The malonyl gramicidin channel: NMR-derived rate constants and comparison of calculated and experimental single-channel currents

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Abstract
Malonyl gramicidin is incorporated into lysolecithin micelles in a manner which satisfies a number of previously demonstrated criteria for the formation of the transmembrane channel structure. By means of sodium-23 nuclear magnetic resonance, two binding sites are observed: a tight site and a weak site with binding constants of approximately 100m −1 and 1m −1, respectively. In addition, off-rate constants from the two sites were estimated from NMR analyses to bek off t ≃3×105/sec andk off w ≃2×107/sec giving, with the binding constants, the on-rate constants,k on t ≃3×107/msec andk on w ≃2×107/m sec. Five different multiple occupancy models with NMR-restricted energy profiles were considered for the purpose of calculating single-channel currents as a function of voltage and concentration utilizing the four NMR-derived rate constants (and an NMR-limit placed on a fifth rate constant for intrachannel ion translocation) in combination with Eyring rate theory for the introduction of voltage dependence. Using the X-ray diffraction results of Koeppe et al. (1979) for limiting the positions of the tight sites, the two-site model and a three-site model in which the weak sites occur after the tight site is filled were found to satisfactorily calculate the experimental currents (also reported here) and to fit the experimental currents extraordinarily well when the experimentally derived values were allowed to vary to a least squares best fit. Surprisingly the “best fit” values differed by only about a factor of two from the NMR-derived values, a variation that is well within the estimated experimental error of the rate constants. These results demonstrate the utility of ion nuclear magnetic resonance to determine rate constants relevant to transport through the gramicidin channel and of the Eyring rate theory to introduce voltage dependence.