A quantitative assessment of models for voltage-dependent gating of ion channels

From Average Transient Transporter Currents to Microscopic Mechanism─A Bayesian Analysis

Electrophysiology studies of secondary active transporters have revealed quantitative mechanistic insights over many decades of research. However, the emergence of new experimental and analytical approaches calls for investigation of the capabilities and limitations of the newer methods. We examine the ability of solid-supported membrane electrophysiology (SSME) to characterize discrete-state kinetic models with >10 rate constants. We use a Bayesian framework applied to synthetic data for three tasks: to quantify and check (i) the precision of parameter estimates under different assumptions, (ii) the ability of computation to guide the selection of experimental conditions, and (iii) the ability of our approach to distinguish among mechanisms based on SSME data. When the general mechanism, i.e., event order, is known in advance, we show that a subset of kinetic parameters can be "practically identified" within ∼1 order of magnitude, based on SSME current traces that visually appear to exhibit simple exponential behavior. This remains true even when accounting for systematic measurement bias and realistic uncertainties in experimental inputs (concentrations) are incorporated into the analysis. When experimental conditions are optimized or different experiments are combined, the number of practically identifiable parameters can be increased substantially. Some parameters remain intrinsically difficult to estimate through SSME data alone, suggesting that additional experiments are required to fully characterize parameters. We also demonstrate the ability to perform model selection and determine the order of events when that is not known in advance, comparing Bayesian and maximum-likelihood approaches. Finally, our studies elucidate good practices for the increasingly popular but subtly challenging Bayesian calculations for structural and systems biology.

Voltage-dependent structural models of the human Hv1 proton channel from long-timescale molecular dynamics simulations

The voltage-gated Hv1 proton channel is a ubiquitous membrane protein that has roles in a variety of cellular processes, including proton extrusion, pH regulation, production of reactive oxygen species, proliferation of cancer cells, and increased brain damage during ischemic stroke. A crystal structure of an Hv1 construct in a putative closed state has been reported, and structural models for the channel open state have been proposed, but a complete characterization of the Hv1 conformational dynamics under an applied membrane potential has been elusive. We report structural models of the Hv1 voltage-sensing domain (VSD), both in a hyperpolarized state and a depolarized state resulting from voltage-dependent conformational changes during a 10-μs-timescale atomistic molecular dynamics simulation in an explicit membrane environment. In response to a depolarizing membrane potential, the S4 helix undergoes an outward displacement, leading to changes in the VSD internal salt-bridge network, resulting in a reshaping of the permeation pathway and a significant increase in hydrogen bond connectivity throughout the channel. The total gating charge displacement associated with this transition is consistent with experimental estimates. Molecular docking calculations confirm the proposed mechanism for the inhibitory action of 2-guanidinobenzimidazole (2GBI) derived from electrophysiological measurements and mutagenesis. The depolarized structural model is also consistent with the formation of a metal bridge between residues located in the core of the VSD. Taken together, our results suggest that these structural models are representative of the closed and open states of the Hv1 channel.

A size-modified poisson-boltzmann ion channel model in a solvent of multiple ionic species: Application to voltage-dependent anion channel

We present a new size-modified Poisson-Boltzmann ion channel (SMPBIC) model and use it to calculate the electrostatic potential, ionic concentrations, and electrostatic solvation free energy for a voltage-dependent anion channel (VDAC) on a biological membrane in a solution mixture of multiple ionic species. In particular, the new SMPBIC model adopts a membrane surface charge density and a natural Neumann boundary condition to reflect the charge effect of the membrane on the electrostatics of VDAC. To avoid the singularity difficulties caused by the atomic charges of VDAC, the new SMPBIC model is split into three submodels such that the solution of one of the submodels is obtained analytically and contains all the singularity points of the SMPBIC model. The other two submodels are then solved numerically much more efficiently than the original SMPBIC model. As an application of this SMPBIC submodel partitioning scheme, we derive a new formula for computing the electrostatic solvation free energy. Numerical results for a human VDAC isoform 1 (hVDAC1) in three different salt solutions, each with up to five different ionic species, confirm the significant effects of membrane surface charges on both the electrostatics and ionic concentrations. The results also show that the new SMPBIC model can describe well the anion selectivity property of hVDAC1, and that the new electrostatic solvation free energy formula can significantly improve the accuracy of the currently used formula. © 2019 Wiley Periodicals, Inc.

Studying Kv Channels Function using Computational Methods

In recent years, molecular modeling techniques, combined with MD simulations, provided significant insights on voltage-gated (Kv) potassium channels intrinsic properties. Among the success stories are the highlight of molecular level details of the effects of mutations, the unraveling of several metastable intermediate states, and the influence of a particular lipid, PIP₂, in the stability and the modulation of Kv channel function. These computational studies offered a detailed view that could not have been reached through experimental studies alone. With the increase of cross disciplinary studies, numerous experiments provided validation of these computational results, which endows an increase in the reliability of molecular modeling for the study of Kv channels. This chapter offers a description of the main techniques used to model Kv channels at the atomistic level.

