## Development of Morphogen Gradients with Spatially Varying Degradation Rates.

- Hamid Teimouri, Behnaz Bozorgui, Anatoly B Kolomeisky
- The journal of physical chemistry. B
- 2016

- Published 2011 in Proceedings of the National Academy of Sciences…

Some aspects of pattern formation in developing embryos can be described by nonlinear reaction-diffusion equations. An important class of these models accounts for diffusion and degradation of a locally produced single chemical species. At long times, solutions of such models approach a steady state in which the concentration decays with distance from the source of production. We present analytical results that characterize the dynamics of this process and are in quantitative agreement with numerical solutions of the underlying nonlinear equations. The derived results provide an explicit connection between the parameters of the problem and the time needed to reach a steady state value at a given position. Our approach can be used for the quantitative analysis of tissue patterning by morphogen gradients, a subject of active research in biophysics and developmental biology.

@article{Gordon2011LocalKO,
title={Local kinetics of morphogen gradients.},
author={Peter V. Gordon and Christine Sample and Alexander M. Berezhkovskii and Cyrill B. Muratov and Stanislav Y. Shvartsman},
journal={Proceedings of the National Academy of Sciences of the United States of America},
year={2011},
volume={108 15},
pages={6157-62}
}