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Partial differential equations for self-organization in cellular and developmental biology

REVIEW ARTICLE

R E Baker1, E A Gaffney1 and P K Maini1,2

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INVITED ARTICLE

Recommended by J A Glazier

Understanding the mechanisms governing and regulating the emergence of structure and heterogeneity within cellular systems, such as the developing embryo, represents a multiscale challenge typifying current integrative biology research, namely, explaining the macroscale behaviour of a system from microscale dynamics. This review will focus upon modelling how cell-based dynamics orchestrate the emergence of higher level structure. After surveying representative biological examples and the models used to describe them, we will assess how developments at the scale of molecular biology have impacted on current theoretical frameworks, and the new modelling opportunities that are emerging as a result. We shall restrict our survey of mathematical approaches to partial differential equations and the tools required for their analysis. We will discuss the gap between the modelling abstraction and biological reality, the challenges this presents and highlight some open problems in the field.


PACS

87.10.-e General theory and mathematical aspects

87.17.Aa Modeling, computer simulation of cell processes

87.18.-h Biological complexity

87.18.Hf Spatiotemporal pattern formation in cellular populations

87.18.Ed Cell aggregation

MSC

92C37 Cell biology

92Bxx Mathematical biology in general

35Qxx Equations of mathematical physics and other areas of application (See also 35J05, 35J10, 35K05, 35L05)

Subjects

Biological physics

Dates

Issue 11 (November 2008)

Received 19 June 2008, in final form 19 September 2008

Published 20 October 2008



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