Validating a Coarse-Grained Voltage Activation Model by Comparing Its Performance to the Results of Monte Carlo Simulations

Simulating the nature of voltage-activated systems is a problem of major current interest, ranging from the action of voltage-gated ion channels to energy storage batteries. However, fully microscopic converging molecular simulations of external voltage effects present a major challenge, and macroscopic models are associated with major uncertainties about the dielectric treatment and the underlying physical basis. Recently we developed a coarse-grained (CG) model that represents explicitly the electrodes, the electrolytes, and the membrane/protein system. The CG model provides a semimacroscopic way of capturing the microscopic physics of voltage-activated systems. Our method was originally validated by reproducing macroscopic and analytical results for key test cases and then used in modeling voltage-activated ion channels and related problems. In this work, we further establish the reliability of the CG voltage model by comparing it to the results of Monte Carlo (MC) simulations with a microscopic electrolyte model. The comparison explores different aspects of membrane, electrolyte, and electrode systems ranging from the Gouy-Chapman model to the determination of the electrolyte charge distribution in the solution between two electrodes (without and with a separating membrane), as well as the evaluation of gating charges. Overall the agreement is very impressive. This provides confidence in the CG model and also shows that the MC model can be used in realistic simulation of voltage activation of membrane proteins with sufficient computer time.

Gating Charge Calculations by Computational Electrophysiology Simulations

Electrical cell signaling requires adjustment of ion channel, receptor, or transporter function in response to changes in membrane potential. For the majority of such membrane proteins, the molecular details of voltage sensing remain insufficiently understood. Here, we present a molecular dynamics simulation-based method to determine the underlying charge movement across the membrane-the gating charge-by measuring electrical capacitor properties of membrane-embedded proteins. We illustrate the approach by calculating the charge transfer upon membrane insertion of the HIV gp41 fusion peptide, and validate the method on two prototypical voltage-dependent proteins, the Kv1.2 K⁺ channel and the voltage sensor of the Ciona intestinalis voltage-sensitive phosphatase, against experimental data. We then use the gating charge analysis to study how the T1 domain modifies voltage sensing in Kv1.2 channels and to investigate the voltage dependence of the initial binding of two Na⁺ ions in Na⁺-coupled glutamate transporters. Our simulation approach quantifies various mechanisms of voltage sensing, enables direct comparison with experiments, and supports mechanistic interpretation of voltage sensitivity by fractional amino acid contributions.

Impact of geometry changes in the channel pore by the gating movements on the channel's conductance

Kv 1.2 are voltage-dependent potassium channels of great biological importance. Despite the existence of many reports considering structure - function relations of the Kv 1.2 channel's quantitative domains, some details of the voltage gating remain ambiguous, or even unknown. One of the examples is the range of the S4-S6 domains motions involved in channel activation and gating. Another important question is to what extent the channel geometry influences the observable channel conductance at different voltages, and what mechanism stands behind. Does the narrowing of the pore reduce the conductance by ohmic resistance growth? The answer is surprisingly negative. But it can be explained in an alternative way by considering the fluctuations. To address these problems, we formulate geometric models that mimic the generic features of voltage sensor movement and trigger the movement of the other domains involved in gating. We carry out a complete simulation of S4-S6 domains translations and tilts. The obtained pore profiles allow to estimate the (ohmic) conductance dependency on the voltage. From a family of analysed models, we choose the one most concurring with the experimental data. The results allow to suggest the most probable scenario of S4-S6 domains movement during channel activation by membrane depolarization.

Refining the treatment of membrane proteins by coarse-grained models

Obtaining a quantitative description of the membrane proteins stability is crucial for understanding many biological processes. However the advance in this direction has remained a major challenge for both experimental studies and molecular modeling. One of the possible directions is the use of coarse-grained models but such models must be carefully calibrated and validated. Here we use a recent progress in benchmark studies on the energetics of amino acid residue and peptide membrane insertion and membrane protein stability in refining our previously developed coarse-grained model (Vicatos et al., Proteins 2014;82:1168). Our refined model parameters were fitted and/or tested to reproduce water/membrane partitioning energetics of amino acid side chains and a couple of model peptides. This new model provides a reasonable agreement with experiment for absolute folding free energies of several β-barrel membrane proteins as well as effects of point mutations on a relative stability for one of those proteins, OmpLA. The consideration and ranking of different rotameric states for a mutated residue was found to be essential to achieve satisfactory agreement with the reference data.

Protein-fluctuation-induced water-pore formation in ion channel voltage-sensor translocation across a lipid bilayer membrane

We have applied a combined fluorescence microscopy and single-ion-channel electric current recording approach, correlating with molecular dynamics (MD) simulations, to study the mechanism of voltage-sensor domain translocation across a lipid bilayer. We use the colicin Ia ion channel as a model system, and our experimental and simulation results show the following: (1) The open-close activity of an activated colicin Ia is not necessarily sensitive to the amplitude of the applied cross-membrane voltage when the cross-membrane voltage is around the resting potential of excitable membranes; and (2) there is a significant probability that the activation of colicin Ia occurs by forming a transient and fluctuating water pore of ∼15 Å diameter in the lipid bilayer membrane. The location of the water-pore formation is nonrandom and highly specific, right at the insertion site of colicin Ia charged residues in the lipid bilayer membrane, and the formation is intrinsically associated with the polypeptide conformational fluctuations and solvation dynamics. Our results suggest an interesting mechanistic pathway for voltage-sensitive ion channel activation, and specifically for translocation of charged polypeptide chains across the lipid membrane under a transmembrane electric field: the charged polypeptide domain facilitates the formation of hydrophilic water pore in the membrane and diffuses through the hydrophilic pathway across the membrane; i.e., the charged polypeptide chain can cross a lipid membrane without entering into the hydrophobic core of the lipid membrane but entirely through the aqueous and hydrophilic environment to achieve a cross-membrane translocation. This mechanism sheds light on the intensive and fundamental debate on how a hydrophilic and charged peptide domain diffuses across the biologically inaccessible high-energy barrier of the hydrophobic core of a lipid bilayer: The peptide domain does not need to cross the hydrophobic core to move across a lipid bilayer.

