SystemC Implementation of Stochastic Petri Nets for Simulation and Parameterization of Biological Networks
Authors: 
Nicola Bombieri, Silvia Scaffeo, Antonio Mastrandrea, Simone Caligola, Tommaso Carlucci, Franco Fummi, Carlo Laudanna, Gabriela Constantin, Rosalba GiugnoAuthors Info & Claims
Nicola Bombieri, Silvia Scaffeo, Antonio Mastrandrea, Simone Caligola, Tommaso Carlucci, Franco Fummi, Carlo Laudanna, Gabriela Constantin, Rosalba GiugnoAuthors Info & ClaimsArticle No.: 31, Pages 1 - 20
Abstract
Model development and simulation of biological networks is recognized as a key task in Systems Biology. Integrated with in vitro and in vivo experimental data, network simulation allows for the discovery of the dynamics that regulate biological systems. Stochastic Petri Nets (SPNs) have become a widespread and reference formalism to model metabolic networks thanks to their natural expressiveness to represent metabolites, reactions, molecule interactions, and simulation randomness due to system fluctuations and environmental noise. In the literature, starting from the network model and the complete set of system parameters, there exist frameworks that allow for dynamic system simulation. Nevertheless, they do not allow for automatic model parameterization, which is a crucial task to identify, in silico, the network configurations that lead the model to satisfy specific temporal properties. To cover such a gap, this work first presents a framework to implement SPN models into SystemC code. Then, it shows how the framework allows for automatic parameterization of the networks. The user formally defines the network properties to be observed and the framework automatically extrapolates, through Assertion-based Verification (ABV), the parameter configurations that satisfy such properties. We present the results obtained by applying the proposed framework to model the complex metabolic network of the purine metabolism. We show how the automatic extrapolation of the system parameters allowed us to simulate the model under different conditions, which led to the understanding of behavioral differences in the regulation of the entire purine network. We also show the scalability of the approach through the modeling and simulation of four biological networks, each one with different structural characteristics.
References
[1]
Luca Albergante, Jon Timmis, Lynette Beattie, and Paul M. Kaye. 2013. A Petri net model of granulomatous inflammation: Implications for IL-10 mediated control of Leishmania donovani infection. PLoS Computational Biology 9, 11 (2013), e1003334.
[2]
Pavel Balazki, Klaus Lindauer, Jens Einloft, Jörg Ackermann, and Ina Koch. 2015. MONALISA for stochastic simulations of Petri net models of biochemical systems. BMC Bioinformatics 16, 1 (2015), 215.
[3]
Albert-Laszlo Barabasi and Zoltan N Oltvai. 2004. Network biology: Understanding the cell’s functional organization. Nature Reviews Genetics 5, 2 (2004), 101.
[4]
B. Behinaein, K. Rudie, and W. Sangrar. 2018. Petri net siphon analysis and graph theoretic measures for identifying combination therapies in cancer. IEEE/ACM Transactions on Computational Biology and Bioinformatics 15, 1 (2018), 231–243.
[5]
Nicola Bombieri, Rosario Distefano, Giovanni Scardoni, Franco Fummi, Carlo Laudanna, and Rosalba Giugno. 2014. Dynamic modeling and simulation of leukocyte integrin activation through an electronic design automation framework. In International Conference on Computational Methods in Systems Biology. Springer, 143–154.
[6]
N. Bombieri, F. Fummi, V. Guarnieri, G. Pravadelli, F. Stefanni, T. Ghasempouri, M. Lora, G. Auditore, and M. N. Marcigaglia. 2015. Reusing RTL assertion checkers for verification of SystemC TLM models. Journal of Electronic Testing: Theory and Applications (JETTA) 31, 2 (2015), 167–180.
[7]
N. Bombieri, F. Fummi, and G. Pravadelli. 2006. On the evaluation of transactor-based verification for reusing TLM assertions and testbenches at RTL. In Proc. of ACM/IEEE DATE, Vol. 1. 1–6.
[8]
M. Boulé and Z. Zilic. 2008. Generating Hardware Assertion Checkers: For Hardware Verification, Emulation, Post-fabrication Debugging and On-line Monitoring. Springer.
[9]
S. Caligola, T. Carlucci, F. Fummi, C. Laudanna, G. Constantin, N. Bombieri, and R. Giugno. 2019. Efficient simulation and parametrization of stochastic Petri nets in SystemC: A case study from systems biology. In Proc. of the 2019 Forum on Specification and Design Languages (FDL’19).
[10]
Yang Cao, Hong Li, and Linda Petzold. 2004. Efficient formulation of the stochastic simulation algorithm for chemically reacting systems. Journal of Chemical Physics 121, 9 (2004), 4059–4067.
[11]
Claudine Chaouiya. 2007. Petri net modelling of biological networks. Briefings in Bioinformatics 8, 4 (2007), 210–219.
[12]
Ming Chen and Ralf Hofestaedt. 2003. Quantitative Petri net model of gene regulated metabolic networks in the cell. In Silico Biology 3, 3 (2003), 347–365.
