Title: Invariance kernel of Biological Regulatory Networks

Authors: Jamil Ahmad, Olivier Roux

Addresses: IRCCyN UMR CNRS 6597, BP 92101, 1 rue de la Noe, 44321 Nantes Cedex 3, France. ' IRCCyN UMR CNRS 6597, BP 92101, 1 rue de la Noe, 44321 Nantes Cedex 3, France

Abstract: The analysis of Biological Regulatory Network (BRN) leads to the computing of the set of the possible behaviours of the biological components. These behaviours are seen as trajectories and we are specifically interested in cyclic trajectories since they stand for stability. The set of cycles is given by the so-called invariance kernel of a BRN. This paper presents a method for deriving symbolic formulae for the length, volume and diameter of a cylindrical invariance kernel. These formulae are expressed in terms of delay parameters expressions and give the existence of an invariance kernel and a hint of the number of cyclic trajectories.

Keywords: BRN; biological regulatory networks; gene networks; hybrid modelling; delays; HyTech; PolyLib; cycles; invariance kernel; bioinformatics; cyclic trajectories.

DOI: 10.1504/IJDMB.2010.035900

International Journal of Data Mining and Bioinformatics, 2010 Vol.4 No.5, pp.553 - 570

Published online: 08 Oct 2010 *

Full-text access for editors Full-text access for subscribers Purchase this article Comment on this article