Nonlinear degradation enhanced transport of morphogens performing subdiffusion

TL;DR

This paper investigates how nonlinear degradation influences morphogen transport under subdiffusion, revealing a power-law stationary profile shaped by anomalous diffusion properties, with implications for biological robustness.

Contribution

It introduces a model combining nonlinear degradation with subdiffusive transport, showing how these interactions produce a power-law morphogen profile.

Findings

Stationary profile is of power-law type.

Profile shape is controlled by the anomalous exponent.

Far from source, production rate changes do not affect the profile.

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 rate of production are not felt.