A Graphical Approach for Hybrid Modelling of Intracellular Calcium Dynamics Based on Coloured Hybrid Petri Nets

Abstract

Intracellular calcium dynamics plays an important role in influencing the outcome of many cellular processes. Constructing and simulating computational models to investigate this biological behaviour are intricate and require the interplay of stochastic and deterministic processes as there are multiple spatial and temporal scales involved. Therefore, many hybrid models have been devised to analyse intracellular calcium dynamics. However, all these models are based on reaction–diffusion equations which are not intuitive for many bioscientists. In contrast, Petri nets do offer an intuitive and graphical approach to model biological processes. To deal with new challenges due to the advances in dynamical modelling, Petri nets have been extended in different directions. Coloured hybrid Petri nets are one of these extensions that support hybrid modelling of complex biological systems using a parametrised language and abstract high-level notations permitting various timing features. In this paper, we present a graphical hybrid model of intracellular calcium dynamics based on coloured hybrid Petri nets. The proposed model can easily be adapted by adjusting a few parameters. Moreover, we illustrate model operations by conducting three simulation experiments in the two-dimensional space. We use Snoopy, a tool to construct and execute qualitative and quantitative Petri nets, to implement the proposed model.