Local kinetics of morphogen gradients

Document Type

Article

Publication Date

4-12-2011

Abstract

Some aspects of pattern formation in developing embryos can be described by nonlinear reaction-diffusion equations. An important class of these models accounts for diffusion and degradation of a locally produced single chemical species. At long times, solutions of such models approach a steady state in which the concentration decays with distance from the source of production. We present analytical results that characterize the dynamics of this process and are in quantitative agreement with numerical solutions of the underlying nonlinear equations. The derived results provide an explicit connection between the parameters of the problem and the time needed to reach a steady state value at a given position. Our approach can be used for the quantitative analysis of tissue patterning by morphogen gradients, a subject of active research in biophysics and developmental biology.

Identifier

79954992391 (Scopus)

Publication Title

Proceedings of the National Academy of Sciences of the United States of America

External Full Text Location

https://doi.org/10.1073/pnas.1019245108

e-ISSN

10916490

ISSN

00278424

First Page

6157

Last Page

6162

Issue

15

Volume

108

Grant

0908279

Fund Ref

National Science Foundation

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