TitleSelf-similar dynamics of morphogen gradients.
Publication TypeJournal Article
Year of Publication2011
AuthorsMuratov, CB, Gordon, PV, Shvartsman, SY
JournalPhys Rev E Stat Nonlin Soft Matter Phys
Issue4 Pt 1
Date Published2011 Oct
KeywordsComputer Simulation, Intracellular Signaling Peptides and Proteins, Models, Biological, Morphogenesis

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.

Alternate JournalPhys Rev E Stat Nonlin Soft Matter Phys