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Relating continuous and discrete PEPA models of signalling pathways. (English) Zbl 1151.68038
Summary: 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. 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 \(\text{PEPA} +\Pi \), 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.

MSC:
68Q85 Models and methods for concurrent and distributed computing (process algebras, bisimulation, transition nets, etc.)
92C37 Cell biology
92C40 Biochemistry, molecular biology
Software:
PEPA
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