Article

Hybrid systems and biology: continuous and discrete modeling for systems biology

Authors:

Luca Bortolussi,

Alberto PolicritiAuthors Info & Claims

SFM'08: Proceedings of the Formal methods for the design of computer, communication, and software systems 8th international conference on Formal methods for computational systems biology

Pages 424 - 448

Published: 02 June 2008 Publication History

Abstract

Hybrid Systems are dynamical systems presenting both discrete and continuous evolution. Hybrid Automata are a formal model for hybrid systems, originally proposed to study embedded systems, where a discrete control acts on a continuously changing environment.

The presence of both discrete and continuous dynamics makes this formalism appealing also for modeling biological systems. However, the situation in this case is subtler, as there is no natural separation into discrete and continuous components. No surprise, then, that hybrid automata have been used in systems biology in rather different ways. Some approaches, like the description of biological switches, concentrate on the use of model-checking routines. Other applications, like the switching between continuous and discrete/stochastic simulation, focus on the exploitation of the interplay between discreteness and continuity in order to reduce the computational burden of numerical simulation, yet maintaining an acceptable precision.

We will survey the use of hybrid automata in systems biology, through a series of cases studies that we deem interesting and paradigmatic.

References

[1]

Alur, R., Belta, C., Ivančić, F.: Hybrid modeling and simulation of biomolecular networks. In: Di Benedetto, M.D., Sangiovanni-Vincentelli, A.L. (eds.) HSCC 2001. LNCS, vol. 2034, pp. 19-32. Springer, Heidelberg (2001)

Digital Library

[2]

Alur, R., Dill, D.L.: A theory of timed automata. Theoretical Computer Science 126(2), 183-235 (1994)

Digital Library

[3]

Batt, G., Belta, C.: Model checking genetic regulatory networks with applications to synthetic biology. Technical Report 2006-IR-0030, CISE Tech. Rep., Boston University (2006)

[4]

Batt, G., Belta, C., Weiss, R.: Model checking liveness properties of genetic regulatory networks. In: Proceedings of TACAS, pp. 323-338 (2007)

Digital Library

[5]

Blossey, R., Cardelli, L., Phillips, A.: A compositional approach to the stochastic dynamics of gene networks. T. Comp. Sys. Biology, pp. 99-122 (2006)

Digital Library

[6]

Bujorianu, M.L., Lygeros, J.: General stochastic hybrid systems: Modeling and optimal control. In: Proceedings of 43rd IEEE Conference on Decision and Control (CDC 2004), pp. 182-187 (2004)

[7]

Brihaye, T., Michaux, C., Rivière, C., Troestler, C.: On O-Minimal Hybrid Systems. In: Alur, R., Pappas, G.J. (eds.) HSCC 2004. LNCS, vol. 2993, pp. 219-233. Springer, Heidelberg (2004)

[8]

Bortolussi, L.: Stochastic concurrent constraint programming. In: Proceedings of 4th International Workshop on Quantitative Aspects of Programming Languages, QAPL 2006. ENTCS, vol. 164, pp. 65-80 (2006)

[9]

Bortolussi, L.: Constraint-based approaches to stochastic dynamics of biological systems. PhD thesis, PhD in Computer Science, University of Udine (preparation 2007)

[10]

Bortolussi, L., Policriti, A.: Stochastic concurrent constraint programming and differential equations. In: Proceedings of QAPL 2007 (2007)

[11]

Bortolussi, L., Policriti, A.: Hybrid approximation of stochastic concurrent constraint programming. In: IFAC 2008 (2008)

[12]

Bortolussi, L., Policriti, A.: Modeling biological systems in stochastic concurrent constraint programming. Constraints 13(1) (2008)

Digital Library

[13]

Casagrande, A., Mysore, V., Piazza, C., Mishra, B.: Independent dynamics hybrid automata in systems biology. In: Proceedings of the First International Conference on Algebraic Biology (AB 2005), November 2005, pp. 61-73. Universal Academy Press, Inc, Tokyo, Japan (2005)

[14]

Casagrande, A., Piazza, C., Mishra, B.: Semi-Algebraic Constant Reset Hybrid Automata - SACoRe. In: Proceedings of the 44rd Conference on Decision and Control and European Control Conference (CDC-ECC 2005), Seville, Spain, December 2005, pp. 678-683. IEEE Computer Society Press, Los Alamitos (2005)

[15]

de Jong, H.: Modeling and simulation of genetic regulatory systems: a literature review. J. Comput. Biol. 9(1), 67-103 (2002)

[16]

Elowitz, M.B., Leibler, S.: A syntetic oscillatory network of transcriptional regulators. Nature 403, 335-338 (2000)

[17]

Emerson, E.A.: Temporal and Modal Logic. In: van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science, vol. B, pp. 995-1072 (1990)

Digital Library

[18]

Gillespie, D.T.: A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J. of Computational Physics 22 (1976)

[19]

Gillespie, D.T.: Exact stochastic simulation of coupled chemical reactions. J. of Physical Chemistry 81(25) (1977)

[20]

Henzinger, T.A.: The theory of hybrid automata. In: LICS 1996: Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science (1996)

Digital Library

[21]

