The gramicidin A channel: comparison of the energy profiles of Na+, K+ and Cs+. Influence of the flexibility of the ethanolamine end chain on the profiles

Permeation redux: thermodynamics and kinetics of ion movement through potassium channels

The fundamental biophysics underlying the selective movement of ions through ion channels was launched by George Eisenman in the 1960s, using glass electrodes. This minireview examines the insights from these early studies and the explosive progress made since then.

Molecular dynamics study of free energy profiles for organic cations in gramicidin A channels

The free energy profiles for four organic cations in right-handed single-helix gramicidin A dimers were computed by using umbrella sampling molecular dynamics with CHARMM. Ion-water column translocations were facilitated by using a novel "water-tunnel" approach. The overlapping pieces of free energy profile for adjacent windows were selected from three trajectories that differed in initial ion rotation and were aligned by the method of umbrella potential differences. Neglected long-range electrostatic energies from the bulk water and the bilayer were computed with DelPhi and added to the profile. The approach was corroborated for the formamidinium-guanidinium pair by using perturbation dynamics at axial positions 0, 6, 12, and 15 A from the channel center. The barrier to ethylammonium entry was prohibitive at 21 kcal/mol, whereas for methylammonium it was 5.5 kcal/mol, and the profile was quite flat through the channel, roughly consistent with conductance measurements. The profile for formamidinium was very similar to that of methylammonium. Guanidinium had a high entry barrier (deltaF = +8.6 kcal/mol) and a narrow deep central well (deltaF = -2.6 kcal/mol), qualitatively consistent with predictions from voltage-dependent potassium current block measurements. Its deep central well, contrasting with the flat profile for formamidinium, was verified with perturbation dynamics and was correlated with its high propensity to form hydrogen bonds with the channel at the dimer junction (not shared by the other three cations). Analysis of the ensemble average radial forces on the ions demonstrates that all four ions undergo compressive forces in the channel that are at maximum at the center of the monomer and relieved at the dimer junction, illustrating increased flexibility of the channel walls in the center of the channel.

Global scientific and engineering simulations on scalar, vector and parallel LCAP-type supercomputers

We present here an example of the global simulation approach to complex systems, selecting, as example, the study of a liquid, specifically water. We start by building the molecules of the liquid from nuclei and electrons using quantum mechanics. Next we obtain the interaction potentials (two, three and four body), again by quantum mechanics. Then we use Monte Carlo and molecular dynamics to study the motions of a water molecule within its Onsager sphere, and the collective properties; subsequently we overlap fluid dynamics by considering a flow along a channel with or without obstacles; finally we extend further and report a preliminary simulation of a Benard problem, using Newton’s equations. These simulations are performed on a parallel supercomputer which we have recently assembled; the system is briefly described in the second part of this work. A number of applications in science and engineering are analysed with attention to the degree of parallelization achievable with and without special hardwares such as busses and bulk shared memory. To conclude the implication of the global simulation methodology and supercomputers evolution is discussed in terms of productivity of information.

Gramicidin channel selectivity. Molecular mechanics calculations for formamidinium, guanidinium, and acetamidinium

Empirical energy function calculations were used to evaluate the effects of minimization on the structure of a gramicidin A channel and to analyze the energies of interaction between three cations (guanidinium, acetamidinium, formamidinium) and the channel as a function of position along the channel axis. The energy minimized model of the gramicidin channel, which was based on the results of Venkatachalam and Urry (1983), has a constriction at the channel entrance. If the channel is not allowed to relax in the presence of the ions (rigid model), there is a large potential energy barrier for all three cations. The barrier varies with cation size and is due to high van der Waals and ion deformation energies. If the channel is minimized in the presence of the ions, the potential energy barrier to formamidinium entry is almost eliminated, but a residual barrier remains for guanidinium and acetamidinium. The residual barrier is primarily due, not to the expansion of the helix, but, to the disruption of hydrogen bonds between the terminal ethanoloamine and the next turn of the helix which occurs when the carbonyls of the outer turn of the helix librate inward toward the ion as it enters the channel. The residual potential energy barriers could be a possible explanation for the measured selectivity of gramicidin for formamidinium over guanidinium. The results of this full-atomic model address the applicability of the size-exclusion concept for the selectivity of the gramicidin channel.

