Ion channels, permeation, and electrostatics: insight into the function of KcsA

Implicit model to capture electrostatic features of membrane environment

Membrane protein structure prediction and design are challenging due to the complexity of capturing the interactions in the lipid layer, such as those arising from electrostatics. Accurately capturing electrostatic energies in the low-dielectric membrane often requires expensive Poisson-Boltzmann calculations that are not scalable for membrane protein structure prediction and design. In this work, we have developed a fast-to-compute implicit energy function that considers the realistic characteristics of different lipid bilayers, making design calculations tractable. This method captures the impact of the lipid head group using a mean-field-based approach and uses a depth-dependent dielectric constant to characterize the membrane environment. This energy function Franklin2023 (F23) is built upon Franklin2019 (F19), which is based on experimentally derived hydrophobicity scales in the membrane bilayer. We evaluated the performance of F23 on five different tests probing (1) protein orientation in the bilayer, (2) stability, and (3) sequence recovery. Relative to F19, F23 has improved the calculation of the tilt angle of membrane proteins for 90% of WALP peptides, 15% of TM-peptides, and 25% of the adsorbed peptides. The performances for stability and design tests were equivalent for F19 and F23. The speed and calibration of the implicit model will help F23 access biophysical phenomena at long time and length scales and accelerate the membrane protein design pipeline.

Implicit model to capture electrostatic features of membrane environment

Membrane protein structure prediction and design are challenging due to the complexity of capturing the interactions in the lipid layer, such as those arising from electrostatics. Accurately capturing electrostatic energies in the low-dielectric membrane often requires expensive Poisson-Boltzmann calculations that are not scalable for membrane protein structure prediction and design. In this work, we have developed a fast-to-compute implicit energy function that considers the realistic characteristics of different lipid bilayers, making design calculations tractable. This method captures the impact of the lipid head group using a mean-field-based approach and uses a depth-dependent dielectric constant to characterize the membrane environment. This energy function Franklin2023 (F23) is built upon Franklin2019 (F19), which is based on experimentally derived hydrophobicity scales in the membrane bilayer. We evaluated the performance of F23 on five different tests probing (1) protein orientation in the bilayer, (2) stability, and (3) sequence recovery. Relative to F19, F23 has improved the calculation of the tilt angle of membrane proteins for 90% of WALP peptides, 15% of TM-peptides, and 25% of the adsorbed peptides. The performances for stability and design tests were equivalent for F19 and F23. The speed and calibration of the implicit model will help F23 access biophysical phenomena at long time and length scales and accelerate the membrane protein design pipeline.

Testing the Limitations of MD-Based Local Electric Fields Using the Vibrational Stark Effect in Solution: Penicillin G as a Test Case

Noncovalent interactions underlie nearly all molecular processes in the condensed phase from solvation to catalysis. Their quantification within a physically consistent framework remains challenging. Experimental vibrational Stark effect (VSE)-based solvatochromism can be combined with molecular dynamics (MD) simulations to quantify the electrostatic forces in solute-solvent interactions for small rigid molecules and, by extension, when these solutes bind in enzyme active sites. While generalizing this approach toward more complex (bio)molecules, such as the conformationally flexible and charged penicillin G (PenG), we were surprised to observe inconsistencies in MD-based electric fields. Combining synthesis, VSE spectroscopy, and computational methods, we provide an intimate view on the origins of these discrepancies. We observe that the electric fields are correlated to conformation-dependent effects of the flexible PenG side chain, including both the local solvation structure and solute conformational sampling in MD. Additionally, we identified that MD-based electric fields are consistently overestimated in three-point water models in the vicinity of charged groups; this cannot be entirely ameliorated using polarizable force fields (AMOEBA) or advanced water models. This work demonstrates the value of the VSE as a direct method for experiment-guided refinements of MD force fields and establishes a general reductionist approach to calibrating vibrational probes for complex (bio)molecules.

Calcium and hydroxyapatite binding site of human vitronectin provides insights to abnormal deposit formation

The human blood protein vitronectin (Vn) is a major component of the abnormal deposits associated with age-related macular degeneration, Alzheimer's disease, and many other age-related disorders. Its accumulation with lipids and hydroxyapatite (HAP) has been demonstrated, but the precise mechanism for deposit formation remains unknown. Using a combination of solution and solid-state NMR experiments, cosedimentation assays, differential scanning fluorimetry (DSF), and binding energy calculations, we demonstrate that Vn is capable of binding both soluble ionic calcium and crystalline HAP, with high affinity and chemical specificity. Calcium ions bind preferentially at an external site, at the top of the hemopexin-like (HX) domain, with a group of four Asp carboxylate groups. The same external site is also implicated in HAP binding. Moreover, Vn acquires thermal stability upon association with either calcium ions or crystalline HAP. The data point to a mechanism whereby Vn plays an active role in orchestrating calcified deposit formation. They provide a platform for understanding the pathogenesis of macular degeneration and other related degenerative disorders, and the normal functions of Vn, especially those related to bone resorption.

Molecular Dynamics of Ion Conduction through the Selectivity Filter of the NaVAb Sodium Channel

The determination of the atomic structures of voltage-gated bacterial sodium channels using X-ray crystallography has provided a first view of this family of membrane proteins. Molecular dynamics simulations offer one approach to clarify the underlying mechanism of permeation and selectivity in these channels. However, it appears that the intracellular gate of the pore domain is either closed or only open partially in the available X-ray structures. The lack of structure with a fully open intracellular gate poses a special challenge to computational studies aimed at simulating ion conduction. To circumvent this problem, we simulated a model of the Na_VAb channel in which the transmembrane S5 and S6 helices of the pore domain have been truncated to provide direct open access to the intracellular entryway to the pore. Molecular dynamics simulations were carried out over a range of membrane potential and ion concentration of sodium and potassium. The simulations show that the Na_VAb selectivity filter is essentially a cationic pore supporting the conduction of ions at a rate comparable to aqueous diffusion with no significant selectivity for sodium. Conductance and selectivity vary as a function of ion concentration for both cations. Permeation occurs primarily via a knock-on mechanism for both sodium and potassium, although the ion ordering in single file along the pore is not strictly maintained. The character of the outward current appears quite different from the inward current, with a buildup on ions in the selectivity filter prior to escape toward the extracellular side, indicating the presence of a rectification effect that is overcome by nonphysiological applied voltages.

