Fedotov Sergei, Falconer Steven
School of Mathematics, The University of Manchester, Manchester M60 1QD, United Kingdom.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Jan;89(1):012107. doi: 10.1103/PhysRevE.89.012107. Epub 2014 Jan 8.
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.
我们研究了非线性降解和次扩散输运下形态发生素梯度的形成。在长时间极限下,我们得到了降解增强扩散的非线性效应,这是由非马尔可夫次扩散输运与非线性反应的相互作用产生的。我们发现了幂律型的稳态分布,其对鲁棒性有影响,分布的形状由反常指数控制。在远离形态发生素源的地方,产量速率的任何变化都不会被感知到。