command of the MetaPlab menu The plugin manager of MetaPlab is the tool which per mits to get advantage of the plugin architecture of the software introduced in 6 Whoever can write a plugin in order to perform a wide variety of operations on MP model data In this section we employ two plugins which are distributed within the software The first one is called dynamics compu tatzon and it is used to compute the dynamics of the model currently loaded To launch the plugin we select its entry in the plugin list prompted by the plugin manager and then we launch it by pressing the Run button Before computing the dynamics the plugin visualizes a window where the user can insert some simulation parameters such as the number of simulation steps which we set to 1000 Then we start the simulation by pressing the Start button After few seconds execution time depends on the number of steps performed the simulation procedure ends and we can go back to the plugin manager by clicking on t
25. d by flux obtained by simulating Sirius model in Section 3 bottom 32 j Log gain tool Log gain regulators Offset parameters Selecta reaction R4 Select a substance Substance C i p i Select a regulator Substance C Select a reaction R2 f gi ee eid G m Add regulator Delete regulator Add reaction Delete reaction Substance A RO Substance A Substance B R1 Substance B Substance C R2 Substance C Substance A Substance B Substance C Substance A Substance B Substance C Substance B Substance B Substance C Run Log Gain Plugin Return to Plugin manager Figure 32 Returning to the plugin manager Then equation 2 is given by Y X6 e 4 where Y R X e R represents the parameters of the regression model and e represents the errors as in the following Y 1 Xy ae XK Gy a v 2 fxs OP MP gal P hell o Ia il Xin nn X kn n En A good estimation of the regression parameters 8 may be computed by means of the method of least squares We denote the least squares estimators of a regression parameter 6 by Bi The objective function S is defined as a sum of squared residuals rj oS ye 6 where each residual is the difference between the observed value and the value calculated by the model k r Y X XyBi 7 i 1 33 and the best fit is obtained when the sum of squared residuals
26. ducing parameters or by modifying the time series values or by changing the components name Finally a check of correctness of the output computed by the tool has been performed by means of Matlab Given the following substances time series 100 0 100 0 1 0 101 8676 96 1727 2 848 103 8088 92 5285 4 5872 105 825 89 0596 6 2241 A 107 9178 p 85 7586 C 7 7646 110 0885 82 6185 9 2143 112 3387 79 6326 10 5786 114 6701 76 7944 11 8628 117 0843 74 098 13 0716 119 5829 71 5375 14 2097 and the fluxes time series below which have been computed by the Log gain plugin 3 7729 0 0189 1 8864 3 84481 0 05418 1 8484 3 91909 0 08829 1 8145 3 99613 0 12152 1 7818 FO 4 0757 Fl 0 1540 F2 1 7510 4 15816 0 18585 127221 4 24364 0 21717 1 69507 4 33207 0 24804 1 66983 4 4235 0 2785 1 64636 38 3 8462 0 0385 3 6983 0 11023 3 55719 0 17769 3 49252 0 24131 F3 3 2941 F4 0 3013 3 17175 0 35781 3 0553 0 41087 2 9444 0 46103 2 83903 0 5086 We load these time series by the MetaPlab input GUI see Section 3 and then we launch the linear regression plugin The following polynomials have been generated through the first interface Poly0 A BxC Polyl Bt Poly2 C B Poly3 AxC Poly4 0 Afterward we pass to the second interface we select the polynomials just inserted and we perform linear regression which compute the following coefficients PolyO 23 8912 0 0022 x A 0 0086 x B x C Polyl 02594
27. e and drag the mouse pointer to the destination node The creation of the edge is automatic thus the user does not need to change the appearance of an edge by hand because the software is able to understand which type of edge has to be generated and it changes accordingly its appearance When we create Please remember that we can always zoom in or zoom out the graph using the com mands of the toolbar or of the View menu If you are not able to see the port of a node please try to zoom in the graph and check that the graph is unlocked You can lock or unlock the graph by using the button of the side bar with a lock as icon or the last command of the View menu JOGate properties dialog FO properties dialog Label IOGate K Identificator FO j Gate orientation Evolution kao q 10 0 02 C 0 02 B A gt Right lt A Left A Up A A Down Time Series none Ld s Add information none kl No errors found while checking user inputs No errors found while checking user inputs Background color Horizontal alignment Background color Horizontal alignment Vertical alignment Vertical alignment Default color Top Default color Center z 4 ite Submit Cancel Submit Edit time series Cancel i oo J Figure 8 The windows to edit the properties of an Input Output gate on the left and of a Flux node on the ri
