TitleFormation of morphogen gradients: local accumulation time.
Publication TypeJournal Article
Year of Publication2011
AuthorsBerezhkovskii, AM, Sample, C, Shvartsman, SY
JournalPhys Rev E Stat Nonlin Soft Matter Phys
Issue5 Pt 1
Date Published2011 May
KeywordsCell Differentiation, Diffusion, Gene Expression Regulation, Models, Biological, Time Factors

Spatial regulation of cell differentiation in embryos can be provided by morphogen gradients, which are defined as the concentration fields of molecules that control gene expression. For example, a cell can use its surface receptors to measure the local concentration of an extracellular ligand and convert this information into a corresponding change in its transcriptional state. We characterize the time needed to establish a steady-state gradient in problems with diffusion and degradation of locally produced chemical signals. A relaxation function is introduced to describe how the morphogen concentration profile approaches its steady state. This function is used to obtain a local accumulation time that provides a time scale that characterizes relaxation to steady state at an arbitrary position within the patterned field. To illustrate the approach we derive local accumulation times for a number of commonly used models of morphogen gradient formation.

Alternate JournalPhys Rev E Stat Nonlin Soft Matter Phys