Stochastic Hybrid Automata with delayed transitions to model biochemical systems with delays

Giulio Caravagna, Alberto D'Onofrio, Marco Antoniotti, Giancarlo Mauri

Research output: Contribution to journalArticle

Abstract

To study the effects of a delayed immune-response on the growth of an immunogenic neoplasm we introduce Stochastic Hybrid Automata with delayed transitions as a representation of hybrid biochemical systems with delays. These transitions abstractly model unknown dynamics for which a constant duration can be estimated, i.e. a delay. These automata are inspired by standard Stochastic Hybrid Automata, and their semantics is given in terms of Piecewise Deterministic Markov Processes. The approach is general and can be applied to systems where (i) components at low concentrations are modeled discretely (so to retain their intrinsic stochastic fluctuations), (ii) abundant component, e.g., chemical signals, are well approximated by mean-field equations (so to simulate them efficiently) and (iii) missing components are abstracted with delays. Via simulations we show in our application that interesting delay-induced phenomena arise, whose quantification is possible in this new quantitative framework.

Original languageEnglish
Pages (from-to)19-34
Number of pages16
JournalInformation and Computation
Volume236
DOIs
Publication statusPublished - 2014

Keywords

  • Biochemical systems with delays
  • Delayed transitions
  • Piecewise Deterministic Markov Processes
  • Stochastic Hybrid Automata

ASJC Scopus subject areas

  • Information Systems
  • Computational Theory and Mathematics
  • Theoretical Computer Science
  • Computer Science Applications

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