Selectivity is one of the most fundamental concepts in natural sciences, and it is also critically important in various technological, industrial, and medical applications. Although there are many experimental methods that allow to separate molecules, frequently they are expensive and not efficient. Recently, a new method of separation of chemical mixtures based on utilization of channels and nanopores has been proposed and successfully tested in several systems. However, mechanisms of selectivity in the molecular transport during the translocation are still not well understood. Here, we develop a simple theoretical approach to explain the origin of selectivity in molecular fluxes through channels. Our method utilizes discrete-state stochastic models that take into account all relevant chemical transitions and can be solved analytically. More specifically, we analyze channels with one and two binding sites employed for separating mixtures of two types of molecules. The effects of the symmetry and the strength of the molecular-pore interactions are examined. It is found that for one-site binding channels, the differences in the strength of interactions for two species drive the separation. At the same time, in more realistic two-site systems, the symmetry of interaction potential becomes also important. The most efficient separation is predicted when the specific binding site is located near the entrance to the nanopore. In addition, the selectivity is higher for large entrance rates into the channel. It is also found that the molecular transport is more selective for repulsive interactions than for attractive interactions. The physical-chemical origin of the observed phenomena is discussed.
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