Abstract
Many biological systems can be modeled using systems of ordinary differential algebraic equations (e.g.,S-systems),thus allowing the study of their solutions and behavior automatically with suitable software tools (e.g.,PLAS, Octave/Matlab tm ).Usually,numerical solutions (traces or trajectories) for appropriate initial conditions are analyzed in order to infer significant properties of the biological systems under study. When several variables are involved and the traces span over a long interval of time,the analysis phase necessitates automation in a scalable and efficient manner. Earlier,we have advocated and experimented with the use of automata and temporal logics for this purpose (XS-systems and Simpathica) and here we continue our investigation more deeply.
We propose the use of hybrid automata and we discuss the use of the notions of bisimulation and collapsing for a “qualitative” analysis of the temporal evolution of biological systems. As compared with our previous proposal,hybrid automata allow maintenance of more information about the differential equations (S-system)than standard automata.The use of the notion of bisimulation in the definition of the projection operation (restrictions to a subset of “interesting”variables)makes possible to work with reduced automata satisfying the same formulae as the initial ones. Finally,the notion of collapsing is introduced to move toward still simpler and equivalent automata taming the complexity of the automata whose number of states depends on the level of approximation allowed.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
R. Alur, C. Belta, F. Ivancic, V. Kumar, M. Mintz, G.J. Pappas, H. Rubin, and J. Schug. Hybrid modeling and simulation of biomolecular networks.In Hybrid Systems: Computation and Control, volume 2034 of LNCS pages 19–22. Springer-Verlag, 2001.60, 62, 67
R. Alur, C. Courcoubetis, T.A. Henzinger, and P.H. Ho.Hybrid automata:An algorithmic approach to the specification and verification of hybrid systems.In R.L. Grossman, A. Nerode, A.P. Ravn, and H. Richel,editors, Hybrid Systems LNCS, pages 209–229. Springer-Verlag, 1992. 66
M. Antoniotti, F.C. Park, A. Policriti, N. Ugel, and B. Mishra. Foundations of a Query and Simulation System for the odeling of Biochemical and Biological Processes. In Proc. of the Pacific Symposium of Biocomputing (PSB’03) 2003. 58, 59
M. Antoniotti, A. Policriti, N. Ugel, and B. Mishra. XS-systems:extended S-systems and algebraic differential automata for modeling cellular behaviour.In Proc. of Int. Conference on High Performance Computing (HiPC’02) 2002. 58, 59, 60, 63, 64, 66, 71
M. Antoniotti, A. Policriti, N. Ugel, and B. Mishra. Model Building and Model Checking for Biological Processes.Cell Biochemistry and Biophysics 2003. To appear. 58
U.S. Bhalla. Data Base of Quatitative Cellular Signaling (DOQCS).Website at http://doqcs.ncbs.res.in/, 2001.58
R.W. Brockett. Dynamical systems and their associated automata. In Systems and Networks: Mathematical Theory and Applications, volume 77. Akademie-Verlag, Berlin, 1994. 59
E.M. Clarke, O. Grumberg, and D.A. Peled. Model checking IT Press, 1999. 63
E.M. Clarke and E.A. Emerson. Design and synthesis of synchronization skeletons using brancing time temporal logic. In Proc. Workshop Logic of Programs volume 131 of LNCS Springer, 1981. 68
M. Curti, P. Degano, C. Priami, and C.T. Baldari. Casualπ-calculus for biochemical modelling. DIT 02, University of Trento, 2002. 60
H. de Jong. Modeling and simulation of genetic regulatory systems:A literature review. DIT 4032, Inria, 2000.59
A. Dovier, C. Piazza, and A. Policriti. A fast bisimulation algorithm. In G. Berry, H. Comon, and A. Finkel, editors, Proc. of Int. Conference on Computer Aided Verification (CAV’01) volume 2102 of LNCS pages 79–90. Springer-Verlag, 2001. 70
M. Elowitz and S. Leibler. A synthetic oscillatory network of transcriptional regulators. Nature 403:335–338, 2000. 59, 65
E.A. Emerson. Temporal and modal logic. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science volume B, pages 995–1072. MIT Press, 1990. 62, 64
T.A. Henzinger. The theory of hybrid automata. In Proc. of IEEE Symposium on Logic in Computer Science (LICS’96) pages 278–292. IEEE Press, 1996. 67, 68
T.A. Henzinger, P.H. Ho, and H. Wong-Toi. HYTECH:A model checker for hybrid systems. International Journal on Software Tools for Technology Transfer 1(1–2):110–122, 1997. 67
J.E. Hopcroft and J.D. Ullman. Introduction to Automata Theory, Languages, and Computation Addison-Wesley, 1979.63
P.D. Karp, M. Riley, S. Paley, and A. Pellegrini-Toole. The etaCyc Database. Nucleic Acid Research 30(1):59, 2002.58
P.D. Karp, M. Riley, M. Saier, and S. Paley A. Pellegrini-Toole.The EcoCyc Database. Nucleic Acids Research 30(1):56, 2002.58
H. Kitano.Systems Biology:an Overview. Science 295:1662–1664, March 2002. 57
O. Müller and T. Stauner. Modelling and verification using linear hybrid automata. Mathematical and Computer Modelling of Dynamical Systems 6(1):71–89, 2000. 67
R. Paige, R.E. Tarjan, and R. Bonic. A linear time solution to the single function coarsest partition problem. Theoretical Computer Science 40:67–84, 1985.70
A. Regev, W. Silverman, and E. Shapiro. Representation and simulation of biochemical processes using the π-calculus process algebra. In Proc. of thePacific Symposium of Biocomputing (PSB’01) pages 459-70, 2003. 60
D. Shasha, A. Kouranov, L. Lejay, C. Chou, and G. Coruzzi. Combinatorial Design to study regulation by multiple input signals:A tool for parsimony in the post-genomics era. Plant Physiology 127:1590–1594, December 2001.59
E.O. Voit. Computational Analysis of Biochemical Systems. A Pratical Guide for Biochemists and Molecular Biologists Cambridge University Press, 2000. 60, 61, 65
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Antoniotti, M., Mishra, B., Piazza, C., Policriti, A., Simeoni, M. (2003). Modeling Cellular Behavior with Hybrid Automata: Bisimulation and Collapsing. In: Priami, C. (eds) Computational Methods in Systems Biology. CMSB 2003. Lecture Notes in Computer Science, vol 2602. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36481-1_6
Download citation
DOI: https://doi.org/10.1007/3-540-36481-1_6
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-00605-3
Online ISBN: 978-3-540-36481-8
eBook Packages: Springer Book Archive