Snoopy A Unifying Petri Net Tool

Transcription

1 Snoopy A Unifying Petri Net Tool Monika Heiner, Mostafa Herajy, Fei Liu, Christian Rohr, and Martin Schwarick Computer Science Institute, Brandenburg University of Technology Cottbus Postbox , 0303 Cottbus, Germany snoopy@informatik.tu-cottbus.de Abstract. The tool Snoopy provides a unifying Petri net framework which has particularly many application scenarios in systems and synthetic biology. The framework consists of two levels: uncoloured and coloured. Each level comprises a family of related Petri net classes, sharing structure, but being specialized by their kinetic information. Petri nets of all net classes within one level can be converted into each other, while changing the level involves user-guided folding or automatic unfolding. Models can be hierarchically structured, allowing for the mastering of larger networks. Snoopy supports the simultaneous use of several Petri net classes; the graphical user interface adapts dynamically to the active one. Built-in animation and simulation (depending on the net class) are complemented by export to various analysis tools. Snoopy facilitates the extension by new Petri net classes thanks to its generic design. Keywords: hierarchical (coloured) qualitative/stochastic/continuous/ hybrid Petri nets, modelling, animation, simulation. Overview Petri nets may easily serve as a convenient umbrella formalism integrating qualitative and quantitative (i.e. stochastic, continuous, or hybrid) modelling and analysis techniques. Thus Petri nets are immediately ready to address distinctive modelling demands in systems and synthetic biology, which particularly include the dealing with biochemical reaction networks in several modelling paradigms. Motivated by this application scenario, Snoopy is set up as a unifying Petri net framework (see Fig. ) which can be divided into two levels: uncoloured [] and coloured [7]. Each level comprises a family of related Petri net models, sharing structure, but being specialized by their kinetic information. Specifically, the uncoloured level contains qualitative (time-free) Place/Transition Petri nets (QPN )aswellasquantitative(time-dependent)petrinetssuchasstochastic Petri nets (SPN), continuous Petri nets (CPN), and generalised hybrid Petri nets (GHPN). The coloured level provides coloured counterparts of the uncoloured level, and thus consists of coloured qualitative Petri nets (QPN C ), coloured stochastic Petri nets (SPN C ), coloured continuous Petri nets (CPN C ) and coloured generalised hybrid Petri nets (GHPN C ). S. Haddad and L. Pomello (Eds.): PETRI NETS 202, LNCS 7347, pp , 202. c Springer-Verlag Berlin Heidelberg 202

2 Snoopy A Unifying Petri Net Tool 399 discrete state space QPN C continuous state space molecules/levels LTS, PO CTL/LTL time-free timed, quantitative SPN C QPN CPN C molecules/levels stochastic rates CTMC CSL/PLTLc SPN CPN concentrations deterministic rates ODEs LTLc folding unfolding abstraction extension approximation GHPN C GHPN molecules and concentrations stochastic and deterministic rates CTMC coupled by Markov jumps PLTLc Fig.. Paradigms integrated in Snoopy s unifying framework Petri nets of these net classes can be converted into each other. Obviously, there may be a loss of information in some directions (cf. arrows labelled with abstraction in Fig. ). The conversion between coloured and uncoloured net classes is accomplished by means of user-guided folding or automatic unfolding (cf. arrows labelled with folding and unfolding in Fig. ). Moving between the coloured and uncoloured level changes the style of representation, but does not change the actual net structure of the underlying reaction network. Therefore, all analysis techniques available for uncoloured Petri nets can be applied to coloured Petri nets as well. Snoopy supports the simultaneous use of different net classes, which provides the grounds to investigate one and the same case study with different modelling abstractions in various complementary ways [0], [], [7]. 2 Basic Functionalities Snoopy offers for its net classes a graphical, unified modelling environment. See Fig. 2 for a snapshot of the user interface with a famous textbook example, the prey predator system. The user interface mainly consists of: graphical elements window (the top left tree control): listing all graphical elements, e.g. node elements and edge elements, hierarchy window (the middle left tree control): showing the model hierarchy,

3 400 M. Heiner et al. declarations window (the bottom left tree control): containing all declarations, e.g. colour sets, constants, and variables for coloured Petri nets, drawing canvas (the right window): drawing and showing models. Fig. 2. User modelling interface Basic modelling functions provided by Snoopy include: define declarations (only for coloured Petri nets), add graphical elements, i.e. places and transitions, from the graphical elements window to the canvas and connect them using edges, edit or modify properties of nodes (e.g. name, initial marking) and edges (multiplicity) in their property dialogues. Snoopy supplies two features for the design and systematic construction of larger Petri nets. Logical nodes (places/transitions) serve as connectors, and coarse transitions (coarse places) help to hide transition-bordered (place-bordered) subnets in order to design hierarchically structured nets. Further features consistently available for all Petri net classes include: editing (cut, copy, paste), colouring of individual net elements and of computed node sets (e.g. support of place/transition invariants, siphons, traps, Parikh vectors), layouting (mirror, flip, rotate, and automatic layouting using OGDF [5]), graphical export to eps, Xfig and FrameMaker (selected net classes), and print. Additionally, Snoopy offers execution capabilities for each net class, see next section for details.

