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Living cells need to exchange nutrients, water, and various other molecules with their environment. Transmembrane structures have evolved to facilitate transport of desired molecules. A similar system is molecular transport through zeolites, which are also comprised of molecular-sized channels. On these scales, continuum descriptions do not capture the nonlinear behavior resulting from finite-sized molecular interactions. A simple one-dimensional lattice model obeying exclusion statistics is used to describe transport across microscopic single-file channels. The finite-sized effects lead to nonlinear coupling between multispecies flow resulting in interesting pumping across molecular pores. The results may qualitatively explain osmosis measurements, propose possible mechanisms for bioenergetic coupling, as well as suggest more systematic experiments. Related ongoing work on collective particle transport will also be outlined.