Gramicidin A channel as a test ground for molecular dynamics force fields

Binding of Organic Cations to Gramicidin A Channel Studied with AutoDock and Molecular Dynamics Simulations

The accurate description of protein-ligand binding energies and configurations is an important problem in molecular biology with many applications in medicine and pharmacology. Molecular dynamics (MD) simulations provide the required accuracy but they are too slow for searching binding positions. Conversely, docking methods are much faster but have limited accuracy. An appropriate combination of the two methods could avoid the shortcomings associated with each, thus offering a better approach to the protein-ligand binding problem. Here we investigate the feasibility of such a combined docking-MD approach in a well-defined system: binding of organic cations to the gramicidin A channel. We use the AutoDock program to generate a set of protein-ligand binding configurations, which are then refined in MD simulations. For each system, we examine the binding configuration in detail and calculate the binding free energy by constructing the potential of mean force for the ligand. Our results show that AutoDock provides suitable initial configurations, which can be used profitably in MD simulations to obtain an accurate description of protein-ligand binding with a reasonable computational effort.

Conduction properties of KcsA measured using brownian dynamics with flexible carbonyl groups in the selectivity filter

In the narrow segment of an ion conducting pathway, it is likely that a permeating ion influences the positions of the nearby atoms that carry partial or full electronic charges. Here we introduce a method of incorporating the motion of charged atoms lining the pore into Brownian dynamics simulations of ion conduction. The movements of the carbonyl groups in the selectivity filter of the KcsA channel are calculated explicitly, allowing their bond lengths, bond angles, and dihedral angels to change in response to the forces acting upon them. By systematically changing the coefficients of bond stretching and of angle bending, the carbon and oxygen atoms can be made to fluctuate from their fixed positions by varying mean distances. We show that incorporating carbonyl motion in this way does not alter the mechanism of ion conduction and only has a small influence on the computed current. The slope conductance of the channel increases by approximately 25% when the root mean-square fluctuations of the carbonyl groups are increased from 0.01 to 0.61 A. The energy profiles and the number of resident ions in the channel remain unchanged. The method we utilized here can be extended to allow the movement of glutamate or aspartate side chains lining the selectivity filters of other ionic channels.

Free energy simulations of single and double ion occupancy in gramicidin A

Simultaneous occupancy of the two binding sites in gramicidin A by monovalent cations is a well known property of this channel, but the energetic feasibility of this process in molecular dynamics simulations has not been established so far. Here the authors study the energetics of single and double ion occupancy in gramicidin A by constructing the potential of mean force for single and pair of cations. As representatives of small and large ions, they consider both Na+ and K+ ions in the calculations. Binding constants of ions are estimated from the free energy profiles. Comparisons with the experimental results indicate 3-4 kT discrepancy in the binding energies. They also study the coordination of the ions in their respective binding sites and the dynamic behavior of the channel water during the double ion binding process.

Structure and energetics of channel-forming protein-polysaccharide complexes inferred via computational statistical thermodynamics

The ion channel protein alpha-hemolysin (alphaHL) forms supramolecular complexes with the polysaccharide beta-cyclodextrin (betaCD). This system has potential uses in nanoscale device engineering. It has been found recently that betaCD formed longer- or shorter-lived complexes with some engineered alphaHL mutants then with a wild type protein (Gu et al. J. Gen. Physiol. 2001, 118, 481-493). However, how changes in the protein sequence affect complex lifetime was not completely understood in part due to the lack of knowledge of structures of these metastable complexes. In this paper, we present an extensive molecular modeling study of the betaCD-alphaHL and selected mutant complexes to gain insights into the betaCD-alphaHL interaction mechanisms and to predict possible structures and energetics of the complexes. Thermodynamic integration (TI) and umbrella sampling (US) techniques (with the weighted histogram analysis method (WHAM)) were used to calculate the relative binding affinities of the complexes formed with the wild type alphaHL and the M113N, M113E, M113A, and M113V mutants. Our results are in excellent agreement with experiment. While betaCD-M113N and betaCD-M113A complexes were stable in the configuration of the wild type complex, the equilibrium configuration of the betaCD-M113V and betaCD-M113E complexes was significantly different. In these cases, TI alone was insufficient to accurately calculate the corresponding free energy differences. By utilizing a TI/US combination in a novel manner, we were able to accurately calculate free energy changes in these flexible systems. The betaCD-M113A and betaCD-M113E complexes, which exhibited shorter lifetimes than other complexes in an experiment, in simulations exhibited greater flexibility and higher water solvation of the betaCD adapter. MD simulations of the betaCD-M113N complex with betaCD in a downward orientation were also performed.

