Theoretical perspectives on ion-channel electrostatics: continuum and microscopic approaches

Computational Investigation of the Effect of Lipid Membranes on Ion Permeation in Gramicidin A

Membrane proteins are embedded in a lipid bilayer and interact with the lipid molecules in subtle ways. This can be studied experimentally by examining the effect of different lipid bilayers on the function of membrane proteins. Understanding the causes of the functional effects of lipids is difficult to dissect experimentally but more amenable to a computational approach. Here we perform molecular dynamics simulations and free energy calculations to study the effect of two lipid types (POPC and NODS) on the conductance of the gramicidin A (gA) channel. A larger energy barrier is found for the K⁺ potential of mean force in gA embedded in POPC compared to that in NODS, which is consistent with the enhanced experimental conductance of cations in gA embedded in NODS. Further analysis of the contributions to the potential energy of K⁺ reveals that gA and water molecules in gA make similar contributions in both bilayers but there are significant differences between the two bilayers when the lipid molecules and interfacial waters are considered. It is shown that the stronger dipole moments of the POPC head groups create a thicker layer of interfacial waters with better orientation, which ultimately is responsible for the larger energy barrier in the K⁺ PMF in POPC.

Approaching the 5-HT₃ receptor heterogeneity by computational studies of the transmembrane and intracellular domains

5-hydroxytryptamine type-3 receptor (5-HT₃), an important target of many neuroactive drugs, is a cation selective transmembrane pentamer whose functional stoichiometries and subunit arrangements are still debated, due to the extreme complexity of the system. The three dimensional structure of the 5-HT₃R subunits has not been solved so far. Moreover, most of the available structural and functional data is related to the extracellular ligand-binding domain, whereas the transmembrane and the intracellular receptor domains are far less characterised, although they are crucial for receptor function. Here, for the first time, 3D homology models of the transmembrane and the intracellular receptor domains of all the known human 5-HT₃ subunits have been built and assembled into homopentameric (5-HT(3A)R, 5-HT(3B)R, 5-HT(3C)R, 5-HT(3D)R and 5-HT(3E)R) and heteropentameric receptors (5-HT(3AB), 5-HT(3AC), 5-HT(3AD) and 5-HT(3AE)), on the basis of the known three-dimensional structures of the nicotinic-acetylcholine receptor and of the ligand gated channel from Erwinia chrysanthemi. The comparative analyses of sequences, modelled structures, and computed electrostatic properties of the single subunits and of the assembled pentamers shed new light both on the stoichiometric composition and on the physicochemical requirements of the functional receptors. In particular, it emerges that a favourable environment for the crossing of the pore at the transmembrane and intracellular C terminus domain levels by Ca²⁺ ions is granted by the maximum presence of two B subunits in the 5-HT₃ pentamer.

Physics of ion channels

We review the basic physics involved in transport of ions across membrane channels in cells. Electrochemical forces that control the diffusion of ions are discussed both from microscopic and macroscopic perspectives. A case is made for use of Brownian dynamics as the minimal phenomenological model that provides a bridge between experiments and more fundamental theoretical approaches. Application of Brownian and molecular dynamics methods to channels with known molecular structures is discussed.

Free energy simulations of single and double ion occupancy in gramicidin A

Simultaneous occupancy of the two binding sites in gramicidin A by monovalent cations is a well known property of this channel, but the energetic feasibility of this process in molecular dynamics simulations has not been established so far. Here the authors study the energetics of single and double ion occupancy in gramicidin A by constructing the potential of mean force for single and pair of cations. As representatives of small and large ions, they consider both Na+ and K+ ions in the calculations. Binding constants of ions are estimated from the free energy profiles. Comparisons with the experimental results indicate 3-4 kT discrepancy in the binding energies. They also study the coordination of the ions in their respective binding sites and the dynamic behavior of the channel water during the double ion binding process.

