Quantitative Modelling with Using Petri nets: A Case Study for the Treatment of Spinal Muscular Atrophy

Randomness and uncertainty are deeply entangled with bioinformatics. Indeed, both concepts are inherited characteristics of biological systems that essentially affect interactions between biological components. Although there exist numerous stochastic and fuzzy methods dealing with these problems, it is not quite sure when which method can be used. In the present work, we model random timing of biomolecular events and uncertainty of biomolecular reaction rates in terms of stochastic Petri nets with fuzzy parameters. The approach is demonstrated through the case study of identification of optimal drug combinations for Spinal Muscular Atrophy. The model of the problem has been created in accordance with deterministic, pure stochastic and fuzzy stochastic approaches. Comparison of deterministic, pure stochastic and fuzzy stochastic approaches shows that all three approaches lead to significantly different results. Since fuzzy stochastic model leads to the best approximation of underlying biological network, it has been concluded that fuzzy stochastic model is the most appropriate modelling approach for the present case study. Keywords: SMN2 expression, fuzzy stochastic Petri nets, quantitative modelling, simulation, validation.