Hybrid representation and simulation of stiff biochemical networks

Abstract

With the progress of computational modelling and simulation of biochemical networks, there is a need to manage multi-scale models, which may contain species or reactions at different scales. A visual language such as Petri nets can provide a valuable tool for representing and simulating such stiff biochemical networks. In this paper, we introduce a new Petri nets class, generalised hybrid Petri nets (GHPNbio), tailored to the specific needs for modelling and simulation of biochemical networks. It provides rich modelling and simulation functionalities by combining all features of continuous Petri nets and generalised stochastic Petri nets, extended by three types of deterministic transition. Herein, we focus on modelling and simulation of stiff biochemical networks, in which some reactions are represented and simulated stochastically, while others are carried out deterministically. Additionally, two related simulation algorithms are presented, supporting static (off-line) partitioning and dynamic (on-line) partitioning. This paper comes with a fully fledged implementation, supporting the introduced net class as well as the discussed simulation algorithms. We discuss three case studies, demonstrating the use of GHPNbio and the efficiency of the developed simulation algorithms.