Proton translocation by the cytochromebc1complexes of phototrophic bacteria: introducing the activated Q-cycle

The cytochrome bc1 complexes are proton-translocating, dimeric membrane ubiquinol:cytochrome c oxidoreductases that serve as "hubs" in the vast majority of electron transfer chains. After each ubiquinol molecule is oxidized in the catalytic center P at the positively charged membrane side, the two liberated electrons head out, according to the Mitchell's Q-cycle mechanism, to different acceptors. One is taken by the [2Fe-2S] iron-sulfur Rieske protein to be passed further to cytochrome c1. The other electron goes across the membrane, via the low- and high-potential hemes of cytochrome b, to another ubiquinone-binding site N at the opposite membrane side. It has been assumed that two ubiquinol molecules have to be oxidized by center P to yield first a semiquinone in center N and then to reduce this semiquinone to ubiquinol. This review is focused on the operation of cytochrome bc1 complexes in phototrophic purple bacteria. Their membranes provide a unique system where the generation of membrane voltage by light-driven, energy-converting enzymes can be traced via spectral shifts of native carotenoids and correlated with the electron and proton transfer reactions. An "activated Q-cycle" is proposed as a novel mechanism that is consistent with the available experimental data on the electron/proton coupling. Under physiological conditions, the dimeric cytochrome bc1 complex is suggested to be continually primed by prompt oxidation of membrane ubiquinol via center N yielding a bound semiquinone in this center and a reduced, high-potential heme b in the other monomer of the enzyme. Then the oxidation of each ubiquinol molecule in center P is followed by ubiquinol formation in center N, proton translocation and generation of membrane voltage.

Histidines, heart of the hydrogen ion channel from influenza A virus: toward an understanding of conductance and proton selectivity

The heart of the H+ conductance mechanism in the homotetrameric M2 H+ channel from influenza A is a set of four histidine side chains. Here, we show that protonation of the third of these imidazoles coincides with acid activation of this transmembrane channel and that, at physiological pH, the channel is closed by two imidazole-imidazolium dimers, each sharing a low-barrier hydrogen bond. This unique construct succeeds in distributing a pair of charges over four rings and many atoms in a low dielectric environment to minimize charge repulsion. These dimers form with identical pKas of 8.2 +/- 0.2, suggesting cooperative H+ binding and clearly illustrating high H+ affinity for this channel. The protonation behavior of the histidine side chains has been characterized by using solid-state NMR spectroscopy on the M2 transmembrane domain in fully hydrated lipid bilayers where the tetrameric backbone structure is known. Furthermore, electrophysiological measurements of multichannel and single-channel experiments confirm that these protein constructs are functional.

Energetics of ion permeation, rejection, binding, and block in gramicidin A from free energy simulations

The rigid force fields currently used in molecular dynamics (MD) simulations of biomolecules are optimized for globular proteins. Whether they can also be used in MD simulations of membrane proteins is an important issue that needs to be resolved. Here we address this issue using the gramicidin A channel, which provides an ideal test case because of the simplicity of its structure and the availability of a wealth of functional data. Permeation properties of gramicidin A can be summarized as "it conducts monovalent cations, rejects anions, and binds divalent cations." Hence, a comprehensive test should consider the energetics of permeation for all three types of ions. To that end, we construct the potential of mean force for K(+), Cl(-), and Ca(2+) ions along the channel axis. For an independent check of the potential-of-mean-force results, we also calculate the free energy differences for these ions at the channel center and binding sites relative to bulk. We find that "rejection of anions" is satisfied but there are difficulties in accommodating the other two properties using the current MD force fields.

Role of protein flexibility in ion permeation: a case study in gramicidin A

Proteins have a flexible structure, and their atoms exhibit considerable fluctuations under normal operating conditions. However, apart from some enzyme reactions involving ligand binding, our understanding of the role of flexibility in protein function remains mostly incomplete. Here we investigate this question in the realm of membrane proteins that form ion channels. Specifically, we consider ion permeation in the gramicidin A channel, and study how the energetics of ion conduction changes as the channel structure is progressively changed from completely flexible to a fixed one. For each channel structure, the potential of mean force for a permeating potassium ion is determined from molecular dynamics (MD) simulations. Using the same molecular dynamics data for completely flexible gramicidin A, we also calculate the average densities and fluctuations of the peptide atoms and investigate the correlations between these fluctuations and the motion of a permeating ion. Our results show conclusively that peptide flexibility plays an important role in ion permeation in the gramicidin A channel, thus providing another reason--besides the well-known problem with the description of single file pore water--why this channel cannot be modeled using continuum electrostatics with a fixed structure. The new method developed here for studying the role of protein flexibility on its function clarifies the contributions of the fluctuations to energy and entropy, and places limits on the level of detail required in a coarse-grained model.

