Taming the complexity of biochemical models through bisimulation and collapsing: Theory and practice

M. Antoniotti, C. Piazza, A. Policriti, M. Simeoni, Bhubaneswar Mishra

Research output: Contribution to journalArticle

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 approach, 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 it 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 automaton taming the complexity in terms of states whose number depends on the attained level of approximation.

Original languageEnglish (US)
Pages (from-to)45-67
Number of pages23
JournalTheoretical Computer Science
Volume325
Issue number1
DOIs
StatePublished - Sep 28 2004

Fingerprint

Collapsing
Bisimulation
Biological systems
Automata
Biological Systems
Hybrid Automata
S-system
Temporal logic
Trace
Octave
Ordinary differential equations
Algebraic Differential Equations
Differential equations
Qualitative Analysis
Several Variables
Automation
Temporal Logic
Software Tools
Trajectories
Model

Keywords

  • Biochemical models
  • Bisimulation
  • Collapsing
  • Hybrid automata

ASJC Scopus subject areas

  • Computational Theory and Mathematics

Cite this

Taming the complexity of biochemical models through bisimulation and collapsing : Theory and practice. / Antoniotti, M.; Piazza, C.; Policriti, A.; Simeoni, M.; Mishra, Bhubaneswar.

In: Theoretical Computer Science, Vol. 325, No. 1, 28.09.2004, p. 45-67.

Research output: Contribution to journalArticle

Antoniotti, M. ; Piazza, C. ; Policriti, A. ; Simeoni, M. ; Mishra, Bhubaneswar. / Taming the complexity of biochemical models through bisimulation and collapsing : Theory and practice. In: Theoretical Computer Science. 2004 ; Vol. 325, No. 1. pp. 45-67.
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