4 Snoopy A Unifying Petri Net Tool 40 3 Net Class Specific Functionalities 3. Overview The hierarchy of the Petri net classes supported by Snoopy is given in Fig. 3. Netclass +name QPN +discreteplaces +discretetransitions +standardedges QPN C +colordeclarations CPN +continuousplaces +continuoustranstions +standardedges + read edges +inhibitoredges +modifieredges SPN +immediatetransitions +deterministictransitions +scheduledtransitions +modifieredges XPN + read edges +inhibitoredges +equaledges + reset edges GHPN +continuousplaces +continuoustransitions +immediatetransitions +deterministictransitions +scheduledtransitions +modifieredges CPN C +colordeclarations SPN C +colordeclarations XPN C +colordeclarations GHPN C +colordeclarations Fig. 3. Snoopy s class hierarchy Qualitative Petri nets (QPN ). QPN contain standard Place/Transition nets (P/T nets) and extended Petri nets (XPN). They do not involve any timing aspects; so they allow a purely qualitative modelling of, e.g., biomolecular networks. Tokens may represent molecules or abstract concentration levels []. XPN enhance standard Petri nets by four special edge types: read edges (often also called test edges), inhibitor edges, equal edges, and reset edges, see [3], [22] for details. Stochastic Petri nets (SPN). This net class extends QPN by assigning to transitions exponentially distributed waiting times, specified by firing rate functions. A rate function is generally state-dependent; it can be an arbitrary arithmetic function deploying the pre-places of a transition as integer variables and user-defined, real-valued constants (often called parameters). Pre-places can be associated with transitions by special modifier edges [22]. They may modify the transition s firing rate, but do not have an influence on the transition s enabledness. Popular kinetics, e.g. mass-action semantics, level semantics [], are supported by pre-defined function patterns. Each transition gets its own rate function, making up together a list of rate functions. Moreover, several rate functions lists and parameter lists as well as multiple initial markings can be maintained,

5 402 M. Heiner et al. allowing for quite flexible models and their systematic evaluation by series of related computational experiments. SPN have been extended to generalised stochastic Petri nets (GSPN) and deterministic and stochastic Petri nets (DSPN ). In our extended stochastic Petri nets (XSPN)[2], there are the four special edge types as for QPN,andthree special transition types: immediate transitions (zero waiting time), deterministic transitions (deterministic waiting time, relative to the time point where the transition gets enabled), and scheduled transitions (scheduled to fire, if any, at single or equidistant, absolute points of the simulation time). The unrestricted use of these extended features destroys the Markov property, but the adaptation of the simulation algorithms is rather straightforward. To simplify our life, Snoopy does not distinguish between these stochastic net classes. Thus, Snoopy s SPN net class is actually XSPN; see Figure 3. Continuous Petri nets (CPN). Continuous Petri nets offer a graphical way to specify unambiguously systems of ordinary differential equations (ODEs) [0]. The real-valued tokens may denote concentrations. The continuous rate functions have to obey similar rules as for SPN.Likewise,theconceptsoffunction lists, parameter lists and initial marking lists are also applied to CPN. Snoopy generates automatically the underlying system of ODEs. CPN and SPN provide an approximation of each other as it is depicted in Fig.. Generalised hybrid Petri nets (GHPN). Snoopy integrates all functionalities of its stochastic and continuous Petri nets into one net class, yielding generalised hybrid Petri nets [4]. GHPN are specifically tailored (but not limited) to models that require an interplay between stochastic and continuous behaviour. They provide a trade-off between accuracy and runtime of model simulation by adjusting the number of stochastic transitions appropriately, which can be done either statically (by the user) or dynamically (by the simulation algorithms). A typical application of GHPN is the hybrid representation of stiff biochemical reactions, where slow reactions are represented by stochastic transitions while fast reactions are modelled by continuous transitions. Coloured extensions. Each uncoloured net class has a coloured counterpart [7] which inherits all features of its corresponding uncoloured net class, e.g., SPN C enjoy all special edge types and transition types of SPN. Snoopy provides various flexible ways to define declarations to be used in the annotations of coloured Petri nets. Data types for colour set definitions include: () simple types: dot, integer, string, boolean, enumeration and index, and (2) compound types: product and union. Variables, constants and functions can be defined to specify arc expressions, guards, and markings. By defining hierarchical colour sets using the product type, one can conveniently model a (biological) system evolving in multi-dimensional, e.g. 2- or 3-dimensional space [8]. Concise initial marking specifications for larger colour sets and individual rate function definitions for each transition instance are supported. Syntax checking ensures the syntactical correctness of constructed models.

