Diffusion of molecules through nanopores under confinement: Time-scale bridging and crowding effects via Markov state model

Passive transport of molecules through nanopores is characterized by the interaction of molecules with pore internal walls and by a general crowding effect due to the constricted size of the nanopore itself, which limits the presence of molecules in its interior. The molecule-pore interaction is treated within the diffusion approximation by introducing the potential of mean force and the local diffusion coefficient for a correct statistical description. The crowding effect can be handled within the Markov state model approximation. By combining the two methods, one can deal with complex free energy surfaces taking into account crowding effects. We recapitulate the equations bridging the two models to calculate passive currents assuming a limited occupancy of the nanopore in a wide range of molecular concentrations. Several simple models are analyzed to clarify the consequences of the model. Eventually, a biologically relevant case of transport of an antibiotic molecule through a bacterial porin is used to draw conclusions (i) on the effects of crowding on transport of small molecules through biological channels, and (ii) to demonstrate its importance for modelling of cellular transport.