Equilibrium fluctuation relations for voltage coupling in membrane proteins

A general theoretical framework is developed to account for the effects of an external potential on the energetics of membrane proteins. The framework is based on the free energy relation between two (forward/backward) probability densities, which was recently generalized to non-equilibrium processes, culminating in the work-fluctuation theorem. Starting from the probability densities of the conformational states along the "voltage coupling" reaction coordinate, we investigate several interconnected free energy relations between these two conformational states, considering voltage activation of ion channels. The free energy difference between the two conformational states at zero (depolarization) membrane potential (i.e., known as the chemical component of free energy change in ion channels) is shown to be equivalent to the free energy difference between the two "equilibrium" (resting and activated) conformational states along the one-dimensional voltage couplin reaction coordinate. Furthermore, the requirement that the application of linear response approximation to the free energy functionals of voltage coupling should satisfy the general free energy relations, yields a novel closed-form expression for the gating charge in terms of other basic properties of ion channels. This connection is familiar in statistical mechanics, known as the equilibrium fluctuation-response relation. The theory is illustrated by considering the coupling of a unit charge to the external voltage in the two sites near the surface of membrane, representing the activated and resting states. This is done using a coarse-graining (CG) model of membrane proteins, which includes the membrane, the electrolytes and the electrodes. The CG model yields Marcus-type voltage dependent free energy parabolas for the response of the electrostatic environment (electrolytes etc.) to the transition from the initial to the final configuratinal states, leading to equilibrium free energy difference and free energy barrier that follow the trend of the equilibrium fluctuation relation and the Marcus theory of electron transfer. These energetics also allow for a direct estimation of the voltage dependence of channel activation (Q-V curve), offering a quantitative rationale for a correlation between the voltage dependence parabolas and the Q-V curve, upon site-directed mutagenesis or drug binding. Taken together, by introducing the voltage coupling as the energy gap reaction coordinate, our framework brings new perspectives to the thermodynamic models of voltage activation in voltage-sensitive membrane proteins, offering an a framework for a better understating of the structure-function correlations of voltage gating in ion channels as well as electrogenic phenomena in ion pumps and transporters. Significantly, this formulation also provides a powerful bridge between the CG model of voltage coupling and the conventional macroscopic treatments.

Electric fingerprint of voltage sensor domains

A dynamic transmembrane voltage field has been suggested as an intrinsic element in voltage sensor (VS) domains. Here, the dynamic field contribution to the VS energetics was analyzed via electrostatic calculations applied to a number of atomistic structures made available recently. We find that the field is largely static along with the molecular motions of the domain, and more importantly, it is minimally modified across VS variants. This finding implies that sensor domains transfer approximately the same amount of gating charges when moving the electrically charged S4 helix between fixed microscopic configurations. Remarkably, the result means that the observed operational diversity of the domain, including the extension, rate, and voltage dependence of the S4 motion, as dictated by the free energy landscape theory, must be rationalized in terms of dominant variations of its chemical free energy.

Molecular mechanism of Mg2+-dependent gating in CorA

CorA is the major transport system responsible for Mg²⁺ uptake in bacteria and can functionally substitute for its homologue Mrs2p in the yeast inner mitochondrial membrane. Although several CorA crystal structures are available, the molecular mechanism of Mg²⁺ uptake remains to be established. Here we use EPR spectroscopy, electrophysiology and molecular dynamic simulations to show that CorA is regulated by cytoplasmic Mg²⁺ acting as a ligand and elucidate the basic conformational rearrangements responsible for Mg²⁺-dependent gating. Mg²⁺ unbinding at the divalent cation sensor triggers a conformational change that leads to the inward motion of the stalk helix, which propagates to the pore forming transmembrane helix TM1. Helical tilting and rotation in TM1 generates an iris-like motion that increases the diameter of the permeation pathway, triggering ion conduction. This work establishes the molecular basis of a Mg²⁺-driven negative feedback loop in CorA as the key physiological event controlling Mg²⁺ uptake and homeostasis in prokaryotes.

Solid state NMR: The essential technology for helical membrane protein structural characterization

NMR spectroscopy of helical membrane proteins has been very challenging on multiple fronts. The expression and purification of these proteins while maintaining functionality has consumed countless graduate student hours. Sample preparations have depended on whether solution or solid-state NMR spectroscopy was to be performed - neither have been easy. In recent years it has become increasingly apparent that membrane mimic environments influence the structural result. Indeed, in these recent years we have rediscovered that Nobel laureate, Christian Anfinsen, did not say that protein structure was exclusively dictated by the amino acid sequence, but rather by the sequence in a given environment (Anfinsen, 1973) [106]. The environment matters, molecular interactions with the membrane environment are significant and many examples of distorted, non-native membrane protein structures have recently been documented in the literature. However, solid-state NMR structures of helical membrane proteins in proteoliposomes and bilayers are proving to be native structures that permit a high resolution characterization of their functional states. Indeed, solid-state NMR is uniquely able to characterize helical membrane protein structures in lipid environments without detergents. Recent progress in expression, purification, reconstitution, sample preparation and in the solid-state NMR spectroscopy of both oriented samples and magic angle spinning samples has demonstrated that helical membrane protein structures can be achieved in a timely fashion. Indeed, this is a spectacular opportunity for the NMR community to have a major impact on biomedical research through the solid-state NMR spectroscopy of these proteins.

