How shortening a channel may lower its conductance. The case of des-Val7-DVal8-gramicidin A

A shortened analog of gramicidin A has been shown by Urry et al. (Biochim. Biophys. Acta 775, 115-119) to have lower conductance than native gramicidin A. They argue this suggests that the major current carrier is the doubly occupied channel. A different perspective is presented here. Channel formation does not alter bilayer width. In a shortened channel an ion approaching the binding site moves further toward the center of the lipid-pore system. The electrostatic contribution to the energy barrier near the constriction mouth is greater for the shorter channel. As long as entry to the channel is rate limiting singly occupied short channels should exhibit lower conductance. The data are not inconsistent with singly occupied channels being the major current carriers. Experiments on other gramicidin analogs are suggested to more clearly distinguish between singly and doubly occupied channels as the dominant conducting species.     

Valence selectivity of the gramicidin channel: a molecular dynamics free energy perturbation study.

The valence selectivity of the gramicidin channel is examined using computer simulations based on atomic models. The channel interior is modeled using a gramicidin-like periodic poly (L,D)-alanine beta-helix. Free energy perturbation calculations are performed to obtain the relative affinity of K+ and Cl- for the channel. It is observed that the interior of the gramicidin channel provides an energetically favorable interaction site for a cation but not for an anion. Relative to solvation in bulk water, the carbonyl CO oxygens can provide a favorable interaction to stabilize K+, whereas the amide NH hydrogens are much less effective in stabilizing Cl-. The results of the calculations demonstrate that, as a consequence of the structural asymmetry of the backbone charge distribution, a K+ cation can partition spontaneously from bulk water to the interior of the gramicidin channel, whereas a Cl- anion cannot.     

Water transport and ion-water interaction in the gramicidin channel

The diffuse permeability and the diffusion coefficient of water (Dw) in the gramicidin channel is determined from the osmotic water permeability of the channel and "single file" pore theory. Dw is about 7% of the self-diffusion coefficient of bulk water. The diffusion coefficient of a single water molecule alone in the channel is also determined and is about equal to the value in bulk water. This provides an estimate of the mobility of water on the channel walls in the absence of water-water interaction. Since the gramicidin channel walls should be representative of uncharged polar protein surfaces, this result provides direct evidence that the presence of a cation in the channel reduces the hydraulic water permeability by a factor ranging from 60 for Tl+ to 5 for Na+. The diffusion coefficient of a cation (Dc) in the channel is estimated and compared with Dw. For Na+ it is found that Dc approximately equal to Dw, which implies that the movement of the row of water molecules through the channel determines the local mobility of Na+. Thus, it seems that short range ion-wall interactions are not important in determining the channel conductance for Na+. In contrast, for Li+, local ion-wall interactions probably do limit the conductance.     

Sodium in gramicidin: an example of a permion.

The reaction path and free energy profile of Na+ were computed in the interior of the channel protein gramicidin, with the program MOIL. Gramicidin was represented in atomic detail, but surrounding water and lipid molecules were not included. Thus, only short range interactions were investigated. The permeation path of the ion was an irregular spiral, far from a straight line. Permeation cannot be described by motions of a single Na+ ion. The minimal energy path includes significant motion of water and channel atoms as well as motion of the permeating ion. We think of permeation as motion of a permion, a quasi-particle that includes the many body character of the permeation process, comparable with quasi-particles like holes, phonons, and electrons of solid-state physics. Na+ is accompanied by a plug of water molecules, and motions of water, Na+, and the atoms of gramicidin are highly correlated. The permion moves like a linear polymer made of waters and ion linked and moving coherently along a zigzag line, following the reptation mechanism of polymer transport. The effective mass, free energy, and memory kernel (of the integral describing time-dependent friction) of short range interactions were calculated. The effective mass of the permion (properly normalized) is much less than Na+. Friction varies substantially along the path. The free energy profile has two deep minima and several maxima. In certain regions, the dominant motions along the reaction path are those of the channel protein, not the permeating ion: there, ion waits while the other atoms move. At these waiting sites, the permion's motion along the reaction path is a displacement of the atoms of gramicidin that prepare the way for the Na+ ion.     

