Transport Driven By A Random Telegraph Force In An Asymmetric Membrane Channel

Channel proteins that selectively conduct molecules across the cell membrane often exhibitrnan asymmetric structure. By means of a stochastic model the channel asymmetry in thernpresence of non equilibrium fluctuations can influence the transport through such channelsrnby a ratchet like mechanism. In general, the ratchet effect refers to the generation ofrndirected motion of Brownian particles in a spatially asymmetric (ratchet) potential inrnthe presence of non equilibrium fluctuations and externally applied time periodic forcernwith mean zero. Using this structure, Schulten and Kosztin [1] have numerically studiedrnthe behavior of steady state flux by considering various cases of an external tilting force.rnBeing interested in seeking analytical results, we model the potential of the channel by arnratchet like potential and obtain analytical expressions for the steady state flux of glycerolrnthrough the channel due to a concentration gradient, constant force, periodically switchingrnforce and non equilibrium fluctuations of the cell membrane. In addition we compare ourrnresults with the numerical results obtained in [1]

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