6 3.2 Executability Snoopy A Unifying Petri Net Tool 403 Animation. Snoopy offers built-in animation for QPN, SPN, QPN C and SPN C, see Fig. 2 for a snapshot of the animation of a SPN C model. Animation visualizes the token flow, which may give first insights in the behaviour and may help to better understand the inherent causality of the model. Animation can be triggered manually or be done in automatic mode with different firing strategies (single/intermediate/maximal step). Snoopy supports a similar animation within a standard web browser for QPN ;seesnoopy swebsiteforasampler. Stochastic simulation. The underlying core semantics of SPN and SPN C are continuous time Markov chains (CTMC); so the simulation follows the standard Gillespie algorithm [9] enhanced by deterministic events of XSPN. Simulation results are available as tables and can be visualized in diagrams, showing the evolution over time of the token numbers on selected places or the firing rates of selected transitions. Simulation traces can be checked on-the fly for reachability of certain states specified by logical expressions over places. Additionally,simulation traces can be exported as averaged/single/exact traces, to be, e.g., evaluated by simulative model checking of PLTLc with the Monte Carlo Model Checker MC2 [4]. Continuous simulation. Snoopy provides 4 stiff/unstiff solvers for the numerical integration of CPN and CPN C. These ODE solvers range from simple fixed-stepsize unstiff solvers (e.g. Euler) to more sophisticated variable-order,variable-step, multi-step stiff solvers (e.g Backward Differentiation Formulas (BDFs)). In the latter case, we use SUNDIALS CVODE [5] to solve the underlying ODEs. Deterministic simulation traces are available as tables, can be visualized in diagrams, and written to files to be, e.g., checked against LTLc properties with MC2, see, e.g., []. Hybrid simulation. The simulation of GHPN can be carried out using either static or dynamic partitioning. In the former case, transition types are decided off-line by the user before the simulation starts, while in the latter case, the running simulation decides on-the-fly which transitions are considered as stochastic or continuous ones based on their current rates. In both cases, continuous transitions are simulated using an ODE solver with event detection, while stochastic transitions are simulated using Gillespie s direct method. Moreover, the user can choose to simulate a net completely as stochastic or continuous one despite of the original place and transition types. Then transitions and places are automatically converted to the required type. This functionality gives the opportunity to experiment with different simulation algorithms without having to change the net. For instance, if the user s Petri net model is drawn to contain only stochastic transitions, later on, it could be simulated using stochastic (e.g. Gillespie) or continuous (e.g. BDFs) algorithms. In the latter case, stochastic transitions will be converted into continuous ones, while transitions of other types (immediate, deterministic, or scheduled) will remain unchanged.

7 404 M. Heiner et al. Coloured extensions. Snoopy supports animation for QPN C and SPN C, which can be run in automatic mode or manually controlled, e.g. with single-step animation by manually choosing a binding. Simulation of coloured Petri nets (SPN C, CPN C, GHPN C ) is done on automatically unfolded Petri nets, and thus all simulation algorithms for uncoloured Petri nets are available for coloured Petri nets as well. In order to improve efficiency, the unfolding adopts a constraint satisfaction approach, which is implemented using the Gecode library [2]. Simulation results of coloured or uncoloured places/transitions can be shown separately or together. In-depth behaviour exploration is supported by auxiliary variables (observers) which depend on coloured places, allowing for extra measures, e.g. the sum of a group of related places. 3.3 Import/Export All net classes can be converted into eachotherthroughexport,whichpermitsto easily switch from one net class to another one and thus to investigate a system under study with different modelling abstractions by deploying simultaneously several Petri net classes. Additionally, there is export to numerous external analysis tools, among them Snoopy s close friends Charlie [24] and Marcie [23] ; see Snoopy s website for a complete list. Charlie s features for P/T nets include structural analysis, P/T invariants computation, and explicit CTL/LTL model checking. Marcie supports qualitative analysis and symbolic CTL model checking based on Interval Decision Diagrams. It also allows a quantitative investigation of SPN by means of CSL and PLTLc model checking based on numerical and simulative analysis engines. A crucial point for the addressed main application area is Snoopy s import and export of the standard exchange format SBML, Level 2, Version 3 [7]. The Petri Net Markup Language [2] is not yet supported, but shortlisted for future plans. Complementary, we developed the Colored Abstract Net Definition Language (CANDL) [8] as a human-readable exchange format for our own toolbox. The ODEs induced by a given CPN or GHPN can be written in Latex format and as plain ASCII text. 4 Architecture Snoopy s architecture has been designed to gain three distinguished characteristics. () It is extensible; its generic design facilitates the implementation of new Petri net classes. (2) It is adaptive by supporting the simultaneous use of several models, with the graphical user interface adapting dynamically to the net class in the active window. (3) It is platform-independent. Snoopy is written in the programming language C++ using the Standard Template Library and the cross-platform toolkit wxwidgets [6]. The main object in the data structure, see Fig. 4, is the graph object which contains modification methods and holds the associated node, edge and metadata classes. Every node class has one prototype and contains a number of nodes that are copied from