Three computational methods for studying permeation, selectivity and dynamics in biological ion channels

The cell membrane, confining some ions and molecules on one side and exchanging others with the other side, is the ultimate unit of the physiology of life. The delicate task of regulating the transport of ions across the membrane is carried out by biological nanotubes called 'ion channels'. Recently, there have been enormous strides in our understanding of the structure-function relationships of biological ion channels. The molecular structures of several ion channels have been determined from crystallographic analysis, including potassium channels, mechanosensitive channels, a chloride channel, as well as gramicidin channels and porins. It is expected that the X-ray structures of other ion channels will soon follow these discoveries, ushering in a new era of ion channel studies in which predicting the function of channels from their atomic structures will become the main quest. In parallel to these experimental findings, there have been important advances in computational biophysics. Here we summarize three theoretical approaches that have been utilized to understand the dynamics of ion permeation across bio-nanotubes, highlighting their advantages and shortcomings, and briefly describe some of the salient properties of ion channels uncovered through computational studies.

Semimicroscopic modeling of permeation energetics in ion channels

The semimicroscopic (SMC) approach to modeling the energetics of ion permeation through biological channels provides an alternative perspective to standard molecular dynamics methods. It exploits the timescale separation between electronic and structural contributions to dielectric stabilization and accounts for electronic polarization by embedding the channel in a milieu that, on average, describes this polarization. Ions, water, and selected peptide moieties are mobile and comprise the reorganizational contribution to dielectric stabilization. The conceptual advantages and limitations of the technique are described. Methodological details are outlined, stressing three convenient electrical geometries. Practical aspects of the SMC procedure are explained, highlighting the areas ripe for further development. Finally, some specific applications are considered.

Ionic permeation free energy in gramicidin: a semimicroscopic perspective

Ion permeation through the gramicidin channel is studied using a model that circumvents two major difficulties inherent to standard simulational methods. It exploits the timescale separation between electronic and structural contributions to dielectric stabilization, accounting for the influence of electronic polarization by embedding the channel in a dielectric milieu that describes this polarization in a mean sense. The explicit mobile moieties are the ion, multipolar waters, and the carbonyls and amides of the peptide backbone. The model treats the influence of aromatic residues and the membrane dipole potential. A new electrical geometry is introduced that treats long-range electrostatics exactly and avoids problems related to periodic boundary conditions. It permits the translocating ion to make a seamless transition from nearby electrolyte to the channel interior. Other degrees of freedom (more distant bulk electrolyte and nonpolar lipid) are treated as dielectric continua. Reasonable permeation free energy profiles are obtained for potassium, rubidium, and cesium; binding wells are shallow and the central barrier is small. Estimated cationic single-channel conductances are smaller than experiment, but only by factors between 2 (rubidium) and 50 (potassium). When applied to chloride the internal barrier is large, with a corresponding miniscule single-channel conductance. The estimated relative single-channel conductances of gramicidin A, B, and C agree well with experiment.

Influence of protein flexibility on the electrostatic energy landscape in gramicidin A

We describe an electrostatic model of the gramicidin A channel that allows protein atoms to move in response to the presence of a permeating ion. To do this, molecular dynamics simulations are carried out with a permeating ion at various positions within the channel. Then an ensemble of atomic coordinates taken from the simulations are used to construct energy profiles using macroscopic electrostatic calculations. The energy profiles constructed are compared to experimentally-determined conductance data by inserting them into Brownian dynamics simulations. We find that the energy landscape seen by a permeating ion changes significantly when we allow the protein atoms to move rather than using a rigid protein structure. However, the model developed cannot satisfactorily reproduce all of the experimental data. Thus, even when protein atoms are allowed to move, the dielectric model used in our electrostatic calculations breaks down when modeling the gramicidin channel.

