Modeling biological systems with delays in Bio-PEPA

Giulio Caravagna
(Dipartimento di Informatica, Universita di Pisa, italy.)
Jane Hillston
(Laboratory for Foundations of Computer Science, The University of Edinburgh, Scotland.)

Delays in biological systems may be used to model events for which the underlying dynamics cannot be precisely observed, or to provide abstraction of some behavior of the system resulting more compact models. In this paper we enrich the stochastic process algebra Bio-PEPA, with the possibility of assigning delays to actions, yielding a new non-Markovian process algebra: Bio-PEPAd. This is a conservative extension meaning that the original syntax of Bio-PEPA is retained and the delay specification which can now be associated with actions may be added to existing Bio-PEPA models. The semantics of the firing of the actions with delays is the delay-as-duration approach, earlier presented in papers on the stochastic simulation of biological systems with delays. These semantics of the algebra are given in the Starting-Terminating style, meaning that the state and the completion of an action are observed as two separate events, as required by delays. Furthermore we outline how to perform stochastic simulation of Bio-PEPAd systems and how to automatically translate a Bio-PEPAd system into a set of Delay Differential Equations, the deterministic framework for modeling of biological systems with delays. We end the paper with two example models of biological systems with delays to illustrate the approach.

In Gabriel Ciobanu and Maciej Koutny: Proceedings Fourth Workshop on Membrane Computing and Biologically Inspired Process Calculi 2010 (MeCBIC 2010), Jena, Germany, 23 August 2010, Electronic Proceedings in Theoretical Computer Science 40, pp. 85–101.
Published: 30th October 2010.

ArXived at: bibtex PDF

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