MODELING AND ANALYZING BIOLOGICAL SYSTEMS USING COLORED HIERARCHICAL PETRI NETS ILLUSTRATED BY C. ELEGANS VULVAL DEVELOPMENT

Colored Petri nets allow compact, parameterizable and scalable representations of large-scale biological models by encoding, e.g., species as colored tokens, and offer a variety of analysis techniques, e.g., structural analysis, simulation and model checking to analyze biological models. However, so far colored Petri nets have not been widely used and well explored in systems biology. In this paper, we aim to present a systematic approach to modeling and analyzing complex biological systems using colored Petri nets in order to help biologists to easily use them. We first describe a framework comprising a family of related colored Petri nets: colored qualitative Petri net (𝒬𝒫𝒩𝒞), colored stochastic Petri net (𝒮𝒫𝒩𝒞) and colored continuous Petri net (𝒞𝒫𝒩𝒞). They share structure, but are specialized by their kinetic information. Based on this framework, we present our colored Petri net approach to modeling and analyzing complex biological systems. First a biological system is modeled as a hierarchical 𝒬𝒫𝒩𝒞 model, animated and analyzed by structural analysis; then it is converted into a 𝒮𝒫𝒩𝒞 or 𝒞𝒫𝒩𝒞 model, to be further analyzed using stochastic or continuous simulation, and simulative or numerical model checking. We demonstrate this approach using a nontrivial example, Caenorhabditis elegans vulval development.

[1]  David R. Gilbert,et al.  A Model Checking Approach to the Parameter Estimation of Biochemical Pathways , 2008, CMSB.

[2]  Iva Greenwald,et al.  Crosstalk Between the EGFR and LIN-12/Notch Pathways in C. elegans Vulval Development , 2004, Science.

[3]  Hartmann J. Genrich,et al.  Executable Petri net models for the analysis of metabolic pathways , 2001, International Journal on Software Tools for Technology Transfer.

[4]  Richard Banks,et al.  A High-Level Petri Net Framework for Genetic Regulatory Networks , 2007, J. Integr. Bioinform..

[5]  Monika Heiner,et al.  Modeling membrane systems using colored stochastic Petri nets , 2013, Natural Computing.

[6]  Doktor der Naturwissenschaften.  Colored Petri Nets for Systems Biology , 2012 .

[7]  Claudine Chaouiya,et al.  Petri net modelling of biological networks , 2007, Briefings Bioinform..

[8]  Monika Heiner,et al.  Petri Nets for Systems and Synthetic Biology , 2008, SFM.

[9]  François Fages,et al.  Machine Learning Biochemical Networks from Temporal Logic Properties , 2006, Trans. Comp. Sys. Biology.

[10]  Amir Pnueli.  The Temporal Semantics of Concurrent Programs , 1981, Theor. Comput. Sci..

[11]  Monika Heiner,et al.  A Unifying Framework for Modelling and Analysing Biochemical Pathways Using Petri Nets , 2007, CMSB.

[12]  Dominique Pontier,et al.  Modeling transmission of directly transmitted infectious diseases using colored stochastic Petri nets. , 2003, Mathematical biosciences.

[13]  Martin Schwarick,et al.  MARCIE - Model Checking and Reachability Analysis Done EffiCIEntly , 2011, 2011 Eighth International Conference on Quantitative Evaluation of SysTems.

[14]  Paul W. Sternberg,et al.  The combined action of two intercellular signaling pathways specifies three cell fates during vulval induction in C. elegans , 1989, Cell.

[15]  Qian Gao,et al.  A systems biology approach to multi-scale modelling and analysis of planar cell polarity in drosophila melanogaster wing , 2013 .

[16]  Thomas Runge.  Application of Coloured Petri Nets in Systems Biology , 2004 .

[17]  Mor Peleg,et al.  Qualitative models of molecular function: linking genetic polymorphisms of tRNA to their functional sequelae , 2002, Proc. IEEE.

[18]  Lars Michael Kristensen,et al.  Design/CPN - A Computer Tool for Coloured Petri Nets , 1997, TACAS.

