The invasion speed of cell migration models with realistic cell cycle time distributions.

Autor: Gavagnin E; Department of Mathematical Sciences University of Bath, Claverton Down, Bath, BA2 7AY, UK. Electronic address: e.gavagnin@bath.ac.uk., Ford MJ; Centre for Research in Reproduction and Development McGill University, Montréal, H3G 1Y6, Québec., Mort RL; Division of Biomedical and Life Sciences Faculty of Health and Medicine Lancaster University, Bailrigg, Lancaster LA1 4YG, UK., Rogers T; Department of Mathematical Sciences University of Bath, Claverton Down, Bath, BA2 7AY, UK., Yates CA; Department of Mathematical Sciences University of Bath, Claverton Down, Bath, BA2 7AY, UK.
Jazyk: angličtina
Zdroj: Journal of theoretical biology [J Theor Biol] 2019 Nov 21; Vol. 481, pp. 91-99. Date of Electronic Publication: 2018 Sep 14.
DOI: 10.1016/j.jtbi.2018.09.010
Abstrakt: Cell proliferation is typically incorporated into stochastic mathematical models of cell migration by assuming that cell divisions occur after an exponentially distributed waiting time. Experimental observations, however, show that this assumption is often far from the real cell cycle time distribution (CCTD). Recent studies have suggested an alternative approach to modelling cell proliferation based on a multi-stage representation of the CCTD. In this paper we investigate the connection between the CCTD and the speed of the collective invasion. We first state a result for a general CCTD, which allows the computation of the invasion speed using the Laplace transform of the CCTD. We use this to deduce the range of speeds for the general case. We then focus on the more realistic case of multi-stage models, using both a stochastic agent-based model and a set of reaction-diffusion equations for the cells' average density. By studying the corresponding travelling wave solutions, we obtain an analytical expression for the speed of invasion for a general N-stage model with identical transition rates, in which case the resulting cell cycle times are Erlang distributed. We show that, for a general N-stage model, the Erlang distribution and the exponential distribution lead to the minimum and maximum invasion speed, respectively. This result allows us to determine the range of possible invasion speeds in terms of the average proliferation time for any multi-stage model.
(Copyright © 2018 Elsevier Ltd. All rights reserved.)
Databáze: MEDLINE
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