RT Journal Article
SR Electronic
T1 Continuum approximations for lattice-free multi-species models of collective cell migration
JF bioRxiv
FD Cold Spring Harbor Laboratory
SP 119586
DO 10.1101/119586
A1 Oleksii M Matsiaka
A1 Catherine J Penington
A1 Ruth E Baker
A1 Matthew J Simpson
YR 2017
UL http://biorxiv.org/content/early/2017/03/22/119586.abstract
AB AbstractCell migration within tissues involves the interaction of many cells from distinct subpopulations. In this work, we present a discrete model of collective cell migration where the motion of individual cells is driven by random forces, short range repulsion forces to mimic crowding, and longer range attraction forces to mimic adhesion. This discrete model can be used to simulate a population of cells that is composed of K ≥ 1 distinct subpopulations. To analyse the discrete model we formulate a hierarchy of moment equations that describe the spatial evolution of the density of agents, pairs of agents, triplets of agents, and so forth. To solve the hierarchy of moment equations we introduce two forms of closure: (i) the mean field approximation, which effectively assumes that the distributions of individual agents are independent; and (ii) a moment dynamics description that is based on the Kirkwood superposition approximation. The moment dynamics description provides an approximate way of incorporating spatial patterns, such as agent clustering, into the continuum description. Comparing the performance of the two continuum descriptions confirms that both perform well when adhesive forces are sufficiently weak. In contrast, the moment dynamics description outperforms the mean field model when adhesive forces are sufficiently large. This is a first attempt to provide an accurate continuum description of a lattice-free, multi-species model of collective cell migration.