28. e A Substance B Substance C IR2 Substance A Substance B Substance C Substance B IR4 Substance C Run Log Gain Plugin Return to Plugin manager Figure 29 Deleting tuners i a reaction tuner entry is selected ii the Delete regulator button is clicked iii the list contain the reaction tuner entry is updated be written by the user as linear combination of monomials of substances and parameters raised to integer powers For instance given the MP system of Figure 9c a parametric function for flux F1 could be Flur1 A B C ao a AC a2 B C In this case the goal of linear regression plug in is to find the coefficients 30 j Log gain tool Log gain regulators Offset parameters Selecta reaction R4 Select a substance Substance C i j j Ww C ga v Select a regulator Substance C Select a reaction R2 r q hae Add regulator Delete regulator Add reaction Delete reaction RO Substance A RO Substance A RO Substance B R1 Substance B RO Substance C R2 Substance C R1 Substance A R1 Substance B R1 Substance C R2 Substance A R2 Substance B R2 Substance C R3 Substance B Substance B R4 Substance C Run Log Gain Plugin Return to Plugin manager Figure 30 Start the flux discovery dg Q and as that make the regulation function of flux F1 fit a known time series for this flux
29. ep 1 000 Range from 0 to 1000 Steps 1 000 _ Use flooring C Permit neg moles _ Guard when false the simulation stops Store last simulation values C Save in Select a file No errors found while checking user inputs Start Stop Return Figure 14 The procedure to simulate the dynamics of an MP model dynamics if possible e setting the number of steps to compute e defining a boolean expression which must be true during the simulation procedure when it becomes false a window is prompted to the user and the simulation is paused e changing the number of steps which the user wants to store in memory if this number is less then the number of simulation steps then only the last values will be maintained in memory e storing to file the time series computed by the software 4 2 Chart plotting plugin When the dynamics of our Sirius model have been computed we plot it by means of another plugin called ChartPlugin which can be launched at the This functionality can be useful when we want to investigate the behavior of an oscillatory phenomenon because it permits to run long simulations without needing a big quantity of memory 16 same way of the previous one Figure 15 This plugin visualizes a window which enables to create different types of chart The plugin window is divided in two parts in the upper side it is depicted the chart that the user wants t
30. eter nodes me Ae eText areas BAS Input Output gates A C lete vi Cust i S Ompic E N EW Submit ae Defaults Cancel S pric ni g Correct Rg Correct Figure 19 The window employed to change the visualization of the current MP graph where J 100 The first thing to do is to modify our MP graph by adding a parameter node The button of the side bar which enables to add parameter nodes is that having an orange rectangle as icon The windows which can be used to edit a parameter node are depicted in Figure 20 and 21 A parameter node can be defined in two different ways by specifying an evolution formula and an initial value or by defining a time series of values to be used during the dynamics computation When in a model one or more parameter nodes are defined by values the number of steps computed by the dynamics compu tation plugin is limited to the minimum length of the time series specified for each parameter There could be some cases nevertheless in which we want to specify by values a parameter that models a periodical function In these cases we add the time series of one oscillation and then we select the Periodical parameter checkbox in order to tell to MetaPlab of to consider the time series of the parameter as a circular vector of datas In these cases the number of steps to be computed by the dynamics computation plugin will be not limited and the dynamics will display a perfect oscillat
31. f Figure 4 all the menu items of this window are reported Many of these commands are replicated in the top toolbar or in the side bar in order to speed up the modelling procedure Particular care must be dedicated to controls collected in the side bar because they have to be used in order to generate new graphs 3 Designing an MP model In this section we create an MP graph by means of the MetaPlab input GUI The model that we consider for this example is an oscillator called Sirius creativus a variant of Sirius model proposed in 19 involving three substances A initial concentration 100 moles molar weight 1 0 gram B initial concentration 100 moles molar weight 1 0 gram C initial concentration 0 02 moles molar weight 1 0 gram and five reactions whose fluxes are tuned by the following regulation func 8 tions where is a constant and its value is 100 10A R1 A gt B YT HI0 0026 0028 R2 A 3 gt C C2 T T0 0 026 0 028 R3 B Tea R4 C D ee 3 1 Adding nodes After having launched MetaPlab we start to generate our model The draw ing area of the input GUI is never completely empty because an Organism node is always displayed This node collects the general information about the current model such as its name its constants and its measure units We begin to draw our model by editing the default information stored into the organism node To do this we either double click on the node or
