Transit probability of biomolecule in nonlinear membranal channel

Based on the generalized Smoluchowski equation that can describe the anomalous diffusion systems, the anomalous facilitated diffusion by which the molecules traverse the membrane in specific channels is studied and the expressions of generalized transit probability are obtained. Two factors of well lengths and power-law parameters on the transit probability are considered. It is shown that the nonlinear property of cell membrane leads to the non-Markov process of Brownian motion and thereby produces the subdiffusive effect. Therefore, it will be expected that our generalized expressions of transit probability are more general and more desired results for complex nonequilibrium systems.