Electric field effects on membranes: Gramicidin A as a test ground

Electric fields due to transmembrane potential differences or ionic gradients across the membrane are presumably crucial for many reactions across membranes or close to membranes like signal transduction, control of ion channels or the generation of neural impulses. Molecular dynamics simulations have been used to study the influence of external electric fields on a mixed gramicidin/phospholipid bilayer system. At high field strengths, formation of membrane electropores occurred both close and distal to the gramicidin. Gramicidin was found to stabilize the membrane adjacent to the protein but also at larger distances of up to 2-3 nm. As a result, membrane pore formation was found to be significantly suppressed for the mixed gramicidin/DMPC system. Moderate field strengths only weakly affected the structure and dynamics of the gramicidin. Spontaneous potassium passage events in external electric fields were observed for both the head-to-head helical conformation as well as for the double helical conformation of gramicidin A. The double-helical conformation was found to facilitate ion passage compared to the head-to-head helical dimer.

A hydrophobic gate in an ion channel: the closed state of the nicotinic acetylcholine receptor

The nicotinic acetylcholine receptor (nAChR) is the prototypic member of the 'Cys-loop' superfamily of ligand-gated ion channels which mediate synaptic neurotransmission, and whose other members include receptors for glycine, gamma-aminobutyric acid and serotonin. Cryo-electron microscopy has yielded a three-dimensional structure of the nAChR in its closed state. However, the exact nature and location of the channel gate remains uncertain. Although the transmembrane pore is constricted close to its center, it is not completely occluded. Rather, the pore has a central hydrophobic zone of radius about 3 A. Model calculations suggest that such a constriction may form a hydrophobic gate, preventing movement of ions through a channel. We present a detailed and quantitative simulation study of the hydrophobic gating model of the nicotinic receptor, in order to fully evaluate this hypothesis. We demonstrate that the hydrophobic constriction of the nAChR pore indeed forms a closed gate. Potential of mean force (PMF) calculations reveal that the constriction presents a barrier of height about 10 kT to the permeation of sodium ions, placing an upper bound on the closed channel conductance of 0.3 pS. Thus, a 3 A radius hydrophobic pore can form a functional barrier to the permeation of a 1 A radius Na+ ion. Using a united-atom force field for the protein instead of an all-atom one retains the qualitative features but results in differing conductances, showing that the PMF is sensitive to the detailed molecular interactions.

Steered Molecular Dynamics Simulations of Na+ Permeation across the Gramicidin A Channel

The potential of mean forces (PMF) governing Na+ permeation through gramicidin A (gA) channels with explicit water and membrane was characterized using steered molecular dynamics (SMD) simulations. Constant-force SMD with a steering force parallel to the channel axis revealed at least seven energy wells in each monomer of the channel dimer. Except at the channel dimer interface, each energy well is associated with at least three and at most four backbone carbonyl oxygens and two water oxygens in a pseudo-hexahedral or pseudo-octahedral coordination with the Na+ ion. Repeated constant-velocity SMD by dragging a Na+ ion from each energy well in opposite directions parallel to the channel axis allowed the computation of the PMF across the gA channel, revealing a global minimum corresponding to Na+ binding sites near the entrance of gA at +/-9.3 A from the geometric center of the channel. The effect of volatile anesthetics on the PMF was also analyzed in the presence of halothane molecules. Although the accuracy of the current PMF calculation from SMD simulations is not yet sufficient to quantify the PMF difference with and without anesthetics, the comparison of the overall PMF profiles nevertheless confirms that the anesthetics cause insignificant changes to the structural makeup of the free energy wells along the channel and the overall permeation barrier. On average, the PMF appears less rugged in the outer part of the channel in the presence of anesthetics, consistent with our earlier finding that halothane interaction with anchoring residues makes the gA channel more dynamic. A causal relationship was observed between the reorientation of the coordinating backbone carbonyl oxygen and Na+ transit from one energy well to another, suggesting the possibility that even minute changes in the conformation of pore-lining residues due to dynamic motion could be sufficient to trigger the ion permeation. Because some of the carbonyl oxygens contribute to Na+ coordination in two adjacent energy wells, our SMD results reveal that the atomic picture of ion "hopping" through a gA channel actually involves a Na+ ion being carried in a relay by the coordinating oxygens from one energy well to the next. Steered molecular dynamics complements other computational approaches as an attractive means for the atomistic interpretation of experimental permeation studies.

Molecular dynamics simulations of gramicidin A in a lipid bilayer: From structure–function relations to force fields

Molecular dynamics simulations of membrane proteins have become a popular tool for studying their dynamic features, which are not easily accessible by experiments. Whether the force fields developed for globular proteins are adequate this purpose is an important question that is often glossed over. Here we determine the permeation properties of potassium ions in the gramicidin A channel in a lipid bilayer from free energy simulations, and compare the results to experimental data. In particular, we check the dependence of the free energy barriers ions face at the channel center on the membrane size. The results indicate that there is a serious problem with the current rigid force fields independent of the membrane size, and new, possibly polarizable, force fields need to be developed to resolve this problem.

Adaptive Brownian Dynamics Simulation for Estimating Potential Mean Force in Ion Channel Permeation

Ion channels are biological nanotubes formed by large protein molecules in the cell membrane. This paper presents a novel multiparticle simulation methodology, which we call adaptive controlled Brownian dynamics, for estimating the force experienced by a permeating ion at each discrete position along the ion-conducting pathway. The profile of this force, commonly known as the potential of mean force, results from the electrostatic interactions between the ions in the conduit and all the charges carried by atoms forming the channel the protein, as well as the induced charges on the protein wall. The current across the channel is solely determined by the potential of mean force encountered by the permeant ions. The simulation algorithm yields consistent estimates of this profile. The algorithm operates on an angstrom unit spatial scale and femtosecond time scale. Numerical simulations on the gramicidin ion channel show that the algorithm yields the potential of mean force profile that accurately reproduces experimental observations.

Ion permeation through a narrow channel: using gramicidin to ascertain all-atom molecular dynamics potential of mean force methodology and biomolecular force fields

We investigate methods for extracting the potential of mean force (PMF) governing ion permeation from molecular dynamics simulations (MD) using gramicidin A as a prototypical narrow ion channel. It is possible to obtain well-converged meaningful PMFs using all-atom MD, which predict experimental observables within order-of-magnitude agreement with experimental results. This was possible by careful attention to issues of statistical convergence of the PMF, finite size effects, and lipid hydrocarbon chain polarizability. When comparing the modern all-atom force fields of CHARMM27 and AMBER94, we found that a fairly consistent picture emerges, and that both AMBER94 and CHARMM27 predict observables that are in semiquantitative agreement with both the experimental conductance and dissociation coefficient. Even small changes in the force field, however, result in significant changes in permeation energetics. Furthermore, the full two-dimensional free-energy surface describing permeation reveals the location and magnitude of the central barrier and the location of two binding sites for K(+) ion permeation near the channel entrance--i.e., an inner site on-axis and an outer site off-axis. We conclude that the MD-PMF approach is a powerful tool for understanding and predicting the function of narrow ion channels in a manner that is consistent with the atomic and thermally fluctuating nature of proteins.

