Self-similar dynamics of morphogen gradients

Cyrill B. Muratov, Peter V. Gordon, Stanislav Y. Shvartsman

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


Morphogen gradients are concentration fields of molecules acting as spatial regulators of cell differentiation in developing tissues and play a fundamental role in various aspects of embryonic development. We discovered a family of self-similar solutions in a canonical class of nonlinear reaction-diffusion models describing the formation of morphogen gradients. These solutions are realized in the limit of infinitely high production rate at the tissue boundary and are given by the product of the steady state concentration profile and a function of the diffusion similarity variable. We solved the boundary value problem for the similarity profile numerically and analyzed the implications of the discovered self-similarity on the dynamics of morphogenetic patterning.

Original languageEnglish (US)
Article number041916
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number4
StatePublished - Oct 14 2011

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Statistics and Probability


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