On the helix sense of gramicidin A single channels

In order to resolve whether gramicidin A channels are formed by right- or left-handed beta-helices, we synthesized an optically reversed (or mirror image) analogue of gramicidin A, called gramicidin A-, to test whether it forms channels that have the same handedness as channels formed by gramicidin M- (F. Heitz et al., Biophys. J. 40:87-89, 1982). In gramicidin M- the four tryptophan residues have been replaced with phenylalanine, and the circular dichroism (CD) spectrum therefore reflects almost exclusively contributions from the polypeptide backbone. The CD spectrum of gramicidin M- in dimyristoylphosphatidylcholine vesicles is consistent with a left-handed helical backbone folding motif (F. Heitz et al., Biophys. Chem. 24:149-160, 1986), and the CD spectra of gramicidins A and A- are essentially mirror images of each other. Based on hybrid channel experiments, gramicidin A- and M- channels are structurally equivalent, while gramicidin A and A- channels are nonequivalent, being of opposite helix sense. Gramicidin A- channels are therefore left-handed, and natural gramicidin A channels in phospholipid bilayers are right-handed beta 6.3-helical dimers.

Ion-water and ion-polypeptide correlations in a gramicidin-like channel. A molecular dynamics study

This work describes a molecular dynamics study of ion-water and ion-polypeptide correlation in a model gramicidin-like channel (the polyglycine analogue) based upon interaction between polarizable, multipolar groups. The model suggests that the vicinity of the dimer junction and of the ethanolamine tail are regions of unusual flexibility. Cs+ binds weakly in the mouth of the channel: there it coordinates five water molecules and the #11CO group with which it interacts strongly and is ideally aligned. In the channel interior it is generally pentacoordinate; at the dimer junction, because of increased channel flexibility, it again becomes essentially hexacoordinate. The ion is also strongly coupled to the #13 CO but not to either #9 or #15, consistent with 13C NMR data. Water in the channel interior is strikingly different from bulk water; it has a much lower mean dipole moment. This correlates with our observation (which differs from that of previous studies) that water-water angular correlations do not persist within the channel, a result independent of ion occupancy or ionic polarity. In agreement with streaming potential measurements, there are seven single file water molecules associated with Cs+ permeation; one of these is always in direct contact with bulk water. At the mouth of an ion-free channel, there is a pattern of dipole moment alteration among the polar groups. Due to differential interaction with water, exo-carbonyls have unusually large dipole moments whereas those of the endo-carbonyls are low. The computed potential of mean force for CS+ translocation is qualitatively reasonable. However, it only exhibits a weakly articulated binding site and it does not quantitatively account for channel energetics. Correction for membrane polarization reduces, but does not eliminate, these problems.

Energetics of ion permeation through membrane channels. Solvation of Na+ by gramicidin A

Calculations of the solvation energetics for a Na+ ion inside the Gramicidin A channel and in water are presented. The protein dipoles Langevin dipoles (PDLD) method is used to obtain an electrostatic free energy profile for ion permeation through the channel. To gauge the quality of the PDLD results the solvation free energy of a Na+ ion in water and in the center of the channel is also calculated using free energy perturbation (FEP) simulations. The effect of the polarisability of the surrounding lipid membrane is taken into account by representing the membrane by a large grid of polarisable point dipoles. The two methods give similar solvation energies in the interior of the channel and these are less than 5 kcal/mol above the solvation free energy for Na+ in water, in good agreement with experimental data on the activation barriers for ion permeation. It appears that the problems associated with previous calculations of energy profiles in membrane channels can be overcome by a consistent treatment of all the relevant electrostatic contributions. In particular, we find that the induced dipoles of the membrane and the protein contributes with approximately 10 kcal/mol to the solvation energy inside the channel and can therefore not be discarded in a realistic description of ion solvation in the Gramicidin channel.

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.

