Colloquium: From microscopic to macroscopic descriptions of cell migration on growing domains
by Professor Ruth Baker
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.
For More Information: Contact Paul Pearce (P.Pearce@ms.unimelb.edu.au) or Paul Norbury (P.Norbury@ms.unimelb.edu.au)