8 Snoopy A Unifying Petri Net Tool 405 graph prototype edgeclass edge prototype node attribute nodeclass metadataclass prototype metadata node attribute graphic edge metadata attribute 0.. widget (a) (b) (c) Fig. 4. (a) Internal data structure of Snoopy. (b) Graphics assigned to the graph elements. (c) Attributes connected with window interactions controls. this prototype. The edge and metadata class are similarly structured, compare Fig. 4a. Every node, edge and metadata can have a list of attributes defining the properties of the graph elements. A graphics is assigned to every displayed element, see Fig. 4b. Attributes of graph elements may be manipulated with widgets as it is shown in Fig. 4c. The object-oriented design uses several design patterns (Model View Controller, Prototype, and Builder), thus special requirements may be added easily. Due to a strict separation of internal data structures and graphical representation it is straightforward to extend Snoopy by a new graph class; see [3] for a demonstration how to do it. Fig. 3 gives the hierarchy of net classes which Snoopy currently supports. 5 Applications Snoopy is in worldwide use for teaching (see, e.g., [6], [20]) and research (see, e.g., [8], [0], [], [2], [4]); see Snoopy s website for more references. In the last year, Snoopy has been downloaded about,400 times. Snoopy s coloured Petri nets have been applied to investigate a variety of largescale biological systems, proving its capability to solve many challenges imposed by biological multi-scale modelling, e.g. repetition, variant, and organization of cells [7]. Case studies deploying coloured Petri nets usually require stochastic and/or continuous simulations over very large underlying uncoloured Petri nets; for specific case studies and related figures see [8]. 6 Comparison with Other Tools There is no tool on the market which supports a comparable family of Petri nets classes as Snoopy does. Usually, modelling tools confine themselves to a few net classes. Contrary, Snoopy provides a set of related net classes: time-free, stochastic, continuous, hybrid and their coloured extensions, as well as plenty of analysis techniques, e.g. built-in animation/simulation and export to external analysis tools. This provides an excellent approach to accomplish the analysis of a (biological) system from different perspectives by relating all these net classes.

9 406 M. Heiner et al. Herein, we compare Snoopy with three popular tools providing similar functionalities for selected net classes: CPN Tools, GreatSPN, and Cell Illustrator. CPN Tools [] are tailored to coloured (timed) Petri nets. They established a landmark in modelling convenience. Their concept of fusion places inspired Snoopy s logical nodes, and the hierarchical organization of substitution transitions triggered Snoopy s coarse nodes. However, there are no special arcs, and CPN Tools do not explicitly support any of the quantitative net classes, which are mandatory for systems and synthetic biology, such as continuous, stochastic or hybrid Petri nets. GreatSPN [3] supports modelling and analysis of GSPN and a coloured extension, but no other net classes. There are neither logical nodes nor hierarchy, but an interesting layer concept. Cell Illustrator [9] is a commercially licensed software tool utilising Hybrid Functional Petri Nets with extensions (HFPNe) to model and simulate biochemical pathways. While Cell Illustrator combines discrete and continuous parts in one model, it does not offer the full interplay between continuous and stochastic transitions as it is given in Snoopy. Crucial features such as modifier edges and immediate or scheduled transitions are not supported. A model can only be simulated using static partitioning. Advanced modelling features like logical nodes, hierarchy, or colour which are imperative when considering large scale models or models with repeated components are not provided. In summary, Snoopy s rich modelling capabilities make it competitive and particularly well suited for scenarios suggesting the simultaneous and consistent use of several modelling paradigms enabling different modelling abstractions. 7 Installation Snoopy is available for Windows, Mac OS X and Linux. It can be obtained free of charge for academic use from its website tu-cottbus.de/snoopy.html. Installation packages contain all dependencies; no other libraries need to be manually installed. See Snoopy s website for more information how to install and use it on different platforms, for Petri net examples in Snoopy s proprietary file format, and for Snoopy s bibliography. Snoopy comes with several further Petri net classes,including time(d)petri nets and modulo Petri nets, as well as a couple of other graph types; see [3]. Snoopy is still evolving we are open for suggestions. Acknowledgement. Substantial contributions to Snoopy s development have been done by former staff members and numerous student projects at Brandenburg University of Technology, chair Data Structures and Software Dependability. References. CPN Tools website, (accessed: March 30, 202) 2. Gecode website, (accessed: March 30, 202)