Evaluation of surface tension and ion occupancy effects on gramicidin A channel lifetime

The surface tension of glycerylmonooleate-hexadecane lipid bilayer membranes and the lifetime of gramicidin A channels were measured at various concentrations of the surrounding solutions. For HCl the surface tension is essentially constant at approximately 5 mN/m up to approximately 1 M, whereas the average lifetime increases approximately 40-fold. At higher concentrations the surface tension decreases markedly. For CsCl the surface tension is constant up to about 1 M then increases with salt level. The average lifetime in this case increases about sixfold. In both cases the lifetime levels off and even decreases at higher salt levels. The increase in lifetime observed with ion activity is therefore qualitatively different from, and not explained by, the established dependence of lifetime on membrane properties (Elliot, J.R., D. Needham, J.P. Dilger, and D.A. Haydon. 1983. Biochim. Biophys. Acta. 735:95-103). We have previously proposed that ion occupancy is a determinant of channel stability, and to test this hypothesis the voltage dependence of channel lifetime was measured in asymmetrical solutions. For the case of a potassium chloride solution on one side of the membrane and a hydrogen chloride solution, on the other, the voltage dependence of the lifetime is asymmetrical. The asymmetry is such that when the electrical field is applied in the direction of the chemical gradient for each of the ions, the channel lifetime approaches, at increasing field strengths, that of a symmetrical solution of the respective ion. The voltage dependence of the surface tension, on the other hand, is negligible for the range of voltages used. These results, and the earlier findings that the order of the lifetimes for the alkali cations generally agree with the order of the permeability selectivity of the gramicidin A channel, support the hypothesis that ion occupancy is a major factor determining the lifetime of gramicidin A channels. The effects of multivalent blockers and osmotic agents were also tested. Ba2", La3+,and Mg2" decrease the lifetime and conductance markedly. Sucrose and urea increase the lifetime and decrease the conductance. The voltage dependence of the lifetime in symmetrical solutions was examined. Contrary to previous reports it was found that the lifetimes for K+, Cs', and H+ are voltage dependent. For 0.5 M HCI the lifetime decreases monotonically by .60% at 150 mV, and for 0.5 M KCI the lifetime increases by -60% at 200 mV. Below 10 mM there is no effect of voltage for H+, K+, and Cs+. These effects of blockers, osmotic agents, and voltage on the lifetime, as well as the lack of effect of voltage at low salt levels, are consistent with the occupancy hypothesis.

The normal modes of the gramicidin-A dimer channel

The dynamics of the gramicidin-A dimer channel is studied in the harmonic approximation by a vibrational analysis of the atomic motions relative to their equilibrium positions. The system is represented by an empirical potential energy function, and all degrees of freedom (bonds lengths, bond angles, and torsional angles) are allowed to vary. The thermal fluctuations in the backbone dihedral angles phi and psi, atomic root mean square displacements, and the correlations between the different amide planes are computed. It is found that only adjacent dihedral psi i and phi i+1 are strongly correlated, while different hydrogen-bonded amide planes are only weakly correlated. Modes with relatively low vibrational frequencies (75-175 cm-1) make the dominant contributions to the carbonyl librations. The general flexibility of the structure and the role of carbonyl librations in the ion transport mechanism are discussed.

Energy profiles in the gramicidin A channel

Gramicidin A (GA) is a linear pentadecapeptide made of alternating D and L residues, in which the N-and C-terminals are blocked by a formyl group (head) and an ethanolamine end (tail), respectively (Sarges & Witkop, 1964):

The interaction of Cl- with a gramicidin-like channel

Molecular dynamics simulations have been used to study the interaction of Cl- with a gramicidin-like channel. The results suggest that there is a high-energy barrier at the entrance of the channel, which would correspond to a permeability 10(-9)-times that of a cation of the same size. This could account for the cationic selectivity of the gramicidin channel and indicates that valence selectivity is kinetically controlled.

Simulation of voltage-driven hydrated cation transport through narrow transmembrane channels

Molecular dynamics studies for the voltage-driven transport of the alkali metal ions lithium, sodium, and potassium through gramicidin A-type channels filled with water molecules are presented. The number of water molecules in the channel is obtained from a previous study (Skerra, A., and J. Brickmann, 1987, Biophys. J., 51:969-976). It is shown that the selectivity of the intrachannel ion diffusion through our model pore conforms to the experimentally observed selectivity of the gramicidin A channel. It is demonstrated that the number of water molecules in the channel plays a key role for the selectivity.

