A spatially heterogeneous Gillespie algorithm modeling framework that enables individual molecule history and tracking

Stochastic models allow investigators to simulate reactions in a discrete way that can account for fluctuations that are otherwise ignored within a deterministic approach. Integrated particle system (IPS) models are a form of stochastic model that take spatial distributions, environmental factors, and agent migration into consideration. Unlike agent based models (ABM), IPS models only rely on a set of general reactions to describe the interactions of molecules/entities, allowing for an easy cause-effect connection between macroscopic phenomena and microscopic behavior. However, IPS models currently do not track individual agents or apply manipulations to individual agent behavior based on their specific location or their individual history. Therefore, IPS models cannot incorporate agent-based manipulations and tracking while still relying on a set of basic assumptions that are needed to easily connect emergent phenomena to simplistic microscopic behaviors. Here we propose an IPS modeling framework where we convert the exact Gillespie algorithm into a 2 dimensional lattice space that allows for environmental factors where molecules can move stochastically, generating an overall heterogeneous molecule distribution. Individual molecules can be tracked without describing the rules of interaction for each specific individual molecule, forming a tracked IPS (TIPS) modeling framework. However, since each individual molecule is tagged, agent-based manipulations and the ability to alter agent behavior due to history can be incorporated into TIPS, allowing one to model biological systems that would otherwise have to rely on a pure ABM. We apply the TIPS modeling framework to STIM1(stromal interaction molecule 1)-Orai1(calcium release-activated calcium channel protein 1) binding and motion, in T cells as a result of T cell receptor activation a key component of the calcium response within lymphocytes that leads to the adaptive response of T cells in an immune response. Within this biological setting we show that observed patterns of reduced motion following activation can be explained by a diffusion trap coming from changes in the environment of interaction without any real change in the molecules movement rates.