We analyze the relaxation of the particle number fluctuations in a membrane channel at arbitrary particle-channel interaction and derive general expressions for the relaxation time and low-frequency limit of the power spectral density. These expressions simplify significantly when the channel is symmetric. For a square-well potential of mean force that occupies the entire channel, we verify the accuracy of the analytical predictions by Brownian dynamics simulations. For such a channel we show that as the depth of the well increases, the familiar scaling of the relaxation time with the channel length squared is transformed into a linear dependence on the length.
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