Abstract
Motivated by in vitro time–lapse images of ovarian cancer spheroids inducing mesothelial cell clearance, the traditional agent–based model of cell migration, based on simple volume exclusion, was extended to include the possibility that a cell seeking to move into an occupied location may push the resident cell, and any cells neighbouring it, out of the way to occupy that location. In traditional discrete models of motile cells with volume exclusion such a move would be aborted. We introduce a new shoving mechanism which allows cells to choose the direction to shove cells that expends the least amount of shoving effort (to account for the likely resistance of cells to being pushed). We call this motility rule ‘smart shoving’. We examine whether agent–based simulations of different shoving mechanisms can be distinguished on the basis of single realisations and averages over many realisations. We emphasise the difficulty in distinguishing cell mechanisms from cellular automata simulations based on snap–shots of cell distributions, site–occupancy averages and the evolution of the number of cells of each species averaged over many realisations. This difficulty suggests the need for higher resolution cell tracking.
Highlights
Data Availability Statement: All relevant data are within the paper
We have analysed a new mechanism for cell motility, which we call ‘smart shoving’, whereby a cell makes motility choices that minimise the shoving effort expended
We have examined the multi-species interaction of invading cells with cells initially present, where each cell species can either shove neighbouring cells out of the way or where a choice to move to an occupied site leads to abortion of the move
Summary
A motivating example for our approach is the experimental work reported by Iwanicki et al [9] and Davidowitz et al [10] They studied an in vitro invasion process in which small clusters of ovarian cancer cells placed on top of an epithelial cell monolayer (grown on a suitable tissue culture substrate) force their way into the epithelial cell layer. Yates et al [17] implemented a single species shoving mechanism, where each cell can shove K neighbouring cells in order to move one space into a chosen occupied site They found good agreement between their agent–based model and the numerical solution of the continuum limit mean–field PDE for all K 2 [0, 4], though there was a slight increase in the error as K increased. We emphasise the need for caution in choosing a particular shoving mechanism to model cell behaviour, since differences between mechanisms may not be revealed by particular experimental measurements
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