The binding site of sodium in the gramicidin A channel: comparison of molecular dynamics with solid-state NMR data

Polarization Effects in Water-Mediated Selective Cation Transport across a Narrow Transmembrane Channel

Despite the progress in modeling complex molecular systems of ever-increasing complexity, a quantitatively accurate computational treatment of ion permeation through narrow membrane channels remains challenging. An important factor to reach this goal is induced electronic polarization, which is likely to impact the permeation rate of small ions through narrow molecular pores. In this work, we extended the recently developed polarizable force field based on the classical Drude oscillators to assess the role of induced polarization effects on the energetics of sodium and potassium ion transport across the gramicidin A (gA) ion channel. The inclusion of induced polarization lowers barriers present in 1D potential of mean force (PMF) for cation permeation by ∼50% compared to those obtained with the additive force field. Conductance properties calculated with 1D PMFs from Drude simulations are in better agreement with experimental results. Polarization of single-file water molecules and protein atoms forming the narrow pore has a direct impact on the free-energy barriers and cation-specific solid-state NMR chemical shifts. Sensitivity analysis indicates that small changes to water-channel interactions can alter the free energy barrier for ion permeation. These results, illustrating polarization effects present in the complex electrostatic environment of the gA channel, have broad implications for revising proposed mechanisms of ion permeation and selectivity in a variety of ion channels.

Deciphering the Structure of the Gramicidin A Channel in the Presence of AOT Reverse Micelles in Pentane Using Molecular Dynamics Simulations

Structural studies of proteins and, in particular, integral membrane proteins (IMPs) using solution NMR spectroscopy approaches are challenging due to not only their inherent structural complexities but also the fact that they need to be solubilized in biomimetic environments (such as micelles), which enhances the slow molecular reorientation. To deal with these difficulties and increase the effective rate of molecular reorientation, the encapsulation of IMPs in the aqueous core of the reverse micelle (RM) dissolved in a low-viscosity solvent has been proven to be a viable approach. However, the effect of the reverse micelle (RM) environment on the IMP structure and function is little known. To gain insight into these aspects, this article presents a series of atomistic unconstrained molecular dynamics (MD) of a model ion channel (gramicidin A, gA) with RMs formed with anionic surfactant diacyl chain bis(2-ethylhexyl) sodium succinate (AOT) in pentane at a water-to-surfactant molar ratio (W₀) of 6. The simulations were carried out with different protocols and starting conditions for a total of 2.4 μs and were compared with other MDs used with the gA channel inserted in models of the SDS micelle or the DMPC membrane. We show here that in the presence of AOT RMs the gA dimer did not look like the "dumbbell-like" model anticipated by experiments, where the C-terminal parts of the gA are capped with two RMs and the rest of the dimer is protected from the oil solvent by the AOT acyl chains. In contrast, the MD simulations reveal that the AOT, Na⁺, and water formed two well-defined and elongated RMs attached to the C-terminal ends of the gA dimer, while the rest is in direct contact with the pentane. The initial β^6.3 secondary structure of the gA is well conserved and filled with 6-9 waters, as in SDS micelles or the DMPC membrane. Finally, the water movement inside the gA is strongly affected by the presence of RMs at each extremity, and no passage of water molecules through the gA channel is observed even after a long simulation period, whereas the opposite was found for gA in SDS and DMPC.

Measurements of Ion Binding to Lipid-Hosted Ionophores by Affinity Chromatography

The binding affinity between antibiotic ionophores and alkali ions within supported lipid bilayers was evaluated using affinity chromatography. We used zonal elution and frontal analysis methods in nanovolume liquid chromatography to characterize the binding selectivity of the carrier and channel ionophores valinomycin and gramicidin A within different phosphatidylcholine bilayers. Distinct binding sensitivity to the lipid phase, both in affinity and selectivity, is observed for valinomycin, whereas gramicidin is less sensitive to changes in a membrane environment, behavior that is consistent with ion binding occurring within the interior of an established channel. There is good agreement between the chromatographic retention and the reported binding selectivity measured by other techniques. Surface potential near the binding site affects ion retention and the apparent association binding constants, but not the binding selectivity or enthalpy measurements. A model accounting for the surface potential contributions of retained ions during frontal analyses yields values close to intrinsic binding constants for gramicidin A (K_A for K⁺ between 70 and 120 M^-1) using reasonable estimates of the initial potential that is postulated to arise from the underlying silica.

