Self-similar dynamics of morphogen gradients

Document Type

Article

Publication Date

10-14-2011

Abstract

Morphogen gradients are concentration fields of molecules acting as spatial regulators of cell differentiation in developing tissues and play a fundamental role in various aspects of embryonic development. We discovered a family of self-similar solutions in a canonical class of nonlinear reaction-diffusion models describing the formation of morphogen gradients. These solutions are realized in the limit of infinitely high production rate at the tissue boundary and are given by the product of the steady state concentration profile and a function of the diffusion similarity variable. We solved the boundary value problem for the similarity profile numerically and analyzed the implications of the discovered self-similarity on the dynamics of morphogenetic patterning. © 2011 American Physical Society.

Identifier

80054915884 (Scopus)

Publication Title

Physical Review E Statistical Nonlinear and Soft Matter Physics

External Full Text Location

https://doi.org/10.1103/PhysRevE.84.041916

e-ISSN

15502376

ISSN

15393755

Issue

4

Volume

84

Grant

0908279

Fund Ref

National Science Foundation

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