A spatially heterogeneous Gillespie algorithm modeling framework that enables individual molecule history and tracking
Authored by Justin Melunis, Uri Hershberg
Date Published: 2017
DOI: 10.1016/j.engappai.2016.09.010
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Abstract
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)-Orail(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.
Tags
activation
lymphocytes
stochastic modeling
immunology
Tracking
Plasma-membrane
Integrated particle system
Gillespie algorithm
Stim
Stromal interaction molecule-1
Operated calcium-entry
Ca2+ store
depletion
Positive selection
Stim1
Oligomerization
Influx