# Modelling Cell Migration and Adhesion During Development

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## Abstract

Cell–cell adhesion is essential for biological development: cells migrate to their target sites, where cell–cell adhesion enables them to aggregate and form tissues. Here, we extend analysis of the model of cell migration proposed by Anguige and Schmeiser (J. Math. Biol. 58(3):395–427, 2009) that incorporates both cell–cell adhesion and volume filling. The stochastic space-jump model is compared to two deterministic counterparts (a system of stochastic mean equations and a non-linear partial differential equation), and it is shown that the results of the deterministic systems are, in general, qualitatively similar to the mean behaviour of multiple stochastic simulations. However, individual stochastic simulations can give rise to behaviour that varies significantly from that of the mean. In particular, individual simulations might admit cell clustering when the mean behaviour does not. We also investigate the potential of this model to display behaviour predicted by the differential adhesion hypothesis by incorporating a second cell species, and present a novel approach for implementing models of cell migration on a growing domain.

## Keywords

Mathematical modelling Cell–cell adhesion Differential adhesion Cell sorting Domain growth## Notes

### Acknowledgements

RNT would like to thank the Centre for Mathematical Biology, University of Oxford, for the opportunity to carry out this research, the Nuffield Foundation for the bursary that allowed this research to begin, and BBSRC for research funding via the Genes to Organisms doctoral training award. He would also like to thank Endre Suli, Michael Thompson and Nik Cunniffe for helpful discussions and support. CAY would like to thank Christ Church College, Oxford, for a Junior Research Fellowship.

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