Heterogeneous dielectric generalized Born model with a van der Waals term provides improved association energetics of membrane-embedded transmembrane helices

The heterogeneous dielectric generalized Born (HDGB) implicit membrane formalism is extended by the addition of a van der Waals dispersion term to better describe the nonpolar components of the free energy of solvation. The new model, termed HDGBvdW, improves the energy estimates in the hydrophobic interior of the membrane, where polar and charged species are rarely found and nonpolar interactions become significant. The implicit van der Waals term for the membrane environment extends the model from Gallicchio et al. (J. Comput. Chem. 2004, 25, 479) by combining separate contributions from each of the membrane components. The HDGBvdW model is validated with a series of test cases ranging from membrane insertion and pair association profiles of amino acid side chain analogs and transmembrane helices. Overall, the HDGBvdW model leads to increased agreement with explicit membrane simulation results and experimental data. © 2016 Wiley Periodicals, Inc.

Constant-pH Molecular Dynamics Study of Kyotorphin in an Explicit Bilayer

To our knowledge, we present the first constant-pH molecular dynamics study of the neuropeptide kyotorphin in the presence of an explicit lipid bilayer. The overall conformation freedom of the peptide was found to be affected by the interaction with the membrane, in accordance with previous results using different methodologies. Analysis of the interactions between the N-terminus amine group of the peptide and several lipid atoms shows that the membrane is able to stabilize both ionized and neutral forms of kyotorphin, resulting in a pKa value that is similar to the one obtained in water. This illustrates how a detailed molecular model of the membrane leads to rather different results than would be expected from simply regarding it as a low-dielectric slab.

Molecular dynamics simulations of biological membranes and membrane proteins using enhanced conformational sampling algorithms

This paper reviews various enhanced conformational sampling methods and explicit/implicit solvent/membrane models, as well as their recent applications to the exploration of the structure and dynamics of membranes and membrane proteins. Molecular dynamics simulations have become an essential tool to investigate biological problems, and their success relies on proper molecular models together with efficient conformational sampling methods. The implicit representation of solvent/membrane environments is reasonable approximation to the explicit all-atom models, considering the balance between computational cost and simulation accuracy. Implicit models can be easily combined with replica-exchange molecular dynamics methods to explore a wider conformational space of a protein. Other molecular models and enhanced conformational sampling methods are also briefly discussed. As application examples, we introduce recent simulation studies of glycophorin A, phospholamban, amyloid precursor protein, and mixed lipid bilayers and discuss the accuracy and efficiency of each simulation model and method. This article is part of a Special Issue entitled: Membrane Proteins edited by J.C. Gumbart and Sergei Noskov.

Representation of Ion-Protein Interactions Using the Drude Polarizable Force-Field

Small metal ions play critical roles in numerous biological processes. Of particular interest is how metalloenzymes are allosterically regulated by the binding of specific ions. Understanding how ion binding affects these biological processes requires atomic models that accurately treat the microscopic interactions with the protein ligands. Theoretical approaches at different levels of sophistication can contribute to a deeper understanding of these systems, although computational models must strike a balance between accuracy and efficiency in order to enable long molecular dynamics simulations. In this study, we present a systematic effort to optimize the parameters of a polarizable force field based on classical Drude oscillators to accurately represent the interactions between ions (K⁺, Na⁺, Ca²⁺, and Cl^–) and coordinating amino-acid residues for a set of 30 biologically important proteins. By combining ab initio calculations and experimental thermodynamic data, we derive a polarizable force field that is consistent with a wide range of properties, including the geometries and interaction energies of gas-phase ion/protein-like model compound clusters, and the experimental solvation free-energies of the cations in liquids. The resulting models display significant improvements relative to the fixed-atomic-charge additive CHARMM C36 force field, particularly in their ability to reproduce the many-body electrostatic nonadditivity effects estimated from ab initio calculations. The analysis clarifies the fundamental limitations of the pairwise additivity assumption inherent in classical fixed-charge force fields, and shows its dramatic failures in the case of Ca²⁺ binding sites. These optimized polarizable models, amenable to computationally efficient large-scale MD simulations, set a firm foundation and offer a powerful avenue to study the roles of the ions in soluble and membrane transport proteins.

Microsecond simulations of DNA and ion transport in nanopores with novel ion-ion and ion-nucleotides effective potentials

We developed a novel scheme based on the grand-canonical Monte Carlo/Brownian dynamics simulations and have extended it to studies of ion currents across three nanopores with the potential for single-stranded DNA (ssDNA) sequencing: solid-state nanopore Si₃N₄, α-hemolysin, and E111N/M113Y/K147N mutant. To describe nucleotide-specific ion dynamics compatible with ssDNA coarse-grained model, we used the inverse Monte Carlo protocol, which maps the relevant ion-nucleotide distribution functions from all-atom molecular dynamics (MD) simulations. Combined with the previously developed simulation platform for Brownian dynamics simulations of ion transport, it allows for microsecond- and millisecond-long simulations of ssDNA dynamics in the nanopore with a conductance computation accuracy that equals or exceeds that of all-atom MD simulations. In spite of the simplifications, the protocol produces results that agree with the results of previous studies on ion conductance across open channels and provide direct correlations with experimentally measured blockade currents and ion conductances that have been estimated from all-atom MD simulations.

