Invariance Kernel of Biological Regulatory Networks

The analysis of biological regulatory network leads to compute the set of the possible behaviors of the biological components. These behaviors are seen as trajectories, some of which are cyclic, and we are specifically interested in these cycles since they stand for stability. The set of cycles is given by the so-called invariance kernel of a biological regulatory network. This article 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. We use PolyLib library for the operations on the polyhedra. The method is explained by using the example of the bacterium Pseudomonas aeruginosa.