The Mathematical Institute, University of Oxford, Eprints Archive

From Microscopic to Macroscopic Descriptions of Cell Migration on Growing Domains

Baker, Ruth E. and Yates, C. A. and Erban, R. (2010) From Microscopic to Macroscopic Descriptions of Cell Migration on Growing Domains. Bulletin of Mathematical Biology . ISSN 0092-8240 (In Press)

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Abstract

Cell migration and growth are essential components of the development of multicellular organisms. The role of various cues in directing cell migration is widespread, in particular, the role of signals in the environment in the control of cell motility and directional guidance. In many cases, especially in developmental biology, growth of the domain also plays a large role in the distribution of cells and, in some cases, cell or signal distribution may actually drive domain growth. There is an almost ubiquitous use of partial differential equations (PDEs) for modelling the time evolution of cellular density and environmental cues. In the last 20 years, a lot of attention has been devoted to connecting macroscopic PDEs with more detailed microscopic models of cellular motility, including models of directional sensing and signal transduction pathways. However, domain growth is largely omitted in the literature. In this paper, individual-based models describing cell movement and domain growth are studied, and correspondence with a macroscopic-level PDE describing the evolution of cell density is demonstrated. The individual-based models are formulated in terms of random walkers on a lattice. Domain growth provides an extra mathematical challenge by making the lattice size variable over time. A reaction–diffusion master equation formalism is generalised to the case of growing lattices and used in the derivation of the macroscopic PDEs.

Item Type:Article
Subjects:O - Z > Partial differential equations
A - C > Biology and other natural sciences
O - Z > Probability theory and stochastic processes
Research Groups:Oxford Centre for Collaborative Applied Mathematics
Centre for Mathematical Biology
ID Code:879
Deposited By:Ruth Baker
Deposited On:13 Jan 2010 07:40
Last Modified:13 Mar 2011 12:42

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