K(+)/Na(+) selectivity of the KcsA potassium channel from microscopic free energy perturbation calculations

Microscopic molecular dynamics free energy perturbation calculations of the K(+)/Na(+) selectivity in the KcsA potassium channel, based on its experimental three-dimensional structure, are reported. The relative binding free energies for K(+) and Na(+) in the most relevant ion occupancy states of the four-site selectivity filter are calculated. The previously proposed mechanism for ion permeation through the KcsA channel is predicted, in agreement with available experimental data, to have a significant selectivity for K(+) over Na(+). The calculations also show that the individual 'binding site' selectivities are generally not additive and the doubly loaded states of the filter thus display cooperative effects. The only site that is not K(+) selective is that which is located at the entrance to the internal water cavity, suggesting the possibility that internal Na(+) could block outward currents.     

The total electrostatic potential in a gramicidin channel

Summary This paper describes a parameter free model of the electrostatic structure of gramicidin channels incorporated into uncharged lipid bilayer membranes. The electrical potential due to all sources is calculated for singly and doubly occupied channels. The model is consistent with all channel properties that are elearly dependent on coulombic interactions. The calculated value of the translocation rate constant and of the binding constant ratio for single and double occupancy are in excellent accord with experiment.     

On the mechanism of channel-length dependence of gramicidin single-channel conductance

Single-channel conductance data on four different gramicidin channel lengths demonstrate that conductance magnitude is neither inversely dependent on the square of the channel length nor on the image force arising from differences in the extent of lipid dimpling (Jordan and Vayl (1985) Biochim. Biophys. Acta 818, 416-420). Rather the conductance differences are consistent with the decreased off-rate constant for the singly occupied state as the ionic radius decreases from that of cesium ion to sodium ion coupled with the decreased probability of the doubly occupied channel due to increased ion-ion repulsion as the channel is shortened (Urry et al. (1984) Biochim. Biophys. Acta 774, 115-119).     

Ion transport in a model gramicidin channel. Structure and thermodynamics.

The potential of mean force for Na+ and K+ ions as a function of position in the interior of a periodic poly(L,D)-alanine model for the gramicidin beta-helix is calculated with a detailed atomic model and realistic interactions. The calculated free energy barriers are 4.5 kcal/mol for Na+ and 1.0 kcal/mol for K+. A decomposition of the free energy demonstrates that the water molecules make a significant contribution to the free energy of activation. There is an increase in entropy at the transition state associated with greater fluctuations. Analysis reveals that the free energy profile of ions in the periodic channel is controlled not by the large interaction energy involving the ion but rather by the weaker water-water, water-peptide and peptide-peptide hydrogen bond interactions. The interior of the channel retains much of the solvation properties of a liquid in its interactions with the cations. Of particular importance is the flexibility of the helix, which permits it to respond to the presence of an ion in a fluidlike manner. The distortion of the helix is local (limited to a few carbonyls) because the structure is too flexible to transmit a perturbation to large distances. The plasticity of the structure (i.e., the property to deform without generating a large energy stress) appears to be an essential factor in the transport of ions, suggesting that a rigid helix model would be inappropriate.     

Ion-specific diffusion rates through transmembrane protein channels. A molecular dynamics study

The migration of different alkali metal cations through a transmembrane model channel is simulated by means of the molecular dynamics technique. The parameters of the model are chosen in close relation to the gramicidin A channel. Coulomb- and van der Waals-type potentials between the ions and flexible carbonyl groups of the pore-forming molecule are used to describe the ion channel interaction. The diffusion properties of the ions are obtained from three-dimensional trajectory calculations. The diffusion rates for the different ions Li+, Na+, K+ and Rb+ are affected not only by the mass of the particles but also very strongly by their size. The latter effect is more pronounced for rigid channels, i.e., for binding vibrational frequencies of the CO groups with v greater than 400 cm-1. In this range the selectivity sequence for the diffusion rates is the inverse of that expected from normal rate theory but agrees with that found in experiments for gramicidin A.     

