Comparison of modelling approaches demonstrated for p16-mediated signalling pathway in higher eukaryotes

Quantitative modelling of biological systems using Petri net technologies has experienced renaissance in the past couple of decades. The overwhelming majority of these models is deterministic though underlying biological systems are usually at the mesoscopic level and small, rather than large, and employ sparse molecular structure. Sparse biological systems are accompanied by randomness due to low molecular density, intrinsic random nature of phenomena and noise in an experiment. On the other hand, biochemical reactions are inherently uncertain due to imprecision and vagueness of kinetic parameters. Stochastic methods are used to cope with randomness while fuzzy methods are developed to deal with uncertainty of biological systems, but there is lack of common voice among researchers regarding the best choice of modelling approach for a particular biological system. The main issues addressed in this paper are the choice between deterministic, stochastic and fuzzy parameters and aspects; that is, which modelling approach to follow to reach the realistic approximation of an underlying biological system, and how to measure parallels and discrepancies between different quantitative paradigms. To this end, we use Petri nets with hybrid, stochastic and fuzzy parameters to create quantitative model of p16-mediated signalling pathway in higher eukaryotes, perform deterministic, pure stochastic and fuzzy stochastic simulations to predict the behaviour of major molecular regulators of p16-mediated pathway. In the meanwhile, we show how uncertain kinetic parameters can be precisely approximated in terms of α cuts. Then we perform statistical analysis of simulation results to measure similarity between the three modelling approaches. The statistical analysis reveals significant deviations between deterministic, pure stochastic and fuzzy stochastic approaches for most of the biological components. Due to rather small size of underlying biological system, it turns out that fuzzy stochastic approach is the most appropriate for modelling of p16-mediated signalling pathway because it successfully deals with both randomness and uncertainty and produces quantitative results with biological relevance.