Site model for channel-facilitated membrane transport: invariance of the translocation time distribution with respect to direction of passage

A particle entering a membrane channel either returns to the initial reservoir from which it entered or goes through to escape on the opposite side. We prove that the probability density of the translocation time is invariant with respect to the direction of passage. This invariance holds at arbitrary asymmetry of the intra-channel potential, i.e., independently of how different the translocation probabilities are in the two directions. Assuming that the particle motion is described as a continuous-time random walk between neighbouring sites representing the channel, we give three proofs of the invariance. The present analysis complements a recent proof of the invariance where we assumed Langevin dynamics of the particle in the channel (Berezhkovskii et al 2006 Phys. Rev. Lett. 97 020601)