From Petri Nets to Differential Equations - An Integrative Approach for Biochemical Network Analysis

Abstract. We report on the results of an investigation into the integration of Petri nets and ordinary differential equations (ODEs) for the modelling and analysis of biochemical networks, and the application of our approach to the model of the influence of the Raf Kinase Inhibitor Protein (RKIP) on the Extracellular signal Regulated Kinase (ERK) signalling pathway. We show that analysis based on a discrete Petri net model of the system can be used to derive the sets of initial concentrations required by the corresponding continuous ordinary differential equation model, and no other initial concentrations produce meaningful steady states. Altogether, this paper represents a tutorial in step-wise modelling and analysis of larger models as well as in structured design of ODEs. 1 Motivation Classical, i.e. time-less discrete Petri nets combine an intuitive modelling style with well-founded analysis techniques. It is for this reason that they are widely used in various application areas, w...

• Type: Conference
• Year: 2006
• Where: APN
• Authors: David Gilbert, Monika Heiner
• Keywords: APN 2006, Artificial Intelligence, Biochemical Networks, Discrete Petri Nets, Petri Nets