Characterization of Lipid-Protein Interactions and Lipid-Mediated Modulation of Membrane Protein Function through Molecular Simulation

The cellular membrane constitutes one of the most fundamental compartments of a living cell, where key processes such as selective transport of material and exchange of information between the cell and its environment are mediated by proteins that are closely associated with the membrane. The heterogeneity of lipid composition of biological membranes and the effect of lipid molecules on the structure, dynamics, and function of membrane proteins are now widely recognized. Characterization of these functionally important lipid-protein interactions with experimental techniques is however still prohibitively challenging. Molecular dynamics (MD) simulations offer a powerful complementary approach with sufficient temporal and spatial resolutions to gain atomic-level structural information and energetics on lipid-protein interactions. In this review, we aim to provide a broad survey of MD simulations focusing on exploring lipid-protein interactions and characterizing lipid-modulated protein structure and dynamics that have been successful in providing novel insight into the mechanism of membrane protein function.

Structural dynamics and conformational equilibria of SERCA regulatory proteins in membranes by solid-state NMR restrained simulations

Solid-state NMR spectroscopy is emerging as a powerful approach to determine structure, topology, and conformational dynamics of membrane proteins at the atomic level. Conformational dynamics are often inferred and quantified from the motional averaging of the NMR parameters. However, the nature of these motions is difficult to envision based only on spectroscopic data. Here, we utilized restrained molecular dynamics simulations to probe the structural dynamics, topology and conformational transitions of regulatory membrane proteins of the calcium ATPase SERCA, namely sarcolipin and phospholamban, in explicit lipid bilayers. Specifically, we employed oriented solid-state NMR data, such as dipolar couplings and chemical shift anisotropy measured in lipid bicelles, to refine the conformational ensemble of these proteins in lipid membranes. The samplings accurately reproduced the orientations of transmembrane helices and showed a significant degree of convergence with all of the NMR parameters. Unlike the unrestrained simulations, the resulting sarcolipin structures are in agreement with distances and angles for hydrogen bonds in ideal helices. In the case of phospholamban, the restrained ensemble sampled the conformational interconversion between T (helical) and R (unfolded) states for the cytoplasmic region that could not be observed using standard structural refinements with the same experimental data set. This study underscores the importance of implementing NMR data in molecular dynamics protocols to better describe the conformational landscapes of membrane proteins embedded in realistic lipid membranes.

Predicting the DNA sequence dependence of nanopore ion current using atomic-resolution Brownian dynamics

It has become possible to distinguish DNA molecules of different nucleotide sequences by measuring ion current passing through a narrow pore containing DNA. To assist experimentalists in interpreting the results of such measurements and to improve the DNA sequence detection method, we have developed a computational approach that has both the atomic-scale accuracy and the computational efficiency required to predict DNA sequence-specific differences in the nanopore ion current. In our Brownian dynamics method, the interaction between the ions and DNA is described by three-dimensional potential of mean force maps determined to a 0.03 nm resolution from all-atom molecular dynamics simulations. While this atomic-resolution Brownian dynamics method produces results with orders of magnitude less computational effort than all-atom molecular dynamics requires, we show here that the ion distributions and ion currents predicted by the two methods agree. Finally, using our Brownian dynamics method, we find that a small change in the sequence of DNA within a pore can cause a large change in the ion current, and validate this result with all-atom molecular dynamics.

Electric field driven changes of a gramicidin containing lipid bilayer supported on a Au(111) surface

Langmuir-Blodgett and Langmuir-Schaeffer methods were employed to deposit a mixed bilayer consisting of 90% of 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) and 10% of gramicidin (GD), a short 15 residue ion channel forming peptide, onto a Au(111) electrode surface. This architecture allowed us to investigate the effect of the electrostatic potential applied to the electrode on the orientation and conformation of DMPC molecules in the bilayer containing the ion channel. The charge density data were determined from chronocoulometry experiments. The electric field and the potential across the membrane were determined through the use of charge density curves. The magnitudes of potentials across the gold-supported biomimetic membrane were comparable to the transmembrane potential acting on a natural membrane. The information regarding the orientation and conformation of DMPC and GD molecules in the bilayer was obtained from photon polarization modulation infrared reflection absorption spectroscopy (PMIRRAS) measurements. The results show that the bilayer is adsorbed, in direct contact with the metal surface, when the potential across the interface is more positive than -0.4 V and is lifted from the gold surface when the potential across the interface is more negative than -0.4 V. This change in the state of the bilayer has a significant impact on the orientation and conformation of the phospholipid and gramicidin molecules. The potential induced changes in the membrane containing peptide were compared to the changes in the structure of the pure DMPC bilayer determined in earlier studies.