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.

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.

Role of protein flexibility in ion permeation: a case study in gramicidin A

Proteins have a flexible structure, and their atoms exhibit considerable fluctuations under normal operating conditions. However, apart from some enzyme reactions involving ligand binding, our understanding of the role of flexibility in protein function remains mostly incomplete. Here we investigate this question in the realm of membrane proteins that form ion channels. Specifically, we consider ion permeation in the gramicidin A channel, and study how the energetics of ion conduction changes as the channel structure is progressively changed from completely flexible to a fixed one. For each channel structure, the potential of mean force for a permeating potassium ion is determined from molecular dynamics (MD) simulations. Using the same molecular dynamics data for completely flexible gramicidin A, we also calculate the average densities and fluctuations of the peptide atoms and investigate the correlations between these fluctuations and the motion of a permeating ion. Our results show conclusively that peptide flexibility plays an important role in ion permeation in the gramicidin A channel, thus providing another reason--besides the well-known problem with the description of single file pore water--why this channel cannot be modeled using continuum electrostatics with a fixed structure. The new method developed here for studying the role of protein flexibility on its function clarifies the contributions of the fluctuations to energy and entropy, and places limits on the level of detail required in a coarse-grained model.

Interfacial tryptophan residues: a role for the cation-pi effect?

Integral membrane proteins are characterized by having a preference for aromatic residues, e.g., tryptophan (W), at the interface between the lipid bilayer core and the aqueous phase. The reason for this is not clear, but it seems that the preference is related to a complex interplay between steric and electrostatic forces. The flat rigid paddle-like structure of tryptophan, associated with a quadrupolar moment (aromaticity) arising from the pi-electron cloud of the indole, interacts primarily with moieties in the lipid headgroup region hardly penetrating into the bilayer core. We have studied the interaction between the nitrogen moiety of lipid molecule headgroups and the pi-electron distribution of gramicidin (gA) tryptophan residues (W9, W11, W13, and W15) using molecular dynamics (MD) simulations of gA embedded in two hydrated lipid bilayers composed of 1-palmitoyl-2-oleoylphosphatidylethanolamine (POPE) and 1-palmitoyl-2-oleoylphosphatidyl-choline (POPC), respectively. We use a force field model for tryptophan in which polarizability is only implicit, but we believe that classical molecular dynamics force fields are sufficient to capture the most prominent features of the cation-pi interaction. Our criteria for cation-pi interactions are based on distance and angular requirements, and the results from our model suggest that cation-pi interactions are relevant for W(PE)1), W(PE)13, W(PE)15, and, to some extent, W(PC)11 and W(PC)13. In our model, W9 does not seem to engage in cation-pi interactions with lipids, neither in POPE nor POPC. The criteria for the cation-pi effect are satisfied more often in POPE than in POPC, whereas the H-bonding ability between the indole donor and the carbonyl acceptor is similar in POPE and POPC. This suggests an increased affinity for lipids with ethanolamine headgroups to transmembrane proteins enriched in interfacial tryptophans.

Three computational methods for studying permeation, selectivity and dynamics in biological ion channels

The cell membrane, confining some ions and molecules on one side and exchanging others with the other side, is the ultimate unit of the physiology of life. The delicate task of regulating the transport of ions across the membrane is carried out by biological nanotubes called 'ion channels'. Recently, there have been enormous strides in our understanding of the structure-function relationships of biological ion channels. The molecular structures of several ion channels have been determined from crystallographic analysis, including potassium channels, mechanosensitive channels, a chloride channel, as well as gramicidin channels and porins. It is expected that the X-ray structures of other ion channels will soon follow these discoveries, ushering in a new era of ion channel studies in which predicting the function of channels from their atomic structures will become the main quest. In parallel to these experimental findings, there have been important advances in computational biophysics. Here we summarize three theoretical approaches that have been utilized to understand the dynamics of ion permeation across bio-nanotubes, highlighting their advantages and shortcomings, and briefly describe some of the salient properties of ion channels uncovered through computational studies.

Surface Tension Effect on Transmembrane Channel Stability in a Model Membrane

The effect of surface tension on the lipid bilayer membrane is a question that has drawn considerable research effort. This interest has been driven both by the desire to determine the surface tension effects on the lipid bilayer and from the suggestion that adding finite surface tension to a small membrane system may provide more realistic lipid properties in molecular dynamics simulations. Here, the effect of surface tension on a palmitololelylphosphatidylcholine (POPC) bilayer membrane containing a four-helix transmembrane alamethicin peptide bundle is investigated. Simulations of 10 ns were undertaken for two different ensembles, NPT and NP(z)gammaT with a surface tension, gamma, of 20 mN m(-1) per interface, which is near the pore-forming region. The significance of differences between the tension-free and surface tension simulations was determined using nonparametric statistical analysis on replicate simulations with different initial conditions. The results suggest that, when the membrane is under surface tension, the peptide helical structure is perturbed from that in the tension-free state but that the bundle conformation is more stable than that in the tension-free state, with hydrogen bonding playing an important stabilizing role. Surface tension counteracts the influence of the transmembrane helix bundle on nearby lipid order, making the lipid order more uniform throughout the membrane in the tension state. Conversely, the lipid mobility was less uniform in the tension state, with lipids far from the bundle being significantly more mobile than those near the bundle. One general implication of the results is that surface tension can affect the membrane nonuniformly, in that the properties of lipids near the peptide are different from those further away.

Molecular dynamics study of bipolar tetraether lipid membranes

Membranes composed of bipolar tetraether lipids have been studied by a series of 25-ns molecular dynamics simulations to understand the microscopic structure and dynamics as well as membrane area elasticity. By comparing macrocyclic and acyclic tetraether and diether archaeal lipids, the effect of tail linkage of the two phytanyl-chained lipids on the membrane properties is elucidated. Tetraether lipids show smaller molecular area and lateral mobility. For the latter, calculated diffusion coefficients are indeed one order-of-magnitude smaller than that of the diether lipid. These two tetraether membranes are alike in many physical properties except for membrane area elasticity. The macrocyclic tetraether membrane shows a higher elastic area expansion modulus than its acyclic counterpart by a factor of three. Free energy profiles of a water molecule crossing the membranes show no major difference in barrier height; however, a significant difference is observed near the membrane center due to the lack of the slip-plane in tetraether membranes.

Semimicroscopic modeling of permeation energetics in ion channels

The semimicroscopic (SMC) approach to modeling the energetics of ion permeation through biological channels provides an alternative perspective to standard molecular dynamics methods. It exploits the timescale separation between electronic and structural contributions to dielectric stabilization and accounts for electronic polarization by embedding the channel in a milieu that, on average, describes this polarization. Ions, water, and selected peptide moieties are mobile and comprise the reorganizational contribution to dielectric stabilization. The conceptual advantages and limitations of the technique are described. Methodological details are outlined, stressing three convenient electrical geometries. Practical aspects of the SMC procedure are explained, highlighting the areas ripe for further development. Finally, some specific applications are considered.

Gramicidin channels

Gramicidin channels are mini-proteins composed of two tryptophan-rich subunits. The conducting channels are formed by the transbilayer dimerization of nonconducting subunits, which are tied to the bilayer/solution interface through hydrogen bonds between the indole NH groups and the phospholipid backbone and water. The channel structure is known at atomic resolution and the channel's permeability characteristics are particularly well defined: gramicidin channels are selective for monovalent cations, with no measurable permeability to anions or polyvalent cations; ions and water move through a pore whose wall is formed by the peptide backbone; and the single-channel conductance and cation selectivity vary when the amino acid sequence is varied, even though the permeating ions make no contact with the amino acid side chains. Given the amount of experimental information that is available--for both the wild-type channels and for channels formed by amino acid-substituted gramicidin analogues--gramicidin channels provide important insights into the microphysics of ion permeation through bilayer-spanning channels. For the same reason, gramicidin channels constitute the system of choice for evaluating computational strategies for obtaining mechanistic insights into ion permeation through the complex channels formed by integral membrane proteins.

