Some investigations concerning the CTMC and the ODE model derived from Bio-PEPA

Ciochetta, F., Degasperi, A., Hillston, J. and Calder, M. (2009) Some investigations concerning the CTMC and the ODE model derived from Bio-PEPA. Electronic Notes in Theoretical Computer Science, 229(1), pp. 145-163. (doi: 10.1016/j.entcs.2009.02.010)

Abstract

<p>Bio-PEPA is a recently defined language for the modelling and analysis of biochemical networks. It supports an abstract style of modelling, in which discrete levels of concentration within a species are considered instead of individual molecules. A finer granularity for the system corresponds to a smaller concentration step size and therefore to a greater number of concentration levels. This style of model is amenable to a variety of different analysis techniques, including numerical analysis based on a CMTC with states reflecting the levels of concentration.</p> <p>In this paper we present a formal definition of the CTMC with levels derived from a Bio-PEPA system. Furthermore we investigate the relationship between this CTMC and the system of ordinary differential equations (ODEs) derived from the same model. Using Kurtz's theorem, we show that the set of ODEs derived from the Bio-PEPA model is able to capture the limiting behaviour of the CTMC obtained from the same system. Finally, we define an empirical methodology to find the granularity of the Bio-PEPA system for which the ODE and the CTMC with levels are in a good agreement. The proposed definition is based on a notion of distance between the two models. We demonstrate our approach on a model of the Repressilator, a simple biochemical network with oscillating behaviour.</p>

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Degasperi, Mr Andrea and Calder, Professor Muffy
• Authors: Ciochetta, F., Degasperi, A., Hillston, J., and Calder, M.
• Subjects: Q Science > QH Natural history > QH345 Biochemistry; Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Computing Science
• Journal Name: Electronic Notes in Theoretical Computer Science
• Journal Abbr.: ENTCS
• Publisher: Elsevier Science
• ISSN: 1571-0661
• ISSN (Online): 1571-0661
• Published Online: 20 February 2009
• Copyright Holders: Copyright © 2009 Elsevier B.V. All rights reserved.
• First Published: First published in Electronic Notes in Theoretical Computer Science 229(1):145-163
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher.