Potassium-39 NMR of K+ interaction with the gramicidin channel and NMR-derived conductance ratios for Na+, K+ and Rb+

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Abstract
A potassium-39 NMR study of potassium ion interaction with the gramicidin transmembrane channel in phospholipid bilayers at high ion activity is reported which allows determination of a weak binding constant, K b w ≃8.3/m, and an off-rate constant for the weak site,k off w ≃2.6×107/sec. These values are interpreted with the aid of additional NMR data as the binding constant for formation of the doubly occupied channel state and the rate constant for an ion leaving the doubly occupied state. Considering the singly occupied channel state for the potassium ion to be “electrically silent” at 1 molar ion activity, as with the sodium ion, the single-channel conductance for 100 mV and 30°C calculated to be 29 pS, and using the same approximation with previous NMR results on the sodium and rubidium ions, reasonable conductance ratios were calculated. Further experimental estimates of the other three constants with the experimental location of binding sites and Eyring rate theory to introduce voltage dependence allowed a more complete calculation of the two-site channel. The single-channel conductance for potassium ion is calculated to be 24 pS at 1m activity and 26 pS at 0.6m activity, which compares for diphytanoyl phosphatidylcholine membranes to an experimental most probable single-channel conductance of 25 pS and a mean channel conductance of 20 pS. The calculated conductance ratios using NMR-derived constants were γ(K)/γ(Na)=2.0 and γ(Rb)/γ(Na)=4.3. These results are close to the experimental values and provide further basis for the use of NMR of quadrupolar ions to provide information on the ionic mechanism of channel transport.