CHARMM fluctuating charge force field for proteins: II protein/solvent properties from molecular dynamics simulations using a nonadditive electrostatic model

A fluctuating charge (FQ) force field is applied to molecular dynamics simulations for six small proteins in explicit polarizable solvent represented by the TIP4P-FQ potential. The proteins include 1FSV, 1ENH, 1PGB, 1VII, 1H8K, and 1CRN, representing both helical and beta-sheet secondary structural elements. Constant pressure and temperature (NPT) molecular dynamics simulations are performed on time scales of several nanoseconds, the longest simulations yet reported using explicitly polarizable all-atom empirical potentials (for both solvent and protein) in the condensed phase. In terms of structure, the FQ force field allows deviations from native structure up to 2.5 A (with a range of 1.0 to 2.5 A). This is commensurate to the performance of the CHARMM22 nonpolarizable model and other currently existing polarizable models. Importantly, secondary structural elements maintain native structure in general to within 1 A (both helix and beta-strands), again in good agreement with the nonpolarizable case. In qualitative agreement with QM/MM ab initio dynamics on crambin (Liu et al. Proteins 2001, 44, 484), there is a sequence dependence of average condensed phase atomic charge for all proteins, a dependence one would anticipate considering the differing chemical environments around individual atoms; this is a subtle quantum mechanical feature captured in the FQ model but absent in current state-of-the-art nonpolarizable models. Furthermore, there is a mutual polarization of solvent and protein in the condensed phase. Solvent dipole moment distributions within the first and second solvation shells around the protein display a shift towards higher dipole moments (increases on the order of 0.2-0.3 Debye) relative to the bulk; protein polarization is manifested via the enhanced condensed phase charges of typical polar atoms such as backbone carbonyl oxygens, amide nitrogens, and amide hydrogens. Finally, to enlarge the sample set of proteins, gas-phase minimizations and 1 ps constant temperature simulations are performed on various-sized proteins to compare to earlier work by Kaminsky et al. (J Comp Chem 2002, 23, 1515). The present work establishes the feasibility of applying a fully polarizable force field for protein simulations and demonstrates the approach employed in extending the CHARMM force field to include these effects.

Permeation of particle through a four-helix-bundle model channel

By using molecular dynamics simulation, the dynamic behaviors of particle permeation through a four-helix-bundle model channel are studied. The interior cavity of the four-helix-bundle provides the "routes" for particle permeation. The main structural properties of the model channel are similar to those that appear in natural four-helix-bundle proteins. It is found that the interior structure of the model channel may greatly influence the permeation process. At the narrow necks of the model channel, the particle would be trapped during the permeation. There is a threshold value for the driving force. When the driving force is larger than this threshold value, the mean first permeation time decreases sharply and tends to be saturated. Increasing the temperature of either the model channel or the particle reservoir can also facilitate the permeation. Enhancing the interaction strength between the particle and monomer on the four-helix-bundle model chain will hinder the permeation. Hence, the electrical current which is induced by the particle permeation is a function of the driving force and temperature. It is found that this current increases monotonically as the strength of the driving force or the temperature increases, but decreases as the interaction strength between the particle and monomer increases. It is also found that the larger the friction coefficient, the slower the permeation is. In addition, the multiparticle (or multi-ion) permeation process is also studied. The permeation of multiparticle is usually quicker than that of the single particle. The permeation of particle through a five-helix-bundle shows similar properties as that through a four-helix-bundle.

