  Transport of molecules across membrane channels is investigated theoretically
using exactly solvable one-dimensional discrete-state stochastic models. An
interaction between molecules and membrane pores is modeled via a set of
binding sites with different energies. It is shown that the interaction
potential strongly influences the particle currents as well as fluctuations in
the number of translocated molecules. For small concentration gradients the
attractive sites lead to largest currents and fluctuations, while the repulsive
interactions yield the largest fluxes and dispersions for large concentration
gradients. Interaction energies that lead to maximal currents and maximal
fluctuations are the same only for locally symmetric potentials, while they
differ for the locally asymmetric potentials. The conditions for the most
optimal translocation transport with maximal current and minimal dispersion are
discussed. It is argued that in this case the interaction strength is
independent of local symmetry of the potential of mean forces. In addition, the
effect of the global asymmetry of the interaction potential is investigated,
and it is shown that it also strongly affects the particle translocation
dynamics. These phenomena can be explained by analyzing the details of the
particle entering and leaving the binding sites in the channel.