Experimental and theoretical study of gramicidin P, an analog of gramicidin A with a methylamine C-terminal

Gramicidin P (a gramicidin A in which the ethanolamine C-terminus is replaced by methylamine) was synthesized and shown to have the same single-channel conductance behavior as gramicidin A. The results are discussed in connection with the energy profile computed in the presence of water in comparison with the corresponding profile for gramicidin A.

Why is gramicidin valence selective? A theoretical study

Calculations contrasting the channel solvation energy for cesium ions and chloride ions associated with water in gramicidin-like channels are presented. The energy profile for the cation exhibits a deep well at the channel entrance; within the single file region the solvation energy is roughly constant. The anion exhibits a totally different energy profile. There is an energy barrier at the channel entrance; if the ion could surmount this barrier, it would be quite stable within the channel. At the channel entrance, the calculated solvation energy difference between anion and cation is approximately 15 kcal mol-1. This is completely consistent with the observation that chloride neither permeates nor blocks the channel since the estimated rate of ion entry would be approximately 0.01-10(-5) s-1, far slower than the rate at which the channel dimer dissociates into monomers.

The gramicidin A channel: energetics and structural characteristics of the progression of a sodium ion in the presence of water

The distribution of water molecules in the Gramicidin A (GA) channel is determined by theoretical computations, and the role of this water on the energetics of the system upon progression of a sodium cation through the channel is investigated. In the absence of the ion, water molecules form a chain along the channel, hydrogen bonded to one another and to the L carbonyl oxygens, while others stay at the entrances of the channel, hydrogen-bonded to the free carbonyl oxygens of the L-Tryptophan residues. According to the definition adopted for the "inside" and the "outside" of the channel, it is found to contain at most 7 or 9 water molecules. When a hydrated sodium cation approaches and enters the channel, the structural properties corresponding to the minimized total energy of the system GA-water-Na+ indicate a reorganization, but not a destruction, of the chain of water molecules. The "energy profile" for the system GA-Na+-(22 waters) is analyzed in terms of its components and in comparison to the corresponding intrinsic profile computed earlier in vacuo. It appears that the presence of water does not unduely modify the pathway or the qualitative features of the energetics of the cation passage, except at the entrance, where the partial and progressive dehydration of the cation plays an important role. The presence and characteristics of the minimum found earlier at 10.5 A from the center are conserved.

Rate theoretical analysis of ion-selectivity in membrane channels with elastically bound ligands

This article demonstrates why a gramicidin-like pore features ion-specific conductivity with the sequence Cs+ greater than Rb+ greater than K+ greater than Na+ greater than Li+. The starting point is a generalized transition state method for escape across multi-dimensional barriers. This model-independent procedure provides an adequate description of the transport process for ions along the interior of a channel-like molecule with flexible ligands. Moreover, the proper treatment of three-dimensional motion of ions within the channel allows for a cross-coupling with the ligands' motion. It is shown that the particle migrating along a sequence of binding sites actually corresponds to a polaron, where the individual dwelling times strongly depend on the ion's radius.

The effect of the amino-acid side chains on the energy profiles for ion transport in the gramicidin A channel

Computations on the energy profiles for Na+ in the gramicidin A (GA) channel have been extended by introducing the effect, previously neglected, of the amino acid side chains of GA, fixed in their most stable conformations. The calculations have been performed in two approximations: 1) with the ethanolamine tail fixed in its most stable conformation, 2) with the tail allowed to optimize its conformation upon the progression of the ion. In both approximations the overall shape of the energy profile is very similar to that obtained in the absence of the side chains. One observes, however, a general lowering of the profile upon the adjunction of the side chains. The analysis of the factors responsible for this energy lowering indicates that it is due essentially to the electrostatic and polarisation components of the interaction which interplay differently, however, in the different parts of the channel. A particular role is attributed in this respect to the tryptophan residues of GA. The role of the 4 tryptophans present, Trp 15, 13, 11 and 9, is individualized by stripping of one of them at a time. The strongest effect on the energy deepening is due to Trp 13 and is particularly prominent in the entrance zone at 14.5A from the center of the channel. The result indicates the possibility of investigating theoretically the effect on the energy profiles of the substitution of the "natural" side chain by others.