Multi-ion distributions in the cytoplasmic domain of inward rectifier potassium channels

Inward rectifier potassium (Kir) channels act as cellular diodes, allowing unrestricted flow of potassium (K(+)) into the cell while preventing currents of large magnitude in the outward direction. The rectification mechanism by which this occurs involves a coupling between K(+) and intracellular blockers-magnesium (Mg(2+)) or polyamines-that simultaneously occupy the permeation pathway. In addition to the transmembrane pore, Kirs possess a large cytoplasmic domain (CD) that provides a favorable electronegative environment for cations. Electrophysiological experiments have shown that the CD is a key regulator of both conductance and rectification. In this study, we calculate and compare averaged equilibrium probability densities of K(+) and Cl(-) in open-pore models of the CDs of a weak (Kir1.1-ROMK) and a strong (Kir2.1-IRK) rectifier through explicit-solvent molecular-dynamics simulations in ~1 M KCl. The CD of both channels concentrates K(+) ions greater than threefold inside the cytoplasmic pore while IRK shows an additional K(+) accumulation region near the cytoplasmic entrance. Simulations carried out with Mg(2+) or spermine (SPM(4+)) show that these ions interact with pore-lining residues, shielding the surface charge and reducing K(+) in both channels. The results also show that SPM(4+) behaves differently inside these two channels. Although SPM(4+) remains inside the CD of ROMK, it diffuses around the entire volume of the pore. In contrast, this polyatomic cation finds long-lived conformational states inside the IRK pore, interacting with residues E224, D259, and E299. The strong rectifier CD is also capable of sequestering an additional SPM(4+) at the cytoplasmic entrance near a cluster of negative residues D249, D274, E275, and D276. Although understanding the actual mechanism of rectification blockade will require high-resolution structural information of the blocked state, these simulations provide insight into how sequence variation in the CD can affect the multi-ion distributions that underlie the mechanisms of conduction, rectification affinity, and kinetics.

Ca(2+) signalling by IP(3) receptors

The Ca(2) (+) signals evoked by inositol 1,4,5-trisphosphate (IP(3)) are built from elementary Ca(2) (+) release events involving progressive recruitment of IP(3) receptors (IP(3)R), intracellular Ca(2) (+) channels that are expressed in almost all animal cells. The smallest events ('blips') result from opening of single IP(3)R. Larger events ('puffs') reflect the near-synchronous opening of a small cluster of IP(3)R. These puffs become more frequent as the stimulus intensity increases and they eventually trigger regenerative Ca(2) (+) waves that propagate across the cell. This hierarchical recruitment of IP(3)R is important in allowing Ca(2) (+) signals to be delivered locally to specific target proteins or more globally to the entire cell. Co-regulation of IP(3)R by Ca(2) (+) and IP(3), the ability of a single IP(3)R rapidly to mediate a large efflux of Ca(2) (+) from the endoplasmic reticulum, and the assembly of IP(3)R into clusters are key features that allow IP(3)R to propagate Ca(2) (+) signals regeneratively. We review these properties of IP(3)R and the structural basis of IP(3)R behavior.

Constant electric field simulations of the membrane potential illustrated with simple systems

Advances in modern computational methods and technology make it possible to carry out extensive molecular dynamics simulations of complex membrane proteins based on detailed atomic models. The ultimate goal of such detailed simulations is to produce trajectories in which the behavior of the system is as realistic as possible. A critical aspect that requires consideration in the case of biological membrane systems is the existence of a net electric potential difference across the membrane. For meaningful computations, it is important to have well validated methodologies for incorporating the latter in molecular dynamics simulations. A widely used treatment of the membrane potential in molecular dynamics consists of applying an external uniform electric field E perpendicular to the membrane. The field acts on all charged particles throughout the simulated system, and the resulting applied membrane potential V is equal to the applied electric field times the length of the periodic cell in the direction perpendicular to the membrane. A series of test simulations based on simple membrane-slab models are carried out to clarify the consequences of the applied field. These illustrative tests demonstrate that the constant-field method is a simple and valid approach for accounting for the membrane potential in molecular dynamics studies of biomolecular systems. This article is part of a Special Issue entitled: Membrane protein structure and function.

Voltage profile along the permeation pathway of an open channel

For ion channels, the transmembrane potential plays a critical role by acting as a driving force for permeant ions. At the microscopic level, the transmembrane potential is thought to decay nonlinearly across the ion permeation pathway because of the irregular three-dimensional shape of the channel's pore. By taking advantage of the current structural and functional understanding of cyclic nucleotide-gated channels, in this study we experimentally explore the transmembrane potential's distribution across the open pore. As a readout for the voltage drop, we engineered cysteine residues along the selectivity filter and scanned the sensitivity of their modification rates by Ag(+) to the transmembrane potential. The experimental data, which indicate that the majority of the electric field drops across the selectivity filter, are in good agreement with continuum electrostatic calculations using a homology model of an open CNG channel. By focusing the transmembrane potential across the selectivity filter, the electromotive driving force is coupled with the movement of permeant ions in the filter, maximizing the efficiency of this process.

APBSmem: a graphical interface for electrostatic calculations at the membrane

Electrostatic forces are one of the primary determinants of molecular interactions. They help guide the folding of proteins, increase the binding of one protein to another and facilitate protein-DNA and protein-ligand binding. A popular method for computing the electrostatic properties of biological systems is to numerically solve the Poisson-Boltzmann (PB) equation, and there are several easy-to-use software packages available that solve the PB equation for soluble proteins. Here we present a freely available program, called APBSmem, for carrying out these calculations in the presence of a membrane. The Adaptive Poisson-Boltzmann Solver (APBS) is used as a back-end for solving the PB equation, and a Java-based graphical user interface (GUI) coordinates a set of routines that introduce the influence of the membrane, determine its placement relative to the protein, and set the membrane potential. The software Jmol is embedded in the GUI to visualize the protein inserted in the membrane before the calculation and the electrostatic potential after completing the computation. We expect that the ease with which the GUI allows one to carry out these calculations will make this software a useful resource for experimenters and computational researchers alike. Three examples of membrane protein electrostatic calculations are carried out to illustrate how to use APBSmem and to highlight the different quantities of interest that can be calculated.

