Qualitative analysis and simulation of nonlinear dynamical models of gene regulatory networks

Abstract

A popular way of modelling gene regulatory networks is to designthe models as if the genes were acting directly on each other.Genes are activated or inhibited by transcription factors whichare direct gene products. The action of a transcription factor ona gene is modelled as a sigmoid around a certain thresholdconcentration. A transcription factor may act on several geneswith equal or different thresholds. The combined effect ofseveral transcription factors on a gene is generally assumed toobey Boolean-like composition rules. A mathematical challengerelated to such network models is to analyse the behaviour in thenarrow domains in phase space where at least one variable isclose to one of its thresholds. This paper summarizes someresults that are necessary and useful for a sound and completeimplementation of an automated analyzer designed for generegulatory networks with steep sigmoids under the biologicallyreasonable assumption that each transcription factor onlyregulates one gene at each of its thresholds. Then, the paperoutlines the design of an algorithm tailored for such analyzer.