Incorporating pushing in exclusion process models of cell migration

Abstract

The macroscale movement behaviour of a wide range of isolated migrating cells has been well characterised experimentally. Recently, attention has turned to understanding the behaviour of cells in crowded environments. In such scenarios it is possible for cells to interact mechanistically, inducing neighbouring cells to move in order to make room for their own movements or progeny. Although the behaviour of interacting cells has been modelled extensively through volume-exclusion processes, no models, thus far, have explicitly accounted for the ability of cells to actively displace each other.\n\nIn this work we consider both on and off-lattice volume-exclusion position-jump processes in which cells are explicitly allowed to induce movements in their near neighbours in order to create space for themselves (which we refer to as pushing). From these simple individual-level representations we derive continuum partial differential equations for the average occupancy of the domain. We find that, for limited amounts of pushing, the comparison between the averaged individual-level simulations and the population-level model is nearly as good as in the scenario without pushing but, that for larger and more complicated pushing events the assumptions used to derive the population-level model begin to break down. Interestingly, we find that, in the on-lattice case, the diffusion coefficient of the population-level model is increased by pushing, whereas, for the particular off-lattice model that we investigate, the diffusion coefficient is reduced. We conclude therefore, that it is important to consider carefully the appropriate individual-level model to use when representing complex cell-cell interactions such as pushing.