A combined computational and functional approach identifies new residues involved in pH-dependent gating of ASIC1a

Acid-sensing ion channels (ASICs) are key receptors for extracellular protons. These neuronal nonvoltage-gated Na(+) channels are involved in learning, the expression of fear, neurodegeneration after ischemia, and pain sensation. We have applied a systematic approach to identify potential pH sensors in ASIC1a and to elucidate the mechanisms by which pH variations govern ASIC gating. We first calculated the pK(a) value of all extracellular His, Glu, and Asp residues using a Poisson-Boltzmann continuum approach, based on the ASIC three-dimensional structure, to identify candidate pH-sensing residues. The role of these residues was then assessed by site-directed mutagenesis and chemical modification, combined with functional analysis. The localization of putative pH-sensing residues suggests that pH changes control ASIC gating by protonation/deprotonation of many residues per subunit in different channel domains. Analysis of the function of residues in the palm domain close to the central vertical axis of the channel allowed for prediction of conformational changes of this region during gating. Our study provides a basis for the intrinsic ASIC pH dependence and describes an approach that can also be applied to the investigation of the mechanisms of the pH dependence of other proteins.

Structures of beta-amyloid peptide 1-40, 1-42, and 1-55-the 672-726 fragment of APP-in a membrane environment with implications for interactions with gamma-secretase

Aggregation of Amyloid beta (Abeta) peptide has been linked to the neurodegenerative Alzheimer's Disease and implicated in other amyloid diseases including cerebral amyloid angiopathy. Abeta peptide is generated by cleavage of the amyloid precursor protein (APP) by transmembrane proteases. It is crucial to determine the structures of beta-amyloid peptides in a membrane to provide a molecular basis for the cleavage mechanism. We report the structures of amyloid beta peptide (Abeta(1-40) and Abeta(1-42)) as well as the 672-726 fragment of APP (referred to as Abeta(1-55)) in a membrane environment determined by replica-exchange molecular dynamics simulation. Abeta(1-40) is found to have two helical domains A (13-22) and B(30-35) and a type I beta-turn at 23-27. The peptide is localized at the interface between membrane and solvent. Substantial fluctuations in domain A are observed. The dominant simulated tertiary structure of Abeta(1-40) is observed to be similar to the simulated Abeta(1-42) structure. However, there are differences observed in the overall conformational ensemble, as characterized by the two-dimensional free energy surfaces. The fragment of APP (Abeta(1-55)) is observed to have a long transmembrane helix. The position of the transmembrane region and ensemble of membrane structures are elucidated. The conformational transition between the transmembrane Abeta(1-55) structure, prior to cleavage, and the Abeta(1-40) structure, following cleavage, is proposed.

Closed-channel block of BK potassium channels by bbTBA requires partial activation

Blockade of large-conductance Ca²⁺-activated K⁺ (BK) channels by the bulky quaternary ammonium compound, N-(4-[benzoyl]benzyl)-N,N,N-tributylammonium (bbTBA), exhibits features consistent with blockade of both closed and open states. Here, we examine block of closed BK channels by bbTBA and how it may differ from block of open channels. Although our observations generally confirm earlier results, we describe three observations that are inconsistent with a model in which closed and open channels are equally accessible to blockade by bbTBA. First, block by bbTBA exhibits Ca²⁺-dependent features that are inconsistent with strictly state-independent block. Second, the steady-state voltage dependence of bbTBA block at negative potentials shows that any block of completely closed states either does not occur or is completely voltage independent. Third, determination of the fractional unblock by bbTBA at either low or high Ca²⁺ reveals deviations from a model in which open- and closed-state block is identical. The results support the view that bbTBA blockade of fully closed channels does not occur. We imagine two general types of explanation. First, a stronger voltage dependence of closed-channel block may minimize the contribution of closed-channel block at negative potentials. Second, voltage-dependent conformational changes among closed-channel states may permit block by bbTBA. The analysis supports the latter view, suggesting that bbTBA blockade of fully closed channels does not occur, but the ability of bbTBA to block a closed channel requires movement of one or more voltage sensors. Models in which block is coupled to voltage sensor movement can qualitatively account for (1) the ability of open-channel block to better fit block of conductance–voltage curves at high Ca²⁺; (2) the voltage dependence of fractional availability; and (3) the fractional unblock at different open probabilities. BK channels appear to undergo voltage-dependent conformational changes among closed states that are permissive for bbTBA block.

Mechanism of potassium-channel selectivity revealed by Na(+) and Li(+) binding sites within the KcsA pore

Potassium channels allow K(+) ions to diffuse through their pores while preventing smaller Na(+) ions from permeating. Discrimination between these similar, abundant ions enables these proteins to control electrical and chemical activity in all organisms. Selection occurs at the narrow selectivity filter containing structurally identified K(+) binding sites. Selectivity is thought to arise because smaller ions such as Na(+) do not bind to these K(+) sites in a thermodynamically favorable way. Using the model K(+) channel KcsA, we examined how intracellular Na(+) and Li(+) interact with the pore and the permeant ions using electrophysiology, molecular dynamics simulations and X-ray crystallography. Our results suggest that these small cations have a separate binding site within the K(+) selectivity filter. We propose that selective permeation from the intracellular side primarily results from a large energy barrier blocking filter entry for Na(+) and Li(+) in the presence of K(+), not from a difference of binding affinity between ions.

Reconstructing potentials of mean force from short steered molecular dynamics simulations of Vpu from HIV-1

Vpu from human immunodeficiency virus type-1 (HIV-1) is an 81 amino acid type I integral membrane protein. Vpu forms ion conducting homooligomeric assemblies. To assess the energy landscape of an ion traversing the channel or pore single ion potentials of mean force (PMF) are reconstructed from short (1.2 ns) steered molecular dynamics (SMD) simulations using the Langevin equation of motion. For the simulations a section of the first 32 amino acids including the transmembrane domain of the Vpu protein is used. The values for the friction coefficient are estimated as a function of time using the velocity autocorrelation method. The PMFs of K(+), Na(+), and C(-) adopt a wave like pattern with a maximum around the hydrophobic stretch of the pore and a minimum at the hydrophilic site (C terminus). Independent of the pore size the amplitude of the PMF of at least one cation is always the lowest.

