title: Nonlinear degradation-enhanced transport of morphogens performing subdiffusion.
abstract: We study a morphogen gradient formation under nonlinear degradation and subdiffusive transport. In the long-time limit, we obtain the nonlinear effect of degradation-enhanced diffusion, resulting from the interaction of non-Markovian subdiffusive transport with a nonlinear reaction. We find the stationary profile of power-law type, which has implications for robustness, with the shape of the profile being controlled by the anomalous exponent. Far away from the source of morphogens, any changes in the rate of production are not felt.
authors.affiliation: School of Mathematics, The University of Manchester, Manchester M60 1QD, United Kingdom.
authors.forename: Sergei
authors.initials: S
authors.lastname: Fedotov
authors.affiliation: School of Mathematics, The University of Manchester, Manchester M60 1QD, United Kingdom.
authors.forename: Steven
authors.initials: S
authors.lastname: Falconer
mesh_terms: D000818:Animals; D003198:Computer Simulation; D004058:Diffusion; D045604:Extracellular Fluid / Q000737:chemistry* / Q000502:physiology*; D006801:Humans; D008954:Models, Biological; D008956:Models, Chemical; D009024:Morphogenesis / Q000502:physiology*; D017711:Nonlinear Dynamics; D011506:Proteins / Q000378:metabolism*
chemical_list: D011506:Proteins