Lattice-free models of directed cell motility

Authored by Michael J Plank, Matthew J Simpson, Carolyn Irons

Date Published: 2016

DOI: 10.1016/j.physa.2015.08.049

Sponsors: Australian Research Council (ARC)

Platforms: No platforms listed

Model Documentation: Other Narrative Mathematical description

Model Code URLs: Model code not found

Abstract

Directed cell migration often occurs when individual cells move in response to an external chemical stimulus. Cells can respond by moving in either the direction of increasing (chemoattraction) or decreasing (chemorepulsion) concentration. Many previous models of directed cell migration use a lattice-based framework where agents undergo a lattice-based random walk and the direction of nearest-neighbour motility events is biased in a preferred direction. Such lattice-based models can lead to unrealistic configurations of agents, since the agents always move on an artificial lattice structure which is never observed experimentally. We present a lattice-free model of directed cell migration that incorporates two key features. First, agents move on a continuous domain, with the possibility that there is some preferred direction of motion. Second, to be consistent with experimental observations, we enforce a crowding mechanism so that motility events that would lead to agent overlap are not permitted. We compare simulation data from the new lattice-free model with a more traditional lattice-based model. To provide additional insight into the lattice-free model, we construct an approximate conservation statement which corresponds to a nonlinear advection-diffusion equation in the continuum limit. The solution of this mean-field model compares well with averaged data from the individual-based model. (C) 2015 Elsevier B.V. All rights reserved.

Tags

proliferation Angiogenesis invasion Tumor-growth Automaton model Diffusion limit Adhesion Biased random-walk Random sequential adsorption Migration assay