Determinants of conductance of a bacterial voltage-gated sodium channel

Through molecular dynamics (MD) and free energy simulations in electric fields, we examine the factors influencing conductance of bacterial voltage-gated sodium channel Na_vMs. The channel utilizes four glutamic acid residues in the selectivity filter (SF). Previously, we have shown, through constant pH and free energy calculations of pKa values, that fully deprotonated, singly protonated, and doubly protonated states are all feasible at physiological pH, depending on how many ions are bound in the SF. With 173 MD simulations of 450 or 500 ns and additional free energy simulations, we determine that the conductance is highest for the deprotonated state and decreases with each additional proton bound. We also determine that the pKa value of the four glutamic residues for the transition between deprotonated and singly protonated states is close to the physiological pH and that there is a small voltage dependence. The pKa value and conductance trends are in agreement with experimental work on bacterial Na_v channels, which show a decrease in maximal conductance with lowering of pH, with pKa in the physiological range. We examine binding sites for Na⁺ in the SF, compare with previous work, and note a dependence on starting structures. We find that narrowing of the gate backbone to values lower than the crystal structure's backbone radius reduces the conductance, whereas increasing the gate radius further does not affect the conductance. Simulations with some amount of negatively charged lipids as opposed to purely neutral lipids increases the conductance, as do simulations at higher voltages.     

Ion coordination in the amphotericin B channel.

The antifungal polyene antibiotic amphotericin B forms channels in lipid membranes that are permeable to ions, water, and nonelectrolytes. Anion, cation, and ion pair coordination in the water-filled pore of the "barrel" unit of the channels was studied by molecular dynamics simulations. Unlike the case of the gramicidin A channel, the water molecules do not create a single-file configuration in the pore, and some cross sections of the channel contain three or four water molecules. Both the anion and cation are strongly bound to ligand groups and water molecules located in the channel. The coordination number of the ions is about six. The chloride has two binding sites in the pore. The binding with water is dominant; more than four water molecules are localized in the anion coordination sphere. Three motifs of the ion coordination were monitored. The dominant motif occurs when the anion is bound to one ligand group. The ion is bound to two or three ligand groups in the less favorable configurations. The strong affinity of cations to the channel is determined by the negatively charged ligand oxygens, whose electrostatic field dominates over the field of the hydrogens. The ligand contribution to the coordination number of the sodium ion is noticeably higher than in the case of the anion. As in the case of the anion, there are three motifs of the cation coordination. The favorable one occurs when the cation is bound to two ligand oxygens. In the less favorable cases, the cation is bound to three or four oxygens. In the contact ion pair, the cation and anion are bound to two ligand oxygens and one ligand hydrogen, respectively. There exist intermediate solvent-shared states of the ion pair. The average distances between ions in these states are twice as large as that of the contact ion pair. The stability of the solvent-shared state is defined by the water molecule oriented along the electrostatic field of both ions.     

Stochastic theory of ion movement in channels with single-ion occupancy. Application to sodium permeation of gramicidin channels.

The electrodiffusion equations were solved for the one-ion channel both by the analytical method due to Levitt and also by Brownian dynamic simulations. For both types of calculations equilibration of ion distribution between the bath and the ends of the channel was assumed. Potential profiles were found that give good fits to published data on Na+ permeation of gramicidin channels. The data were best fit by profiles that have no relative energy maximum at the mouth of the channel. This finding suggests that alignment of waters or channel charged groups inside the channel in response to an ion's approach may provide an energetically favorable situation for entry sufficient to overcome the energy required for removing bulk waters of hydration. An alternative possibility is that the barrier to ion entry is situated outside the region restricted to single-ion occupancy. Replacement of valine with more polar amino acids at the No. 1 location was found to correspond to a deepening of the potential minima near the channel mouths, an increase in height of the central barrier to ion translocation across the channel, and possibly a reduction in the mobility of the ion-water complex in the channel. The Levitt theory was extended to calculate passage times for ions to cross the channel and the blocking effects of ions that entered the channel but didn't cross. These quantities were also calculated by the Brownian dynamics method.     

Stochastic theory of singly occupied ion channels. II. Effects of access resistance and potential gradients extending into the bath.