A structural model for K2P potassium channels based on 23 pairs of interacting sites and continuum electrostatics

K(2P)Ø, the two-pore domain potassium background channel that determines cardiac rhythm in Drosophila melanogaster, and its homologues that establish excitable membrane activity in mammals are of unknown structure. K(2P) subunits have two pore domains flanked by transmembrane (TM) spans: TM1-P1-TM2-TM3-P2-TM4. To establish spatial relationships in K(2P)Ø, we identified pairs of sites that display electrostatic compensation. Channels silenced by the addition of a charge in pore loop 1 (P1) or P2 were restored to function by countercharges at specific second sites. A three-dimensional homology model was determined using the crystal structure of K(V)1.2, effects of K(2P)Ø mutations to establish alignment, and compensatory charge-charge pairs. The model was refined and validated by continuum electrostatic free energy calculations and covalent linkage of introduced cysteines. K(2P) channels use two subunits arranged so that the P1 and P2 loops contribute to one pore, identical P loops face each other diagonally across the pore, and the channel complex has bilateral symmetry with a fourfold symmetric selectivity filter.

Long-pore electrostatics in inward-rectifier potassium channels

Inward-rectifier potassium (Kir) channels differ from the canonical K⁺ channel structure in that they possess a long extended pore (∼85 Å) for ion conduction that reaches deeply into the cytoplasm. This unique structural feature is presumably involved in regulating functional properties specific to Kir channels, such as conductance, rectification block, and ligand-dependent gating. To elucidate the underpinnings of these functional roles, we examine the electrostatics of an ion along this extended pore. Homology models are constructed based on the open-state model of KirBac1.1 for four mammalian Kir channels: Kir1.1/ROMK, Kir2.1/IRK, Kir3.1/GIRK, and Kir6.2/KATP. By solving the Poisson-Boltzmann equation, the electrostatic free energy of a K⁺ ion is determined along each pore, revealing that mammalian Kir channels provide a favorable environment for cations and suggesting the existence of high-density regions in the cytoplasmic domain and cavity. The contribution from the reaction field (the self-energy arising from the dielectric polarization induced by the ion's charge in the complex geometry of the pore) is unfavorable inside the long pore. However, this is well compensated by the electrostatic interaction with the static field arising from the protein charges and shielded by the dielectric surrounding. Decomposition of the static field provides a list of residues that display remarkable correspondence with existing mutagenesis data identifying amino acids that affect conduction and rectification. Many of these residues demonstrate interactions with the ion over long distances, up to 40 Å, suggesting that mutations potentially affect ion or blocker energetics over the entire pore. These results provide a foundation for understanding ion interactions in Kir channels and extend to the study of ion permeation, block, and gating in long, cation-specific pores.

Calculating free-energy profiles in biomolecular systems from fast nonequilibrium processes

Often gaining insight into the functioning of biomolecular systems requires to follow their dynamics along a microscopic reaction coordinate (RC) on a macroscopic time scale, which is beyond the reach of current all atom molecular dynamics (MD) simulations. A practical approach to this inherently multiscale problem is to model the system as a fictitious overdamped Brownian particle that diffuses along the RC in the presence of an effective potential of mean force (PMF) due to the rest of the system. By employing the recently proposed FR method [I. Kosztin, J. Chem. Phys. 124, 064106 (2006)], which requires only a small number of fast nonequilibrium MD simulations of the system in both forward and time reversed directions along the RC, we reconstruct the PMF: (1) of deca-alanine as a function of its end-to-end distance, and (2) that guides the motion of potassium ions through the gramicidin A channel. In both cases the computed PMFs are found to be in good agreement with previous results obtained by different methods. Our approach appears to be about one order of magnitude faster than the other PMF calculation methods and, in addition, it also provides the position-dependent diffusion coefficient along the RC. Thus, the obtained PMF and diffusion coefficient can be used in an overdamped Brownian model to estimate important characteristics of the studied systems, e.g., the mean folding time of the stretched deca-alanine and the mean diffusion time of the potassium ion through gramicidin A.

The membrane potential and its representation by a constant electric field in computer simulations

A theoretical framework is elaborated to account for the effect of a transmembrane potential in computer simulations. It is shown that a simulation with a constant external electric field applied in the direction normal to the membrane is equivalent to the influence of surrounding infinite baths maintained to a voltage difference via ion-exchanging electrodes connected to an electromotive force. It is also shown that the linearly-weighted displacement charge within the simulation system tracks the net flow of charge through the external circuit comprising the electromotive force and the electrodes. Using a statistical mechanical reduction of the degrees of freedom of the external system, three distinct theoretical routes are formulated and examined for the purpose of characterizing the free energy of a protein embedded in a membrane that is submitted to a voltage difference. The W-route is constructed from the variations in the voltage-dependent potential of mean force along a reaction path connecting two conformations of the protein. The Q-route is based on the average displacement charge as a function of the conformation of the protein. Finally, the G-route considers the relative charging free energy of specific residues, with and without applied membrane potentials. The theoretical formulation is illustrated with a simple model of an ion crossing a vacuum slab surrounded by two aqueous bulk phases and with a fragment of the voltage-sensor of the KvAP potassium channel.