32. fers their tuners by means of a non linear regression technique based on neural networks 40 Initial flux discovery automatically computes initial flux values used by the Log gain plugin to generate flux time series Covering discovery automatically generates sets of reactions satisfying the Covering Offset Log Gain Property These sets are used by the Log gain plugin Tuners discovering by statistical correlation it looks for substances and parameters which can be employed as tuners for regulation functions Regulation functions discovery by step wise regression employs the step wise regression techniques in order to generate regulation func tions XML exportation manages the translation of MP models to the XML standard References 1 2 L Bianco and A Castellini Psim a computational platform for Metabolic P systems In LNCS 4860 pages 1 20 Springer 2007 L Bianco V Manca and F Fontana Reaction driven membrane sys tems In Advances in Natural Computation LNCS 3611 pages 1155 1158 Springer 2005 L Bianco F Fontana G Franco and V Manca P systems for biolog ical dynamics In 10 pages 81 126 Springer 2006 L Bianco F Fontana and V Manca P systems with reaction maps International Journal of Foundations of Computer Science 17 1 27 48 2006 L Bianco V Manca L Marchetti and M Petterlini Psim a simula tor for biochemical dynamics based on P systems In IEEE CEC2007 V
33. ght 12 we a ow g 6 Figure 9 The Sirius model at different modelling steps after the editing of Flux nodes a after the insertion of Reaction edges b and finally the complete model c the reaction edges for rule R1 we need to change the multiplicity of the edge which connects node R1 to node At To do this we double click on the edge and than we change the value using the window depicted in Figure 12 The model is now completed and its graphical aspect is shown in Figure 9c 3 3 Checking model correctness During the modelling procedure the application visualizes a small framed label at the bottom of the side bar which checks the correctness of the model If any mistake occurs it is possible to visualize a window which prompts a list of errors that must be eliminated in order to use the model Figure 13 To visualize the window we click on the framed label of the side bar If we correctly followed all the modeling steps the MetaPlab checker confirms the model correctness otherwise a list of errors is prompted and the user Please remember that each reaction edge which does not display the number of its multiplicity has this value set to 1 the default value e N e Figure 10 A magnification of a reaction edge with three control points 13 Figure 11 A magnification of MP nodes where it is possible to see the port of each node Each Gate node the last on the right in the picture has
34. ght command of the Edit menu The area of the MP graph to be visualized or hidden have to be selected before launching the visualization window or it can be defined specifying a particular type of node or edge 4 4 Adding parameters to MP models In this subsection we propose a little modification of the Sirius model where we add some random noise to flux functions To do this we add to the model a parameter node N which represents the noise and then we change each flux formula to the following ones 18 A MetaPlab 1 0 chart plugin MetaPlab 1 0 chart plugin mo File File MetaPlab simulation Sirius creativus MetaPlab simulation Sirius creativus 1 100 4 1 000 900 800 700 n 600 s S 500 40 30 20 10 o 100 200 300 00 5 600 800 900 1 000 100 200 300 400 500 600 700 800 900 1 000 Time Time A moles B moles C moles A moles B moles C moles ar ar Line chart Phase chart Options Line chart Phase chart Options N Values to plot for each series Val p aci ies H v Do data sampling v Do data sampling Data sampling factor for line charts 1H Charts are updated every 20 seconds Data sampling factor for line charts 30 l re updated every Data sampling factor for phase charts 1H i Data sampling factor for phase charts 1H ng 10 0 40 0 0 1 20 3 ie
