Ionic permeation free energy in gramicidin: a semimicroscopic perspective

Protein Motifs for Proton Transfers That Build the Transmembrane Proton Gradient

Biological membranes are barriers to polar molecules, so membrane embedded proteins control the transfers between cellular compartments. Protein controlled transport moves substrates and activates cellular signaling cascades. In addition, the electrochemical gradient across mitochondrial, bacterial and chloroplast membranes, is a key source of stored cellular energy. This is generated by electron, proton and ion transfers through proteins. The gradient is used to fuel ATP synthesis and to drive active transport. Here the mechanisms by which protons move into the buried active sites of Photosystem II (PSII), bacterial RCs (bRCs) and through the proton pumps, Bacteriorhodopsin (bR), Complex I and Cytochrome c oxidase (CcO), are reviewed. These proteins all use water filled proton transfer paths. The proton pumps, that move protons uphill from low to high concentration compartments, also utilize Proton Loading Sites (PLS), that transiently load and unload protons and gates, which block backflow of protons. PLS and gates should be synchronized so PLS proton affinity is high when the gate opens to the side with few protons and low when the path is open to the high concentration side. Proton transfer paths in the proteins we describe have different design features. Linear paths are seen with a unique entry and exit and a relatively straight path between them. Alternatively, paths can be complex with a tangle of possible routes. Likewise, PLS can be a single residue that changes protonation state or a cluster of residues with multiple charge and tautomer states.

Dielectric screening effect of electronic polarization and intramolecular hydrogen bonding

Recent site-resolved hydrogen exchange measurements have uncovered significant discrepancies between simulations and experimental data during protein folding, including the excessive intramolecular hydrogen bonds in simulations. This finding indicates a possibility that intramolecular charge-charge interactions have not included sufficient dielectric screening effect of the electronic polarization. Scaling down peptide atomic charges according to the optical dielectric constant is tested in this study. As a result, the number of intramolecular hydrogen bonds is lower than using unscaled atomic charges while reaching the same levels of helical contents or β-hairpin backbone hydrogen bonds, because van der Waals interactions contribute substantially to peptide folding in water. Reducing intramolecular charge-charge interactions and hydrogen bonding increases conformational search efficiency. In particular, it reduces the equilibrium helical content in simulations using AMBER force field and the energy barrier in folding simulations using CHARMM force field.

Structure based computational assessment of channel properties of assembled ORF-8a from SARS-CoV

ORF 8a is a short 39 amino acid bitopic membrane protein encoded by severe acute respiratory syndrome causing corona virus (SARS‐CoV). It has been identified to increase permeability of the lipid membrane for cations. Permeability is suggested to occur due to the assembly of helical bundles. Computational models of a pentameric assembly of 8a peptides are generated using the first 22 amino acids, which include the transmembrane domain. Low energy structures reveal a hydrophilic pore mantled by residues Thr‐8, and −18, Ser‐11, Cys‐13, and Arg‐22. Potential of mean force (PMF) profiles for mono (Na⁺, K⁺, Cl⁻) and divalent (Ca²⁺) ions along the pore are calculated. The data support experimental findings of a weak cation selectivity of the channel. Calculations on 8a are compared to data derived for a pentameric bundle consisting of the M2 helices of the bacterial pentameric ligand gated ion channel GLIC (3EHZ). PMF curves of both, bundles 8a and M2, show sigmoidal shaped profiles. In comparison to the data for the M2‐GLIC model, data of the 8a bundle show lower amplitude of the PMF values between maximum and minimum and less discrimination amongst ions. Proteins 2015; 83:300–308. © 2014 Wiley Periodicals, Inc.

Ion selectivity of alpha-hemolysin with a beta-cyclodextrin adapter. I. Single ion potential of mean force and diffusion coefficient

The alpha-hemolysin (alphaHL) is a self-assembling exotoxin that binds to the membrane of a susceptible host cell and causes its death. Experimental studies show that electrically neutral beta-cyclodextrin (betaCD) can insert into the alphaHL channel and significantly increase its anion selectivity. To understand how betaCD can affect ion selectivity, molecular dynamics simulations and potential of mean force (PMF) calculations are carried out for different alphaHL channels with and without the betaCD adapter. A multiscale approach based on the generalized solvent boundary potential is used to reduce the size of the simulated system. The PMF profiles reveal that betaCD has no anion selectivity by itself but can increase the Cl(-) selectivity of the alphaHL channel when lodged into the pore lumen. Analysis shows that betaCD causes a partial desolvation of ions and affects the orientation of nearby charged residues. The ion selectivity appears to result from increased electrostatic interaction between the ion and the channel due to a reduction in dielectric shielding by the solvent. These observations suggest a reasonable explanation of the ion selectivity and provide important information for further ion channel modification.