In a previous paper (Jakobsson, E., and S. W. Chiu. 1987. Biophys. J. 52:33-46), we presented the stochastic theory of the singly occupied ion channel as applied to sodium permeation of gramicidin channels, with the assumption of perfect equilibration between the bathing solutions and the ends of the ion channel. In the present paper we couple the previous theory to electrodiffusion of ions from the bulk of the bathing solution to the channel mouth. Our electrodiffusion calculations incorporate estimates of the potential gradients near the channel mouth due to image forces and due to the fraction of the applied potential that falls beyond the ends of the channel. To keep the diffusion calculation one-dimensional, we make the assumption that the electrical potentials in the bath exhibit hemispherical symmetry. As in the previous paper, the flux equations are fit to data on sodium permeation of normal gramicidin A, and gramicidins modified by the fluorination of the valine at the No. 1 position (Barrett Russell, E. W., L. B. Weiss, F. I. Navetta, R. E. Koeppe II, and O. S. Anderson. 1986. Biophys. J. 49:673-686). The conclusions of our previous paper with respect to the effect of fluorination on the mobility, surface potential well depth, and central barrier, are confirmed. However the absolute values of these quantities are somewhat changed when diffusive resistance to the mouth is taken into account, as in the present paper. Future possibilities for more accurate calculations by other methods are outlined.     

Protonation state of the selectivity filter of bacterial voltage-gated sodium channels is modulated by ions

The selectivity filter (SF) of bacterial voltage-gated sodium channels consists of four glutamate residues arranged in a C₄ symmetry. The protonation state population of this tetrad is unclear. To address this question, we simulate the pore domain of bacterial voltage-gated sodium channel of Magnetococcus sp. (Na_vMs) through constant pH methodology in explicit solvent and free energy perturbation calculations. We find that at physiological pH the fully deprotonated as well as singly and doubly protonated states of the SF appear feasible, and that the calculated pKa decreases with each additional bound ion, suggesting that a decrease in the number of ions in the pore can lead to protonation of the SF. Previous molecular dynamics simulations have suggested that protonation can lead to a decrease in the conductance, but no pKa calculations were performed. We confirm a decreased ionic population of the pore with protonation, and also observe structural symmetry breaking triggered by protonation; the SF of the deprotonated channel is closest to the C₄ symmetry observed in crystal structures of the open state, while the SF of protonated states display greater levels of asymmetry which could lead to transition to the inactivated state which possesses a C₂ symmetry in the crystal structure. We speculate that the decrease in the number of ions near the mouth of the channel, due to either random fluctuations or ion depletion due to conduction, could be a self-regulatory mechanism resulting in a nonconducting state that functionally resembles inactivated states.     

Molecular dynamics study of water and Na+ ions in models of the pore region of the nicotinic acetylcholine receptor.

The nicotinic acetylcholine receptor (nAChR) is an integral membrane protein that forms ligand-gated and cation-selective channels. The central pore is lined by a bundle of five approximately parallel M2 helices, one from each subunit. Candidate model structures of the solvated pore region of a homopentameric (alpha7)5 nAChR channel in the open state, and in two possible forms of the closed state, have been studied using molecular dynamics simulations with restraining potentials. It is found that the mobility of the water is substantially lower within the pore than in bulk, and the water molecules become aligned with the M2 helix dipoles. Hydrogen-bonding patterns in the pore, especially around pore-lining charged and hydrophilic residues, and around exposed regions of the helix backbone, have been determined. Initial studies of systems containing both water and sodium ions together within the pore region have also been conducted. A sodium ion has been introduced into the solvated models at various points along the pore axis and its energy profile evaluated. It is found that the ion causes only a local perturbation of the water structure. The results of these calculations have been used to examine the effectiveness of the central ring of leucines as a component of a gate in the closed-channel model.     

Energy levels and ion wave functions in gramicidin channels

A model study of the motion of Na+ ions in the cavity of membrane gramicidin channels was performed by the methods of quantum mechanics. An approximation of the distribution of the electrostatic potential along the channel axis, determined by charges on the atoms of the gramicidin A molecule, was obtained. The energy distribution and the wave functions for the stationary states of the ions were determined. The solutions of the Schr?dinger equation for two conformers were compared.     

