Nuclear magnetic resonance of 23Na ions interacting with the gramicidin channel.

Basic nuclear magnetic resonance (NMR) features of 23Na ions bound to the gramicidin channel (packaged into lecithin liposomes) were studied. The first binding constant K1 of Na+ was not significantly dependent on channel models employed. With the two-identical-site model (Model I), K1 was 13.7 (+/- 1.4) molal-1 (in the activity basis) at 25 degrees C; when the binding of a third ion was included (Model II), it was 13.0 (+/- 2.0) molal-1. The second binding constant K2 was model dependent; it was 1.6 (+/- 0.2) and 3-4 molal-1 for Models I and II, respectively. The rate constants, k-1 and k-2, of Na+ for exit from singly and doubly loaded channels, respectively, were 8 X 10(5) s-1 less than or equal to k-1 less than or equal to 3 X 10(6) s-1 and 8 X 10(5) s-1 less than or equal to k-2 less than or equal to 1.0 X 10(7) s-1 at 25 degrees C; the lower bound represents a rough approximation of k-1. The ratio k-2/k-1 was greater than one and did not greatly exceed 20. From the competition experiment, K1 of T1+ was 5.7 (+/- 0.6) X 10(2) molal-1. The longitudinal relaxation time T1 of bound 23Na in the state of single occupancy (T 1B sing) was virtually independent of models, 0.56 (+/- 0.03) and 0.55 (+/- 0.04) ms at 25 degrees C for Models I and II, respectively. For the state of double occupancy, T1 of bound 23Na (T 1B doub) was model dependent: 0.27 (+/- 0.01) and 0.4-0.6 ms for Models I and II. The correlation time tau c of bound 23Na was 2.2 (+/- 0.2) ns at 25 degrees C for single occupancy; tau c for double occupancy was not significantly different from this value. The estimated tau c was found to involve no appreciable contribution of the exchange of 23Na between the channel and the bulk solution. Thé quadrupole coupling constant chi was 1.0 (+/- 0.1) MHz for 23Na in single occupancy; chi for double occupancy was 0.9-1.4 MHz, depending on models. A lower bound of the average quadrupole coupling constant chi alpha was 0.13-0.26 MHz at 25 degrees C for 23Na in single occupancy; this value represents a rough approximation of chi alpha at this temperature. An argument based on the estimated chi alpha and the known conformation of the gramicidin channel suggests that the binding site is a small domain near the channel end. Within the framework of Model I, Tb was faster than Tljn; this inequality was attributed to an increased chi in the presence ofa second cation, which was not explained in terms of electrostatic interactions between bound cations, implying a conformation change upon binding of cations

Effects of alkali cations on the nuclear magnetic resonance intensity of 23Na in rat liver homogenate.

Effects of alkali cations on the nuclear magnetic resonance intensity of 23Na were studied in rat liver homogenate. The loss in the resonance intensity of 23Na in the homogenate was able to be divided into two components, one of which is abolished by the addition of Cs+ ("Cs-sensitive component"), the other being insensitive to Cs+ ("Cs-insensitive component"). Both components were sensitive to guanidinium ion. In a pH range of 7.4-4.9, the Cs-sensitive component varied remarkably, but the Cs-insensitive component remained virtually unchanged. The sequence of effectiveness of alkali cations (300 mmol/kg sample) in restoring the fractional intensity of 23Na was: Cs approximately Na greater than Li approximately Rb greater than K. It was suggested that the sequences of effectiveness of alkali cations in abolishing the two components are quite different from each other. The present results were examined within the framework of a simple model. Within this framework, the results suggest that there occur, in particulate fractions, sites whose affinity for Cs+ is sufficiently lower than that for Na+

Energy-minimized conformation of gramicidin-like channels. II. Periodicity of the lowest energy conformation of an infinitely long poly-(L,D)-alanine beta 6.3-helix.

If an infinitely long polymer has a primary structure characterized by an N-residue periodicity, a minimum energy conformation of the polymer under the constraint of the conformational N-residue periodicity corresponds to an equilibrium structure (energy minimal or unstable equilibrium structure) when this constraint is absent. Molecular mechanics calculations showed that with an infinitely long poly-(L,D)-alanine single-stranded beta 6.3-helix (which has a 2-residue periodicity with respect to the primary structure), its lowest energy conformation within the framework of the conformational 2-residue periodicity is also the lowest energy form of this beta 6.3-helix even when no conformational periodicity is assumed. In the course of this study, contour maps of helix parameters and conformation energies for beta structures of poly-(L,D)-alanine were examined. It was also found that beta 6.3-, beta 4.5-, alpha L,D-, and tau L,D-helices constitute the global minima in the whole conformational space of this polypeptide. In the present calculation, an improved formulation of the conformation energy was introduced to estimate the structure and conformation energy of an infinite periodic chain from results on a chain of finite length

