Counting translocations of strongly repelling particles through single channels: fluctuation theorem for membrane transport.

Transport of strongly repelling particles through a single membrane channel is analyzed assuming that the channel cannot be occupied by more than one particle. An exact solution is found for the Laplace transform of the probability P_{n}(t) that n particles have been transported in time t. This transform is used to find the flux through the channel and to show that P_{n}(t) and P_{-n}(t) are related by the fluctuation theorem. The solution is obtained using an observation that P_{n}(t) is the propagator for a non-Markovian random walk, which can be found by solving a set of integral equations.