The free energy governing K ؉ conduction through gramicidin A channels is characterized by using over 0.1 s 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 singlechannel 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 kcal͞mol, roughly half the bulk solvation free energy. M olecular dynamics (MD) simulation has become an essential tool for investigating a wide range of chemical and biological systems. Greater computational resources, improvements in simulation methodologies, and refinement of interaction potentials have made it possible to model increasingly complex processes that previously were intractable (1). It is important that the approach be thoroughly tested on systems that are small and yet possess the same ingredients and challenges as much larger and more complex biomolecular systems. These benchmarks serve to set standards on which studies of more complex problems can find foundation. For example, a single key protein secondary structure, the ␤ hairpin, has been used as a benchmark test in protein-folding studies (2). In the present study, we tackle the problem of ion permeation with a similar mindset. Ion permeation involves a seemingly straightforward process of an ion passing across the membrane through a molecular pore. However, this process is difficult to model because it entails the accurate representation of intermolecular interactions in vastly different environments (aqueous solution and narrow protein pore) for which there is little direct experimental data (3). As a rigorous examination of an all-atom force field to model ion permeation, we combine free energy methods with fully atomistic, dynamical simulations on a benchmark system. Atomic structures have been reported for many ion channels, but none is structurally and functionally as well characterized (4), or as amenable to computer simulation, as the gramicidin A (gA) channel. gA channels form by transmembrane dimerization of single-stranded, right-handed ␤ 6.3 -helices (5) with the sequence (underlined residues are D-amino acids): formyl-Val-Gly-AlaLeu-Ala-Val-Val-Val-Trp-Leu-Trp-Leu-Trp-Leu-Trp-ethanolamine (6). High resolution structures have been obtained for gA embedded in detergent micelles by using liquid-state NMR (7,8) and oriented dimyristoyl...

Biological membranes consist of bilayer arrangements of lipids forming a hydrophobic core that presents a physical barrier to all polar and charged molecules. This long-held notion has recently been challenged by biological translocon-based experiments that report small apparent free energies to insert charged side chains near the center of a transmembrane (TM) helix. We have carried out fully atomistic simulations to provide the free-energy profile for moving a TM helix containing a protonated Arg side chain across a lipid bilayer. Our results reveal the fundamental thermodynamics governing the stability of charged side chains in membranes and the microscopic interactions involved. Despite local membrane deformations, where large amounts of water and lipid head groups are pulled into the bilayer to interact with Arg, the free-energy barrier is 17 kcal/mol. We provide a rationale for the differences in our microscopic free energies and cell biological experiments using free-energy calculations that indicate that a protonated Arg at the central residue of a TM helix of the Leader peptidase might reside close to the interface and not at the membrane center. Our findings have implications for the gating mechanisms of voltage-gated ion channels, suggesting that movements of protonated Arg residues through the membrane will be prohibited.

Abstract. The goal of this review is to establish a broad and rigorous theoretical framework to describe ion permeation through biological channels. This framework is developed in the context of atomic models on the basis of the statistical mechanical projection-operator formalism of Mori and Zwanzig. The review is divided into two main parts. The first part introduces the fundamental concepts needed to construct a hierarchy of dynamical models at different level of approximation. In particular, the potential of mean force (PMF) as a configuration-dependent free energy is introduced, and its significance concerning equilibrium and non-equilibrium phenomena is discussed. In addition, fundamental aspects of membrane electrostatics, with a particular emphasis on the influence of the transmembrane potential, as well as important computational techniques for extracting essential information from all-atom molecular dynamics (MD) simulations are described and discussed. The first part of the review provides a theoretical formalism to 'translate ' the information from the atomic structure into the familiar language of phenomenological models of ion permeation. The second part is aimed at reviewing and contrasting results obtained in recent computational studies of three very different channels : the gramicidin A (gA) channel, which is a narrow one-ion pore (at moderate concentration), the KcsA channel from Streptomyces lividans, which is a narrow multi-ion pore, and the outer membrane matrix porin F (OmpF) from Escherichia coli, which is a trimer of three b-barrel subunits each forming wide aqueous multi-ion pores. Comparison with experiments demonstrates that current computational models are approaching semi-quantitative accuracy and are able to provide significant insight into the microscopic mechanisms of ion conduction and selectivity. We conclude that all-atom MD with explicit water molecules can represent important structural features of complex biological channels accurately, including such features as the location of ion-binding sites along the permeation pathway. We finally discuss the broader issue of the validity of ion permeation models and an outlook to the future.