The different interactions of lysine and arginine side chains with lipid membranes

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.

Voltage-dependent processes in the electroneutral amino acid exchanger ASCT2

Neutral amino acid exchange by the alanine serine cysteine transporter (ASCT)2 was reported to be electroneutral and coupled to the cotransport of one Na⁺ ion. The cotransported sodium ion carries positive charge. Therefore, it is possible that amino acid exchange is voltage dependent. However, little information is available on the electrical properties of the ASCT2 amino acid transport process. Here, we have used a combination of experimental and computational approaches to determine the details of the amino acid exchange mechanism of ASCT2. The [Na⁺] dependence of ASCT2-associated currents indicates that the Na⁺/amino acid stoichiometry is at least 2:1, with at least one sodium ion binding to the amino acid–free apo form of the transporter. When the substrate and two Na⁺ ions are bound, the valence of the transport domain is +0.81. Consistently, voltage steps applied to ASCT2 in the fully loaded configuration elicit transient currents that decay on a millisecond time scale. Alanine concentration jumps at the extracellular side of the membrane are followed by inwardly directed transient currents, indicative of translocation of net positive charge during exchange. Molecular dynamics simulations are consistent with these results and point to a sequential binding process in which one or two modulatory Na⁺ ions bind with high affinity to the empty transporter, followed by binding of the amino acid substrate and the subsequent binding of a final Na⁺ ion. Overall, our results are consistent with voltage-dependent amino acid exchange occurring on a millisecond time scale, the kinetics of which we predict with simulations. Despite some differences, transport mechanism and interaction with Na⁺ appear to be highly conserved between ASCT2 and the other members of the solute carrier 1 family, which transport acidic amino acids.

Voltage-gated proton channels: molecular biology, physiology, and pathophysiology of the H(V) family

Voltage-gated proton channels (H(V)) are unique, in part because the ion they conduct is unique. H(V) channels are perfectly selective for protons and have a very small unitary conductance, both arguably manifestations of the extremely low H(+) concentration in physiological solutions. They open with membrane depolarization, but their voltage dependence is strongly regulated by the pH gradient across the membrane (ΔpH), with the result that in most species they normally conduct only outward current. The H(V) channel protein is strikingly similar to the voltage-sensing domain (VSD, the first four membrane-spanning segments) of voltage-gated K(+) and Na(+) channels. In higher species, H(V) channels exist as dimers in which each protomer has its own conduction pathway, yet gating is cooperative. H(V) channels are phylogenetically diverse, distributed from humans to unicellular marine life, and perhaps even plants. Correspondingly, H(V) functions vary widely as well, from promoting calcification in coccolithophores and triggering bioluminescent flashes in dinoflagellates to facilitating killing bacteria, airway pH regulation, basophil histamine release, sperm maturation, and B lymphocyte responses in humans. Recent evidence that hH(V)1 may exacerbate breast cancer metastasis and cerebral damage from ischemic stroke highlights the rapidly expanding recognition of the clinical importance of hH(V)1.

Consequences of dimerization of the voltage-gated proton channel

The human voltage-gated proton channel, hHV1, appears to exist mainly as a dimer. Teleologically, this is puzzling because each protomer retains the main properties that characterize this protein: proton conduction that is regulated by conformational (channel opening and closing) changes that occur in response to both voltage and pH. The HV1 dimer is mainly linked by C-terminal coiled-coil interactions. Several types of mutations produce monomeric constructs that open approximately five times faster than the wild-type dimeric channel but with weaker voltage dependence. Intriguingly, the quintessential function of the HV1 dimer, opening to allow H(+) conduction, occurs cooperatively. Both protomers undergo a conformational change, but both must undergo this transition before either can conduct. The teleological purpose of dimerization may be to steepen the voltage dependence of channel opening, at least in phagocytes. In other cells, the purpose is not understood. Finally, several single-celled species have HV that are likely monomeric.

Emerging approaches to probing ion channel structure and function

Ion channels, as membrane proteins, are the sensors of the cell. They act as the first line of communication with the world beyond the plasma membrane and transduce changes in the external and internal environments into unique electrical signals to shape the responses of excitable cells. Because of their importance in cellular communication, ion channels have been intensively studied at the structural and functional levels. Here, we summarize the diverse approaches, including molecular and cellular, chemical, optical, biophysical, and computational, used to probe the structural and functional rearrangements that occur during channel activation (or sensitization), inactivation (or desensitization), and various forms of modulation. The emerging insights into the structure and function of ion channels by multidisciplinary approaches allow the development of new pharmacotherapies as well as new tools useful in controlling cellular activity.

A theoretical model for calculating voltage sensitivity of ion channels and the application on Kv1.2 potassium channel

Voltage sensing confers conversion of a change in membrane potential to signaling activities underlying the physiological processes. For an ion channel, voltage sensitivity is usually experimentally measured by fitting electrophysiological data to Boltzmann distributions. In our study, a two-state model of the ion channel and equilibrium statistical mechanics principle were used to test the hypothesis of empirically calculating the overall voltage sensitivity of an ion channel on the basis of its closed and open conformations, and determine the contribution of individual residues to the voltage sensing. We examined the theoretical paradigm by performing experimental measurements with Kv1.2 channel and a series of mutants. The correlation between the calculated values and the experimental values is at respective level, R(2) = 0.73. Our report therefore provides in silico prediction of key conformations and has identified additional residues critical for voltage sensing.