Gramicidin A backbone and side chain dynamics evaluated by molecular dynamics simulations and nuclear magnetic resonance experiments. I: molecular dynamics simulations

Gramicidin A (gA) channels provide an ideal system to test molecular dynamics (MD) simulations of membrane proteins. The peptide backbone lines a cation-selective pore, and due to the small channel size, the average structure and extent of fluctuations of all atoms in the peptide will influence ion permeation. This raises the question of how well molecular mechanical force fields used in MD simulations and potential of mean force (PMF) calculations can predict structure and dynamics as well as ion permeation. To address this question, we undertook a comparative study of nuclear magnetic resonance (NMR) observables predicted by fully atomistic MD simulations on a gA dimer embedded in a sodium dodecyl sulfate (SDS) micelle with measurements of the gA dimer backbone and tryptophan side chain dynamics using solution-state (15)N NMR on gA dimers in SDS micelles (Vostrikov, V. V.; Gu, H.; Ingólfsson, H. I.; Hinton, J. F.; Andersen, O. S.; Roux, B.; Koeppe, R. E., II. J. Phys. Chem. B2011, DOI 10.1021/jp200906y , accompanying article). This comparison enables us to examine the robustness of the MD simulations done using different force fields as well as their ability to predict important features of the gA channel. We find that MD is able to predict NMR observables, including the generalized order parameters (S(2)), the (15)N spin-lattice (T(1)) and spin-spin (T(2)) relaxation times, and the (1)H-(15)N nuclear Overhauser effect (NOE), with remarkable accuracy. To examine further how differences in the force fields can affect the channel conductance, we calculated the PMF for K(+) and Na(+) permeation through a gA channel in a dimyristoylphosphatidylcholine (DMPC) bilayer. In this case, we find that MD is less successful in quantitatively predicting the single-channel conductance.

The structural and topological analysis of membrane-associated polypeptides by oriented solid-state NMR spectroscopy: established concepts and novel developments

Solid-state NMR spectroscopy is a powerful technique for the investigation of membrane-associated peptides and proteins as well as their interactions with lipids, and a variety of conceptually different approaches have been developed for their study. The technique is unique in allowing for the high-resolution investigation of liquid disordered lipid bilayers representing well the characteristics of natural membranes. Whereas magic angle solid-state NMR spectroscopy follows approaches that are related to those developed for solution NMR spectroscopy the use of static uniaxially oriented samples results in angular constraints which also provide information for the detailed analysis of polypeptide structures. This review introduces this latter concept theoretically and provides a number of examples. Furthermore, ongoing developments combining solid-state NMR spectroscopy with information from solution NMR spectroscopy and molecular modelling as well as exploratory studies using dynamic nuclear polarization solid-state NMR will be presented.

The gramicidin channel ion permeation free-energy profile: direct and indirect effects of CHARMM force field improvements

A revised CHARMM force field for tryptophan residues is studied as well as a new grid-based correction algorithm, called CMAP, using molecular dynamics simulations of gramicidin A (1JNO) embedded in a lipid bilayer (DMPC) with 1 mol/kg NaCl or KCl saline solution. The conformational stability of the interfacial side chains is studied, which shows good stability on the 10 ns time scale. The revised force field for the tryptophan side chain produces, in the decomposition, a Na(+) PMF(Trp) profile that is consonant with the prediction from the experimental results, analyzed with rate theory by Durrant et al. (2006), but in stark contrast to the prediction of the original CHARMM force field, version 22. However, the effect is diluted in the PMF profile due to indirect effects mediated by other components of the system (polypeptide, lipid molecules, ions, and water molecules). CMAP corrections to the L-amino acids help reduce the excessive translocation barrier. Decomposition demonstrates that this effect is due to effects on the K(+) PMF(H(2)O) profile rather than on the K(+) PMF(gA) profile. The results have been confirmed to be robust using an alternative umbrella-potential method. Further force field balancing efforts (direct and indirect) are required for future studies to evaluate whether these effects give rise to predictions that are consistent with those observables extracted from real experiments.

Application of the fuzzy-oil-drop model to membrane protein simulation

The analysis of structural properties and biological activity of membrane proteins requires long lasting simulation of molecular dynamics. The large number of atoms present in protein molecule, membrane (phospholipids), and water environment makes the simulation of large scale. The implementation of simplified model representing the natural environment for membrane proteins is presented and compared with the vacuum simulation and simulation in the presence of water molecules and membrane phospholipids presented explicite. The comparative structural analysis and computational times for these three models makes the simplified model promising.

CHARMM: the biomolecular simulation program

CHARMM (Chemistry at HARvard Molecular Mechanics) is a highly versatile and widely used molecular simulation program. It has been developed over the last three decades with a primary focus on molecules of biological interest, including proteins, peptides, lipids, nucleic acids, carbohydrates, and small molecule ligands, as they occur in solution, crystals, and membrane environments. For the study of such systems, the program provides a large suite of computational tools that include numerous conformational and path sampling methods, free energy estimators, molecular minimization, dynamics, and analysis techniques, and model-building capabilities. The CHARMM program is applicable to problems involving a much broader class of many-particle systems. Calculations with CHARMM can be performed using a number of different energy functions and models, from mixed quantum mechanical-molecular mechanical force fields, to all-atom classical potential energy functions with explicit solvent and various boundary conditions, to implicit solvent and membrane models. The program has been ported to numerous platforms in both serial and parallel architectures. This article provides an overview of the program as it exists today with an emphasis on developments since the publication of the original CHARMM article in 1983.

