In this paper we present a formalism based on stochastic automata to describe the stochastic dynamics of signal transduction networks that are specified by rule-sets. Our formalism gives a modular description of the underlying stochastic process, in the sense that it is a composition of smaller units, agent-views. The view of an agent is an automaton that identifies all local modification changes of that agent (internal state modifications, binding and unbinding), but also those of interacting agents, which are tested within the same rule. We show how to represent the generator matrix of the underlying Markov process of the whole rule-set as Kronecker sums of the rate matrices belonging to individual view-automata. In the absence of birth the automata are finite, since the number of different contexts in which one agent can appear in a rule-set is finite. We illustrate the framework by an example that is related to cellular signaling events.
Stochastic semantics of signaling as a composition of agent-view automata / Koeppl, H., Petrov, T.. - In: ELECTRONIC NOTES IN THEORETICAL COMPUTER SCIENCE. - ISSN 1571-0661. - 272:1(2011), pp. 3-17. (Stochastic Semantics of Signaling as a Composition of Agent-view Automata Author links open overlay panelHeinz Koeppl 1, Tatjana Petrov Show more Add to Mendeley Share Cite https://doi.org/10.1016/j.entcs.2011.04.002 Get rights and content Under a Creative Commons license open access Abstract In this paper we present a formalism based on stochastic automata to describe the stochastic dynamics of signal transduction networks that are specified by rule-sets. Our formalism gives a modular description of the underlying stochastic process, in the sense that it is a composition of smaller units, agent-views. The view of an agent is an automaton that identifies all local modification changes of that agent (internal state modifications, binding and unbinding), but also those of interacting agents, which are tested within the same rule. We show how to represent the generator matrix of the underlying Markov process of the whole rule-set as Kronecker sums of the rate matrices belonging to individual view-automata. In the absence of birth the automata are finite, since the number of different contexts in which one agent can appear in a Previous articleNext article Keywords Cell signalingContinuous-time Markov chainStochastic automata composition View PDF References [1] C. Baier, B. Haverkort, H. Hermanns, J.-P. Katoen Model-checking algorithms for continuous-time Markov chains IEEE Transactions on Software Engineering, 29 (2003), p. 2003 Google Scholar [2] N.M. Borisov, N.I. Markevich, J.B. Hoek, B.N. Kholodenko Signaling through receptors and scaffolds: Independent interactions reduce combinatorial complexity Biophys J, 89 (2005), pp. 951-966 View PDFView articleCrossRefView in ScopusGoogle Scholar [3] P. Buchholz, P. Kemper Kronecker based matrix representations for large Markov models Validation of Stochastic Systems, Lecture Notes in Computer Science, vol. 2925 (2004), pp. 256-295 CrossRefView in ScopusGoogle Scholar [4] J.-P. Changeux, S.J. Edelstein Allosteric mechanisms of signal transduction Science, 308 (2005), pp. 1424-1428 CrossRefView in ScopusGoogle Scholar [5] H. Conzelmann, J. Saez-Rodriguez, T. Sauter, B.N. Kholodenko, E.D. Gilles A domain oriented approach to the reduction of combinatorial complexity in signal transduction networks BMC Syst Biol, 7 (2006) Google Scholar [6] Danos, V., J. Feret, W. Fontana and J. Krivine, Abstract interpretation of cellular signalling networks, 4905, 2008, pp. 42–58. Google Scholar [7] V. Danos, C. Laneve Core formal molecular biology Theoretical Computer Science, 325 (2003), pp. 69-110 Google Scholar [8] J. Feret, V. Danos, J. Krivine, R. Harmer, W. Fontana Internal coarse-graining of molecular systems Proc. Natl. Acad. Sci. USA, 106 (2009), pp. 6453-6458 CrossRefView in ScopusGoogle Scholar [9] Feret, J., T. A. Henzinger, H. Koeppl and