Membrane bending is critical for the stability of voltage sensor segments in the membrane

The interaction between membrane proteins and the surrounding membrane is becoming increasingly appreciated for its role in regulating protein function, protein localization, and membrane morphology. In particular, recent studies have suggested that membrane deformation is needed to stably accommodate proteins harboring charged amino acids in their transmembrane (TM) region, as it is energetically prohibitive to bury charge in the hydrophobic core of the bilayer. Unfortunately, current computational methods are poorly equipped for describing such deformations, as atomistic simulations are often too short to observe large-scale membrane reorganization and most continuum approaches assume a flat membrane. Previously, we developed a method that overcomes these shortcomings by using elasticity theory to characterize equilibrium membrane distortions in the presence of a TM protein, while using traditional continuum electrostatic and nonpolar energy models to determine the energy of the protein in the membrane. Here, we linked the elastostatics, electrostatics, and nonpolar numeric solvers to permit the calculation of energies for nontrivial membrane deformations. We then coupled this procedure to a robust search algorithm that identifies optimal membrane shapes for a TM protein of arbitrary chemical composition. This advance now permits us to explore a host of biological phenomena that were beyond the scope of our original method. We show that the energy required to embed charged residues in the membrane can be highly nonadditive, and our model provides a simple mechanical explanation for this nonadditivity. Our results also predict that isolated voltage sensor segments do not insert into rigid membranes, but membrane bending dramatically stabilizes these proteins in the bilayer despite their high charge content. Additionally, we use the model to explore hydrophobic mismatch with regard to nonpolar peptides and mechanosensitive channels. Our method is in quantitative agreement with molecular dynamics simulations at a tiny fraction of the computational cost.

The sliding-helix voltage sensor: mesoscale views of a robust structure-function relationship

The voltage sensor (VS) domain of voltage-gated ion channels underlies the electrical excitability of living cells. We simulate a mesoscale model of the VS domain to determine the functional consequences of some of its physical elements. Our mesoscale model is based on VS charges, linear dielectrics, and whole-body motion, applied to an S4 "sliding helix." The electrostatics under voltage-clamped boundary conditions are solved consistently using a boundary-element method. Based on electrostatic configurational energy, statistical-mechanical expectations of the experimentally observable relation between displaced charge and membrane voltage are predicted. Consequences of the model are investigated for variations of S4 configuration (α- and 3(10)-helical), countercharge alignment with S4 charges, protein polarizability, geometry of the gating canal, screening of S4 charges by the baths, and fixed charges located at the bath interfaces. The sliding-helix VS domain has an inherent electrostatic stability in the explored parameter space: countercharges present in the region of weak dielectric always retain an equivalent S4 charge in that region but allow sliding movements displacing 3-4 e (0). That movement is sensitive to small energy variations (<2 kT) along the path dependent on a number of electrostatic parameters tested in our simulations. These simulations show how the slope of the relation between displaced charge and voltage could be tuned in a channel.

Autonomous transmembrane segment S4 of the voltage sensor domain partitions into the lipid membrane

The S4 transmembrane segment in voltage-gated ion channels, a highly basic alpha helix, responds to changes in membrane potential and induces channel opening. Earlier work by others indicates that the S4 segment interacts with lipids in plasma membrane, but its mechanism is unclear. Working with synthetic tryptophan-labeled S4 peptides, we characterized binding of autonomous S4 to lipid membranes. The binding free energy (5.2 +/- 0.2 kcal/mol) of the peptide-lipid interaction was estimated from the apparent dissociation constants, determined from the changes in anisotropy of tryptophan fluorescence induced by addition of lipid vesicles with 30 mol% phosphatidylglycerol. The results are in good agreement with the prediction based on the Wimley-White hydrophobicity scale for interfacial (IF) binding of an alpha-helical peptide to the lipid bilayer (6.98 kcal/mol). High salt inhibited the interaction, thus indicating that the peptide/membrane interaction has both electrostatic and non-electrostatic components. Furthermore, the synthetic S4 corresponding to the Shaker potassium channel was found to spontaneously penetrate into the negatively charged lipid membrane to a depth of about 9 A. Our results revealed important biophysical parameters that influence the interaction of S4 with the membrane: they include fluidity, surface charge, and surface pressure of the membrane, and the at helicity and regular spacing of basic amino-acid residues in the S4 sequence.

Voltage sensing in ion channels: mesoscale simulations of biological devices

Electrical signaling via voltage-gated ion channels depends upon the function of a voltage sensor (VS), identified with the S1-S4 domain in voltage-gated K(+) channels. Here we investigate some energetic aspects of the sliding-helix model of the VS using simulations based on VS charges, linear dielectrics, and whole-body motion. Model electrostatics in voltage-clamped boundary conditions are solved using a boundary element method. The statistical mechanical consequences of the electrostatic configurational energy are computed to gain insight into the sliding-helix mechanism and to predict experimentally measured ensemble properties such as gating charge displaced by an applied voltage. Those consequences and ensemble properties are investigated for two alternate S4 configurations, α and 3(10) helical. Both forms of VS are found to have an inherent electrostatic stability. Maximal charge displacement is limited by geometry, specifically the range of movement where S4 charges and countercharges overlap in the region of weak dielectric. Charge displacement responds more steeply to voltage in the α-helical than in the 3(10)-helical sensor. This difference is due to differences on the order of 0.1 eV in the landscapes of electrostatic energy. As a step toward integrating these VS models into a full-channel model, we include a hypothetical external load in the Hamiltonian of the system and analyze the energetic input-output relation of the VS.