An ion gating mechanism of gastric H,K-ATPase based on molecular dynamics simulations

Gastric H,K-ATPase is an electroneutral transmembrane pump that moves protons from the cytoplasm of the parietal cell into the gastric lumen in exchange for potassium ions. The mechanism of transport against the established electrochemical gradients includes intermediate conformations in which the transferred ions are trapped (occluded) within the membrane domain of the pump. The pump cycle involves switching between the E1 and E2P states. Molecular dynamics simulations on homology models of the E2P and E1 states were performed to investigate the mechanism of K(+) movement in this enzyme. We performed separate E2P simulations with one K(+) in the luminal channel, one K(+) ion in the occlusion site, two K(+) ions in the occlusion site, and targeted molecular dynamics from E2P to E1 with two K(+) ions in the occlusion site. The models were inserted into a lipid bilayer system and were stable over the time course of the simulations, and K(+) ions in the channel moved to a consistent location near the center of the membrane domain, thus defining the occlusion site. The backbone carbonyl oxygen from residues 337 through 342 on the nonhelical turn of M4, as well as side-chain oxygen from E343, E795, and E820, participated in the ion occlusion. A single water molecule was stably bound between the two K(+) ions in the occlusion site, providing an additional ligand and partial shielding the positive charges from one another. Targeted molecular dynamics was used to transform the protein from the E2P to the E1 state (two K(+) ions to the cytoplasm). This simulation identified the separation of the water column in the entry channel as the likely gating mechanism on the luminal side. A hydrated exit channel also formed on the cytoplasmic side of the occlusion site during this simulation. Hence, water molecules became available to hydrate the ions. The movement of the M1M2 transmembrane segments, and the displacement of residues Q159, E160, Q110, and T152 during the conformational change, as well as the motions of E343 and L346, acted as the cytoplasmic-side gate.

PBEQ-Solver for online visualization of electrostatic potential of biomolecules

PBEQ-Solver provides a web-based graphical user interface to read biomolecular structures, solve the Poisson-Boltzmann (PB) equations and interactively visualize the electrostatic potential. PBEQ-Solver calculates (i) electrostatic potential and solvation free energy, (ii) protein–protein (DNA or RNA) electrostatic interaction energy and (iii) pKa of a selected titratable residue. All the calculations can be performed in both aqueous solvent and membrane environments (with a cylindrical pore in the case of membrane). PBEQ-Solver uses the PBEQ module in the biomolecular simulation program CHARMM to solve the finite-difference PB equation of molecules specified by users. Users can interactively inspect the calculated electrostatic potential on the solvent-accessible surface as well as iso-electrostatic potential contours using a novel online visualization tool based on MarvinSpace molecular visualization software, a Java applet integrated within CHARMM-GUI (http://www.charmm-gui.org). To reduce the computational time on the server, and to increase the efficiency in visualization, all the PB calculations are performed with coarse grid spacing (1.5 Å before and 1 Å after focusing). PBEQ-Solver suggests various physical parameters for PB calculations and users can modify them if necessary. PBEQ-Solver is available at http://www.charmm-gui.org/input/pbeqsolver.

Intrinsic electrostatic potential in the BK channel pore: role in determining single channel conductance and block

The internal vestibule of large-conductance Ca²⁺ voltage-activated K⁺ (BK) channels contains a ring of eight negative charges not present in K⁺ channels of lower conductance (Glu386 and Glu389 in hSlo) that modulates channel conductance through an electrostatic mechanism (Brelidze, T.I., X. Niu, and K.L. Magleby. 2003. Proc. Natl. Acad. Sci. USA. 100:9017–9022). In BK channels there are also two acidic amino acid residues in an extracellular loop (Asp326 and Glu329 in hSlo). To determine the electrostatic influence of these charges on channel conductance, we expressed wild-type BK channels and mutants E386N/E389N, D326N, E329Q, and D326N/E329Q channels on Xenopus laevis oocytes, and measured the expressed currents under patch clamp. Contribution of E329 to the conductance is negligible and single channel conductance of D326N/E329Q channels measured at 0 mV in symmetrical 110 mM K⁺ was 18% lower than the control. Current–voltage curves displayed weak outward rectification for D326N and the double mutant. The conductance differences between the mutants and wild-type BK were caused by an electrostatic effect since they were enhanced at low K⁺ (30 mM) and vanished at high K⁺ (1 M K⁺). We determine the electrostatic potential change, Δφ, caused by the charge neutralization using TEA⁺ block for the extracellular charges and Ba²⁺ for intracellular charges. We measured 13 ± 2 mV for Δφ at the TEA⁺ site when turning off the extracellular charges, and 17 ± 2 mV for the Δφ at the Ba²⁺ site when the intracellular charges were turned off. To understand the electrostatic effect of charge neutralizations, we determined Δφ using a BK channel molecular model embedded in a lipid bilayer and solving the Poisson-Boltzmann equation. The model explains the experimental results adequately and, in particular, gives an economical explanation to the differential effect on the conductance of the neutralization of charges D326 and E329.

Is the mobility of the pore walls and water molecules in the selectivity filter of KcsA channel functionally important?

We performed in-depth analysis of the forces which act on the K(+) ions in the selectivity filter of the KcsA channel in order to estimate the relative importance of static and dynamic influence of the filter wall and water molecules on ion permeation and selectivity. The forces were computed using the trajectories of all-atom molecular dynamics simulations. It is shown that the dynamics of the selectivity filter contributes about 3% to the net force acting on the ions and can be neglected in the studies focused on the macroscopic properties of the channel, such as the current. Among the filter atoms, only the pore-forming carbonyl groups can be considered as dynamic in the studies of microscopic events of conduction, while the dynamic effects from all other atoms are negligible. We also show that the dynamics of the water molecules in the filter can not be neglected. The fluctuating forces from the water molecules can be as strong as net forces from the pore walls and can effectively drive the ions through the local energy barriers in the filter.

Implicit membrane models for membrane protein simulation

Implicit models of membrane environments offer computational advantages in simulations of membrane-interacting proteins and peptides. Such methods are especially useful for studies of long time scale processes, such as folding and aggregation, or very large complexes that are otherwise intractable with explicit lipid environments. Implicit models replace explicit solute-solvent interactions with a mean-field approach. In the most physical models, continuum dielectric electrostatics is combined with empirical formulations for the nonpolar components of the free energy of solvation. The practical use of a number of implicit membrane models ranging from the empirical IMM1 method to generalized Born-based methods with two-dielectric and multidielectric representations of biological membrane characteristics is presented.

