Stochastic simulation algorithms for Interacting Particle Systems

Interacting Particle Systems (IPSs) are used to model spatio-temporal stochastic systems in many disparate areas of science. We design an algorithmic framework that reduces IPS simulation to simulation of well-mixed Chemical Reaction Networks (CRNs). This framework minimizes the number of associated reaction channels and decouples the computational cost of the simulations from the size of the lattice. Decoupling allows our software to make use of a wide class of techniques typically reserved for well-mixed CRNs. We implement the direct stochastic simulation algorithm in the open source programming language Julia. We also apply our algorithms to several complex spatial stochastic phenomena. including a rock-paper-scissors game, cancer growth in response to immunotherapy, and lipid oxidation dynamics. Our approach aids in standardizing mathematical models and in generating hypotheses based on concrete mechanistic behavior across a wide range of observed spatial phenomena.

Automated summary

Interacting Particle Systems (IPSs) are simplified to well-mixed Chemical Reaction Networks (CRNs) using an algorithmic framework, allowing for a wide range of techniques to be applied. The approach is implemented in Julia and applied to complex spatial stochastic phenomena, aiding in standardizing mathematical models and generating hypotheses based on observed spatial phenomena.