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bioRxiv · 10.1101/267708

Spatial moment description of birth-death-movementprocesses incorporating the effects of crowding andobstacles

Surendran, A.·Plank, M.·Simpson, M. J.
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Abstract

Birth-death-movement processes, modulated by interactions between individuals, are fundamental to many cell biology processes. A key feature of the movement of cells within in vivo environments are the interactions between motile cells and stationary obstacles. Here we propose a multi-species model of individual-level motility, proliferation and death. This model is a spatial birth-death-movement stochastic process, a class of individual-based model (IBM) that is amenable to mathematical analysis. We present the IBM in a general multi-species framework, and then focus on the case of a population of motile, proliferative agents in an environment populated by stationary, non-proliferative obstacles. To analyse the IBM, we derive a system of spatial moment equations governing the evolution of the density of agents and the density of pairs of agents. This approach avoids making the usual mean-field assumption so that our models can be used to study the formation of spatial structure, such as clustering and aggregation, and to understand how spatial structure influences population-level outcomes. Overall the spatial moment model provides a reasonably accurate prediction of the system dynamics, including important effects such as how varying the properties of the obstacles leads to different spatial patterns in the population of agents.

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Surendran, A., Plank, M., Simpson, M. J.. 2018-02-18. Spatial moment description of birth-death-movementprocesses incorporating the effects of crowding andobstacles. https://doi.org/10.1101/267708

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