title: Collective Cell Behaviour with Neighbour-Dependent Proliferation, Death and Directional Bias.
abstract: Collective cell migration and proliferation are integral to tissue repair, embryonic development, the immune response and cancer. Central to collective cell migration and proliferation are interactions among neighbouring cells, such as volume exclusion, contact inhibition and adhesion. These individual-level processes can have important effects on population-level outcomes, such as growth rate and equilibrium density. We develop an individual-based model of cell migration and proliferation that includes these interactions. This is an extension of a previous model with neighbour-dependent directional bias to incorporate neighbour-dependent proliferation and death. A deterministic approximation to this individual-based model is derived using a spatial moment dynamics approach, which retains information about the spatial structure of the cell population. We show that the individual-based model and spatial moment model match well across a range of parameter values. The spatial moment model allows insight into the two-way interaction between spatial structure and population dynamics that cannot be captured by traditional mean-field models.
authors.affiliation: School of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand.|Te Pūnaha Matatini, A New Zealand Centre of Research Excellence, Auckland, New Zealand.|Landcare Research, Lincoln, New Zealand.
authors.forename: Rachelle N
authors.initials: RN
authors.lastname: Binny
authors.affiliation: School of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand.|Te Pūnaha Matatini, A New Zealand Centre of Research Excellence, Auckland, New Zealand.
authors.forename: Alex
authors.initials: A
authors.lastname: James
authors.affiliation: School of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand. michael.plank@canterbury.ac.nz.|Te Pūnaha Matatini, A New Zealand Centre of Research Excellence, Auckland, New Zealand. michael.plank@canterbury.ac.nz.
authors.forename: Michael J
authors.identifier: 0000-0002-7539-3465
authors.initials: MJ
authors.lastname: Plank
mesh_terms: D002448:Cell Adhesion / Q000502:physiology; D016923:Cell Death / Q000502:physiology; D002465:Cell Movement / Q000502:physiology*; D049109:Cell Proliferation / Q000502:physiology*; D003260:Contact Inhibition / Q000502:physiology; D006801:Humans; D055641:Mathematical Concepts; D008954:Models, Biological
keywords: Cell adhesion; Contact inhibition; Crowding effects; Pair correlation function; Spatial moment dynamics