35. he Return button All the steps described before are depicted in Figure 14 The simulation plugin of MetaPlab offers to the user many functionalities which can be used to manage the simulation process Among them we point out the possibilities of e stopping or resuming the dynamics computation by using the Start and Stop buttons e changing the initial step from which to start the computation of the 15 MetaPlab 11 simulation plugin 2 Simulation parameters MetaPlab 1 1 input GUI home marchet SABES HY AE HPI SALE File Edit View MetaPlab Help Initial step 0 Range from 0 to 0 fia B gt Q Q a Steps 1 000 Use flooring C Permit neg moles 2 Bo n is fs Ff p le poe ja C Guard when false the simulation stops Da Store last H simulation values C Save in Select a file No errors found while checking user inputs MetaPlab 1 1 plugin manager Local MP plugins Available plugins Plugin description Flux Discovery Log Gain Simulation Plugin 2 Chart Plugin HTML Plugin Online MP plugins This tool computes the dynamics of an MP system Step 0 0 Return Repositories MetaPlab 1 1 simulation plugin 2 Plugins of the selected repositor Plugin description Simulation parameters Fluxes by function by tim Initial st
36. iations of r The following sets of tuners have been assigned to Sirius by the analysis of its structure Here we don t enter into the details of tuners discovery To TR Tro _ A B C Tr B Tra C The Covering Offset Log Gain Property the reader can find more details 23 about this property in 20 establishes that a rule of R X rules where X occurs has to be assigned to ant substance X In our case let us provide the following covering Ro R0 R1 R2 with RO R A R1 R B R2 R C Tuners and covering are the inputs required by the Log gain plugin along with substance and parameter time series for inferring flux time series tald 1 2 m Loading initial fluxes and time series Before starting the plugin we load observed substance and parameter time series as explained in Section 3 and we also insert the initial value of each flux which is fundamental to generate flux time series by the Log gain theory We then launch the plugin manager by clicking on the right button of the MetaPlab top toolbar or by using the corresponding command of the MetaPlab menu this procedure has been explained in Section 4 To launch the plugin we select Flux discovery Log Gain as showed in Figure 23 in the list prompted by the plugin man ager and then we click on the Run button After these steps the plugin GUI is visualized as shown in Figure 24 It is essentially divided in two parts MetaPlab 1
37. ilable matter of each substance is partitioned among all reactions which need to consume it The policy of matter partition is regulated at each instant by flux regulation maps or simply flux maps The notion of MP system we introduce here generalizes that one given originally in 17 A discrete dynamical system is specified by a set of states and by a discrete dynamics on them that is by a function from the set N of natural numbers to the states of the system 26 In this context the natural numbers which are argument of dynamics are called instants or steps Definition 1 A reaction r over substances X is represented by a pair of elements separated by an arrow a 2 where a and B are strings over the alphabet X Given a symbol x we denote by ar and by 3 the number of occurrences of the symbol x ina and B respectively The stoichiometric matrix A of a set R of reactions over a set X of substances is A A r X r R where Az Gr 2 Qr z The set of reactions having the substance x as a reactant is Ro x r R a z gt 0 and the set of rules consuming 2 or producing x is R x r R Azsr 0 Two reactions r1 ro compete forx X ifr r2 Ralx for some substance x X Definition 2 An MP system is a discrete dynamical system specified by a construct M X R V Q v u T qo where X R V are finite disjoint sets and the following conditions hold with n m k
38. in order to infer the time series of fluxes the user must return to the MP graph and inserts these fluxes values e the covering of substances by reactions is not complete and the user 2 Log gain tool Log gain regulators Offset parameter Select a reaction R4 elect a substance Substance A Select a regulator Substance C KA elect a reaction Add regulator Delete regulator Add reaction Delete reaction RO Substance A RO Substance B RO Substance C R1 Substance A R1 Substance B R1 Substance C R2 Substance A R2 Substance B R2 Substance C R3 Substance B R4 Substance B R4 Substance C Run Log Gain Plugin Return to Plugin manager Log gain tool Log gain regulators Offset parameters Select a reaction R4 Select a substance Substance A f tance C Select a reaction RO Select a regulator Subs Add regulator Delete regulator i Delete reaction Substance A Substance B Substance C Substance A Substance B Substance C Substance A Substance B Substance C Substance B Substance B Substance C Run Log Gain Plugin Return to Plugin manager Log gain tool Log gain regulators Offset parameters Select a reaction R4 v Select a substance Substance A L Select a regulator Substance c v Select a reaction RO Add regulator Delete