Effects of internal Na+ on the Ca channel outward current in mouse neoplastic B lymphocytes

The whole-cell configuration of the patch-clamp technique was used to study the outward Na+ current through Ca channels in hybridoma cell lines (202B and 206), constructed by fusion of S194 myeloma cells with murine splenic B lymphocytes. The concentration of Na+ in the electrode solution, [Na+]p, was changed by isosmotic replacement of Na+ with N-methyl-D-glucamine+ ions. When 2.5 mM calcium was present in the bath, neither the current nor the reversal potential was significantly altered by changes in the level of external Na+ [( Na+]o. By contrast, both of those properties were strongly affected by [Na+]p. At fixed depolarizing potentials, the outward current increased approximately as the square power of [Na+]p, a feature that cannot be easily explained by one-ion models for a channel or by "continuum" theories based on electrodiffusion. Instead, all the data could be well described by a "single-file" model for a two-site pore that admits up to two ions. Although double occupancy of the Ca channel by divalent cations has been proposed previously (Hess and Tsien. 1984. Nature. 309: 453-456; Almers et al., 1984. J. Physiol. 353: 585-608), this study indicates that, in our system, states of the channel with two Na+ ions must also be considered in order to explain the dependence of the outward current on [Na+]p. A good fit to the data could be obtained by assuming that both sites in the channel are "electrically" close to its cytoplasmic end and that most of the voltage dependence pertains to the rates for ion exit to the external medium. The values of the parameters suggest that: (a) Ca2+ is bound most strongly by the site nearest to the cytoplasm (in both singly and doubly occupied channels); (b) in channels with two Ca2+ ions, the dissociation constant of the site close to the external mouth must be greater than 2.5 mM; and (c) in pores occupied by two Na+ ions, the rate constant for Na+ exit to the external solution is larger than the rate constant for Na+ exit to the cytoplasm.     

Energy profile of Cs+ in gramicidin A in the presence of water. Problem of the ion selectivity of the channel

The effect of water present at the mouth and inside the channel of Gramicidin A on the energy profile calculated for a caesium ion is determined. The total optimal interaction energy computed for the system GA-Cs+-(22 waters) leads to an energy profile characterized by a deep minimum at 11 A followed by an entrance energy barrier of 7 Kcal/mol expanding until 9 A from the center. After this point, a second minimum less deep than the previous one is observed, itself followed by a central barrier. The shape of the profile at the entrance is governed by the balance between the progressive desolvation process of the ion and the increase of favorable hydrogen bond interactions implying both the water molecules and GA. The comparison of this energy profile with that obtained in vacuo shows that the presence of water molecules does not modify the pathway of the ion which, owing to its size, is constrained essentially to remain on the channel axis. The comparison Na+ versus Cs+ indicates that although the phenomena involved are globally the same, differences between the two profiles appear due firstly to the difference in the affinity of the two ions for water and secondly to their respective size. This last difference implies that the number of water molecules present in the interior of the channel during the cation progression is reduced roughly by one in the case of caesium. The desolvation barrier computed for Cs+ is half the corresponding value for Na+, a result in agreement with the observed selectivity.     

Thermodynamic stability of water molecules in the bacteriorhodopsin proton channel: a molecular dynamics free energy perturbation study.

The proton transfer activity of the light-driven proton pump, bacteriorhodopsin (bR) in the photochemical cycle might imply internal water molecules. The free energy of inserting water molecules in specific sites along the bR transmembrane channel has been calculated using molecular dynamics simulations based on a microscopic model. The existence of internal hydration is related to the free energy change on transfer of a water molecule from bulk solvent into a specific binding site. Thermodynamic integration and perturbation methods were used to calculate free energies of hydration for each hydrated model from molecular dynamics simulations of the creation of water molecules into specific protein-binding sites. A rigorous statistical mechanical formulation allowing the calculation of the free energy of transfer of water molecules from the bulk to a protein cavity is used to estimate the probabilities of occupancy in the putative bR proton channel. The channel contains a region lined primarily by nonpolar side-chains. Nevertheless, the results indicate that the transfer of four water molecules from bulk water to this apparently hydrophobic region is thermodynamically permitted. The column forms a continuous hydrogen-bonded chain over 12 A between a proton donor, Asp 96, and the retinal Schiff base acceptor. The presence of two water molecules in direct hydrogen-bonding association with the Schiff base is found to be strongly favorable thermodynamically. The implications of these results for the mechanism of proton transfer in bR are discussed.