Time-resolved dynamics of proton transfer in proteinous systems

The dynamics of proton dissociation from an acidic moiety and its subsequent dispersion in the bulk is regulated by the physical chemical properties of the solvent. The solvent has to provide a potential well to accommodate the discharged proton, screen it from the negative charge of the conjugated base, and provide an efficient mode for the diffusion of the proton to the bulk. On measuring the dynamics of proton dissociation in the time-resolved domain, the kinetic analysis of the reaction can quantitate the properties of the immediate environment. In this review we implement the kinetic analysis for evaluating the properties of small cavities in proteins and the diffusion of protons within narrow channels. On the basis of this analysis,we discuss how the clustering of proton-binding sites on a surface can endow the surface with enhanced capacity to attract protons and to funnel them toward a specific site.

Gating gramicidin channels in lipid bilayers: reaction coordinates and the mechanism of dissociation

The dissociation of gramicidin A (gA) channels into monomers is the simplest example of a channel gating process. The initial steps in this process are studied via a computational model that simulates the reaction coordinate for dimer-monomer dissociation. The nonbonded interaction energy between the monomers is determined, allowing for their free relative translational and rotational motion. Lowest energy pathways and reaction coordinates of the gating process are determined. Partial rupture of the six hydrogen bonds (6HB) at the dimer junction takes place by coupling monomer rotation and lateral displacement. Coupling rotation with axial separation is far more expensive energetically. The transition state for channel dissociation occurs when monomers are displaced laterally by approximately 4-6 A, separated by approximately 1.6-2 A, and rotated by approximately 120 degrees, breaking two hydrogen bonds. In membranes with significant hydrophobic mismatch there is a much greater likelihood of forming 4HB and possibly even 2HB states. In the 4HB state the pore remains fully open and conductive. However, transitions from the 6HB to 4HB and 4HB to 2HB states take place via intermediates in which the gA pore is closed and nonconductive. These lateral monomer displacements give rise to transitory pore occlusion at the dimer junction, which provides a rationale for fast closure events (flickers). Local dynamics of gA monomers also leads to lateral and rotational diffusion of the whole gA dimer, giving rise to diffusional rotation of the dimer about the channel axis.

Improved 3D continuum calculations of ion flux through membrane channels

A continuum model, based on the Poisson-Nernst-Planck (PNP) theory, is applied to simulate steady-state ion flux through protein channels. The PNP equations are modified to explicitly account (1) for the desolvation of mobile ions in the membrane pore and (2) for effects related to ion sizes. The proposed algorithm for a three-dimensional self-consistent solution of PNP equations, in which final results are refined by a focusing technique, is shown to be suitable for arbitrary channel geometry and arbitrary protein charge distribution. The role of the pore shape and protein charge distribution in formation of basic electrodiffusion properties, such as channel conductivity and selectivity, as well as concentration distributions of mobile ions in the pore region, are illustrated by simulations on model channels. The influence of the ionic strength in the bulk solution and of the externally applied electric field on channel properties are also discussed.

The implementation of slab geometry for membrane-channel molecular dynamics simulations

Slab geometric boundary conditions are applied in the molecular dynamics simulation of a simple membrane-channel system. The results of the simulation were compared to those of an analogous system using normal three-dimensional periodic boundary conditions. Analysis of the dynamics and electrostatics of the system show that slab geometric periodicity eliminates the artificial bulk water orientational polarization that is present while using normal three-dimensional periodicity. Furthermore, even though the water occupancy and volume of our simple channel is the same when using either method, the electrostatic properties are considerably different when using slab geometry. In particular, the orientational polarization of water is seen to be different in the interior of the channel. This gives rise to a markedly different electric field within the channel. We discuss the implications of slab geometry for the future simulation of this type of system and for the study of channel transport properties.

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

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

Role of the dielectric constants of membrane proteins and channel water in ion permeation

Using both analytical solutions obtained from simplified systems and numerical results from more realistic cases, we investigate the role played by the dielectric constant of membrane proteins epsilon(p) and pore water epsilon(w) in permeation of ions across channels. We show that the boundary and its curvature are the crucial factors in determining how an ion's potential energy depends on the dielectric constants near an interface. The potential energy of an ion outside a globular protein has a dominant 1/epsilon(w) dependence, but this becomes 1/epsilon(p) for an ion inside a cavity. For channels, where the boundaries are in between these two extremes, the situation is more complex. In general, we find that variations in epsilon(w) have a much larger impact on the potential energy of an ion compared to those in epsilon(p). Therefore a better understanding of the effective epsilon(w) values employed in channel models is desirable. Although the precise value of epsilon(p) is not a crucial determinant of ion permeation properties, it still needs to be chosen carefully when quantitative comparisons with data are made.

