Modeling cellular behavior with hybrid automata: Bisimulation and collapsing

Marco Antoniotti, Bhubaneswar Mishra, Carla Piazza, Alberto Policriti, Marta Simeoni

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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/Matlabtm). 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.

Original languageEnglish (US)
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
EditorsCorrado Priami
PublisherSpringer Verlag
Pages57-74
Number of pages18
ISBN (Print)3540006052, 9783540006053
DOIs
StatePublished - Jan 1 2003
Event1st International Workshop on Computational Methods in Systems Biology, CMSB 2003 - Rovereto, Italy
Duration: Feb 24 2003Feb 26 2003

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2602
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other1st International Workshop on Computational Methods in Systems Biology, CMSB 2003
CountryItaly
CityRovereto
Period2/24/032/26/03

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ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Antoniotti, M., Mishra, B., Piazza, C., Policriti, A., & Simeoni, M. (2003). Modeling cellular behavior with hybrid automata: Bisimulation and collapsing. In C. Priami (Ed.), Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (pp. 57-74). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2602). Springer Verlag. https://doi.org/10.1007/3-540-36481-1_6