Molecular dynamics simulations of voltage-gated cation channels: insights on voltage-sensor domain function and modulation

Since their discovery in the 1950s, the structure and function of voltage-gated cation channels (VGCC) has been largely understood thanks to results stemming from electrophysiology, pharmacology, spectroscopy, and structural biology. Over the past decade, computational methods such as molecular dynamics (MD) simulations have also contributed, providing molecular level information that can be tested against experimental results, thereby allowing the validation of the models and protocols. Importantly, MD can shed light on elements of VGCC function that cannot be easily accessed through “classical” experiments. Here, we review the results of recent MD simulations addressing key questions that pertain to the function and modulation of the VGCC’s voltage-sensor domain (VSD) highlighting: (1) the movement of the S4-helix basic residues during channel activation, articulating how the electrical driving force acts upon them; (2) the nature of the VSD intermediate states on transitioning between open and closed states of the VGCC; and (3) the molecular level effects on the VSD arising from mutations of specific S4 positively charged residues involved in certain genetic diseases.

Realistic simulation of the activation of voltage-gated ion channels

Understanding the detailed mechanism of the activation of voltage-gated ion channels has been a problem of great current interest. Reliable molecular simulations of voltage effects present a major challenge because meaningful converging microscopic simulations are not yet available and macroscopic treatments involve major uncertainties regarding the dielectric constant used and other key features. The current work has overcome some of the above challenges by using our recently developed coarse-grained (CG) model in simulating the activation of the Kv1.2 channel. The CG model has allowed us to explore problems that cannot be addressed at present by fully microscopic simulations, while providing insights on some features that are not usually considered in continuum models, including the distribution of the electrolytes between the membrane and the electrodes during the activation process and thus the nature of the gating current. Furthermore, the clear connection to microscopic descriptions combined with the power of CG modeling offers a powerful tool for exploring the energy balance between the protein conformational energy and the interaction with the external potential in voltage-activated channels. Our simulations have reproduced the observed experimental trend of the gating charge and, most significantly, the correct trend in the free energies, where the closed channel is more stable at negative potential and the open channel is more stable at positive potential. Moreover, we provide a unique view of the activation landscape and the time dependence of the activation process.

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 dependence of a stochastic model of activation of an alpha helical S4 sensor in a K channel membrane

The voltage dependence of the ionic and gating currents of a K channel is dependent on the activation barriers of a voltage sensor with a potential function which may be derived from the principal electrostatic forces on an S4 segment in an inhomogeneous dielectric medium. By variation of the parameters of a voltage-sensing domain model, consistent with x-ray structures and biophysical data, the lowest frequency of the survival probability of each stationary state derived from a solution of the Smoluchowski equation provides a good fit to the voltage dependence of the slowest time constant of the ionic current in a depolarized membrane, and the gating current exhibits a rising phase that precedes an exponential relaxation. For each depolarizing potential, the calculated time dependence of the survival probabilities of the closed states of an alpha helical S4 sensor are in accord with an empirical model of the ionic and gating currents recorded during the activation process.

Coarse grained model for exploring voltage dependent ion channels

The relationship between the membrane voltage and the gating of voltage activated ion channels and other systems have been a problem of great current interest. Unfortunately, reliable molecular simulations of external voltage effects present a major challenge, since meaningful converging microscopic simulations are not yet available and macroscopic treatments involve major uncertainties in terms of the dielectric used and other key features. This work extends our coarse grained (CG) model to simulations of membrane/protein systems under external potential. Special attention is devoted to a consistent modeling of the effect of external potential due to the electrodes, emphasizing semimacroscopic description of the electrolytes in the solution regions between the membranes and the electrodes, as well as the coupling between the combined potential from the electrodes plus the electrolytes and the protein ionized groups. We also provide a clear connection to microscopic treatment of the electrolytes and thus can explore possible conceptual problems that are hard to resolve by other current approaches. For example, we obtain a clear description of the charge distribution in the entire electrolyte system, including near the electrodes in membrane/electrodes systems (where continuum models do not seem to provide the relevant results). Furthermore, the present treatment provides an insight on the distribution of the electrolyte charges before and after equilibration across the membrane, and thus on the nature of the gating charge. The different aspects of the model have been carefully validated by considering problems ranging for the simple Debye-Huckel, and the Gouy-Chapman models to the evaluation of the electrolyte distribution between two electrodes, as well as the effect of extending the simulation system by periodic replicas. Overall the clear connection to microscopic descriptions combined with the power of the CG modeling seems to offer a powerful tool for exploring the balance between the protein conformational energy and the interaction with the external potential in voltage activated channels. To illustrate these features we present a preliminary study of the gating charge in the voltage activated Kv1.2 channel, using the actual change in the electrolyte charge distribution rather than the conventional macroscopic estimate. We also discuss other special features of the model, which include the ability to capture the effect of changes in the protonation states of the protein residues during the close to open voltage induced transition. This article is part of a Special Issue entitled: Membrane protein structure and function.

