Location of ion-binding sites in the gramicidin channel by X-ray diffraction.

We report the first X-ray diffraction on gramicidin in its membrane-active form by using uniformly aligned multilayer samples of membranes containing gramicidin and ions (T1+, K+, Ba2+, Mg2+ or without ions). From the difference electron density profiles, we found a pair of symmetrically located ion-binding sites for T1- at 9.6 (+/- 0.3) A and for Ba2+ at 13.0 (+/- 0.2) A from the midpoint of the gramicidin channel. The location of Ba(2+)-binding sites is near the ends of the channel, consistent with the experimental observation that divalent cations do not permeate but block the channel. The location of T1(+)-binding sites is somewhat of a surprise. It was generally thought that monovalent cations bind to the first turn of the helix from the mouth of the channel. (It is now generally accepted that the gramicidin channel is a cylindrical pore formed by two monomers, each a single-stranded beta 6.3 helix and hydrogen-bonded head-to-head at their N termini.) But our experiment shows that the T1(+)-binding site is either near the bottom of or below the first helix turn.     

Small iminium ions block gramicidin channels in lipid bilayers.

Guanidinium and acetamidinium, when added to the bathing solution in concentrations of approximately 0.1M, cause brief blocks in the single channel potassium currents from channels formed in planar lipid bilayers by gramicidin A. Single channel lifetimes are not affected indicating that the channel structure is not modified by the blockers. Guanidinium block durations and interblock times are approximately exponential in distribution. Block frequencies increase with guanidinium concentration whereas block durations are unaffected. Increases in membrane potential cause an increase in block frequency as expected for a positively charged blocker but a decrease in block duration suggesting that the block is relieved when the blocker passes through the channel. At low pH, urea, formamide, and acetamide cause similar blocks suggesting that the protonated species of these molecules also block. Arginine and several amines do not block. This indicates that only iminium ions which are small enough to enter the channel can cause blocks in gramicidin channels.     

Theoretical study of the antiparallel double-stranded helical dimer of gramicidin as an ion channel.

Recent experimental studies by Durkin, J. T., O. S. Andersen, F. Heitz, Y. Trudelle, and R. E. Koeppe II (1987. Biophys. J. 51:451a) have suggested that the antiparallel double-stranded helical (APDS) dimer of gramicidin can form a transmembrane cation channel. This article reports a theoretical study that successfully rationalizes the channel properties of the APDS dimer. As in the case of the head-to-head (HH) dimer, the APDS exhibits a high potential energy barrier as anions approach the channel mouth, according for the observation of valence selectivity. The calculated potential energies of cations show two binding sites near the channel mouths, a typical feature of the HH channel. The potential energies of hydrated cations in the APDS are generally higher than those in the HH channel and show a larger pseudoperiodicity and higher barriers, an observation which suggests that the APDS should exhibit lower single channel conductance.     

Gramicidin tryptophans mediate formamidinium-induced channel stabilization.

Compared with alkali metal cations, formamidinium ions stabilize the gramicidin A channel molecule in monoolein bilayers (Seoh and Busath, 1993a). A similar effect is observed with N-acetyl gramicidin channel molecules in spite of the modified forces at the dimeric junction (Seoh and Busath, 1993b). Here we use electrophysiological measurements with tryptophan-to-phenylalanine-substituted gramicidin analogs to show that the formamidinium-induced channel molecule stabilization is eliminated when the four gramicidin tryptophans are replaced with phenylalanines in gramicidin M-. This suggests that the stabilization is mediated by the tryptophan side chains. Tryptophan residues 9, 13, and 15 must cooperate to produce the effect because replacement of any one of the three with phenylalanine significantly reduces stabilization; replacement of Trp-11 with phenylalanine causes negligible decrease in stabilization. In addition, formamidinium-related current-voltage supralinearity and open-channel noise are absent with gramicidin M-. When the lipid bilayer was formed with monoolein ether rather than monoolein ester, the channel lifetimes were reduced markedly and, at low voltage and relative to those in KCl solution, were decreased by a factor of 2, whereas the open-channel noise was unaffected and the current-voltage relation was only modestly affected. These results suggest that formamidinium modifies the state of the tryptophan side chains, which, in turn, affects channel lifetime, current-voltage supralinearity, and open-channel noise through interactions with water or lipid headgroup atoms including the lipid ester carbonyl.     

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.     

The permeation properties of small organic cations in gramicidin A channels.