Nuclear Magnetic Resonance of Tissue (23)Na: II. Theoretical Line Shape

The theoretical line-shape function of the nuclear magnetic resonance (NMR) signal of (23)Na in biological tissue (and other unoriented systems) was obtained under the following conditions: (I) there occur two states of (23)Na in the system, (II) the exchange of (23)Na between the two states is rapid (but not too rapid), (III) in the absence of exchange, the (23)Na in one state is characterized by a single transverse relaxation time T(2) and a single Larmor frequency, and (IV) in the absence of exchange, the (23)Na in the other state possesses (a) two different values of T(2) and/or (b) more than one Larmor frequencies in the first order perturbation effect. The theoretical signal obtained consists of two Lorentzian components, which are centered at the same frequency, but characterized by different T(2). Only the narrower component, comprising 40% of the total intensity, is visible, when the fast T(2) is sufficiently short. The theoretical line-shape function of (23)Na signal was also calculated for oriented systems in which the above conditions are fulfilled

Energy-minimized conformation of gramicidin-like channels. I. Infinitely long poly-(L,D)-alanine beta 6.3-helix.

The energy-minimized conformation of an infinitely long poly-(L,D)-alanine in single-stranded beta 6.3-helix was calculated by the molecular mechanics method. When energy minimization was started from a wide range of initial geometries, six optimized conformations were obtained and identified as the right- and left-handed counterparts of the beta 4.5-, beta 6.3-, and beta 8.2-helices. It was found that their conformation energies increase in this order, the beta 4.5-helix having the lowest energy. The backbone dihedral angles of the energy-minimized beta 6.3-helix were: phi L = -116 degrees (or -131 degrees), psi L = 122 degrees (or 111 degrees), phi D = 131 degrees (or 116 degrees), psi D = -111 degrees (or -122 degrees), omega L = 173 degrees (or 173 degrees), and omega D = -173 degrees (or -173 degrees) for the right-handed (or left-handed) helix. This helix was composed of 6.30 residues/turn with a pitch of 4.97 A. All the alpha-carbons of L- and D-configurations appeared on one common circular helix. Interestingly, small deviations (approximately 7 degrees) of the peptide bonds from the planar structure caused a considerable lowering of the conformation energy, and, at the same time, they produced more favorable fitting of the hydrogen bonds; the carbonyl oxygens and the nearest-neighbor alpha-hydrogens also took more favorable relative positions

Nuclear Magnetic Resonance of Tissue (23)Na: I. (23)Na Signal and Na(+) Activity in Homogenate

The ability to depress the resonance intensity of (23)Na in rat liver tissue was not found in the supernatant fraction. It was exclusively localized in particulate fractions. The intensity and saturation behavior of the (23)Na signal was examined in suspensions containing various amounts of the particulate fraction of rat liver homogenate. The results strongly suggest that the (23)Na signal of tissue reflects quadrupole interactions and does not result from a slow exchange between the free and bound fractions of Na(+). The activity coefficient of Na(+) in rat liver homogenate (no medium was added) was 0.59, about 20% less than that in the isotonic saline. Available evidences and discussion indicate that the bound Na(+) in the homogenate is much less than the so-called “NMR-invisible” fraction of Na(+)

Na+ interacting with gramicidin D. A nuclear magnetic resonance study.

23Na nuclei in a milk-white emulsion composed to nonionic surfactant and higher alcohol in saline were characterized by single values of T1 and T2 and a single Larmor frequency. In the presence of small amounts of gramicidin D (Dubos), the relaxations of 23Na were greatly accelerated, and the transverse relaxation was a sum of two decaying exponentials. But only a single T1 was observed; it was roughly equal to the slow T2. The slow T2 accounted for about 40% of the total resonance intensity. The relaxation rates increased linearly with the increase of the gramicidin concentration. The absorption signal consisted of a narrow and a broad line, both centered at the same frequency. The present results suggest that nuclear magnetic resonance spectroscopy is a useful tool for studying the nature of ion-permeable channels of biological membranes, even when the channel has no ionizable groups

Effective pore radius of the gramicidin channel. Electrostatic energies of ions calculated by a three-dielectric model.

Electrostatic calculation of the gramicidin channel is performed on the basis of a three-dielectric model in which the peptide backbone of the channel is added as a third dielectric region to the conventional two-dielectric channel model (whose pore radius is often referred to as the effective pore radius reff). A basic principle for calculating electrostatic fields in three-dielectric models is introduced. It is shown that the gramicidin channel has no unique value of reff. The reff with respect to the "self-image energy" (i.e., the image energy in the presence of a single ion) is 2.6-2.7 A, slightly depending upon the position of the ion (the least-square value over the whole length of the pore is 2.6 A). In contrast, the reff with respect to the electric potential due to an ion (and hence the reff with respect to the interaction energy between two ions) is dependent upon the distance s of separation; it ranges from 2.6 to greater than 5 A, increasing with an increase in s. However, for the purpose of rough estimation, the reff with respect to the self-image energy can also be used in calculating the electric potential and the interaction energy, because the error introduced by this approximation is an overestimation of the order of 30% at most. It is also shown that the apparent dielectric constant for the interaction between two charges depends markedly upon the positions of the charges. In the course of this study, the dielectric constant and polarizability of the peptide backbone in the beta-sheet structure is estimated to be 10 and 8.22 A3