Fifty Years of Progress in Ion Channel Research

Fifty years ago, ion channels were but a reasonable hypothesis. I outline some major steps in transforming this idea from a plausible description of the biological assemblies responsible for controlling passive ion transport across membranes to established fact. Important electrophysiological, biochemical, molecular biological, structural, and theoretical tools are discussed in the context of the transition from studying whole cell preparations, containing many channels, to investigating single channel behavior. Six channel families are exemplified: the model peptide, gramicidin, the acetylcholine receptor, and the sodium, potassium, calcium, and chloride channels. Some questions of current interest are posed.

Test of molecular dynamics force fields in gramicidin A

The force fields commonly used in molecular dynamics simulations of proteins are optimized under bulk conditions. Whether the same force fields can be used in simulations of membrane proteins is not well established, although they are increasingly being used for such purposes. Here we consider ion permeation in the gramicidin A channel as a test of the AMBER force field in a membrane environment. The potentials of mean force for potassium ions are calculated along the channel axis and compared with the one deduced from the experimental conductance data. The calculated result indicates a rather large central barrier similar to those obtained from other force fields, which are incompatible with the conductance data. We suggest that lack of polarizability is the most likely cause of this problem, and, therefore, urge development of polarizable force fields for simulations of membrane proteins.

Ionic permeation free energy in gramicidin: a semimicroscopic perspective

Ion permeation through the gramicidin channel is studied using a model that circumvents two major difficulties inherent to standard simulational methods. It exploits the timescale separation between electronic and structural contributions to dielectric stabilization, accounting for the influence of electronic polarization by embedding the channel in a dielectric milieu that describes this polarization in a mean sense. The explicit mobile moieties are the ion, multipolar waters, and the carbonyls and amides of the peptide backbone. The model treats the influence of aromatic residues and the membrane dipole potential. A new electrical geometry is introduced that treats long-range electrostatics exactly and avoids problems related to periodic boundary conditions. It permits the translocating ion to make a seamless transition from nearby electrolyte to the channel interior. Other degrees of freedom (more distant bulk electrolyte and nonpolar lipid) are treated as dielectric continua. Reasonable permeation free energy profiles are obtained for potassium, rubidium, and cesium; binding wells are shallow and the central barrier is small. Estimated cationic single-channel conductances are smaller than experiment, but only by factors between 2 (rubidium) and 50 (potassium). When applied to chloride the internal barrier is large, with a corresponding miniscule single-channel conductance. The estimated relative single-channel conductances of gramicidin A, B, and C agree well with experiment.

Computer simulations of membrane proteins

Computer simulations are rapidly becoming a standard tool to study the structure and dynamics of lipids and membrane proteins. Increasing computer capacity allows unbiased simulations of lipid and membrane-active peptides. With the increasing number of high-resolution structures of membrane proteins, which also enables homology modelling of more structures, a wide range of membrane proteins can now be simulated over time spans that capture essential biological processes. Longer time scales are accessible by special computational methods. We review recent progress in simulations of membrane proteins.

Influence of protein flexibility on the electrostatic energy landscape in gramicidin A

We describe an electrostatic model of the gramicidin A channel that allows protein atoms to move in response to the presence of a permeating ion. To do this, molecular dynamics simulations are carried out with a permeating ion at various positions within the channel. Then an ensemble of atomic coordinates taken from the simulations are used to construct energy profiles using macroscopic electrostatic calculations. The energy profiles constructed are compared to experimentally-determined conductance data by inserting them into Brownian dynamics simulations. We find that the energy landscape seen by a permeating ion changes significantly when we allow the protein atoms to move rather than using a rigid protein structure. However, the model developed cannot satisfactorily reproduce all of the experimental data. Thus, even when protein atoms are allowed to move, the dielectric model used in our electrostatic calculations breaks down when modeling the gramicidin channel.

