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

Abstract

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 gramicidindoped planar lipid bilayers. The calculated results for the twoand 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., effects conductance of cations across planar lipid bilayer membranes (2) by means of discrete increments (3-5). The conductance steps are due to the formation of a continuous transmembrane channel (5, 6), with a single transmembrane channel being capable of conducting 107 ions/sec at 1 M salt, 100 mV transmembrane potential, and 25°C (7,8). This is a single-channel conductance of the order of 10 pS.As proposed in 1971 (9, 10) and now widely accepted (11, 12), the transmembrane channel is formed from the formyl-toformyl hydrogen-bonded dimerization of two helical monomers containing 6.3 residues per turn and a 4 A diameter channel (Fig. 1). The length of the channel is about 26 A (see figure 6 of ref. 13 It has recently been demonstrated that functional gramicidin channels can be packaged in lipid micelles (17,18). This allows for spectroscopic characterization during ion titrations without the development of complicating electrochemical gradients that would make difficult the analysis of cation interactions with channels incorporated into lipid vesicles. Interestingly, the energy of activation for sodium exchange with the micellar channel, at approximately equimolar sodium and channel concentrations, is essentially the same as the overall energy of activation for transport through the channel (19). Accordingly, any other translocation rate for movements within the channel are taken to be faster than the off-rate from the tight-binding site.The first rate analysis of ion transport through the grarnicidin channel was carried out by Lauger (20 to give an x-axis intercept of -K1' when Na concentration is sufficiently greater than the site concentration (24). Fig. 2 shows such a plot for GA with Na concentration ranging Abbreviation: GA, gramicidin A. 2028The publication costs of this article were defrayed in part by page charge payment. This article must therefore be hereby marked "advertisement" in accordance with 18 U. S. C. §1734 solely to indicate thi...

Estimation of Na+ dwell time in the gramicidin A channel. Na+ ions as blockers of H+ currents

“…The two models for Na + transport make appreciably different predictions for i at very low Na + eoncentra- 3) adjusted to data as shown in Fig. 2.…”

“…1A. For the solid curve the starting values of the fit were the 'weak binding' rate constants of Finkelstein and Andersen [1], while for the dotted curve the "tight binding' values of Urry et al [3,4] were used. The fitted values (listed in Table If) are very similar to the starting values, and fit the experimental points indistinguishable well even dtough two of the rate constants differ by two orders of magnitude between the two sets.…”

“…In the other case, low affinity of Na + for the channel would cause it to act as a classical 'one ion" channel, with saturation corresponding to the occupation of one of the binding sites. Supported by Z3Na nuclear magnetic resonance (NMR) experiments, Urry et al [3,4] proposed a tight binding of the first sodium ion of 30-100 M-I; experiments with gramicidin anaCorrespondence: S.H. Heinemann.…”

Carbon-13 nuclear magnetic resonance study of potassium and thallium ion binding to the Gramicidin A transmembrane channel

“…9, 14 and see Discussion below). The method of analysis for studying ion nmr data has been already discussed in detail elsewhere (4)(5)(6)8). Slight modification in procedure is required for analyzing the "C chemical shifts.…”

“…Sodium-23 (4,5) and lithium-7 (6) nuclear magnetic resonance (nmr) and dielectric relaxation (7) studies have been carried out on this system to provide estimates of binding constants and rate constants, and these constants in the case of sodium ion have been shown to be capable of calculating single channel currents over wide ranges of ion activity and of applied potential when Eyring rate theory is utilized to introduce voltage dependence to the rate constants derived in the absence of an applied field (5,8). It is useful, however, to have verification that the ion-nrnr-derived binding constants are indeed due to ion binding within the channel and not due to interaction with lipid components.…”