Tilt and azimuthal angles of a transmembrane peptide: a comparison between molecular dynamics calculations and solid-state NMR data of sarcolipin in lipid membranes

We report molecular dynamics simulations in the explicit membrane environment of a small membrane-embedded protein, sarcolipin, which regulates the sarcoplasmic reticulum Ca-ATPase activity in both cardiac and skeletal muscle. In its monomeric form, we found that sarcolipin adopts a helical conformation, with a computed average tilt angle of 28 +/- 6 degrees and azymuthal angles of 66 +/- 22 degrees, in reasonable accord with angles determined experimentally (23 +/- 2 degrees and 50 +/- 4 degrees, respectively) using solid-state NMR with separated-local-field experiments. The effects of time and spatial averaging on both (15)N chemical shift anisotropy and (1)H/(15)N dipolar couplings have been analyzed using short-time averages of fast amide out-of-plane motions and following principal component dynamic trajectories. We found that it is possible to reproduce the regular oscillatory patterns observed for the anisotropic NMR parameters (i.e., PISA wheels) employing average amide vectors. This work highlights the role of molecular dynamics simulations as a tool for the analysis and interpretation of solid-state NMR data.

Noncontact dipole effects on channel permeation. III. Anomalous proton conductance effects in gramicidin

Proton transport on water wires, of interest for many problems in membrane biology, is analyzed in side-chain analogs of gramicidin A channels. In symmetrical 0.1N HCl solutions, fluorination of channel Trp(11), Trp-(13), or Trp(15) side chains is found to inhibit proton transport, and replacement of one or more Trps with Phe enhances proton transport, the opposite of the effects on K(+) transport in lecithin bilayers. The current-voltage relations are superlinear, indicating that some membrane field-dependent process is rate limiting. The interfacial dipole effects are usually assumed to affect the rate of cation translocation across the channel. For proton conductance, however, water reorientation after proton translocation is anticipated to be rate limiting. We propose that the findings reported here are most readily interpreted as the result of dipole-dipole interactions between channel waters and polar side chains or lipid headgroups. In particular, if reorientation of the water column begins with the water nearest the channel exit, this hypothesis explains the negative impact of fluorination and the positive impact of headgroup dipole on proton conductance.

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.

Tryptophan contributions to the empirical free-energy profile in gramicidin A/M heterodimer channels

Gramicidin A/gramicidin M heterodimer conductances were measured in planar lipid bilayers and found to form two distinguishable populations about halfway between the gramicidin A and gramicidin M homodimer conductances. This implies that the principle difference in the gramicidin A and gramicidin M transport free-energy profiles occurs at the channel center, where it would produce similar effects on the rate-limiting barrier for the two heterodimers. Kinetic analysis based on this and nearly all previously published homodimer conductance data for both gramicidin A and gramicidin M channels confirms this conclusion, indicating that the translocation step is approximately 100-fold slower in gramicidin M homodimers than in gramicidin A homodimers and that first- and second-ion exit-rate constants are higher by factors of 24 and 10, respectively. Assuming that the ratios of rate constants are related to the free-energy difference between gramicidin A and gramicidin M, we construct an effective ion-Trp free-energy interaction profile that has a minimum at the channel center.

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.

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.

Poisson–Nernst–Planck Theory Approach to the Calculation of Current Through Biological Ion Channels

The Poisson-Nernst-Planck (PNP) theory of electro-diffusion is reviewed. Techniques for numerical solution of the three-dimensional PNP equations are summarized, and several illustrative applications to ion transport through protein channels are presented. Strengths and weaknesses of the theory are discussed, as well as attempts to improve it via increasingly realistic evaluation of the force acting on each ion due to the protein/membrane environment.

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.

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.

The role of the dielectric barrier in narrow biological channels: a novel composite approach to modeling single-channel currents

