Filled pore approximation: a theoretical framework for solute-solvent coupling in narrow water channels

A phenomenological model is presented of water and solute transport that is applicable to water pores with radii less than approximately 2 A. This includes such examples as gramicidin A, the proximal tubule basolateral membrane, and the aquaporin 1 (CHIP28) water channel. The model differs from the conventional single-file model by allowing for a variation of unoccupied volume within the pores. It is shown that the accessible or free portion of the unoccupied volume can be related to the mechanical frictional coefficients and thereby to the filtration and diffusive permeabilities by the filled pore approximation. In general, the smallness of the unoccupied volume represents the compactness of the molecules within the pore and is indicative of the single-file character of the motion of water and solute moving together. When that volume is equal to a single water volume, the results are identical to the conventional single-file model. An important result is that, despite very low diffusive permeabilities, the reflection coefficient of a solute can remain at approximately 0.5 if its frictional interaction with the channel walls is comparable with its frictional interaction with neighboring water molecules. This is consistent with values previously reported for NaCl in cell membranes of proximal tubule. The model predicts a minimum effective pore radius for a water channel of 1.78 A and corresponds to a maximum filtration-to-diffusion permeability ratio that is proportional to the length of the effective pore or channel. This limiting condition corresponds to a water channel completely filled by water and may be applicable to the aquaporin 1 water channel.