Diffusion of large particles through small pores: From entropic to enthalpic transport

We present a statistical model for solving and predicting the transport of large molecules through small flexible channels. The average radius of the channel and the average radius of the molecule are the only two quantities determining the steric part of the potential of mean force for the translocation, in the case of a small rigid particle and a large rigid channel: the barrier is completely entropic and is described by the Fick-Jacobs model. However, the flexibility of the channel's cross section and that of the molecule's size have a significant effect on transport, especially when a large molecule goes through a narrow channel. In this case, the steric barrier changes its statistical nature becoming enthalpic, and we predict a strong temperature enhancement of the diffusion current through the channel. The flexibility is described in terms of the equilibrium fluctuations of the channel and of the molecule. The model is compared with the all-atom MD simulations of the transport of hard spheres of various radii and of drug molecules through a biological nanochannel. For the case of Gaussian fluctuations, we derived a simple analytical expression for the steric barrier, which can be quantified using average size and fluctuations of the channel and of the molecule.