Structural dynamics of the S4 voltage-sensor helix in lipid bilayers lacking phosphate groups

Voltage-dependent K(+) (Kv) channels require lipid phosphates for functioning. The S4 helix, which carries the gating charges in the voltage-sensing domain (VSD), inserts into membranes while being stabilized by a protein-lipid interface in which lipid phosphates play an essential role. To examine the physical basis of the protein-lipid interface in the absence of lipid phosphates, we performed molecular dynamics (MD) simulations of a KvAP S4 variant (S4mut) in bilayers with and without lipid phosphates. We find that, in dioleoyltrimethylammoniumpropane (DOTAP) bilayers lacking lipid phosphates, the gating charges are solvated by anionic counterions and, hence, lack the bilayer support provided by phosphate-containing palmitoyloleoylglycerophosphocholine (POPC) bilayers. The result is a water-permeable bilayer with significantly smaller deformations around the peptide. Together, these results provide an explanation for the nonfunctionality of VSDs in terms of a destabilizing protein-lipid interface.

Intermediate states of the Kv1.2 voltage sensor from atomistic molecular dynamics simulations

The response of a membrane-bound Kv1.2 ion channel to an applied transmembrane potential has been studied using molecular dynamics simulations. Channel deactivation is shown to involve three intermediate states of the voltage sensor domain (VSD), and concomitant movement of helix S4 charges 10-15 Å along the bilayer normal; the latter being enabled by zipper-like sequential pairing of S4 basic residues with neighboring VSD acidic residues and membrane-lipid head groups. During the observed sequential transitions S4 basic residues pass through the recently discovered charge transfer center with its conserved phenylalanine residue, F(233). Analysis indicates that the local electric field within the VSD is focused near the F(233) residue and that it remains essentially unaltered during the entire process. Overall, the present computations provide an atomistic description of VSD response to hyperpolarization, add support to the sliding helix model, and capture essential features inferred from a variety of recent experiments.

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.

Voltage-induced bending and electromechanical coupling in lipid bilayers

The electrical properties of the cellular membrane are important for ion transport across cells and electrophysiology. Plasma membranes also resist bending and stretching, and mechanical properties of the membrane influence cell shape and forces in membrane tethers pulled from cells. There exists a coupling between the electrical and mechanical properties of the membrane. Previous work has shown that applied voltages can induce forces and movements in the lipid bilayer. We present a theory that computes membrane bending deformations and forces as the applied voltage is changed. We discover that electromechanical coupling in lipid bilayers depends on the voltage-dependent adsorption of ions into the region occupied by the phospholipid head groups. A simple model of counter-ion absorption is investigated. We show that electromechanical coupling can be measured using membrane tethers and we use our model to predict the membrane tether tension as a function of applied voltage. We also discuss how electromechanical coupling in membranes may influence transmembrane protein function.

Structure and hydration of membranes embedded with voltage-sensing domains

Despite the growing number of atomic-resolution membrane protein structures, direct structural information about proteins in their native membrane environment is scarce. This problem is particularly relevant in the case of the highly charged S1-S4 voltage-sensing domains responsible for nerve impulses, where interactions with the lipid bilayer are critical for the function of voltage-activated ion channels. Here we use neutron diffraction, solid-state nuclear magnetic resonance (NMR) spectroscopy and molecular dynamics simulations to investigate the structure and hydration of bilayer membranes containing S1-S4 voltage-sensing domains. Our results show that voltage sensors adopt transmembrane orientations and cause a modest reshaping of the surrounding lipid bilayer, and that water molecules intimately interact with the protein within the membrane. These structural findings indicate that voltage sensors have evolved to interact with the lipid membrane while keeping energetic and structural perturbations to a minimum, and that water penetrates the membrane, to hydrate charged residues and shape the transmembrane electric field.

The electrostatics of VDAC: implications for selectivity and gating

The voltage-dependent anion channel (VDAC) is the major pathway mediating the transfer of metabolites and ions across the mitochondrial outer membrane. Two hallmarks of the channel in the open state are high metabolite flux and anion selectivity, while the partially closed state blocks metabolites and is cation selective. Here we report the results from electrostatics calculations carried out on the recently determined high-resolution structure of murine VDAC1 (mVDAC1). Poisson-Boltzmann calculations show that the ion transfer free energy through the channel is favorable for anions, suggesting that mVDAC1 represents the open state. This claim is buttressed by Poisson-Nernst-Planck calculations that predict a high single-channel conductance indicative of the open state and an anion selectivity of 1.75--nearly a twofold selectivity for anions over cations. These calculations were repeated on mutant channels and gave selectivity changes in accord with experimental observations. We were then able to engineer an in silico mutant channel with three point mutations that converted mVDAC1 into a channel with a preference for cations. Finally, we investigated two proposals for how the channel gates between the open and the closed state. Both models involve the movement of the N-terminal helix, but neither motion produced the observed voltage sensitivity, nor did either model result in a cation-selective channel, which is observed experimentally. Thus, we were able to rule out certain models for channel gating, but the true motion has yet to be determined.

A multiscale model linking ion-channel molecular dynamics and electrostatics to the cardiac action potential

Ion-channel function is determined by its gating movement. Yet, molecular dynamics and electrophysiological simulations were never combined to link molecular structure to function. We performed multiscale molecular dynamics and continuum electrostatics calculations to simulate a cardiac K(+) channel (I(Ks)) gating and its alteration by mutations that cause arrhythmias and sudden death. An all-atom model of the I(Ks) alpha-subunit KCNQ1, based on the recent Kv1.2 structure, is used to calculate electrostatic energies during gating. Simulations are compared with experiments where varying degrees of positive charge-added via point mutation-progressively reduce current. Whole-cell simulations show that mutations cause action potential and ECG QT interval prolongation, consistent with clinical phenotypes. This framework allows integration of multiscale observations to study the molecular basis of excitation and its alteration by disease.