The conductance properties of organic cations in single gramicidin A channels were studied using planar lipid bilayers. From measurements at 10 mM and at 27 mV the overall selectivity sequence was found to be NH4+ > K+ > hydrazinium > formamidinium > Na+ > methylammonium, which corresponds to Eisenman polyatomic cation sequence X'. Methylammonium and formamidinium exhibit self block, suggesting multiple occupancy and single filing. Formamidinium has an apparent dissociation constant (which is similar to those of alkali metal cations) for the first ion being 22 mM from the Eadie-Hofstee plot (G0 vs. G0/C), 12 mM from the rate constants of a three-step kinetic model. The rate-limiting step for formamidinium is translocation judging from supralinear I-V relations at low concentrations. 1 M formamidinium solutions yields exceptionally long single channel lifetimes, 20-fold longer than methylammonium, which yields lifetimes similar to those found with alkali metal cations. The average lifetime in formamidinium solution significantly decreases with increasing voltage up to 100 mV but is relatively voltage independent between 100 and 200 mV. At lower voltages (< or = 100 mV), the temperature and concentration dependences of the average lifetime of formamidinium were steep. At very low salt concentrations (0.01 M, 100 mV), there was no significant difference in average lifetime from that formed with 0.01 M methylammonium or hydrazinium. We conclude that formamidinium very effectively stabilizes the dimeric channel while inside the channel and speculate that it does so by affecting tryptophan-reorientation or tryptophan-lipid interactions at binding sites.     

Constant helical pitch of the gramicidin channel in phospholipid bilayers.

X-ray diffraction has been applied in measuring the helical pitch of the gramicidin channel in oriented bilayers of dilauroylphosphatidylcholine (DLPC) and dimyristoylphosphatidylcholine (DMPC) at a polypeptide concentration of 9.1 mol %. The diffraction data show the helical pitch of gramicidin to be 4.7 +/- 0.2 A in both gel and liquid-crystalline phase bilayers, with and without monovalent cations. In addition, the width of the reflection due to the pitch of the helical gramicidin channel is consistent with a five turn helix.     

Formamidinium-induced dimer stabilization and flicker block behavior in homo- and heterodimer channels formed by gramicidin A and N-acetyl gramicidin A.

Compared to the N-formyl gramicidin A (GA), the N-acetyl gramicidin A (NAG) channel has unchanged conductance in 1 M NH4+ (gamma NN/gamma GG = 1, conductance ratio) but reduced conductance in 1 M K+ (gamma NN/gamma GG = 0.6) methylammonium (gamma NN/gamma GG = 0.3), and formamidinium (gamma NN/gamma GG = 0.1) solutions. Except with formamidinium, "flicker blocks" are evident even at low cutoff frequencies. For all cations studied, channel lifetimes of N-acetyl homodimers (NN) are approximately 50-fold shorter than those of the GA homodimer (GG). The novel properties of GA channels in formamidinium solution (supralinear current-voltage relations and dimer stabilization (Seoh and Busath, 1993)) also appear in NN channels. The average single channel lifetime in 1 M formamidinium solution at 100 mV is 6-7-fold longer than in K+ and methylammonium solutions and, like in the GA channel, significantly decreases with increasing membrane potential. Experiments with mixtures of the two peptides, GA and NAG, showed three main conductance peaks. Oriented hybrids were formed utilizing the principle that monomers remain in one leaflet of the bilayer (O'Connell et al., 1990). With GA at the polarized side and NAG at the grounded side, at positive potentials (in which case hybrids were designated GN) and at negative potentials (in which case hybrids were designated NG), channels had the same conductances and channel properties at all potentials studied. Flicker blocks were not evident in the hybrid channels, which suggests that both N-acetyl methyl groups at the junction of the dimer are required to cause flickers. Channel lifetimes in hybrids are only approximately threefold shorter than those of the GG channels, and channel conductances are similar to those of GG rather than NN channels. We suggest that acetyl-acetyl crowding at the dimeric junction in NN channels cause dimer destabilization, flickers, and increased selectivity in N-acetyl gramicidin channels.     

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.     

Energetics of ion permeation, rejection, binding, and block in gramicidin A from free energy simulations

The rigid force fields currently used in molecular dynamics (MD) simulations of biomolecules are optimized for globular proteins. Whether they can also be used in MD simulations of membrane proteins is an important issue that needs to be resolved. Here we address this issue using the gramicidin A channel, which provides an ideal test case because of the simplicity of its structure and the availability of a wealth of functional data. Permeation properties of gramicidin A can be summarized as "it conducts monovalent cations, rejects anions, and binds divalent cations." Hence, a comprehensive test should consider the energetics of permeation for all three types of ions. To that end, we construct the potential of mean force for K(+), Cl(-), and Ca(2+) ions along the channel axis. For an independent check of the potential-of-mean-force results, we also calculate the free energy differences for these ions at the channel center and binding sites relative to bulk. We find that "rejection of anions" is satisfied but there are difficulties in accommodating the other two properties using the current MD force fields.     

