Local kinetics of morphogen gradients

Gordon Peter V., Christine Sample, Alexander M. Berezhkovskii, Cyrill B. Muratov, Stanislav Y. Shvartsman

Research output: Contribution to journalArticlepeer-review

50 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)6157-6162
Number of pages6
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number15
StatePublished - Apr 12 2011

All Science Journal Classification (ASJC) codes

  • General


  • Concentration gradient
  • Robustness
  • Tissue regulation


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