Exploiting stochastic Petri nets with fuzzy parameters to predict efficient drug combinations for Spinal Muscular Atrophy

Randomness and uncertainty are two major problems one faces while modeling nonlinear dynamics of molecular systems. Stochastic and fuzzy methods are used to cope with these problems, but there is no consensus among researchers regarding which method should be used when. This is because the areas of applications of these methods are overlapping with differences in opinions. In the present work, we demonstrate how to use stochastic Petri nets with fuzzy parameters to manage random timing of biomolecular events and deal with the uncertainty of reaction rates in biological networks. The approach is demonstrated through a case study of simulation-based prediction of efficient drug combinations for spinal muscular atrophy, for which we obtained very promising results. The feasibility of the approach is assessed through statistical analysis of deterministic, pure stochastic and fuzzy stochastic simulation results. Statistical analysis reveals that all three models produce significantly different results which, when coupled with the fact that fuzzy stochastic model provides the closest approximation of underlying biological network, successfully coping not only with randomness but also uncertainty, suggests that fuzzy stochastic model is the most appropriate choice for the present case study. The proposed approach can be adapted or extended to other biological networks.