A composite continuum theory for calculating ion current through a protein channel of known structure is proposed, which incorporates information about the channel dynamics. The approach is utilized to predict current through the Gramicidin A ion channel, a narrow pore in which the applicability of conventional continuum theories is questionable. The proposed approach utilizes a modified version of Poisson-Nernst-Planck (PNP) theory, termed Potential-of-Mean-Force-Poisson-Nernst-Planck theory (PMFPNP), to compute ion currents. As in standard PNP, ion permeation is modeled as a continuum drift-diffusion process in a self-consistent electrostatic potential. In PMFPNP, however, information about the dynamic relaxation of the protein and the surrounding medium is incorporated into the model of ion permeation by including the free energy of inserting a single ion into the channel, i.e., the potential of mean force along the permeation pathway. In this way the dynamic flexibility of the channel environment is approximately accounted for. The PMF profile of the ion along the Gramicidin A channel is obtained by combining an equilibrium molecular dynamics (MD) simulation that samples dynamic protein configurations when an ion resides at a particular location in the channel with a continuum electrostatics calculation of the free energy. The diffusion coefficient of a potassium ion within the channel is also calculated using the MD trajectory. Therefore, except for a reasonable choice of dielectric constants, no direct fitting parameters enter into this model. The results of our study reveal that the channel response to the permeating ion produces significant electrostatic stabilization of the ion inside the channel. The dielectric self-energy of the ion remains essentially unchanged in the course of the MD simulation, indicating that no substantial changes in the protein geometry occur as the ion passes through it. Also, the model accounts for the experimentally observed saturation of ion current with increase of the electrolyte concentration, in contrast to the predictions of standard PNP theory.

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

We use the well-known structural and functional properties of the gramicidin A channel to test the appropriateness of force fields commonly used in molecular dynamics (MD) simulations of ion channels. For this purpose, the high-resolution structure of the gramicidin A dimer is embedded in a dimyristoylphosphatidylcholine bilayer, and the potential of mean force of a K(+) ion is calculated along the channel axis using the umbrella sampling method. Calculations are performed using two of the most common force fields in MD simulations: CHARMM and GROMACS. Both force fields lead to large central barriers for K(+) ion permeation, that are substantially higher than those deduced from the physiological data by inverse methods. In long MD simulations lasting over 60 ns, several ions are observed to enter the binding site but none of them crossed the channel despite the presence of a large driving field. The present results, taken together with many earlier studies, highlights the shortcomings of the standard force fields used in MD simulations of ion channels and calls for construction of more appropriate force fields for this purpose.

Ion permeation through the gramicidin channel: atomically detailed modeling by the Stochastic Difference Equation

Atomically detailed descriptions of ionic solution, membrane, and the gramicidin channel are used to compute molecular dynamics trajectories of ion permeation. The microsecond trajectories are calculated with the Stochastic Difference Equation (SDE), which provides approximate solutions to the equations of motions (with filtered high-frequency modes) of extended timescales. The relative permeations of lithium, sodium, and potassium are estimated by using a novel, kinetic cycle protocol and are compared with experiment. The transport through native gramicidin and one fluoro-valine variant is considered as well. Qualitative agreement between theory and experiment is obtained. The faster permeation rate of sodium compared to lithium is reproduced in the calculations. The calculations also reproduce the slower diffusion through a gramicidin with fluorinated valine compared to native gramicidin. The calculations are inconclusive about the relative rates of potassium and sodium. The experiment suggests that potassium permeates more quickly. We directly probe the kinetics of a biophysical process at a relevant time window without reducing the atomically detailed description of the system. The calculations were able to capture subtle balances between binding and diffusion that determine permeation rates. The same model gave the correct ordering of diffusion rates for cases in which electrostatic binding has opposite effects and must be supplemented by dynamic factors. Diffusion rates are faster when favorable electrostatic interactions of ions in the channel (compared to the solvent) are observed. Studies of a gramicidin variant suggest an opposite effect, in which permeation is faster for the less polar channel, indicating dynamic effects. Although both trends can be explained qualitatively, it is not possible to predict (before doing the SDE calculations) which factor is more important.

Recent advances in ion channel research

The field of ion channels has entered into a rapid phase of development in the last few years, partly due to the breakthroughs in determination of the crystal structures of membrane proteins and advances in computer simulations of biomolecules. These advances have finally enabled the long-dreamed goal of relating function of a channel to its underlying molecular structure. Here we present simplified accounts of the competing permeation theories and then discuss their application to the potassium, gramicidin A and calcium channels.

Continuum electrostatics fails to describe ion permeation in the gramicidin channel

We investigate the validity of continuum electrostatics in the gramicidin A channel using a recently determined high-resolution structure. The potential and electric field acting on ions in and around the channel are computed by solving Poisson's equation. These are then used in Brownian dynamics simulations to obtain concentration profiles and the current passing through the channel. We show that regardless of the effective dielectric constant used for water in the channel or the channel protein, it is not possible to reproduce all the experimental data on gramicidin A; thus, continuum electrostatics cannot provide a valid framework for the description of ion dynamics in gramicidin channels. Using experimental data and molecular dynamics simulations as guides, we have constructed potential energy profiles that can satisfactorily describe the available physiological data. These profiles provide useful benchmarks for future potential of mean force calculations of permeating ions from molecular dynamics simulations of gramicidin A. They also offer a convenient starting point for studying structure-function relationships in modified gramicidin channels.

