Event Driven Approach for Simulating Gene Regulation Networks Marco Berardi 1,2 and Nicoletta Del Buono 2, ⋆ 1 IRSA-CNR, via F. De Blasio,5 70132 Bari, Italy 2 Dipartimento di Matematica, Universit` a degli Studi di Bari Aldo Moro, via E.Orabona 4, 70125 Bari, Italy {marco.berardi,nicoletta.delbuono}@uniba.it Abstract. Gene regulatory networks can be described by continuous models in which genes are acting directly on each other. Genes are ac- tivated or inhibited by transcription factors which are direct gene prod- ucts. The action of a transcription factor on a gene is modeled as a binary on-off response function around a certain threshold concentra- tion. Different thresholds can regulate the behaviors of genes, so that the combined effect on a gene is generally assumed to obey Boolean-like composition rules. Analyzing the behavior of such network model is a challenging task in mathematical simulation, particularly when at least one variable is close to one of its thresholds, called switching domains. In this paper, we briefly review a particular class model for gene regu- lation networks, namely, the piece-wise linear model and we present an event-driven method to analyze the motion in switching domains. Keywords: Gene regulatory networks, piecewise-linear differential equation, event-driven method. 1 Introduction Many physical phenomena are described by discontinuous time-dependent prob- lems in which relations between the state variables are subject to irregularities or discontinuities. The study of discontinuous dynamical systems has been under- taken for several decades and has produced several theoretical results and a wide range of applications in various fields as Biological Sciences, Medicine and Engi- neering. Particular importance is covered by the mathematical models described by systems of differential equations characterized by discontinuities that occur when the state variable reaches a surface, said switching surface. Among the different kind of discontinuity there is the well known discontinuity of Filippov type [17,22,15], where the vector field is discontinuous on a switching region of the space. These systems have an interesting dynamic behavior, since the state of the system can be forced to remain on the discontinuity surface, in order to ⋆ This paper has been supported by the project “Modelli Matematici Discontinui per l’Analisi delle Reti di Geni: Applicazioni al Diabete”, sponsored by Fondazione Cassa di Risparmio di Puglia-FCRP (Anno 2013). B. Murgante et al. (Eds.): ICCSA 2014, Part VI, LNCS 8584, pp. 415–425, 2014. c ⃝ Springer International Publishing Switzerland 2014