[13]
K.-T. Cheng and A. S. Krishnakumar. 1996. Automatic generation of functional vectors using the extended finite state machine model. ACM TODAES 1, 1 (1996), 57–79.
[14]
I.-Chun Chou, Harald Martens, and Eberhard O. Voit. 2006. Parameter estimation in biochemical systems models with alternating regression. Theoretical Biology and Medical Modelling 3, 1 (2006), 25.
[15]
D. Coati, R. Distefano, N. Bombieri, F. Fummi, M. Mirenda, C. Laudanna, and R. Giugno. 2016. A SystemC-based platform for assertion-based verification and mutation analysis in systems biology. 17th IEEE Latin-American Test Symposium (LATS’16), 159–164.
[16]
Claudionor-Nunes Coelho Jr. and Harry D. Foster. 2008. Assertion-Based Verification. Vol. 4. Springer.
[17]
R. Distefano, F. Fummi, C. Laudanna, N. Bombieri, and R. Giugno. 2015. A systemc platform for signal transduction modelling and simulation in systems biology. In Proc. of the ACM Great Lakes Symposium on VLSI (GLSVLSI’15), 233–236.
[18]
R. Distefano, N. Goncharenko, F. Fummi, R. Giugno, G. D. Badery, and N. Bombieri. 2016. SyQUAL: A platform for qualitative modelling and simulation of biological systems. In 2016 IEEE International High Level Design Validation and Test Workshop (HLDVT’16), 155–161.
[19]
Cristian Dittamo and Davide Cangelosi. 2009. Optimized parallel implementation of Gillespie’s first reaction method on graphics processing units. In International Conference on Computer Modeling and Simulation (ICCMS’09). IEEE, 156–161.
[20]
T. Eleftheriadis, G. Pissas, A. Karioti, G. Antoniadi, S. Golfinopoulos, V. Liakopoulos, A. Mamara, M. Speletas, G. Koukoulis, and I. Stefanidis. 2013. Uric acid induces caspase-1 activation, IL-1 secretion and P2X7 receptor dependent proliferation in primary human lymphocytes. Hippokratia 17, 2 (2013), 141.
[21]
Philippe Darondeau, Eric Badouel, and Luca Bernardinello. 2015. Petri Net Synthesis. Springer-Verlag, Berlin.
[22]
Jasmin Fisher and Thomas A. Henzinger. 2007. Executable cell biology. Nature Biotechnology 25 (2007), 1239–1249.
[23]
Hartmann Genrich, Robert Küffner, and Klaus Voss. 2001. Executable Petri net models for the analysis of metabolic pathways. International Journal on Software Tools for Technology Transfer (STTT) 3, 4 (2001), 394–404.
[24]
Daniel T. Gillespie. 1976. A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. Journal of Computational Physics 22, 4 (1976), 403–434.
[25]
Daniel T. Gillespie. 1977. Exact stochastic simulation of coupled chemical reactions. Journal of Physical Chemistry 81, 25 (1977), 2340–2361.
[26]
Gautam Goel, I.-Chun Chou, and Eberhard O. Voit. 2008. System estimation from metabolic time-series data. Bioinformatics 24, 21 (2008), 2505–2511.
[27]
Anja Hartmann and Falk Schreiber. 2015. Integrative analysis of metabolic models–from structure to dynamics. Frontiers in Bioengineering and Biotechnology 2 (2015), 91.
[28]
Monika Heiner, Mostafa Herajy, Fei Liu, Christian Rohr, and Martin Schwarick. 2012. Snoopy–a unifying Petri net tool. In Int. Conf. on Application and Theory of Petri Nets and Concurrency. Springer, 398–407.
[29]
Monika Heiner and Ina Koch. 2004. Petri net based model validation in systems biology. In ICATPN, Vol. 3099. Springer, 216–237.
[30]
Alexander Hoffmann, Andre Levchenko, Martin L. Scott, and David Baltimore. 2002. The IB-NF-B signaling module: Temporal control and selective gene activation. Science 298, 5596 (2002), 1241–1245.
[31]
M. Hucka, A. Finney, H. M. Sauro, H. Bolouri, J. C. Doyle, H. Kitano, A. P. Arkin, B. J. Bornstein, D. Bray, A. Cornish-Bowden, A. A. Cuellar, S. Dronov, E. D. Gilles, M. Ginkel, V. Gor, I. I. Goryanin, W. J. Hedley, T. C. Hodgman, J.-H. Hofmeyr, P. J. Hunter, N. S. Juty, J. L. Kasberger, A. Kremling, U. Kummer, N. Le Novre, L. M. Loew, D. Lucio, P. Mendes, E. Minch, E. D. Mjolsness, Y. Nakayama, M. R. Nelson, P. F. Nielsen, T. Sakurada, J. C. Schaff, B. E. Shapiro, T. S. Shimizu, H. D. Spence, J. Stelling, K. Takahashi, M. Tomita, J. Wagner, and J. Wang. 2003. The systems biology markup language (SBML): A medium for representation and exchange of biochemical network models. Bioinformatics 19, 4 (2003), 524–531. cited By 1920.
