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From microscopic to macroscopic descriptions of cell migration on growing domains

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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 a ubiquitous use of partial differential equations (PDEs) for modelling the time evolution of cellular density and environmental cues. In the last twenty 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 talk, individual-based models describing cell movement and domain growth are outlined, and correspondence with a macroscopic-level PDE describing the evolution of cell density is demonstrated. The individual-basedmodels are formulated in terms of randomwalkers 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.

Biography: Ruth Baker is an RCUK Academic Fellow in Mathematical Biology at the Centre for Mathematical Biology, part of the Mathematical Institute, University of Oxford. She is a Junior Research Fellow at St Hugh’s College and holds a Microsoft Research European Fellowship. She has also held a Lloyds Tercentenary Foundation Fellowship.

Ruth completed her M.Math (1997-2001) and D.Phil (2001-2005) at Wadham College and also held a Stipendiary Lectureship in Applied Mathematics at St John’s College (2004-2005).

This talk is part of the Microsoft Research Symposium series.

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