Rate theory calculation of gramicidin single-channel currents using NMR-derived rate constants

By means of 23Na NMR, two ion binding sites were observed in phospholipid-packaged gramicidin channels and the four associated rate constants were approximated. Limits also were placed on a fifth rate constant for an intrachannel ion translocation. By using Eyring rate theory to introduce voltage dependence, these rate constants were used in steady-state-current equations for calculation of gramicidin single-channel currents for two- and three-site models. Calculated single-channel currents are compared with previously published experimental single-channel currents obtained by electrical measurements on Na+ transport across gramicidin-doped planar lipid bilayers. The calculated results for the two- and three-site models compare favorably with the experimental results. Accordingly, it is demonstrated that NMR-derived rate constants can be coupled with Eyring rate theory to calculate currents through a transmembrane channel and to do so within levels of variation that compare with the differences obtained on planar lipid bilayers formed with different lipids.