Spatial structure arising from neighbour-dependent bias in collective cell movement
Authored by Richard Law, Michael J Plank, Rachelle N Binny, Alex James, Parvathi Haridas, Matthew J Simpson
Date Published: 2016
DOI: 10.7717/peerj.1689
Sponsors:
Royal Society of New Zealand Marsden Fund
Platforms:
MATLAB
Model Documentation:
Other Narrative
Mathematical description
Model Code URLs:
https://dfzljdn9uc3pi.cloudfront.net/2016/1689/1/MATLAB_code_IBM.zip
Abstract
Mathematical models of collective cell movement often neglect the
effects of spatial structure, such as clustering, on the population
dynamics. Typically, they assume that individuals interact with one
another in proportion to their average density (the mean-field
assumption) which means that cell - cell interactions occurring over
short spatial ranges are not accounted for. However, in vitro cell
culture studies have shown that spatial correlations can play an
important role in determining collective behaviour. Here, we take a
combined experimental and modelling approach to explore how
individual-level interactions give rise to spatial structure in a moving
cell population. Using imaging data from in vitro experiments, we
quantify the extent of spatial structure in a population of 3T3
fibroblast cells. To understand how this spatial structure arises, we
develop a lattice-free individual-based model (IBM) and simulate cell
movement in two spatial dimensions. Our model allows an individual's
direction of movement to be affected by interactions with other cells in
its neighbourhood, providing insights into how directional bias
generates spatial structure. We consider how this behaviour scales up to
the population level by using the IBM to derive a continuum description
in terms of the dynamics of spatial moments. In particular, we account
for spatial correlations between cells by considering dynamics of the
second spatial moment (the average density of pairs of cells). Our
numerical results suggest that the moment dynamics description can
provide a good approximation to averaged simulation results from the
underlying IBM. Using our in vitro data, we estimate parameters for the
model and show that it can generate similar spatial structure to that
observed in a 3T3 fibroblast cell population.
Tags
Migration
proliferation
models
invasion
growth
Mechanisms
Equations
Contact inhibition
Moment dynamics
Point-processes