Efficient modelling of yeast cell cycles based on multisite phosphorylation using coloured hybrid Petri nets with marking-dependent arc weights

With the increasing interest in systems biology to investigate the dynamics and behaviour of biological reaction networks, the scales as well as the complexities of the models under study grew rapidly and continue to grow at even faster pace. Traditional single-scale simulation methods become more and more impractical and inefficient to study these complex reaction networks. A daunting example of biological systems that falls into this category is the cell cycle regulation. In order to accurately model repeated cell growth and division, the corresponding reaction network should exhibit some sort of nonlinearity. One of the techniques able to reproduce this nonlinear behaviour is to include a series of phosphorylation and dephosphorylation reactions of the regulating proteins. However, this modelling approach results in two main challenges: the existence of components with different abundance of molecules and substantially larger biochemical networks in terms of number of reactions and species, with many of them exposing equivalent structure and behaviour. In this paper, we address these two issues by exploiting the modelling power of coloured hybrid Petri nets (HPNC). HPNC are a hybrid Petri net class that combines stochastic and deterministic events over a continuous time scale at the coloured level. Moreover, motivated by this case study we extend HPNC to include marking-dependent arc weights instead of just having constant values to define such weights.