## 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.

Original language | English (US) |
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Pages (from-to) | 46-63 |

Number of pages | 18 |

Journal | Mathematical Modelling of Natural Phenomena |

Volume | 5 |

Issue number | 5 |

DOIs | |

State | Published - Jan 2010 |

## All Science Journal Classification (ASJC) codes

- Modeling and Simulation
- Applied Mathematics

## Keywords

- cell communication
- front propagation
- traveling waves