A free boundary model of epithelial dynamics.

Author: 

Baker, R
Parker, A
Simpson, M

Publication Date: 

19 December 2018

Journal: 

Journal of theoretical biology

Last Updated: 

2019-08-18T18:01:03.87+01:00

DOI: 

10.1016/j.jtbi.2018.12.025

abstract: 

In this work we analyse a one-dimensional, cell-based model of an epithelial sheet. In the model, cells interact with their nearest neighbouring cells and move deterministically. Cells also proliferate stochastically, with the rate of proliferation specified as a function of the cell length. This mechanical model of cell dynamics gives rise to a free boundary problem. We construct a corresponding continuum-limit description where the variables in the continuum limit description are expanded in powers of the small parameter 1/N, where N is the number of cells in the population. By carefully constructing the continuum limit description we obtain a free boundary partial differential equation description governing the density of the cells within the evolving domain, as well as a free boundary condition that governs the evolution of the domain. We show that care must be taken to arrive at a free boundary condition that conserves mass. By comparing averaged realisations of the cell-based model with the numerical solution of the free boundary partial differential equation, we show that the new mass-conserving boundary condition enables the coarse-grained partial differential equation model to provide very accurate predictions of the behaviour of the cell-based model, including both evolution of the cell density, and the position of the free boundary, across a range of interaction potentials and proliferation functions in the cell based model.

Symplectic id: 

954924

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article