TitlePhysical interpretation of mean local accumulation time of morphogen gradient formation.
Publication TypeJournal Article
Year of Publication2011
AuthorsBerezhkovskii, AM, Shvartsman, SY
JournalJ Chem Phys
Date Published2011 Oct 21
KeywordsAlgorithms, Diffusion, Models, Biological, Morphogenesis, Time Factors

The paper deals with a reaction-diffusion problem that arises in developmental biology when describing the formation of the concentration profiles of signaling molecules, called morphogens, which control gene expression and, hence, cell differentiation. The mean local accumulation time, which is the mean time required to reach the steady state at a fixed point of a patterned tissue, is an important characteristic of the formation process. We show that this time is a sum of two times, the conditional mean first-passage time from the source to the observation point and the mean local accumulation time in the situation when the source is localized at the observation point.

Alternate JournalJ Chem Phys