T. Petrov, Lumpability abstractions of rule-based systems, MeCBIC (2010), pp. 142–161. Google Scholar [10] Feret, J., H. Koeppl and T. Petrov, Stochastic fragments: A framework for the exact reduction of the stochastic semantics of rule-based models, International Journal of Software and Informatics in press (2010). Google Scholar [11] D.T. Gillespie Exact stochastic simulation of coupled chemical reactions J Phys Chem, 81 (1977), pp. 2340-2361 CrossRefView in ScopusGoogle Scholar [12] P. Kemper Numerical analysis of superposed GSPNs IEEE T Software Eng, 9 (1996), pp. 615-628 View in ScopusGoogle Scholar [13] T. Mori, D.R. Willams, M.O. Bryne, X. Qin, M. Egli, H.S. Mchaourab, P.L. Stewart, C.H. Johnson Elucidating the ticking of an in vitro circadian clockwork PLoS Biol, 5 (2007), pp. 841-853 View in ScopusGoogle Scholar [14] M. Nakajima, K. Imai, H. Ito, T. Nishiwaki, Y. Murayama, H. Iwasaki, T. Oyama, T. Kondo Reconstitution of circadian oscillation of cyanobacterial KaiC phosphorylation in vitro Science, 308 (2005), pp. 414-415 CrossRefView in ScopusGoogle Scholar [15] T. Nishiwaki, Y. Satomi, Y. Kitayama, K. Terauchi, R. Kiyohara, T. Takao, T. Kondo A sequential program of dual phosphorylation of KaiC as a basis for circadian rhythm in cyanobacteria EMBO J, 26 (2007), pp. 4029-4037 CrossRefView in ScopusGoogle Scholar [16] Plateau, B., On the stochastic structure of parallelism and synchronization models for distributed algorithms, 13, 1985, pp. 147–154. Google Scholar [17] C. Salazar, T. Höfer Multisite protein phosphorylation – from molecular mechanisms to kinetic models FEBS J, 276 (2009), pp. 3177-3198 CrossRefView in ScopusGoogle Scholar [18] R.G. Smock, L.M. Gierasch Sending signals dynamically Science, 324 (2009), pp. 198-203 CrossRefView in ScopusGoogle Scholar [19] C.F. Van Loan The ubiquitous kronecker product Comput Appl Math, 123 (2000), pp. 85-100 Google Scholar [20] J.S. van Zon, D.K. Lubensky, P.R.H. Altena An allosteric model of circadian KaiC phosphorylation Proc Natl Acad Sci USA, 104 (2007), pp. 7420-7425 CrossRefView in ScopusGoogle Scholar [21] C.T. Walsh Posttranslation Modification of Proteins: Expanding Natureʼs Inventory Roberts and Co. Publisher (2006) Google Scholar [22] V. Wolf Modelling of biochemical reactions by stochastic automata networks Electron. Notes Theor. Comput. Sci., 171 (2007), pp. 197-208 View PDFView articleView in ScopusGoogle Scholar Cited by (0) 1 Heinz Koeppl acknowledges the support from the Swiss National Science Foundation, grant no. 200020-117975/1. Tatjana Petrov acknowledges the support from SystemsX.ch, the Swiss Initiative in Systems Biology. Copyright © 2011 Elsevier B.V. Part of special issue Proceedings of the 1st International Workshop on Static Analysis and Systems Biology (SASB 2010) Perpignan, France 2010) [10.1016/j.entcs.2011.04.002].
Stochastic semantics of signaling as a composition of agent-view automata
Petrov, T.
2011-01-01
Abstract
In this paper we present a formalism based on stochastic automata to describe the stochastic dynamics of signal transduction networks that are specified by rule-sets. Our formalism gives a modular description of the underlying stochastic process, in the sense that it is a composition of smaller units, agent-views. The view of an agent is an automaton that identifies all local modification changes of that agent (internal state modifications, binding and unbinding), but also those of interacting agents, which are tested within the same rule. We show how to represent the generator matrix of the underlying Markov process of the whole rule-set as Kronecker sums of the rate matrices belonging to individual view-automata. In the absence of birth the automata are finite, since the number of different contexts in which one agent can appear in a rule-set is finite. We illustrate the framework by an example that is related to cellular signaling events.Pubblicazioni consigliate
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