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.

The basic amino acids lysine (Lys) and arginine (Arg) play important roles in membrane protein activity, the sensing of membrane voltages, and the actions of antimicrobial, toxin, and cell-penetrating peptides. These roles are thought to stem from the strong interactions and disruptive influences of these amino acids on lipid membranes. In this study, we employ fully atomistic molecular dynamics simulations to observe, quantify, and compare the interactions of Lys and Arg with saturated phosphatidylcholine membranes of different thickness. We make use of both charged (methylammonium and methylguanidinium) and neutral (methylamine and methylguanidine) analogue molecules, as well as Lys and Arg side chains on transmembrane helix models. We find that the free energy barrier experienced by a charged Lys crossing the membrane is strikingly similar to that of a charged Arg (to within 2 kcal/mol), despite the two having different chemistries, H-bonding capability, and hydration free energies that differ by ∼10 kcal/mol. In comparison, the barrier for neutral Arg is higher than that for neutral Lys by around 5 kcal/mol, being more selective than that for the charged species. This can be explained by the different transport mechanisms for charged or neutral amino acid side chains in the membrane, involving membrane deformations or simple dehydration, respectively. As a consequence, we demonstrate that Lys would be deprotonated in the membrane, whereas Arg would maintain its charge. Our simulations also reveal that Arg attracts more phosphate and water in the membrane, and can form extensive H-bonding with its five H-bond donors to stabilize Arg-phosphate clusters. This leads to enhanced interfacial binding and membrane perturbations, including the appearance of a trans-membrane pore in a thinner membrane. These results highlight the special role played by Arg as an amino acid to bind to, disrupt, and permeabilize lipid membranes, as well as to sense voltages for a range of peptide and protein activities in nature and in engineered bionanodevices.

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

The mechanisms underlying ion transport and selectivity in calcium channels are examined using electrostatic calculations and Brownian dynamics simulations. We model the channel as a rigid structure with fixed charges in the walls, representing glutamate residues thought to be responsible for ion selectivity. Potential energy profiles obtained from multi-ion electrostatic calculations provide insights into ion permeation and many other observed features of L-type calcium channels. These qualitative explanations are confirmed by the results of Brownian dynamics simulations, which closely reproduce several experimental observations. These include the current-voltage curves, current-concentration relationship, block of monovalent currents by divalent ions, the anomalous mole fraction effect between sodium and calcium ions, attenuation of calcium current by external sodium ions, and the effects of mutating glutamate residues in the amino acid sequence.

The issue of ionizable protein side chains interacting with lipid membranes has been the focus of much attention since the proposal of the paddle model of voltage-gated ion channels, which suggested multiple arginine (Arg) side chains may move through the hydrocarbon core of a lipid membrane. Recent cell biology experiments have also been interpreted to suggest that these side chains would face only small free energy penalties to cross membranes, challenging a long-standing view in membrane biophysics. Here, we employ side chain analog and transmembrane helix models to determine the free energy of an Arg side chain, as a function of protonation state, across a membrane. We observe high free energy barriers for both the charged and neutral states that would prohibit lipid-exposed movement. The mechanisms for charged and neutral Arg transport are, however, very different, with the neutral state experiencing simple dehydration, whereas the charged state experiences a complex mechanism involving connections to the bilayer interfaces that deform the local membrane structure. We employ special methods to ensure sampling of these interfacial connections and decompose the free energy to shed light on the mechanisms. These deformations are found to preferentially stabilize the protonated form, such that the Arg side chain remains almost exclusively charged inside the membrane, with a pKa shift of