Dynamics of the Kv1.2 voltage-gated K+ channel in a membrane environment

All-atom molecular dynamics simulations are used to better understand the dynamic environment experienced by the Kv1.2 channel in a lipid membrane. The structure of the channel is stable during the trajectories. The pore domain keeps a well-defined conformation, whereas the voltage-sensing domains undergo important lateral fluctuations, consistent with their modular nature. A channel-like region at the center of the S1-S4 helical bundle fills rapidly with water, reminiscent of the concept of high-dielectric aqueous crevices. The first two arginines along S4 (R294 and R297) adopt an interfacial position where they interact favorably with water and the lipid headgroups. The following two arginines (R300 and R303) interact predominantly with water and E226 in S2. Despite the absence of a structurally permanent gating pore formed by protein residues and surrounding the S4 helix, as traditionally pictured, the charged residues are located in a favorable environment and are not extensively exposed to the membrane nonpolar region. Continuum electrostatic computations indicate that the transmembrane potential sensed by the charged residues in the voltage sensor varies abruptly over the outer half of the membrane in the arginine-rich region of S4; thus, the voltage gradient or membrane electric field is "focused". Interactions of basic residues with the lipid headgroups at the intracellular membrane-solution interface reduce the membrane thickness near the channel, resulting in an increased transmembrane field.

A quantitative description of KcsA gating II: single-channel currents

The kinetic transitions of proton-activated WT KcsA and the noninactivating E71A mutant were studied at the single-channel level in purified, liposome-reconstituted preparations. Single-channel currents were recorded using patch-clamp techniques under nonstationary and steady-state conditions. Maximum-likelihood analyses reveal that the key influence of acidic pH is to increase the frequency of bursting without an effect on the intraburst open and closed dwell times, consistent with the finding from macroscopic currents that protons promote activation without a significant effect on inactivation. However, in steady-conditions of pH, voltage not only alters the burst frequency but also affects their properties, such as the frequency of the flickers and the dwell times of the closed and open states. This is to be expected if voltage modulates pathways connecting open and inactivated states. Upon opening, KcsA can enter at least two closed states that are not part of the activation pathway. The frequency and duration of these closed states was found to be voltage dependent and therefore these are likely to represent short-lived inactivated states. Single-channel recordings of WT KcsA also show varying propensity for the presence of subconductance states. The probability of occurrence of these states did not show clear modulation by voltage or pH and their origin remains unclear and a focus for further investigation. A kinetic model is proposed to describe the gating events in KcsA that recapitulates its macroscopic and single-channel behavior. The model has been constrained by the single-channel analyses presented in this work along with data from macroscopic currents in the preceding paper.

Ion conductance vs. pore gating and selectivity in KcsA channel: Modeling achievements and perspectives

KcsA potassium channel belongs to a wide family of allosteric proteins that switch between closed and open states conformations in response to a stimulus, and act as a regulator of cation activity in living cells. The gating mechanism and cation selectivity of such channels have been extensively studied in the literature, with a revival emphasis these latter years, due to the publication of the crystallized structure of KcsA. Despite the increasing number of research and review papers on these topics, quantitative interpretation of these processes at the atomic scale is far from achieved. On the basis of available experimental and theoretical data, and by including our recent results, we review the progresses in this field of activity and discuss the weaknesses that should be corrected. In this spirit, we partition the channel into the filter, cavity, extra and intracellular media, in order to analyze separately the specificity of each region. Special emphasis is brought to the study of an open state for the channel and to the different properties generated by the opening. The influence of water as a structural and dynamical component of the channel properties in closed and open states, as well as in the sequential motions of the cations, is analyzed using molecular dynamics simulations and ab initio calculations. The polarization and charge transfer effects on the ions' dynamics and kinetics are discussed in terms of partial charge models.

Insight into the origins of the barrier-less knock-on conduction in the KcsA channel: molecular dynamics simulations and ab initio calculations

Since the pioneering work of Zhou et al. (Y. Zhou, J. H. Morais-Cabral, A. Kaufman and R. MacKinnon, Nature, 2001, 414, 43-48) it is now well established that the streptomyces lividans potassium channel (KcsA) can accommodate more than one ion, namely between 2 and 3. As a result, it is usually assumed that the conduction of ions proceeds through a barrier-less knock-on mechanism. This one is an alternation of two sequences containing either 2 or 3 ions which have nearly the same energies. However, the origin of such knock-on mechanism is not clearly known. The entry and the exit of ion in or out of the selectivity filter are suspected to be due to the repulsive interactions between ions. In this work, molecular dynamics simulations running over nanoseconds have been done in order to identify such events. Two specific situations, namely (S(1), S(3)) containing 2 ions and (S(2), S(4)) containing 3 ions, have been investigated regarding the different locations that ions can occupy during their diffusion through the selectivity filter of KcsA. We show that contractions of the (S(1), S(3)) file and dilation of the (S(2), S(4)) file are at the origin of the passage from one sequence to the other. The comparison between the experimentally observed diffusion rate and the occurrence's frequency of such contractions or dilation confirm the importance of such events. Ab initio calculations have also been conducted in order to examine the effect of ion polarization in the filter of KcsA. During the contraction of the ion/water file, one charge at the extra-cellular mouth of the channel strongly deviates from the others. This behavior could guide the diffusion direction to a certain extent since the contraction of the (S(1), S(3)) is favored.

Effect of different treatments of long-range interactions and sampling conditions in molecular dynamic simulations of rhodopsin embedded in a dipalmitoyl phosphatidylcholine bilayer

The present study analyzes the effect of the simulation conditions on the results of molecular dynamics simulations of G-protein coupled receptors (GPCRs) performed with an explicit lipid bilayer. Accordingly, the present work reports the analysis of different simulations of bovine rhodopsin embedded in a dipalmitoyl phosphatidylcholine (DPPC) lipid bilayer using two different sampling conditions and two different approaches for the treatment of long-range electrostatic interactions. Specifically, sampling was carried out either by using the statistical ensembles NVT or NPT (constant number of atoms, a pressure of 1 atm in all directions and fixed temperature), and the electrostatic interactions were treated either by using a twin-cutoff, or the particle mesh Ewald summation method (PME). The results of the present study suggest that the use of the NPT ensemble in combination with the PME method provide more realistic simulations. The use of NPT during the equilibration avoids the need of an a priori estimation of the box dimensions, giving the correct area per lipid. However, once the system is equilibrated, the simulations are irrespective of the sampling conditions used. The use of an electrostatic cutoff induces artifacts on both lipid thickness and the ion distribution, but has no direct effect on the protein and water molecules.

