Waves of Autocrine Signaling in Patterned Epithelia

C. B. Muratov; S. Y. Shvartsman

Mathematical Modelling of Natural Phenomena (2010)

  • Volume: 5, Issue: 5, page 46-63
  • ISSN: 0973-5348

Abstract

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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.

How to cite

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Muratov, C. B., and Shvartsman, S. Y.. "Waves of Autocrine Signaling in Patterned Epithelia." Mathematical Modelling of Natural Phenomena 5.5 (2010): 46-63. <http://eudml.org/doc/197683>.

@article{Muratov2010,
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.},
author = {Muratov, C. B., Shvartsman, S. Y.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {cell communication; front propagation; traveling waves; strong heterogeneity; global bifurcation structure},
language = {eng},
month = {7},
number = {5},
pages = {46-63},
publisher = {EDP Sciences},
title = {Waves of Autocrine Signaling in Patterned Epithelia},
url = {http://eudml.org/doc/197683},
volume = {5},
year = {2010},
}

TY - JOUR
AU - Muratov, C. B.
AU - Shvartsman, S. Y.
TI - Waves of Autocrine Signaling in Patterned Epithelia
JO - Mathematical Modelling of Natural Phenomena
DA - 2010/7//
PB - EDP Sciences
VL - 5
IS - 5
SP - 46
EP - 63
AB - 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.
LA - eng
KW - cell communication; front propagation; traveling waves; strong heterogeneity; global bifurcation structure
UR - http://eudml.org/doc/197683
ER -

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