Cell invasion with proliferation mechanisms motivated by time-lapse data

Abstract

Cell invasion involves a population of cells which are motile and proliferative. Traditional
discrete models of proliferation involve agents depositing daughter agents on nearest-
neighbor lattice sites. Motivated by time-lapse images of cell invasion, we propose and analyze two new discrete proliferation models in the context of an exclusion process with an
undirected motility mechanism. These discrete models are related to a family of reaction-
diffusion equations and can be used to make predictions over a range of scales appropriate for interpreting experimental data. The new proliferation mechanisms are biologically
relevant and mathematically convenient as the continuum-discrete relationship is more
robust for the new proliferation mechanisms relative to traditional approaches.