Modelling Disease - Drug Networks with Petri Nets

Abstract

Quantitative modelling of biological systems with Petri nets has undergone a renaissance over the past two decades. In spite of ever-growing numbers of models, it is still a question whether such models are biologically relevant. Despite the fact that most of the biological processes are mesoscopic in scale, the majority of models uses deterministic predictions, which cannot quantify uncertainties and randomness inherent in such biological processes. Choice between deterministic, stochastic and fuzzy parameters and aspects; that is, what modelling approach to use to approximate biological systems to the desired relevance, and how to measure the parallels and discrepancies between modelling paradigms, are the main questions addressed in this work. We use Petri nets with discrete, continuous, hybrid, stochastic and fuzzy extensions and parameters to exemplify our approach. For the case study of Spinal Motor Neuron production network, the statistical analysis reveals significant deviations between simulation results collected from three modelling approaches. Since the underlying biological system is at the mesoscopic-scale, we conclude that fuzzy stochastic approach produces quantitative results with the most biological relevance. © 2023 IEEE.