Math. Model. Nat. Phenom.
Volume 5, Number 5, 2010Reaction-diffusion waves
|Page(s)||46 - 63|
|Published online||27 July 2010|
Waves of Autocrine Signaling in Patterned Epithelia
Department of Mathematical Sciences, New Jersey Institute of Technology Newark,
2 Department of Chemical Engineering and Lewis Sigler Institute for Integrative Genomics Princeton University, Princeton, NJ 08544, USA
* Corresponding author. E-mail:
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.
Mathematics Subject Classification: 35K55 / 35J60 / 35J20 / 35K57
Key words: cell communication / front propagation / traveling waves
© EDP Sciences, 2010
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.