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Waves of Autocrine Signaling in PatternedEpithelia

Published online by Cambridge University Press:  27 July 2010

C. B. Muratov  and
S. Y. Shvartsman
C. B. Muratov*
Affiliation:
Department of Mathematical Sciences, New Jersey Institute of Technology Newark, NJ 07102, USA
S. Y. Shvartsman
Affiliation:
Department of Chemical Engineering and Lewis Sigler Institute for Integrative Genomics Princeton University, Princeton, NJ 08544, USA
*
* Corresponding author. E-mail:muratov@njit.edu
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Abstract

A biophysical model describing long-range cell-to-cell communication by a diffusiblesignal mediated by autocrine loops in developing epithelia in the presence of amorphogenetic pre-pattern is introduced. Under a number of approximations, the modelreduces to a particular kind of bistable reaction-diffusion equation with strongheterogeneity. In the case of the heterogeneity in the form of a long strip a detailedanalysis of signal propagation is possible, using a variational approach. It is shown thatunder a number of assumptions which can be easily verified for particular sets of modelparameters, the equation admits a unique (up to translations) variational traveling wavesolution. A global bifurcation structure of these solutions is investigated in a number ofparticular cases. It is demonstrated that the considered setting may provide a robustdevelopmental regulatory mechanism for delivering chemical signals across large distancesin developing epithelia.

Keywords

cell communicationfront propagationtraveling waves
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 5 , Issue 5: Reaction-diffusion waves , 2010 , pp. 46 - 63
Copyright
© EDP Sciences, 2010

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