39. ins are listed on the left side of the Plugin manager and they can be launched by the Run button substance concentrations and parameter values of the biological system To insert a new substance parameter in a polynomial we select the substance parameter variable from the list called substances and parameters on the right side of Figure 34 we raise it to a proper power and if necessary we multiply or add it to other substance and parameter variables by clicking respectively on and buttons While writing a polynomial its ele ments are visualized step by step in a text box see polynomial V1 C M in Figure 34 When all substance and parameter variables have been inserted we write a polynomial description in the bottom text box and we click on the OK button to add the new polynomial to the list of polynomials available for reaction Rt where Ri depends on the reaction selected before Poly nomials can be deleted from this list by clicking the Remove button The overall process has to be repeated for each reaction of the inspected model until each reaction is associated with at least one polynomial At that point we click on the Nezt button which opens the second GUI described in the section below and creates a text file for each reaction e g R1 txt R2 txt etc and saves inside of them the polynomials generated so far 30 G j Linear Regression step 1 generation of polynomials Erim
40. ionary Computation IEEE CEC 2009 Trondheim Norway 2009 V Manca L Bianco and F Fontana Evolutions and oscillations of P systems Application to biological phenomena In Membrane Comput ing WMC 2004 LNCS 3365 pages 63 84 Springer 2005 V Manca G Franco and G Scollo State transition dynamics ba sic concepts and molecular computing perspectives In M Gheorghe editor Molecular Computational Models Unconventional Approachers chapter 2 pages 32 55 Idea Group Inc UK 2005 V Manca R Pagliarini and S Zorzan A Photosynthetic pro cess modeled by a metabolic P system Natural Computing DOI 10 1007 S11047 008 9104 X 2008 E O Voit Computational Analisys of Biochemical Systems Cambridge University Press 2000 43
41. is minimized From the theory of linear least squares the parameter estimators are found by solving the normal equations which can be written as XTX B XTY 8 and the we compute the estimators of regression parameters along with the following formula CeO Ge te Gun 4 9 6 2 Running linear regression plugin In the following a comprehensive step by step procedure leads the user through the computation of MP regulation functions by the linear regression plugin Launching the plugin In order to launch the linear regression tool we firstly launch MetaPlab by clicking on the MetaPlab jar file or on one of the batch files called MetaPlab windows xxxM or MetaPlab linux macOS xxxM that enable to allocate specific amounts of memory to the software Afterwards we load an MP model mps file or we generate it from scratch paying attention to enclose in the model file substance parameter and flux time series required to perform the linear regression lime series can be im ported from external files or computed by Dynamic computation and Log gain plug ins more details about these tools are available in the MetaPlab web site Once all these data have been collected the linear regression plug in can be launched by means of the Plug in manager highlighted in Figure 33 It displays the list of all the available plug ins and enables the user to select and run them in a couple of clicks First interface Polynomials generation
42. is presented and finally we discuss the main features of the linear regression tool which can be employed in the context of MetaPlab software to automatically generate regulation functions from data A main task of MP modeling process concerns the synthesis of MP reg ulation functions from experimental data Nowadays biologists have several high and low throughput experimental techniques able to provide time series of substance quantities and chemo physical parameters These data are em ployed into MP models for regulation functions Given some substance and parameter time series collected by experimental observations two main steps have to be performed in order to infer flux regulation functions i to compute flux time series from substance and parameter time series ii to synthesise regulation functions from substance parameter and flux time series The Log gain theory 19 supports the first step while the second one requires a regression technique to compute sound regulation functions from observed data Linear regression plug in is a tool devised to automatically synthesize MP regulation functions from time series of substances parameters and fluxes by means of linear regression It takes as input both observed data and a parametric form of every regulation function and it returns as output a set of regulation functions that fit observed data Polynomial functions have to 29 j Log gain tool Log gain regulators Offset para