The role of Trp side chains in tuning single proton conduction through gramicidin channels

We present an extensive set of measurements of proton conduction through gramicidin A (gA), B (gB), and M (gM) homodimer channels which have 4, 3, or 0 Trp residues at each end of the channel, respectively. In gA we find a shoulder separating two domains of conductance increasing with concentration, confirming the results of Eisenman, G., B. Enos, J. Hagglund, and J. Sandblom. 1980. Ann. NY. Acad. Sci. 339:8-20. In gB, the shoulder is shifted by approximately 1/2 pH unit to higher H(+) concentrations and is very sharply defined. No shoulder appears in the gM data, but an associated transition from sublinear to superlinear I-V values occurs at a 100-fold higher [H(+)] in gM than in gA. The data in the low concentration domain are analyzed using a configuration space model of single-proton conduction, assuming that the difference in the proton potential of mean force (PMF) between gA and its analogs is constant, similar to the results of Anderson, D., R. B. Shirts, T. A. Cross, and D. D. Busath. 2001. Biophys. J. 81:1255-1264. Our results suggest that the average amplitudes of the calculated proton PMFs are nearly correct, but that the water reorientation barrier calculated for gA by molecular dynamics using the PM6 water model (Pomès, R., and B. Roux. 1997. Biophys. J. 72:246a) must be reduced in amplitude by 1.5 kcal/mol or more, and is not rate-limiting for gA.

Computational studies of the gramicidin channel

Ion channels are highly specific membrane-spanning protein structures which serve to facilitate the passage of selected ions across the lipid barrier. In the past decade, molecular dynamics simulations based on atomic models and realistic microscopic interactions with explicit solvent and membrane lipids have been used to gain insight into the function of these complex systems. These calculations have considerably expanded our view of ion permeation at the microscopic level. This Account will mainly focus on computational studies of the gramicidin A channel, one of the simplest and best characterized molecular pore.

Theoretical and computational models of ion channels

Computational studies can make meaningful contributions to our understanding of biological ion channels. A wide variety of methods, at different levels of approximation, can be used. Over the past few years, progress in the experimental determination of three-dimensional structures has given a fresh impetus to the theorists. Noteworthy progress has been made in carefully constructing realistic models of a number of complex biological channels to address important questions about their function.

Cellular microtransport processes: intercellular, intracellular, and aggregate behavior

Ionic and molecular transfer among cells occurs by a variety of transport processes operative at different length scales. Cell membrane permeability and electrical conductance derive from channel proteins producing pores at the molecular (ultrastructural) scale. Intracellular mobility involves the dynamics of motion through the complex ultrastructure of the cytoplasm. These phenomena unite in the larger-scale (microscopic) process of gross intercellular transfer. When such movement occurs among sufficiently many cells, it in turn begins to reflect their average collective (macroscopic) behavior as bulk tissue. This article surveys selected aspects of intercellular and intracellular transport, with emphasis on detailed mechanistic theory, experimental probes of cellular permeability, and systematic transcendence from small to large length scales.

Noncontact dipole effects on channel permeation. V. Computed potentials for fluorinated gramicidin

Experimental and theoretical calculations indicate that the dipole moment of the four Trp side chains in gramicidin A (gA) channels modify channel conductance through long-range electrostatic interactions. Electrostatic ion/side-chain interaction energies along the channel were computed with CHARMM using ab initio atom charges for native and 4-, 5-, or 6-fluorinated Trp side chains. The bulk water reaction to the polar side chains was included using the method of images as implemented by, and channel waters in idealized structures were included. Ion/Trp interaction energies were approximately -0.6 kcal/mol throughout the channel for all four of the native Trp pairs. Channel waters produced a modest reduction in the magnitude of interactions, essentially offsetting images representing the bulk water outside the channel. The effects of side-chain fluorination depended on ring position and, to a lesser extent, residue number. Compared with native Trp, 5-fluorination reduces the translocation barrier with minor effects on the exit barrier. In contrast, 6-fluorination primarily reduces exit barrier. 4-Fluorination produces a more complex double-well energy profile. Effects of measured side-chain movements resulting from fluorination or change in lipid bilayer were negligible whereas thermal side chain librations cause large effects, especially in the region of the ion-binding sites.

