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The effect of domain growth on spatial correlations

Robert J. H. Ross, C. A. Yates, R. E. Baker
doi: https://doi.org/10.1101/041491
Robert J. H. Ross
1Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG
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C. A. Yates
2Centre for Mathematical Biology, Department of Mathematical Sciences, University of Bath, Claverton Down, Bath, BA2 7AY
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R. E. Baker
1Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG
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Abstract

Mathematical models describing cell movement and proliferation are important research tools for the understanding of many biological processes. In this work we present methods to include the effects of domain growth on the evolution of spatial correlations between agent locations in a continuum approximation of a one-dimensional lattice-based model of cell motility and proliferation. This is important as the inclusion of spatial correlations in continuum models of cell motility and proliferation without domain growth has previously been shown to be essential for their accuracy in certain scenarios. We include the effect of spatial correlations by deriving a system of ordinary differential equations that describe the expected evolution of individual and pair density functions for agents on a growing domain. We then demonstrate how to simplify this system of ordinary differential equations by using an appropriate approximation. This simplification allows domain growth to be included in models describing the evolution of spatial correlations between agents in a tractable manner.

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The copyright holder for this preprint is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. All rights reserved. No reuse allowed without permission.
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Posted February 26, 2016.
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The effect of domain growth on spatial correlations
Robert J. H. Ross, C. A. Yates, R. E. Baker
bioRxiv 041491; doi: https://doi.org/10.1101/041491
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The effect of domain growth on spatial correlations
Robert J. H. Ross, C. A. Yates, R. E. Baker
bioRxiv 041491; doi: https://doi.org/10.1101/041491

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