43. meters Selecta reaction R3 Select a substance Substance C Selecta regulator Substance A Select a reaction R2 Add regulator Delete regulator Add reaction Delete reaction B L d Substance A IRO Substance A Substance B R1 Substance B Substance C R2 Substance C R1 Substance A R1 Substance B Substance C Substance A Substance B R2 Substance C Substance B Certs ance R3 Substance A Run Log Gain Plugin Return to Plugin manager 4 Log gain tool Log gain regulators Offset parameters Select a reaction R3 Selecta substance Substance C Select a regulator Substance A Select a reaction R2 Add regulator Delete regulator Add reaction Delete reaction Substance A RO Substance A Substance B R1 Substance B Substance C R2 Substance C Substance A R1 Substance B Substance C Substance A Substance B Substance C Substance B Substance C Substance A Run Log Gain Plugin Return to Plugin manager j Log gain tool Log gain regulators Offset parameters Select a reaction R3 Selecta substance Substance C Select a regulator Substance A Select a reaction R2 Add regulator Delete regulator Add reaction Delete reaction RO Substance A RO Substance A Substance B R1 Substance B Substance C R2 Substance C Substanc
44. o study in the bottom side there are three panels which enables to create line charts phase charts and to set some general options First of all we create a line chart which displays the concentration of the three substances of the model The result of this operation is depicted in the right side of Figure 15 Moreover we can create phase charts using the second panel of the plugin window as depicted in Figure 16 Charts created by the plugin can be exported to file printed and zoomed In order to reduce memory load the creation of each chart is performed by means of an algorithm which uses data sampling In the third panel it is possible to set a parameter which modifies the accuracy of the chart plotting Its default value is set to 1 but it can be changed to any rational numbert Figure 17 displays the same line chart plotted using different parameter values for data sampling 4 3 Result analysis When we close the plugin and the plugin manager a window is prompted asking to update the current model by new values computed during the plugins execution Confirming the operation the update is performed in a few seconds If we click on substance node A in order to check its properties we find the new time series computed during the simulation as displayed in Figure 18 Values grater then 1 reduces the accuracy of the plot while smaller values increase it MetaPlab 1 1 chart plugin Available plugins Plugin description
45. olume pages 883 887 2007 A Castellini and V Manca MetaPlab A computational framework for metabolic P systems In LNCS volume 5391 pages 157 168 Springer Verlag 2009 A Castellini V Manca and L Marchetti MP systems and Hybrid Petri Nets In Studies in Computational Intelligence volume 129 pages 53 62 Springer 2008 Al 8 12 13 14 16 17 18 A Castellini G Franco and V Manca Hybrid functional Petri nets as MP systems Natural Computing 9121 2009 DOI 10 1007 s11047 009 9121 4 A Castellini G Franco and V Manca Toward a representation of hybrid functional Petri nets by MP systems In Y Suzuki et al edi tor Natural computing volume PICT 1 pages 28 37 Springer Verlag Tokyo 2009 G Ciobanu G Paun and M J P rez Jim nez editors Applications of Memebrane Computing Springer 2006 F Fontana and V Manca Discrete solutions of differential equations by metabolic P systems Theoretical Computer Science 3712 165 182 2007 F Fontana and V Manca Predator prey dynamics in P systems ruled by metabolic algorithm BioSystems 91 3 545 557 2008 F Fontana L Bianco and V Manca P systems and the modelling of biochemical oscillations In Membrane Computing WMC 2005 LNCS 3850 pages 199 208 Springer 2005 G Franco and V Manca A membrane system for leukocyte selective re cruitment In A Alhazov C Martin Vide and G Paun editors Mem br
46. ory behavior The parameter node which we add to the MP graph in order to add a noisy signal is defined by values and set to be periodical First of all we modify the lFor example it could be considered as periodical a parameter which models the in tensity of the light during a day 20 Noise JEJ eo ei aiaiog Identificator N Name Noise Evolution 0 0 Initial value 1 225221805516884 Add information jnone Parameter type Parameter options O Defined by an evolution formula E J v Periodical parameter Defined by a set of values No errors found while checking user inputs Background color Horizontal alignment Center v Vertical alignment Default color Center v a Submit Ei Edit time series Cancel Figure 20 The MP graph of the Sirius model with noise on the left and the window to set the noise Parameter node on the right values of the parameter as depicted in the right side of Figure 20 and then we edit the parameter time series To do this we have to click on the Edit time series button which enables the visualization of the first window of Figure 21 It is not the first time that we use this kind of window indeed it is the same that we have used before to specify the initial concentration of substances but this time we insert more values
