Physical interpretation of mean local accumulation time of morphogen gradient formation

Alexander M. Berezhkovskii, Stanislav Y. Shvartsman

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22 Scopus citations


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.

Original languageEnglish (US)
Article number154115
JournalJournal of Chemical Physics
Issue number15
StatePublished - Oct 21 2011

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy
  • Physical and Theoretical Chemistry


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