Simulation of multicellular populations with Petri nets and genome scale intracellular networks

Abstract We present a new distributed architecture allowing simulation of living cells in spatial structures. Each cell is represented with a Quasi-Steady State Petri Net that integrates dynamic regulatory network expressed with a Petri net and Genome Scale Metabolic Network (GSMN) where linear programming is used to explore the steady-state metabolic flux distributions in the whole-cell model. The combination of Petri net and GSMN has already been used in simulations of single cells, but we present an extension to the model and an architecture to simulate populations of millions of interacting cells organised in spatial structures which can be used to model tumour growth or formation of tuberculosis lesions. The crucial element of this solution is the ability of cells to communicate by producing and detecting substances such as cytokines and chemokines. This ability is modeled by allowing cells to share tokens in places called communicators. To make the simulation of such a huge model possible we use the Spark framework and organise the computation in an agent-based “think like a vertex” fashion as in Pregel-like systems. In the cluster we introduce a special kind of per node caching to speed up computation of the steady-state metabolic flux. We demonstrate capabilities of the new architecture by simulating communication of liver cells through FGF19 cytokine during the homeostatic response to cholesterol burst. Our approach can be used for mechanistic modelling of the emergence of multicellular system behaviour from interaction between genome and environment.