47. ovide a new theory based on the Log Gain Principle 20 for inferring models from experimental data They allow to determine metabolic fluxes associated with each reaction by using algebraic manipulations of observed data Since flux discovery is the first step towards the generation of MP models from experimental data MetaPlab offers a plugin based on Log gain theory 22 MetaPlab simulation Sirius creativus with noise 1 1004 A moles B moles C moles AN N 1 000 4 Values Time MetaPlab simulation Sirius creativus A moles B moles C moles N A S f fi l f 1 j j j j 1 100 1 000 Values Figure 22 The charts which plot 500 simulation steps of the Sirius model with noise on the top and of the classical one on the bottom which automates this process In this section we describe how to use the Log Gain plugin to infer fluxes related to observed dynamics We will refer to Sirius the synthetic oscillator already introduced in Section 3 We suppose to know 1000 steps of substance and parameter time series and the initial value of each flux We remark that the i th value of substance j parameter vj and flux y will be denoted respectively by x 2 v and u 2 Moreover we define tuners or regulators of a reaction r as substances and parameters which influence by their variations the flux var
48. re is a framed text box which prompts an error message if we insert wrong values for example if we insert a textual value where the application needs a number Using this window we can also start to edit the model constants list in order to add the constant J defined before To do this we click on the button Edit constants and then we use the window subsequently displayed as shown in the right side of Figure 5 After having changed the Organism node values we submit them by clicking on the Submit button The Organism node updates its content as in the following picture Now we add to the drawing area three Substance nodes needed to define the stoichiometry of the system To do this we click on the button identified by a blue circle icon in the side bar of Figure 4 When we do this the mouse pointer changes its shape because the software has entered into the insertion mode At this point we can add Substance nodes by moving the pointer to the position where we want to create the new node and then clicking by the left button of the mouse After the three Substance nodes have been created we exit from the insertion mode by clicking on the side bar button having an arrow as icon Now we can change the default values of the nodes 10 a b Figure 7 Sirius at different modelling steps after the insertion of Substance nodes a and after the insertion of Reaction Flux and Gate nodes b just created by the window
49. regulator Add reaction Delete reaction Ro Substance A RO Substance A IRO Substance B IRO Substance C R1 Substance A Substance B Substance C Substance A Substance B Substance C Substance B Substance B Substance C Run Log Gain Plugin Return to Plugin manager Figure 27 Adding reactions which fulfill the Covering Offset Log Gain Prop erty i a reaction tuner entry is selected ii the Add reaction button is clicked iii the entry is inserted into the list click on the Run Log Gain Plugin button 28 j Log gain tool Log gain regulators Offset parameters Selecta reaction R4 Select a substance Substance C Select a regulator Substance C Select a reaction R2 Add regulator Delete regulator Add reaction Delete reaction Substance A RO Substance A Substance B R1 Substance B Substance C R2 Substance C Substance A Substance B Substance C Substance A Substance B Substance C Substance B Substance B Substance C Run Log Gain Plugin Return to Plugin manager Figure 28 Covering set Ro for Sirius 6 Linear regression plugin In this section some basic concepts are reported which are necessary to un derstand how the Linear Regression tool works and the theory behind it we firstly introduce the problem of discovering regulation functions in MP systems then linear regression
50. s among them the Belousov Zhabotinsky reac tion Brusselator 3 4 the Lotka Volterra dynamics 25 3 4 a Susceptible Infected Recovered epidemic 3 the Leukocyte Selective Recruitment in the immune response 14 3 the Protein Kinase C Activation 4 Mitotic Cycles 23 the Pseudomonas Quorum Sensing the Non Photochemical Quenching NPQ phenomenon 27 and the lac operon gene regulatory mechanism in the glycolitic pathway of Escherichia coli 9 8 Each of these models is based on the definition of a different MP system whose evolution in time presents the same behavior of the biological dynamics under examination In the following we focus on MetaPlab a software conceived and devel oped by Prof Vincenzo Manca Dr Luca Bianco Alberto Castellini Dr Giuditta Franco Luca Marchetti and Roberto Pagliarini at the Computer science department of the University of Verona with the support of the Computational BioMedicine Center CBMC In the following we will not explain the theory behind the software but we only define MP systems and employ the graphical representation of MP graphs in order to avoid complex mathematical formalisms Detailed mathematical justifications can be found in works listed in the Bibliography section at the end of this document 1 1 Metabolic P Systems MP systems are deterministic P systems where the transition to the next state is calculated according to a mass partition strategy that is the ava