[19]  A. Kupfer,et al.  Modelling and Simulation of the TLR4 Pathway with Coloured Petri Nets , 2006, 2006 International Conference of the IEEE Engineering in Medicine and Biology Society.

[20]  Thomas A. Henzinger,et al.  Predictive Modeling of Signaling Crosstalk during C. elegans Vulval Development , 2007, PLoS Comput. Biol..

[21]  Henri E. Bal,et al.  Executing multicellular differentiation: quantitative predictive modelling of C.elegans vulval development , 2009, Bioinform..

[22]  Monika Heiner,et al.  Snoopy - a unifying Petri net framework to investigate biomolecular networks , 2010, Bioinform..

[23]  Monika Heiner,et al.  Multiscale modelling of coupled Ca2+ channels using coloured stochastic Petri nets. , 2013, IET systems biology.

[24]  Monika Heiner,et al.  Colouring Space - A Coloured Framework for Spatial Modelling in Systems Biology , 2013, Petri Nets.

[25]  Barry L. Nelson,et al.  Statistical Analysis of Simulation Results , 2007 .

[26]  Doktor der Naturwissenschaften.  Computational Steering of Multi-Scale Biochemical Networks , 2013 .

[27]  Kurt Jensen.  Coloured Petri Nets , 1992, EATCS Monographs in Theoretical Computer Science.

[28]  Martin Schwarick,et al.  Snoopy - A Unifying Petri Net Tool , 2012, Petri Nets.

[29]  Marta Simeoni,et al.  Petri nets for modelling metabolic pathways: a survey , 2010, Natural Computing.

[30]  Kurt Lautenbach,et al.  The Analysis of Distributed Systems by Means of Predicate ? Transition-Nets , 1979, Semantics of Concurrent Computation.

[31]  Lydia E. Kavraki,et al.  Computational challenges in systems biology , 2009, Comput. Sci. Rev..

[32]  Sunwon Park,et al.  Colored Petri net modeling and simulation of signal transduction pathways. , 2006, Metabolic engineering.

[33]  Annegret Wagler,et al.  Petri nets as a framework for the reconstruction and analysis of signal transduction pathways and regulatory networks , 2011, Natural Computing.

[34]  Monika Heiner,et al.  A multiscale approach to modelling planar cell polarity in Drosophila wing using hierarchically coloured Petri nets , 2011, CMSB.

[35]  Edmund M. Clarke,et al.  Model Checking , 1999, Handbook of Automated Reasoning.

[36]  Monika Heiner,et al.  BioModel engineering for multiscale Systems Biology. , 2013, Progress in biophysics and molecular biology.

[37]  Monika Heiner,et al.  Multiscale Modeling and Analysis of Planar Cell Polarity in the Drosophila Wing , 2013, IEEE/ACM Transactions on Computational Biology and Bioinformatics.

[38]  Denis Thieffry,et al.  Qualitative Petri Net Modelling of Genetic Networks , 2006, Trans. Comp. Sys. Biology.

[39]  Paul W Sternberg,et al.  Intercellular coupling amplifies fate segregation during Caenorhabditis elegans vulval development , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[40]  Robert K. Brayton,et al.  Verifying Continuous Time Markov Chains , 1996, CAV.

[41]  Monika Heiner,et al.  Modelling and Analysis of Phase Variation in Bacterial Colony Growth , 2013, CMSB.

[42]  Masao Nagasaki,et al.  Simulation-based model checking approach to cell fate specification during Caenorhabditis elegans vulval development by hybrid functional Petri net with extension , 2009, BMC Systems Biology.

[43]  Monika Heiner,et al.  Steady state analysis of metabolic pathways using Petri nets , 2003, Silico Biol..

[44]  Kurt Jensen,et al.  Coloured Petri Nets and the Invariant-Method , 1981, Theor. Comput. Sci..

[45]  D. Gillespie.  Exact Stochastic Simulation of Coupled Chemical Reactions , 1977 .

[46]  Monika Heiner,et al.  Colored Petri nets to Model and Simulate Biological Systems , 2010, ACSD/Petri Nets Workshops.

[47]  Hanna Klaudel,et al.  Modeling Multi-valued Genetic Regulatory Networks Using High-Level Petri Nets , 2005, ICATPN.