Henzinger, M.R., Henzinger, T.A., Kopke, P.W.: Computing simulations on finite and infinite graphs. In: Proceedings of the Thirty-Sixth Annual Symposium on Foundations of Computer Science (FOCS 1995), Washington, DC, USA, p. 453 (1995)

Digital Library

[22]

Hillston, J.: Fluid flow approximation of pepa models. In: Proceedings of the Second International Conference on the Quantitative Evaluation of Systems (QEST 2005) (2005)

Digital Library

[23]

Henzinger, T.A., Kopke, P.W.: State Equivalences for Rectangular Hybrid Automata. In:Montanari, U., Sassone, V. (eds.) Proc. of Int. Conference on Concurrency Theory (Concur 1996), vol. 1119, pp. 530-545 (1996)

Digital Library

[24]

Hardy, S., Robillard, P.N.: Modeling and simulation of molecular biology systems using petri nets: Modeling goals of various approaches. Journal of Bioinformatics and Computational Biology 2(4), 619-637 (2004)

[25]

Kopke, P.W.: The Theory of Rectangular Hybrid Automata. PhD thesis, Faculty of the Graduate School, Cornell University, Advisor - T. A. Henzinger (1996)

Digital Library

[26]

Lafferriere, G., Pappas, G.J., Sastry, S.: O-Minimal Hybrid Systems. Mathematics of Control, Signals, and Systems 13, 1-21 (2000)

[27]

Neogi, N.A.: Dynamic partitioning of large discrete event biological systems for hybrid simulation and analysis. In: Alur, R., Pappas, G.J. (eds.) HSCC 2004. LNCS, vol. 2993, pp. 463-476. Springer, Heidelberg (2004)

[28]

Piazza, C., Antoniotti, M., Mysore, V., Policriti, A., Winkler, F., Mishra, B.: Algorithmic algebraic model checking i: Challenges from systems biology. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, pp. 5-19. Springer, Heidelberg (2005)

Digital Library

[29]

Puri, A., Varaiya, P.: Decidability of hybrid systems with rectangular differential inclusions. In: Dill, D.L. (ed.) CAV 1994. LNCS, vol. 818, pp. 95-104. Springer, Heidelberg (1994)

Digital Library

[30]

Ross, S.M.: Stochastic Processes. Wiley, New York (1996)

[31]

Saraswat, V.A.: Concurrent Constraint Programming. MIT Press, Cambridge (1993)

Digital Library

[32]

Wilkinson, D.J.: Stochastic Modelling for Systems Biology. Chapman and Hall, Boca Raton (2006)

Cited By

Herranz JLaguillaumie FRífols C(2011)Relations between semantic security and anonymity in identity-based encryptionInformation Processing Letters10.1016/j.ipl.2011.02.002111:10(453-460)Online publication date: 1-Apr-2011
https://dl.acm.org/doi/10.1016/j.ipl.2011.02.002
Bortolussi LPolicriti A(2010)Hybrid dynamics of stochastic programsTheoretical Computer Science10.1016/j.tcs.2010.02.008411:20(2052-2077)Online publication date: 1-Apr-2010
https://dl.acm.org/doi/10.1016/j.tcs.2010.02.008
Ciocchetta FHillston J(2009)Bio-PEPATheoretical Computer Science10.1016/j.tcs.2009.02.037410:33-34(3065-3084)Online publication date: 1-Aug-2009
https://dl.acm.org/doi/10.1016/j.tcs.2009.02.037
Show More Cited By

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cover image Guide Proceedings

SFM'08: Proceedings of the Formal methods for the design of computer, communication, and software systems 8th international conference on Formal methods for computational systems biology

June 2008

524 pages

ISBN:3540688927

Editors:
Marco Bernardo
Università di Urbino "Carlo Bo", Istituto di Scienze e Tecnologie dell'Informazione, Urbino, Italy
,
Pierpaolo Degano
Università di Pisa, Dipartimento di Informatica, Pisa, Italy
,
Gianluigi Zavattaro
Università di Bologna, Dipartimento di Scienze dell'Informazione, Bologna, Italy

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University Bologna: University Bologna

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 02 June 2008

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Cited By

Herranz JLaguillaumie FRífols C(2011)Relations between semantic security and anonymity in identity-based encryptionInformation Processing Letters10.1016/j.ipl.2011.02.002111:10(453-460)Online publication date: 1-Apr-2011
https://dl.acm.org/doi/10.1016/j.ipl.2011.02.002
Bortolussi LPolicriti A(2010)Hybrid dynamics of stochastic programsTheoretical Computer Science10.1016/j.tcs.2010.02.008411:20(2052-2077)Online publication date: 1-Apr-2010
https://dl.acm.org/doi/10.1016/j.tcs.2010.02.008
Ciocchetta FHillston J(2009)Bio-PEPATheoretical Computer Science10.1016/j.tcs.2009.02.037410:33-34(3065-3084)Online publication date: 1-Aug-2009
https://dl.acm.org/doi/10.1016/j.tcs.2009.02.037
Casagrande APiazza CPolicriti A(2009)Discrete Semantics for Hybrid AutomataDiscrete Event Dynamic Systems10.1007/s10626-009-0082-719:4(471-493)Online publication date: 1-Dec-2009
https://dl.acm.org/doi/10.1007/s10626-009-0082-7

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