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

Gavagnin, Enrico and Ford, Matthew J and Mort, Richard L and Rogers, Tim and Yates, Christian A (2018) The invasion speed of cell migration models with realistic cell cycle time distributions. Journal of Theoretical Biology. ISSN 0022-5193

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Abstract

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.

Item Type: Journal Article
Journal or Publication Title: Journal of Theoretical Biology
Additional Information: Copyright © 2018. Published by Elsevier Ltd.
Uncontrolled Keywords: /dk/atira/pure/subjectarea/asjc/2700
Subjects:
Departments: Faculty of Health and Medicine > Biomedical & Life Sciences
ID Code: 127715
Deposited By: ep_importer_pure
Deposited On: 28 Sep 2018 15:08
Refereed?: Yes
Published?: Published
Last Modified: 27 Feb 2020 04:32
URI: https://eprints.lancs.ac.uk/id/eprint/127715

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