[32]
IEEE. 2017. Property Specification Language - PSL. https://standards.ieee.org/findstds/standard/1850-2010.html.
[33]
Hawoong Jeong, Sean P. Mason, A.-L. Barabási, and Zoltan N. Oltvai. 2001. Lethality and centrality in protein networks. Nature 411, 6833 (2001), 41.
[34]
Steffen Klamt, Julio Saez-Rodriguez, Jonathan A. Lindquist, Luca Simeoni, and Ernst D. Gilles. 2006. A methodology for the structural and functional analysis of signaling and regulatory networks. BMC Bioinformatics 7, 1 (2006), 56.
[35]
I. Koch. 2015. Petri nets in systems biology. Software and Systems Modeling 14, 2 (2015), 703–710.
[36]
L. Napione et al. 2009. On the use of stochastic Petri nets in the analysis of signal transduction pathways for angiogenesis process. In International Conference on Computational Methods in Systems Biology. Springer, 281–295.
[37]
Hiroshi Matsuno, Yukiko Tanaka, Hitoshi Aoshima, Mika Matsui, Satoru Miyano, et al. 2003. Biopathways representation and simulation on hybrid functional Petri net. In Silico Biology 3, 3 (2003), 389–404.
[38]
James M. McCollum, Gregory D. Peterson, Chris D. Cox, Michael L. Simpson, and Nagiza F. Samatova. 2006. The sorting direct method for stochastic simulation of biochemical systems with varying reaction execution behavior. Computational Biology and Chemistry 30, 1 (2006), 39–49.
[39]
Melody K. Morris, Julio Saez-Rodriguez, Peter K. Sorger, and Douglas A. Lauffenburger. 2010. Logic-based models for the analysis of cell signaling networks. Biochemistry 49, 15 (2010), 3216–3224.
[40]
Jacek Puchałka and Andrzej M. Kierzek. 2004. Bridging the gap between stochastic and deterministic regimes in the kinetic simulations of the biochemical reaction networks. Biophysical Journal 86, 3 (2004), 1357–1372.
[41]
G. Russo, M. Pennisi, R. Boscarino, and F. Pappalardo. 2018. Continuous Petri nets and microRNA analysis in melanoma. IEEE/ACM Transactions on Computational Biology and Bioinformatics 15, 5 (2018), 1492–1499.
[42]
Andrea Sackmann, Dorota Formanowicz, Piotr Formanowicz, Ina Koch, and Jacek Blazewicz. 2007. An analysis of the Petri net based model of the human body iron homeostasis process. Computational Biology and Chemistry 31, 1 (2007), 1–10.
[43]
Karsten Schmidt. 2005. Controllability of open workflow nets. In EMISA. 236–249.
[44]
Ralf Steuer and Bjorn H. Junker. 2009. Computational models of metabolism: Stability and regulation in metabolic networks. Advances in Chemical Physics 142 (2009), 105.
[45]
Synopsys Inc.2003. Assertion-Based Verification. White paper, http://www.synopsys.com.
[46]
Systems Biology - A portal suite for Systems Biology. 2019. Model Repositories. http://systems-biology.org/resources/model-repositories.
[47]
Vo Hong Thanh, Corrado Priami, and Roberto Zunino. 2014. Efficient rejection-based simulation of biochemical reactions with stochastic noise and delays. Journal of Chemical Physics 141, 13 (2014), 10B602_1.
[48]
Siren R. Veflingstad, Jonas Almeida, and Eberhard O. Voit. 2004. Priming nonlinear searches for pathway identification. Theoretical Biology and Medical Modelling 1, 1 (2004), 8.
[49]
L. Watanabe, T. Nguyen, M. Zhang, Z. Zundel, Z. Zhang, C. Madsen, N. Roehner, and C. Myers. 2019. IBIOSIM 3: A tool for model-based genetic circuit design. ACS Synthetic Biology 8, 7 (2019), 1560–1563. cited By 2.
[50]
Karsten Wolf. 2019. How Petri Net Theory Serves Petri Net Model Checking: A Survey. Springer, Berlin, 36–63.
[51]
Y. Abarbanel et al. 2000. FOCS–Automatic generation of simulation checkers from formal specifications. In Computer Aided Verification. Springer, 538–542.
[52]
Choujun Zhan and Lam F. Yeung. 2011. Parameter estimation in systems biology models using spline approximation. BMC Systems Biology 5, 1 (2011), 14.
Index Terms
- SystemC Implementation of Stochastic Petri Nets for Simulation and Parameterization of Biological Networks
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Publication History
Published: 29 May 2021
Accepted: 01 September 2020
Revised: 01 August 2020
Received: 01 January 2020
Published in TECS Volume 20, Issue 4
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