Permeation of ions across the potassium channel: brownian dynamics studies

The physical mechanisms underlying the transport of ions across a model potassium channel are described. The shape of the model channel corresponds closely to that deduced from crystallography. From electrostatic calculations, we show that an ion permeating the channel, in the absence of any residual charges, encounters an insurmountable energy barrier arising from induced surface charges. Carbonyl groups along the selectivity filter, helix dipoles near the oval chamber, and mouth dipoles near the channel entrances together transform the energy barrier into a deep energy well. Two ions are attracted to this well, and their presence in the channel permits ions to diffuse across it under the influence of an electric field. Using Brownian dynamics simulations, we determine the magnitude of currents flowing across the channel under various conditions. The conductance increases with increasing dipole strength and reaches its maximum rapidly; a further increase in dipole strength causes a steady decrease in the channel conductance. The current also decreases systematically when the effective dielectric constant of the channel is lowered. The conductance with the optimal choice of dipoles reproduces the experimental value when the dielectric constant of the channel is assumed to be 60. The current-voltage relationship obtained with symmetrical solutions is linear when the applied potential is less than approximately 100 mV but deviates from Ohm's law at a higher applied potential. The reversal potentials obtained with asymmetrical solutions are in agreement with those predicted by the Nernst equation. The conductance exhibits the saturation property observed experimentally. We discuss the implications of these findings for the transport of ions across the potassium channels and membrane channels in general.     

Ionic selectivity, saturation, and block in sodium channels. A four- barrier model

Ionic fluxes in Na channels of myelinated axons show ionic competition, block, and deviations from simple flux independence. These phenomena are particularly evident when external Na+ ions are replaced by other permeant or impermeant ions. The observed currents require new flux equations not based on the concepts of free diffusion. A specific permeability model for the Na channel is developed from Eyring rate theory applied to a chain of saturable binding sites. There are four energy barriers in the pore and only one ion is allowed inside at a time. Deviations from independence arise from saturation. The model shows that ionic permeability ratios measured from zero-current potentials can differ from those measured from relative current amplitudes or conductances. The model can be fitted to experiments with various external sodium substitutes by varying only two parameters: For each ion the height of the major energy barrier (the selectivity filter) determines the biionic zero-current potential and the depth of the energy well (binding site) just external to that barrier then determines the current amplitudes. Voltage clamp measurements with myelinated nerve fibers are given showing numerous examples of deviations from independence in ionic fluxes. Strong blocks of ionic currents by guanidinium compounds and Tl+ ions are fitted by binding within the channel with apparent dissociation constants in the range 50-122 mM. A small block with high Na+ concentrations can be fitted by Na+ ion binding with a dissociation constant of 368 mM. The barrier model is given a molecular interpretation that includes stepwise dehydration of the permeating ion as it interacts with an ionized carboxylic acid.     

Extended dipolar chain model for ion channels: electrostriction effects and the translocational energy barrier.

We reinvestigate the dipolar chain model for an ion channel. Our goal is to account for the influence that ion-induced electrostriction of channel water has on the translocational energy barriers experienced by different ions in the channel. For this purpose, we refine our former model by relaxing the positional constraint on the ion and the water dipoles and by including Lennard-Jones contributions in addition to the electrostatic interactions. The positions of the ion and the waters are established by minimization of the free energy. As before, interaction with the external medium is described via the image forces. Application to alkali cations show that the short range interactions modulate the free energy profiles leading to a selectivity sequence for translocation. We study the influence of some structural parameters on this sequence and compare our theoretical predictions with observed results for gramicidin.     

Effect of pore structure on energy barriers and applied voltage profiles. I. Symmetrical channels.

This paper presents calculations of the image potential for an ion in an aqueous pore spanning a lipid membrane and for the electric field produced in such a pore when a transmembrane potential is applied. The pore diameter may be variable. As long as the length-to-radius ratio in the narrow portion of a channel is large enough, the image potential for an ion in or near the mouth of a channel is determined by the geometry of the mouth. Within the constriction, the image potential of the ion-pore system may be reasonably approximated by constructing an "equivalent pore" of uniform diameter spanning a somewhat thinner membrane. When a transmembrane potential is applied the electric field within a constricted, constant radius, section of the model pore is constant. If the length-to-radius ratio of the narrow part of the channel is not too large or the channel ensemble has wide mouths, the field extends a significant distance into the aqueous region. The method is used to model features of the gramicidin A channel. The energy barrier for hydration (for exiting the channel) is identified with the activation energy for gramicidin conductance (Bamberg and Läuger, 1974, Biochim. Biophys. Acta. 367:127).     

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.     

