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Stochastic concurrent constraint programming and differential equations. (English) Zbl 1279.92031
Aldini, Alessandro (ed.) et al., Proceedings of the fifth workshop on quantitative aspects of programming languages (QAPL 2007), Braga, Portugal, March 24–25, 2007. Amsterdam: Elsevier. Electronic Notes in Theoretical Computer Science 190, No. 3, 27-42 (2007).
Summary: We tackle the problem of relating models of systems (mainly biological systems) based on stochastic process algebras (SPA) with models based on differential equations. We define a syntactic procedure that translates programs written in stochastic concurrent constraint programming (sCCP) into a set of ordinary differential equations (ODE), and also the inverse procedure translating ODEs into sCCP programs. For the class of biochemical reactions, we show that the translation is correct w.r.t. the intended rate semantics of the models. Finally, we show that the translation does not generally preserve the dynamical behavior, giving a list of open research problems in this direction.
For the entire collection see [Zbl 1275.68011].

MSC:
92C42 Systems biology, networks
68Q85 Models and methods for concurrent and distributed computing (process algebras, bisimulation, transition nets, etc.)
34A99 General theory for ordinary differential equations
Software:
PEPA
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[1] Alur, R.; Courcoubetis, C.; Halbwachs, N.; Henzinger, T.A.; Ho, P.-H.; Nicollin, X.; Olivero, A.; Sifakis, J.; Yovine, S., The algorithmic analysis of hybrid systems, Theoretical computer science, 138, 1, 3-34, (1995) · Zbl 0874.68206
[2] Bortolussi, L., Stochastic concurrent constraint programming, () · Zbl 1279.92031
[3] L. Bortolussi. Constraint-based approaches to stochastic dynamics of biological systems. PhD thesis, PhD in Computer Science, University of Udine, 2007. In preparation. Available on request from the author
[4] Bortolussi, L.; Policriti, A., Modeling biological systems in concurrent constraint programming, () · Zbl 1144.92001
[5] L. Bortolussi and A. Policriti Relating stochastic process algebras and differential equations for biological modeling. Proceedings of PASTA 2006, 2006
[6] ()
[7] Calder, M.; Gilmore, S.; Hillston, J., Modelling the influence of rkip on the erk signalling pathway using the stochastic process algebra pepa, Transactions on computational systems biology, 4230, 1-23, (2006)
[8] L. Cardelli. From Processes to ODEs by Chemistry. Draft, 2006
[9] L. Cardelli. On process rate semantics. draft, 2006 · Zbl 1133.68054
[10] Cornish-Bowden, A., Fundamentals of chemical kinetics, (2004), Portland Press
[11] Elowitz, M.B.; Leibler, S., A syntetic oscillatory network of transcriptional regulators, Nature, 403, 335-338, (2000)
[12] Gillespie, D., The chemical Langevin equation, Journal of chemical physics, 113, 1, 297-306, (2000)
[13] Gillespie, D.; Petzold, L., System modelling in cellular biology, Numerical simulation for biochemical kinetics, (2006), MIT Press, chapter
[14] Gillespie, D.T., Exact stochastic simulation of coupled chemical reactions, J. of physical chemistry, 81, 25, (1977)
[15] Hillston, J., A compositional approach to performance modelling, (1996), Cambridge University Press
[16] J. Hillston. Fluid flow approximation of pepa models. In Proceedings of the Second International Conference on the Quantitative Evaluation of Systems (QEST05), 2005
[17] Kitano, H., Foundations of systems biology, (2001), MIT Press
[18] Kitano, H., Computational systems biology, Nature, 420, 206-210, (2002)
[19] Norris, J.R., Markov chains, (1997), Cambridge University Press · Zbl 0873.60043
[20] Priami, C., Stochastic π-calculus, The computer journal, 38, 6, 578-589, (1995)
[21] Rao, C.V.; Arkin, A.P., Stochastic chemical kinetics and the quasi-steady state assumption: application to the Gillespie algorithm, Journal of chemical physics, 118, 11, 4999-5010, (March 2003)
[22] Regev, A.; Shapiro, E., Cellular abstractions: cells as computation, Nature, 419, (2002)
[23] Saraswat, V.A., Concurrent constraint programming, (1993), MIT press · Zbl 1002.68026
[24] Wilkinson, Darren J., Stochastic modelling for systems biology, (2006), Chapman & Hall · Zbl 1099.92004
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