title: Formation of morphogen gradients: local accumulation time.
abstract: 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.
authors: Mathematical and Statistical Computing Laboratory, Division of Computational Bioscience, Center for Information Technology, National Institutes of Health, Bethesda, Maryland 20892, USA.
authors: Alexander M
authors: AM
authors: Berezhkovskii
authors: Christine
authors: C
authors: Sample
authors: Stanislav Y
authors: SY
authors: Shvartsman
mesh_terms: D002454:Cell Differentiation; D004058:Diffusion; D005786:Gene Expression Regulation; D008954:Models, Biological; D013997:Time Factors