Sequence specific stabilization of a linear analog of the antifungal lipopeptide iturin A2 by sodium during low energy electrospray ionization mass spectrometry conditions

The structures and stability of sodiated species of 8-Beta, a linear lipopeptide analog (beta-aminotetradecanoyl-NYNQPNS) of the antifungal peptide iturin A2, were evaluated by electrospray ionization mass spectrometry (ESI-MS). Association of the lipopeptide, 8-Beta, with sodium afforded protection from fragmentation at high cone voltages and increasing collision energy conditions in the ESI-MS. The order of decreasing stability was found as 8-Beta 1Na > 8-Beta 2Na > 8-Beta 3Na > 8-Beta. Substantial differences were found between fragmentation patterns of the free and sodiated molecular species. Breakage of the N-terminal peptide bond of L-Pro generated the major product ions of the free 8-Beta parent ion. Impaired fragmentation of the sodium adducts of 8-Beta, indicated that this bond is protected by sodium complexation. Fragmentation patterns of the sodiated lipopeptide further revealed two specific binding sites for a nonsolvated sodium ion within the two type II beta-turn sequences (beta-aminotetradecanoyl-NYN and QPNS) of the natural iturin A2. It is proposed that specific interaction with sodium takes place with most of the peptide bond oxygens in these turns, and with the Gln sidechain. This interaction leads to stabilized structures in which the peptide backbone, specifically the peptide bonds in which L-Pro participates, is protected against low-energy fragmentation during ESI-MS.

A Grand Canonical Monte Carlo-Brownian dynamics algorithm for simulating ion channels

A computational algorithm based on Grand Canonical Monte Carlo (GCMC) and Brownian Dynamics (BD) is described to simulate the movement of ions in membrane channels. The proposed algorithm, GCMC/BD, allows the simulation of ion channels with a realistic implementation of boundary conditions of concentration and transmembrane potential. The method is consistent with a statistical mechanical formulation of the equilibrium properties of ion channels (; Biophys. J. 77:139-153). The GCMC/BD algorithm is illustrated with simulations of simple test systems and of the OmpF porin of Escherichia coli. The approach provides a framework for simulating ion permeation in the context of detailed microscopic models.

The binding site of sodium in the gramicidin A channel

The available information concerning the structure and location of the main binding site for sodium in the gramicidin A channel is reviewed and discussed. Results from molecular dynamics simulations using an atomic model of the channel embedded in a lipid bilayer are compared with experimental observations. The combined information from experiment and simulation suggests that the main binding sites for sodium are near the channel's mouth, approximately 9.2 A from the centre of the dimer channel, although the motion along the axis could be as large as 1 to 2 A. In the binding site, the sodium ion is lying off axis, making contact with two carbonyl oxygens and two single-file water molecules. The main channel ligand is provided by the carbonyl group of the Leu10-Trp11 peptide linkage, which exhibits the largest deflection from the ion-free channel structure.

Can we use rate constants and state models to describe ion transport through gramicidin channels?

Can we use rate constants and state models to describe ion transport through gramicidin channels? Maybe, but only if rate constants are just proportionality constants between rates and probabilities of observing states of the channel. This approach is natural if the system of channel plus ions (plus water) is almost always in one or another of a small number of identifiable states. Many features of ion transport through gramicidin, including the conductance-concentration relationship, concentration-dependent permeability ratios, anomalous mole fraction effect and to some extent flux ratio exponents, are consistent with a description in which there are four occupation 'states' of the pore: only water; an ion at one end; an ion at the other; and ions at both ends. Current-voltage relationships can (and must) also be fitted, but until there is a theory to predict the potential dependence of the rate constants this success will remain hollow. Other features have resisted interpretation. These include the failures to determine 'binding constants' consistent with all the data; the variation of flux ratio exponents with ion type; and, probably, the variation of the currents with asymmetrical ion concentrations. Nevertheless, state models still have one attractive feature, they allow consideration of the effects that one ion within the pore has on the movements of another.

Ionic interactions in multiply occupied channels

A significant number of physiologically important ion channels function via multi-ion mechanisms where repulsion between ions at slightly separated locations is believed to be critical for permeation. We apply the semi-microscopic Monte Carlo approach and analyse how multiple occupancy affects permeation energetics and ion-water-peptide correlations. We consider double occupancy in idealized models of two systems: gramicidin A and the KcsA K+ channel. We focus on the excess repulsion energy due to ion-water and ion-peptide correlations (repulsion energy adjusted for direct ion-ion interaction). Gramicidin, where multiple occupancy is marginally important functionally, is ideal for correlating structure and ion interactions. Pair occupancy is stabilized by interaction with bulk solvent, destabilized by interaction with both the channel water and, as binding sites are far apart, the peptide backbone. In the KcsA K+ channel, double occupancy is promoted by the uneven spacing and the large ion-water separations in the selectivity filter. The carbonyls forming the binding cavities are equally important for pair stabilization. Due to the binding pocket's design, net ionic repulsion is approximately 25-30% of what it would be in a gramicidin-like structure with the same interionic spacing.