Saturation of conductance in single ion channels: the blocking effect of the near reaction field

The ionic current flowing through a protein channel in the membrane of a biological cell depends on the concentration of the permeant ion, as well as on many other variables. As the concentration increases, the rate of arrival of bath ions to the channel's entrance increases, and typically so does the net current. This concentration dependence is part of traditional diffusion and rate models that predict Michaelis-Menten current-concentration relations for a single ion channel. Such models, however, neglect other effects of bath concentrations on the net current. The net current depends not only on the entrance rate of ions into the channel, but also on forces acting on ions inside the channel. These forces, in turn, depend not only on the applied potential and charge distribution of the channel, but also on the long-range Coulombic interactions with the surrounding bath ions. In this paper, we study the effects of bath concentrations on the average force on an ion in a single ion channel. We show that the force of the reaction field on a discrete ion inside a channel embedded in an uncharged lipid membrane contains a blocking (shielding) term that is proportional to the square root of the ionic bath concentration. We then show that different blocking strengths yield different behavior of the current-concentration and conductance-concentration curves. Our theory shows that at low concentrations, when the blocking force is weak, conductance grows linearly with concentration, as in traditional models, e.g., Michaelis-Menten formulations. As the concentration increases to a range of moderate shielding, conductance grows as the square root of concentration, whereas at high concentrations, with high shielding, conductance may actually decrease with increasing concentrations: the conductance-concentration curve can invert. Therefore, electrostatic interactions between bath ions and the single ion inside the channel can explain the different regimes of conductance-concentration relations observed in experiments.

Energetics of ion conduction through the gramicidin channel

The free energy governing K(+) conduction through gramicidin A channels is characterized by using over 0.1 micros of all-atom molecular dynamics simulations with explicit solvent and membrane. The results provide encouraging agreement with experiments and insights into the permeation mechanism. The free energy surface of K(+), as a function of both axial and radial coordinates, is calculated. Correcting for simulation artifacts due to periodicity and the lack of hydrocarbon polarizability, the calculated single-channel conductance for K(+) ions is 0.8 pS, closer to experiment than any previous calculation. In addition, the estimated single ion dissociation constants are within the range of experimental determinations. The relatively small free energy barrier to ion translocation arises from a balance of large opposing contributions from protein, single-file water, bulk electrolyte, and membrane. Mean force decomposition reveals a remarkable ability of the single-file water molecules to stabilize K(+) by -40 kcal/mol, roughly half the bulk solvation free energy. The importance of the single-file water confirms the conjecture of Mackay et al. [Mackay, D. H. J., Berens, P. H., Wilson, K. R. & Hagler, A. T. (1984) Biophys. J. 46, 229-248]. Ion association with the channel involves gradual dehydration from approximately six to seven water molecules in the first shell, to just two inside the narrow pore. Ion permeation is influenced by the orientation of the single-file water column, which can present a barrier to conduction and give rise to long-range coupling of ions on either side of the pore. Small changes in the potential function, including contributions from electronic polarization, are likely to be sufficient to obtain quantitative agreement with experiments.

Modeling permeation energetics in the KcsA potassium channel

The thermodynamics of cation permeation through the KcsA K(+) channel selectivity filter is studied from the perspective of a physically transparent semimicroscopic model using Monte Carlo free energy integration. The computational approach chosen permits dissection of the separate contributions to ionic stabilization arising from different parts of the channel (selectivity filter carbonyls, single-file water, cavity water, reaction field of bulk water, inner helices, ionizable residues). All features play important roles; their relative significance varies with the ion's position in the filter. The cavity appears to act as an electrostatic buffer, shielding filter ions from structural changes in the inner pore. The model exhibits K(+) vs. Na(+) selectivity, and roughly isoenergetic profiles for K(+) and Rb(+), and discriminates against Cs(+), all in agreement with experimental data. It also indicates that Ba(2+) and Na(+) compete effectively with permeant ions at a site near the boundary between the filter and the cavity, in the vicinity of the barium blocker site.