Document Detail

From microscopic to macroscopic descriptions of cell migration on growing domains.
MedLine Citation:
PMID:  19862577     Owner:  NLM     Status:  MEDLINE    
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.
Ruth E Baker; Christian A Yates; Radek Erban
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Publication Detail:
Type:  Journal Article     Date:  2009-10-28
Journal Detail:
Title:  Bulletin of mathematical biology     Volume:  72     ISSN:  1522-9602     ISO Abbreviation:  Bull. Math. Biol.     Publication Date:  2010 Apr 
Date Detail:
Created Date:  2010-03-22     Completed Date:  2010-06-10     Revised Date:  -    
Medline Journal Info:
Nlm Unique ID:  0401404     Medline TA:  Bull Math Biol     Country:  United States    
Other Details:
Languages:  eng     Pagination:  719-62     Citation Subset:  IM    
Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford OX1 3LB, UK.
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MeSH Terms
Cell Movement / physiology*
Computer Simulation
Models, Biological*
Signal Transduction
Stochastic Processes*

From MEDLINE®/PubMed®, a database of the U.S. National Library of Medicine

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