# 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

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topMuratov, 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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