Initial response of the potassium channel voltage sensor to a transmembrane potential

Early transition events of the voltage sensor (VS) of Kv1.2 potassium channel embedded in a lipid membrane are triggered using full atomistic molecular dynamics (MD) simulations. When subject to an applied hyperpolarized transmembrane (TM) voltage, the VS undergoes conformational changes and reaches a stable kinetic intermediate state, beta', within 20 ns. The gating charge ( approximately 2e) associated with this fast transition results mainly from salt-bridge rearrangements involving negative charges in S2 and S3 and all but the two top residues R(294) and R(297) of S4. Interactions of the latter with phosphomoieties of the lipid head groups appear to stabilize the kinetic state beta'.

Free-energy profiles of membrane insertion of the M2 transmembrane peptide from influenza A virus

The insertion of the M2 transmembrane peptide from influenza A virus into a membrane has been studied with molecular-dynamics simulations. This system is modeled by an atomically detailed peptide interacting with a continuum representation of a membrane bilayer in aqueous solution. We performed replica-exchange molecular-dynamics simulations with umbrella-sampling techniques to characterize the probability distribution and conformation preference of the peptide in the solution, at the membrane interface, and in the membrane. The minimum in the calculated free-energy surface of peptide insertion corresponds to a fully inserted, helical peptide spanning the membrane. The free-energy profile also shows that there is a significant barrier for the peptide to enter into this minimum in a nonhelical conformation. The sequence of the peptide is such that hydrophilic amino acid residues at the ends of the otherwise primarily hydrophobic peptide create a trapped, U-shaped conformation with the hydrophilic residues associated with the aqueous phase and the hydrophobic residues embedded in the membrane. Analysis of the free energy shows that the barrier to insertion is largely enthalpic in nature, whereas the membrane-spanning global minimum is favored by entropy.

Potential of mean force and pKa profile calculation for a lipid membrane-exposed arginine side chain

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 <or=4.5 units. In contrast, the analog models are found to exaggerate the variations in energetics across the membrane and have larger pKa shifts. These results have implications for models of voltage gated ion channels, suggesting that although Arg side chains are ideally suited for carrying charge, the thermodynamics dictate that they must remain sequestered from the lipid bilayer environment.

Theoretical and computational analysis of the membrane potential generated by cytochrome c oxidase upon single electron injection into the enzyme

We have developed theory and the computational scheme for the analysis of the kinetics of the membrane potential generated by cytochrome c oxidase upon single electron injection into the enzyme. The theory allows one to connect the charge motions inside the enzyme to the membrane potential observed in the experiments by using data from the "dielectric topography" map of the enzyme that we have created. The developed theory is applied for the analysis of the potentiometric data recently reported by the Wikström group [I. Belevich, D.A. Bloch, N. Belevich, M. Wikström and M.I. Verkhovsky, Exploring the proton pump mechanism of cytochrome c oxidase in real time, Proc. Natl. Acad. Sci. U. S. A. 104 (2007) 2685-2690] on the O to E transition in Paracoccus denitrificans oxidase. Our analysis suggests, that the electron transfer to the binuclear center is coupled to a proton transfer (proton loading) to a group just "above" the binuclear center of the enzyme, from which the pumped proton is subsequently expelled by the chemical proton arriving to the binuclear center. The identity of the pump site could not be determined with certainty, but could be localized to the group of residues His326 (His291 in bovine), propionates of heme a(3), Arg 473/474, and Trp164. The analysis also suggests that the dielectric distance from the P-side to Fe a is 0.4 or larger. The difficulties and pitfalls of quantitative interpretation of potentiometric data are discussed.

A continuum method for determining membrane protein insertion energies and the problem of charged residues

Continuum electrostatic approaches have been extremely successful at describing the charged nature of soluble proteins and how they interact with binding partners. However, it is unclear whether continuum methods can be used to quantitatively understand the energetics of membrane protein insertion and stability. Recent translation experiments suggest that the energy required to insert charged peptides into membranes is much smaller than predicted by present continuum theories. Atomistic simulations have pointed to bilayer inhomogeneity and membrane deformation around buried charged groups as two critical features that are neglected in simpler models. Here, we develop a fully continuum method that circumvents both of these shortcomings by using elasticity theory to determine the shape of the deformed membrane and then subsequently uses this shape to carry out continuum electrostatics calculations. Our method does an excellent job of quantitatively matching results from detailed molecular dynamics simulations at a tiny fraction of the computational cost. We expect that this method will be ideal for studying large membrane protein complexes.

Distribution of amino acids in a lipid bilayer from computer simulations

We have calculated the distribution in a lipid bilayer of small molecules mimicking 17 natural amino acids in atomistic detail by molecular dynamics simulation. We considered both charged and uncharged forms for Lys, Arg, Glu, and Asp. The results give detailed insight in the molecular basis of the preferred location and orientation of each side chain as well the preferred charge state for ionizable residues. Partitioning of charged and polar side chains is accompanied by water defects connecting the side chains to bulk water. These water defects dominate the energetic of partitioning, rather than simple partitioning between water and a hydrophobic phase. Lys, Glu, and Asp become uncharged well before reaching the center of the membrane, but Arg may be either charged or uncharged at the center of the membrane. Phe has a broad distribution in the membrane but Trp and Tyr localize strongly to the interfacial region. The distributions are useful for the development of coarse-grained and implicit membrane potentials for simulation and structure prediction. We discuss the relationship between the distribution in membranes, bulk partitioning to cyclohexane, and several amino acid hydrophobicity scales.