Permeability of the squid giant axon to organic cations and small nonelectrolytes

Summary The permeability of the Na channel of squid giant axon to organic cations and small nonelectrolytes was studied. The compounds tested were guanidinium, formamidinium, and¹⁴C-labeled urea, formamide, thiourea, and acetone. Permeability was calculated from measurements of reversal potential and influx on internally perfused, voltage clamped squid axons. The project had two objectives: (1) to determine whether different methods of measuring the permeability of organic cations yield similar values and (2) to see whether neutral analogs of the organic cations can permeate the Na channel. Our results show that the permeability ratio of sodium to a test ion depends upon the ionic composition of the solution used. This finding is consistent with the view put forward previously that the Na channel can contain more than one ion at a time. In addition, we found that the uncharged analogs of permeant cations are not measurably permeant through the Na channel, but instead probably pass through the lipid bilayer.     

The ionic selectivity of two voltage activated channels and an acetylcholine activated channel in an Onchidium neuron

1. The selectivities of the ion channels underlying the action potential and the hyperpolarizing response to acetylcholine of the GH cell of Onchidium have been analysed. 2. The rising phase of the action potential is due to an increase in the permeability of the membrane to both Na+ and Ca2+. The Na+ channel is permeable to Li+ and is somewhat permeable to formamidinium, guanidinium and ammonium ions. The Ca2+ channel is permeable to Sr2+ and Ba2+, but not to Mn2+ and Mg2+. 3. The Cl- channel operated by ACh is permeable to chlorate, but not to formate and propionate ions. 4. The selectivities of these channels are similar to those of a number of other channels in other organisms.     

Molecular dynamics - potential of mean force calculations as a tool for understanding ion permeation and selectivity in narrow channels

Ion channels catalyze the permeation of charged molecules across cell membranes and are essential for many vital physiological functions, including nerve and muscle activity. To understand better the mechanisms underlying ion conduction and valence selectivity of narrow ion channels, we have employed free energy techniques to calculate the potential of mean force (PMF) for ion movement through the prototypical gramicidin A channel. Employing modern all-atom molecular dynamics (MD) force fields with umbrella sampling methods that incorporate one hundred 1-2 ns trajectories, we find that it is possible to achieve semi-quantitative agreement with experimental binding and conductance measurements. We also examine the sensitivity of the MD-PMF results to the choice of MD force field and compare PMFs for potassium, calcium and chloride ions to explore the basis for the valence selectivity of this narrow and uncharged ion channel. A large central barrier is observed for both anions and divalent ions, consistent with lack of experimental conductance. Neither anion or divalent cation is seen to be stabilized inside the channel relative to the bulk electrolyte and each leads to large disruptions to the protein and membrane structure when held deep inside the channel. Weak binding of calcium ions outside the channel corresponds to a free energy well that is too shallow to demonstrate channel blocking. Our findings emphasize the success of the MD-PMF approach and the sensitivity of ion energetics to the choice of biomolecular force field.     

Activation of diol dehydrase by formamidinium or guanidinium ion, polyatomic monovalent cations having sp2 nitrogen

Coenzyme B₁₂-dependent diol dehydrase was activated by formamidinium or guanidinium ion. These polyatomic monovalent cations having sp² hybrid atomic orbitals and trigonal orientation were much more effective in activating the enzyme than methylammonium ion, but less active than NH₄+ or K⁺. Formamidinium and guanidinium ions were also effective both in forming and maintaining the binding of coenzyme B₁₂ to the apoenzyme. There is a close relationship between the effectiveness in activating the enzyme and those in forming and maintaining the holoenzyme, suggesting that these polyatomic monovalent cations play the same role in the diol dehydrase system as alkali metal monovalent cation such as K⁺.     

Electrostatic calculations for an ion channel. I. Energy and potential profiles and interactions between ions

The electrostatic energy profile of one, two, or three ions in an aqueous channel through a lipid membrane is calculated. It is shown that the previous solution to this problem (based on the assumption that the channel is infinitely long) significantly overestimates the electrostatic energy barrier. For example, for a 3-A radius pore, the energy is 16 kT for the infinite channel and 6.7 kT for an ion in the center of a channel 25 A long. The energy as a function of the position of the ion is also determined. With this energy profile, the rate of crossing the membrane (using the Nernst-Planck equation) was estimated and found to be compatible with the maximum conductance observed for the gramicidin A channel. The total electrostatic energy (as a function of position) required to place two or three ions in the channel is also calculated. The electrostatic interaction is small for two ions at opposite ends of the channel and large for any positioning of the three ions. Finally, the gradient through the channel of an applied potential is calculated. The solution to these problems is based on solving an equivalent problem in which an appropriate surface charge is placed on the boundary between the lipid and aqueous regions. The magnitude of the surface charge is obtained from the numerical solution for a system of coupled integral equations.