Waves of autocrine signaling in patterned epithelia

Document Type

Article

Publication Date

1-1-2010

Abstract

A biophysical model describing long-range cell-to-cell communication by a diffusible signal mediated by autocrine loops in developing epithelia in the presence of a morphogenetic pre-pattern is introduced. Under a number of approximations, the model reduces to a particular kind of bistable reaction-diffusion equation with strong heterogeneity. In the case of the heterogeneity in the form of a long strip a detailed analysis of signal propagation is possible, using a variational approach. It is shown that under a number of assumptions which can be easily verified for particular sets of model parameters, the equation admits a unique (up to translations) variational traveling wave solution. A global bifurcation structure of these solutions is investigated in a number of particular cases. It is demonstrated that the considered setting may provide a robust developmental regulatory mechanism for delivering chemical signals across large distances in developing epithelia. © EDP Sciences, 2010.

Identifier

79960794557 (Scopus)

Publication Title

Mathematical Modelling of Natural Phenomena

External Full Text Location

https://doi.org/10.1051/mmnp/20105504

e-ISSN

17606101

ISSN

09735348

First Page

46

Last Page

63

Issue

5

Volume

5

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