Membrane assembly of simple helix homo-oligomers studied via molecular dynamics simulations

The assembly of simple transmembrane helix homo-oligomers is studied by combining a generalized Born implicit membrane model with replica exchange molecular dynamics simulations to sample the conformational space of various oligomerization states and the native oligomeric conformation. Our approach is applied to predict the structures of transmembrane helices of three proteins--glycophorin A, the M2 proton channel, and phospholamban--using only peptide sequence and the native oligomerization state information. In every case, the methodology reproduces native conformations that are in good agreement with available experimental structural data. Thus, our method should be useful in the prediction of native structures of transmembrane domains of other peptides. When we ignore the experimental constraint on the native oligomerization state and attempt de novo prediction of the structure and oligomerization state based only on sequence and simple energetic considerations, we identify the pentamer as the most stable oligomer for phospholamban. However, for the glycophorin A and the M2 proton channels, we tend to predict higher oligomers as more stable. Our studies demonstrate that reliable predictions of the structure of transmembrane helical oligomers can be achieved when the observed oligomerization state is imposed as a constraint, but that further efforts are needed for the de novo prediction of both structure and oligomeric state.

Modeling electrostatic effects in proteins

Electrostatic energies provide what is perhaps the most effective tool for structure-function correlation of biological molecules. This review considers the current state of simulations of electrostatic energies in macromolecules as well as the early developments of this field. We focus on the relationship between microscopic and macroscopic models, considering the convergence problems of the microscopic models and the fact that the dielectric 'constants' in semimacroscopic models depend on the definition and the specific treatment. The advances and the challenges in the field are illustrated considering a wide range of functional properties including pK(a)'s, redox potentials, ion and proton channels, enzyme catalysis, ligand binding and protein stability. We conclude by pointing out that, despite the current problems and the significant misunderstandings in the field, there is an overall progress that should lead eventually to quantitative descriptions of electrostatic effects in proteins and thus to quantitative descriptions of the function of proteins.

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

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

The barrier for proton transport in aquaporins as a challenge for electrostatic models: The role of protein relaxation in mutational calculations

The origin of the barrier for proton transport through the aquaporin channel is a problem of general interest. It is becoming increasingly clear that this barrier is not attributable to the orientation of the water molecules across the channel but rather to the electrostatic penalty for moving the proton charge to the center of the channel. However, the reason for the high electrostatic barrier is still rather controversial. It has been argued by some workers that the barrier is due to the so-called NPA motif and/or to the helix macrodipole or to other specific elements. However, our works indicated that the main reason for the high barrier is the loss of the generalized solvation upon moving the proton charge from the bulk to the center of the channel and that this does not reflect a specific repulsive electrostatic interaction but the absence of sufficient electrostatic stabilization. At this stage it seems that the elucidation and clarification of the origin of the electrostatic barrier can serve as an instructive test case for electrostatic models. Thus, we reexamine the free-energy surface for proton transport in aquaporins using the microscopic free-energy perturbation/umbrella sampling (FEP/US) and the empirical valence bond/umbrella sampling (EVB/US) methods as well as the semimacroscopic protein dipole Langevin dipole model in its linear response approximation version (the PDLD/S-LRA). These extensive studies help to clarify the nature of the barrier and to establish the "reduced solvation effect" as the primary source of this barrier. That is, it is found that the barrier is associated with the loss of the generalized solvation energy (which includes of course all electrostatic effects) upon moving the proton charge from the bulk solvent to the center of the channel. It is also demonstrated that the residues in the NPA region and the helix dipole cannot be considered as the main reasons for the electrostatic barrier. Furthermore, our microscopic and semimacroscopic studies clarify the problems with incomplete alternative calculations, illustrating that the effects of various electrostatic elements are drastically overestimated by macroscopic calculations that use a low dielectric constant and do not consider the protein reorganization. Similarly, it is pointed out that microscopic potential of mean force calculations that do not evaluate the electrostatic barrier relative to the bulk water cannot be used to establish the origin of the electrostatic barrier. The relationship between the present study and calculations of pK(a)s in protein interiors is clarified, pointing out that approaches that are applied to study the aquaporin barrier should be validated by pK(a)s calculations. Such calculations also help to clarify the crucial role of solvation energies in establishing the barrier in aquaporins.

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.

Balancing solvation and intramolecular interactions: toward a consistent generalized Born force field

The efficient and accurate characterization of solvent effects is a key element in the theoretical and computational study of biological problems. Implicit solvent models, particularly generalized Born (GB) continuum electrostatics, have emerged as an attractive tool to study the structure and dynamics of biomolecules in various environments. Despite recent advances in this methodology, there remain limitations in the parametrization of many of these models. In the present work, we demonstrate that it is possible to achieve a balanced implicit solvent force field by further optimizing the input atomic radii in combination with adjusting the protein backbone torsional energetics. This parameter optimization is guided by the potentials of mean force (PMFs) between amino acid polar groups, calculated from explicit solvent free energy simulations, and by conformational equilibria of short peptides, obtained from extensive folding and unfolding replica exchange molecular dynamics (REX-MD) simulations. Through the application of this protocol, the delicate balance between the competing solvation forces and intramolecular forces appears to be better captured, and correct conformational equilibria for a range of both helical and beta-hairpin peptides are obtained. The same optimized force field also successfully folds both beta-hairpin trpzip2 and mini-protein Trp-Cage, indicating that it is quite robust. Such a balanced, physics-based force field will be highly applicable to a range of biological problems including protein folding and protein structural dynamics.