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. © 2009 Society for Mathematical Biology.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 719-762 |
| Number of pages | 44 |
| Journal | Bulletin of Mathematical Biology |
| Volume | 72 |
| Issue number | 3 |
| DOIs | |
| State | Published - Oct 28 2009 |
| Externally published | Yes |
Bibliographical note
KAUST Repository Item: Exported on 2020-10-01Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: R.E.B. would like to thank Microsoft Research for a European Postdoctoral Fellowship,Research Councils UK for an RCUK Fellowship in Mathematical Biology, and St Hugh’sCollege, Oxford, for a Junior Research Fellowship. C.A.Y. would like to thank EPSRCand BBSRC for funding via the Systems Biology Doctoral Training Centre, Universityof Oxford. This publication is based on work (R.E.) supported by Award No. KUK-C1-013-04, made by the King Abdullah University of Science and Technology (KAUST).R.E. would also like to thank Somerville College, Oxford, for a Fulford Junior ResearchFellowship.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.