title: Spatial structure arising from neighbour-dependent bias in collective cell movement.
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.
authors.affiliation: School of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand; Te Pūnaha Matatini, New Zealand; Landcare Research-Manaaki Whenua, Lincoln, New Zealand.
authors.forename: Rachelle N
authors.initials: RN
authors.lastname: Binny
authors.affiliation: Institute of Health and Biomedical Innovation, Queensland University of Technology , Brisbane , Australia.
authors.forename: Parvathi
authors.initials: P
authors.lastname: Haridas
authors.affiliation: School of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand; Te Pūnaha Matatini, New Zealand.
authors.forename: Alex
authors.initials: A
authors.lastname: James
authors.affiliation: York Centre for Complex Systems Analysis, Ron Cooke Hub, University of York , York , United Kingdom.
authors.forename: Richard
authors.initials: R
authors.lastname: Law
authors.affiliation: Institute of Health and Biomedical Innovation, Queensland University of Technology, Brisbane, Australia; School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia.
authors.forename: Matthew J
authors.initials: MJ
authors.lastname: Simpson
authors.affiliation: School of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand; Te Pūnaha Matatini, New Zealand.
authors.forename: Michael J
authors.initials: MJ
authors.lastname: Plank
keywords: Cell migration; Collective movement; Directed movement; Individual-based model; Spatial correlations; Spatial moment dynamics