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.

Gramicidin A Channel in a Matrix from a Semifluorinated Surfactant Monolayer

Gramicidin A, a polypeptide antibiotic forming transmembrane ion channels, has been incorporated into a Langmuir monolayer formed by a semifluorinated alkane (SFA). In this work, partially fluorinated tetracosane, perfluorohexyloctadecane (F6H18), has been applied, aiming at finding a suitable matrix for gramicidin A to be transferred onto solid support for a biosensor design. For this purpose, the physiological conditions were of special interest (mixed monolayers containing low gramicidin proportion and the surface pressure of 30 mN/m). Mixed monolayers of gramicidin and SFA were found to be miscible within the whole range of mole fractions. A very significant increase of the stability of SFA monolayer has been found in the presence of gramicidin, even at such a low proportion as X(gramicidin) = 0.1, which is reflected in a 3.5-fold increase of the collapse pressure value of mixed monolayer as compared to the film from pure SFA. This interesting phenomenon has been interpreted as being due to the existence of a strong dipole-dipole interaction between both film-forming molecules. Opposite sign of the measured electric surface potential for gramicidin and SFA, resulting from different directions of the dipole moment vectors in both film molecules, implies that the ordered, antiparallel orientation of the dipole moments in the mixed gramicidin/SFA system can be responsible for its extremely high stability.

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.

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.

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.

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.

On the importance of atomic fluctuations, protein flexibility, and solvent in ion permeation

Proteins, including ion channels, often are described in terms of some average structure and pictured as rigid entities immersed in a featureless solvent continuum. This simplified view, which provides for a convenient representation of the protein's overall structure, incurs the risk of deemphasizing important features underlying protein function, such as thermal fluctuations in the atom positions and the discreteness of the solvent molecules. These factors become particularly important in the case of ion movement through narrow pores, where the magnitude of the thermal fluctuations may be comparable to the ion pore atom separations, such that the strength of the ion channel interactions may vary dramatically as a function of the instantaneous configuration of the ion and the surrounding protein and pore water. Descriptions of ion permeation through narrow pores, which employ static protein structures and a macroscopic continuum dielectric solvent, thus face fundamental difficulties. We illustrate this using simple model calculations based on the gramicidin A and KcsA potassium channels, which show that thermal atomic fluctuations lead to energy profiles that vary by tens of kcal/mol. Consequently, within the framework of a rigid pore model, ion-channel energetics is extremely sensitive to the choice of experimental structure and how the space-dependent dielectric constant is assigned. Given these observations, the significance of any description based on a rigid structure appears limited. Creating a conducting channel model from one single structure requires substantial and arbitrary engineering of the model parameters, making it difficult for such approaches to contribute to our understanding of ion permeation at a microscopic level.

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.

Water and ion permeation in bAQP1 and GlpF channels: a kinetic Monte Carlo study

The kinetic Monte Carlo reaction-path-following technique is applied to determine the lowest-energy water pathway and the coordinating amino acids in bAQP1 and GlpF channels, both treated as rigid. In bAQP1, water molecules pass through the pore between the asparagine-proline-alanine (NPA) and selectivity filter (SF) sites one at a time. The water chain is interrupted at the SF where one water forms three stable hydrogen bonds with protein atoms. In this SF, water's conformation depends on the protonation locus of H182. In GlpF, two water molecules bond simultaneously to the NPA asparagines and pass through the SF in zigzag fashion. No water single-file forms in rigid GlpF. To accommodate a single file of waters requires narrowing the GlpF pore. Our results reveal that in both proteins a proposed bipolar water arrangement is thermally disrupted in the NPA region, especially in the cytoplasmic part of the pore. The equilibrium hydrogen-bonded chain is occasionally interrupted in the hydrophobic zones adjacent to the NPA motifs. The permeation of alkali cations through bAQP1 and GlpF is barred due to a large free-energy barrier in the NPA region as well as a large energy barrier blocking entry from the cytoplasm. Permeation of halides is prevented due to two large energy barriers in the cytoplasmic and periplasmic pores as well as a large free-energy barrier barring entry from the periplasm. Our results, based on modeling charge permeation, support an electrostatic rather than orientational basis for proton exclusion. Binding within the aquaporin pore cannot compensate sufficiently for dehydration of the protonic charge; there is also an electrostatic barrier in the NPA region blocking proton transport. The highly ordered single file of waters, which is drastically interrupted at the SF of bAQP1, may also contribute to proton block.