51. sist biologists to under stand the internal mechanisms of biological systems and to reproduce and analyze in silico biological phenomena responses to external stimuli envi ronmental condition alterations and structural changes It extends an MP systems simulator called Psim 1 5 The lates version of MetaPlab is avail able at the MetaPlab website http mplab sci univr it 5 Organism node Parameter node e or Parameter node Figure 2 A toy MP graph with a legenda of different nodes and edges and it requires Java 1 6 or later versions installed on the user s computer in order to be run The Java implementation of MetaPlab ensures the cross platform portability of the software which is released under the GPL open source license 2 1 Plugin framework The new computational framework we propose is based on an extensible set of plugins namely Java tools for solving specific tasks relevant in the framework of MP systems Among these tasks regulation function discovery simula tion visualization graphical and statistical curve analysis importation of biological networks from on line databases and possibly other aspects result to be significant for further investigations Figure 3 depicts this framework which involves four main layers the first deals with the model definition and visualization by MP graphs the second is dedicated to the representation and storing of MP systems by a suitable data structure called
52. the left side the list of all the tuners of each reaction Assigning covering reactions After the tuner definition we move to the right side of the interface in order to insert the set of reactions which has the Covering Offset Log Gain Property that is the reactions that belong to the set Rp The procedure is very similar to that performed to insert tuners In this case we cover every substance by a reaction of Ro Let we suppose we want to insert the reaction RO which covers the substance A We select entry RO from the upper drop down list and entry Substance A from the lower drop down list and then we click on the Add reaction button After these steps graphically represented in Figure 27 the entry RO A is added to the list panel below In the same way we add reactions R1 and R2 which cover respectively substances B and C Figure 28 shows the list containing the complete set Ro Deleting wrong tuners and or wrong covering reactions Let us suppose to have inserted a wrong tuner such as substance A as tuner for reaction R3 In this case we can delete entry R3 A from the corresponding list in a very simple way It is sufficient to select this couple from the list and click on the Delete regulator button This step is depicted in Figure 29 In the same manner it is possible to delete a covering reaction from the list 20 Log gain tool Log gai Offset parameters Select a reaction RO elect a substance
53. tor Description Model of the mitotic oscillator found in early amphibian embryos Model constants N Protease activation and deactivation Figure 1 An MP graph representation of the mitotic oscillator model devised by Goldbeter 15 17 1 2 Metabolic P graphs In order to allow a better and simpler understanding of the behavior of MP systems the graphical formalism of MP graphs has been recently intro duced 23 An MP graph is a graphical representation of MP systems by means of bipartite graphs having two levels in which the first level describes the stoichiometry of reactions while the second level expresses the regula tion which tunes the flux of every reaction i e the quantity of chemicals transformed at each step depending on the state of the system see for ex ample Figure 1 As shown in Figure 2 seven types of node and three types of edge are employed 1 Organism node rounded corner box it stores general information of a model specifying title description constants and measure units of the system Each MP graph must have one and only one Organism node 2 Substance nodes blue circles they represent substances specifying their name concentration values and molar weight Similar graphical formalisms were developed in the context of complex reaction net works SNA Stoichiometric Network Analysis and MCA Metabolic Control Analysis see also 28 10

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