Discrete and continuous mathematical models of sharp-fronted collective cell migration and invasion.

Autor:	Simpson MJ; School of Mathematical Sciences, Queensland University of Technology, Brisbane, Queensland, Australia., Murphy KM; School of Mathematical Sciences, Queensland University of Technology, Brisbane, Queensland, Australia., McCue SW; School of Mathematical Sciences, Queensland University of Technology, Brisbane, Queensland, Australia., Buenzli PR; School of Mathematical Sciences, Queensland University of Technology, Brisbane, Queensland, Australia.
Jazyk:	angličtina
Zdroj:	Royal Society open science [R Soc Open Sci] 2024 May 15; Vol. 11 (5), pp. 240126. Date of Electronic Publication: 2024 May 15 (Print Publication: 2024).
DOI:	10.1098/rsos.240126
Abstrakt:	Mathematical models describing the spatial spreading and invasion of populations of biological cells are often developed in a continuum modelling framework using reaction-diffusion equations. While continuum models based on linear diffusion are routinely employed and known to capture key experimental observations, linear diffusion fails to predict well-defined sharp fronts that are often observed experimentally. This observation has motivated the use of nonlinear degenerate diffusion; however, these nonlinear models and the associated parameters lack a clear biological motivation and interpretation. Here, we take a different approach by developing a stochastic discrete lattice-based model incorporating biologically inspired mechanisms and then deriving the reaction-diffusion continuum limit. Inspired by experimental observations, agents in the simulation deposit extracellular material, which we call a substrate , locally onto the lattice, and the motility of agents is taken to be proportional to the substrate density. Discrete simulations that mimic a two-dimensional circular barrier assay illustrate how the discrete model supports both smooth and sharp-fronted density profiles depending on the rate of substrate deposition. Coarse-graining the discrete model leads to a novel partial differential equation (PDE) model whose solution accurately approximates averaged data from the discrete model. The new discrete model and PDE approximation provide a simple, biologically motivated framework for modelling the spreading, growth and invasion of cell populations with well-defined sharp fronts. Open-source Julia code to replicate all results in this work is available on GitHub. Competing Interests: We declare we have no competing interests. (© 2024 The Authors.)
Databáze:	MEDLINE
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