Unitary Water Channel Permeability and Arrhenius Activation Energy are Intricately Linked

Measurements of the Gibbs activation energy barrier ΔG‡t constitute the traditional way of showing the presence of an aqueous pore. The expected ΔG‡t value of about 4 kcal/mol corresponds to the activation energy for the self-diffusion of water. However, structural investigations within the last two decades have revealed radical differences in the water environment for molecules in the narrow channel lumen, which casts doubt on the validity of the standard argumentation. Water molecules may lose up to two of their four hydrogen bonds when entering channels where they are lined up in single file. Moreover, the number of hydrogen bonds which permeating water molecules may eventually form with pore-lining residues is known to determine the unitary water permeability pf.1 Here we present a different line of argumentation in favor of ΔG‡t≈4 kcal/mol: high pf values indicate bulk-like water mobility. pf can be converted into the transport rate r. Transition state theory intricately links r to ΔG‡t: r=νoexp(-ΔG‡t/kBT) where T, kB, and νo≈1013s−1 are the absolute temperature, the Boltzmann constant, and the universal transition state theory attempt frequency. Calculating theoretical pf values from ΔG‡t, we find a satisfactory match to experimentally obtained pf values of aquaporins1, potassium channels1, gramicidinA2 and other channels that we have measured to bolster the experimental basis for the link between r and ΔG‡t. Only channels in which water retains bulk mobility require ΔG‡t≈4 kcal/mol, while less permeable channels exhibit a higher barrier to water transport. 1. Horner, A.; ...; Pohl, P., The mobility of single-file water molecules is governed by the number of H-bonds they may form with channel-lining residues. Science Adv. 2015, 1, e1400083. 2. Pohl, P.; Saparov, S. M., Solvent drag across gramicidin channels demonstrated by microelectrodes. Biophys. J. 2000, 78, 2426.