10 Snoopy A Unifying Petri Net Tool GreatSPN website, (accessed: March 30, 202) 4. MC2 website, (accessed: March 30, 202) 5. OGDF - Open graph drawing framework website, (accessed: March 30, 202) 6. Wxwidgets website, (accessed: March 30, 202) 7. Bornstein, B.J., Keating, S.M., Jouraku, A., Hucka, M.: LibSBML: an API library for SBML. Bioinformatics 24(6) (2008) 8. Gilbert, D., Heiner, M.: Petri nets for multiscale Systems Biology. Brunel University, Uxbridge/London (20), 9. Gillespie, D.T.: Exact stochastic simulation of coupled chemical reactions. Journal of Physical Chemistry 8(25), (977) 0. Heiner, M., Gilbert, D.: How Might Petri Nets Enhance Your Systems Biology Toolkit. In: Kristensen, L.M., Petrucci, L. (eds.) PETRI NETS 20. LNCS, vol. 6709, pp Springer, Heidelberg (20). Heiner, M., Gilbert, D., Donaldson, R.: Petri Nets for Systems and Synthetic Biology. In: Bernardo, M., Degano, P., Zavattaro, G. (eds.) SFM LNCS, vol. 506, pp Springer, Heidelberg (2008) 2. Heiner, M., Lehrack, S., Gilbert, D., Marwan, W.: Extended Stochastic Petri Nets for Model-Based Design of Wetlab Experiments. In: Priami, C., Back, R.-J., Petre, I. (eds.) Transactions on Computational Systems Biology XI. LNCS (LNBI), vol. 5750, pp Springer, Heidelberg (2009) 3. Heiner, M., Richter, R., Schwarick, M., Rohr, C.: Snoopy-a tool to design and execute graph-based formalisms. Petri Net Newsletter 74, 8 22 (2008) 4. Herajy, M., Heiner, M.: Hybrid representation and simulation of stiff biochemical networks through generalised hybrid Petri nets. Tech. Rep. 02, BTU Cottbus, Computer Science Institute (20) 5. Hindmarsh, A., Brown, P., Grant, K., Lee, S., Serban, R., Shumaker, D., Woodward, C.: Sundials: Suite of nonlinear and differential/algebraic equation solvers. ACM Trans. Math. Softw. 3, (2005) 6. Kafura, D., Tatar, D.: Initial experience with a computational thinking course for computer science students. In: Proc. SIGCSE 20, pp ACM (20) 7. Liu, F.: Colored Petri Nets for Systems Biology. Ph.D. thesis, BTU Cottbus, Computer Science Institute (January 202) 8. Liu, F., Heiner, M., Rohr, C.: Manual for Colored Petri Nets in Snoopy. Tech. Rep. 02 2, BTU Cottbus, Computer Science Institute (March 202) 9. Nagasaki, M., Saito, A., Jeong, E., Li, C., Kojima, K., Ikeda, E., Miyano, S.: Cell Illustrator 4.0: a Comp. Platform for Systems Biology. Silico Biology 0 (200) 20. Petre, I.: Introduction to Computational and Systems Biology, Collection of Modelling Reports, Åbo Akademi, Department of IT (20) 2. Petri Net Markup Language (PNML): Systems and software engineering Highlevel Petri nets Part 2: Transfer format, ISO/IEC :20 (2009) 22. Rohr, C., Marwan, W., Heiner, M.: Snoopy - a unifying Petri net framework to investigate biomolecular networks. Bioinformatics 26(7), (200) 23. Schwarick, M., Rohr, C., Heiner, M.: MARCIE - Model checking And Reachability analysis done efficiently. In: Proc. QEST 20. pp (20) 24. Wegener, J., Schwarick, M., Heiner, M.: A Plugin System for Charlie. In: Proc. CS&P 20, pp Bia lystok University of Technology (20)