Collective Cell Behaviour with Neighbour-Dependent Proliferation, Death and Directional Bias

Authored by Michael J Plank, Rachelle N Binny, Alex James

Date Published: 2016

DOI: 10.1007/s11538-016-0222-9

Sponsors: Royal Society of New Zealand

Platforms: No platforms listed

Model Documentation: Other Narrative Mathematical description

Model Code URLs: Model code not found

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.

Tags

Migration models movement invasion Biology Predator-prey dynamics Forces Spatial moment equations Contact inhibition Guidance