Gramicidin D conformation, dynamics and membrane ion transport

The linear pentadecapeptide antibiotic, gramicidin D, a heterogeneous mixture of six components, is a naturally occurring product of Bacillus brevis known to form ion channels in synthetic and natural membranes. The conformation of gramicidin A in the solid state, in organic solvents, and in planar lipid bilayers and the relationship between the composition and the conformation of gramicidin and its selective transport of ions across membranes has been the subject of intense investigation for over 50 years. The x-ray crystal structure and nmr solution spectroscopy agree fully with one another and reveal that entirely different conformations of gramicidin are present in uncomplexed and ion complexed forms. Precise refinements of the three-dimensional structures of naturally occurring gramicidin D in crystals obtained from methanol, ethanol, and n-propanol demonstrate the unexpected presence of stable left-handed antiparallel double-helical heterodimers that vary with the crystallization solvent. The side chains of Trp residues in the three structures exhibit sequence-specific patterns of conformational preference. Tyr substitution for Trp at position 11 appears to favor beta ribbon formation and stabilization of the antiparallel double helix. This conformation acts as a template for gramicidin folding and nucleation of the different crystal forms. The fact that a minor component in a heterogeneous mixture influences aggregation and crystal nucleation has potential applications to other systems in which anomalous behavior is exhibited by aggregation of apparently homogeneous materials, such as the enigmatic behavior of prion proteins. The crystallographically determined structures of cesium, potassium, rubidium, and hydronium ion complexes of gramicidin A are in excellent agreement with the nmr structure determination of the cesium ion gramicidin complex in a methanol chloroform mixture (50 : 50). The right-handed antiparallel double stranded double helical structures (DSDHR) also exhibit geometric features compatible with the solid-state 15N and 2H nmr data recorded for gramicidin in planar lipid bilayers and attributed to the active form of gramicidin A. The DSDHR crystal structures reveal an ion channel with a single partially solvated cation distributed over three ion binding sites. The channel lumen is relatively smooth and electrostatically negative as required for cation passage, while the exterior is electrostatically neutral, a requirement for membrane insertion. The "coordination" of the Cs+ ion is achieved by interaction with the pi orbitals of the carbonyls which do not point toward the ions. The K+ binding sites, which are similar in position to Cs+ binding sites, are shifted off center slightly toward the wall of the channel.

Statistical mechanical equilibrium theory of selective ion channels

A rigorous statistical mechanical formulation of the equilibrium properties of selective ion channels is developed, incorporating the influence of the membrane potential, multiple occupancy, and saturation effects. The theory provides a framework for discussing familiar quantities and concepts in the context of detailed microscopic models. Statistical mechanical expressions for the free energy profile along the channel axis, the cross-sectional area of the pore, and probability of occupancy are given and discussed. In particular, the influence of the membrane voltage, the significance of the electric distance, and traditional assumptions concerning the linearity of the membrane electric field along the channel axis are examined. Important findings are: 1) the equilibrium probabilities of occupancy of multiply occupied channels have the familiar algebraic form of saturation properties which is obtained from kinetic models with discrete states of denumerable ion occupancy (although this does not prove the existence of specific binding sites; 2) the total free energy profile of an ion along the channel axis can be separated into an intrinsic ion-pore free energy potential of mean force, independent of the transmembrane potential, and other contributions that arise from the interfacial polarization; 3) the transmembrane potential calculated numerically for a detailed atomic configuration of the gramicidin A channel embedded in a bilayer membrane with explicit lipid molecules is shown to be closely linear over a distance of 25 A along the channel axis. Therefore, the present analysis provides some support for the constant membrane potential field approximation, a concept that has played a central role in the interpretation of flux data based on traditional models of ion permeation. It is hoped that this formulation will provide a sound physical basis for developing nonequilibrium theories of ion transport in selective biological channels.

Structural consequences of anesthetic and nonimmobilizer interaction with gramicidin A channels

Although interactions of general anesthetics with soluble proteins have been studied, the specific interactions with membrane bound-proteins that characterize general anesthesia are largely unknown. The structural modulations of anesthetic interactions with synaptic ion channels have not been elucidated. Using gramicidin A as a simplified model for transmembrane ion channels, we have recently demonstrated that a pair of structurally similar volatile anesthetic and nonimmobilizer, 1-chloro-1,2,2-trifluorocyclobutane (F3) and 1,2-dichlorohexafluorocyclobutane (F6), respectively, have distinctly different effects on the channel function. Using high-resolution NMR structural analysis, we show here that neither F3 nor F6 at pharmacologically relevant concentrations can significantly affect the secondary structure of the gramicidin A channel. Although both the anesthetic F3 and the nonimmobilizer F6 can perturb residues at the middle section of the channel deep inside the hydrophobic region in the sodium dodecyl sulfate micelles, only F3, but not F6, can significantly alter the chemical shifts of the tryptophan indole N-H protons near the channel entrances. The results are consistent with the notion that anesthetics cause functional change of the channel by interacting with the amphipathic domains at the peptide-lipid-water interface.