Relating continuous and discrete PEPA models of signalling pathways

Nil Geisweiller, Jane Hillston, Marco Stenico

Research output: Contribution to journalArticlepeer-review

Abstract

PEPA and its semantics have recently been extended to model biological systems. In order to cope with massive quantities of processes (as is usually the case when considering biological reactions) the model is interpreted in terms of a small set of coupled ordinary differential equations (ODEs) instead of a large state space continuous time Markov chain (CTMC). So far the relationship between these two semantics of PEPA had not been established. This is the goal of the present paper. After introducing a new extension of PEPA, denoted PEPA+[Pi], that allows models to capture both mass action law and bounded capacity law cooperations, the relationship between these two semantics is demonstrated. The result relies on Kurtz's Theorem that expresses that a set of ODEs can be, in some sense, considered as the limit of pure jump Markov processes.
Original languageEnglish
Pages (from-to)97-111
Number of pages15
JournalTheoretical Computer Science
Volume404
Issue number1-2
DOIs
Publication statusPublished - Sep 2008

Keywords

  • Kurtz
  • PEPA
  • ODEs
  • CTMC

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