TitleLocal kinetics of morphogen gradients.
Publication TypeJournal Article
Year of Publication2011
AuthorsGordon, PV, Sample, C, Berezhkovskii, AM, Muratov, CB, Shvartsman, SY
JournalProc Natl Acad Sci U S A
Volume108
Issue15
Pagination6157-62
Date Published2011 Apr 12
KeywordsBody Patterning, Models, Biological
Abstract

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.

Alternate JournalProc. Natl. Acad. Sci. U.S.A.