Modeling permeation energetics in the KcsA potassium channel

The thermodynamics of cation permeation through the KcsA K(+) channel selectivity filter is studied from the perspective of a physically transparent semimicroscopic model using Monte Carlo free energy integration. The computational approach chosen permits dissection of the separate contributions to ionic stabilization arising from different parts of the channel (selectivity filter carbonyls, single-file water, cavity water, reaction field of bulk water, inner helices, ionizable residues). All features play important roles; their relative significance varies with the ion's position in the filter. The cavity appears to act as an electrostatic buffer, shielding filter ions from structural changes in the inner pore. The model exhibits K(+) vs. Na(+) selectivity, and roughly isoenergetic profiles for K(+) and Rb(+), and discriminates against Cs(+), all in agreement with experimental data. It also indicates that Ba(2+) and Na(+) compete effectively with permeant ions at a site near the boundary between the filter and the cavity, in the vicinity of the barium blocker site.

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

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

Functional properties of threefold and fourfold channels in ferritin deduced from electrostatic calculations

The iron storage protein ferritin contains threefold and fourfold symmetric channels that are thought to provide pathways for the transfer of Fe(2+) ions in and out of the protein. Using the known crystal structure of the ferritin protein, we perform electrostatic potential energy calculations to elucidate the functional properties of these channels. The threefold channel is shown to be responsible for the transit of Fe(2+) ions. Monovalent ions can also diffuse through the threefold channel but presence of divalent ions in the pore retards this process leading to a selectivity mechanism similar to the one observed in calcium channels. The fourfold channel is found to be impermeant to all cations with the possible exception of protons. Because proton transfer is essential to maintain the electroneutrality of the protein during iron deposition, we suggest that the function of the fourfold channel is to form a "proton wire" that facilitates their transfer in and out of ferritin.

A fast in silico simulation of ion flux through the large-pore channel proteins

The PSST program (see accompanying article) utilizes the detailed structure of a large-pore channel protein as the sole input for selection of trajectories along which negative and positive ions propagate. In the present study we applied this program to reconstruct the ion flux through five large-pore channel proteins (PhoE, OmpF, the WT R. blastica general diffusion porin and two of its mutants). The conducting trajectories, one for positive and one for negative particles, are contorted pathways that run close to arrays of charged residues on the inner surface of the channel. In silico propagation of the charged particles yielded passage time values that are compatible with the measured average passage time of ions. The calculated ionic mobilities are close to those of the electrolyte solution of comparable concentrations. Inspection of the transition probabilities along the channel revealed no region that could impose a rate-limiting step. It is concluded that the ion flux is a function of the whole array of local barriers. Thus, the conductance of the large-pore channel protein is determined by the channel's shape and charge distribution, while the selectivity also reflects the features of the channel's vestibule.

Recent advances in ion channel research

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

Continuum electrostatics fails to describe ion permeation in the gramicidin channel

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

The alpha-helix and the organization and gating of channels

The structures of an increasing number of channels and other alpha-helical membrane proteins have been determined recently, including the KcsA potassium channel, the MscL mechanosensitive channel, and the AQP1 and GlpF members of the aquaporin family. In this chapter, the orientation and packing characteristics of bilayer-spanning helices are surveyed in integral membrane proteins. In the case of channels, alpha-helices create the sealed barrier that separates the hydrocarbon region of the bilayer from the permeation pathway for solutes. The helices surrounding the permeation pathway tend to be rather steeply tilted relative to the membrane normal and are consistently arranged in a right-handed bundle. The helical framework further provides a supporting scaffold for nonmembrane-spanning structures associated with channel selectivity. Although structural details remain scarce, the conformational changes associated with gating transitions between closed and open states of channels are reviewed, emphasizing the potential roles of helix-helix interactions in this process.

Electrostatic properties of the anion selective porin Omp32 from Delftia acidovorans and of the arginine cluster of bacterial porins

The functional properties of the anion-selective porin Omp32 from the bacterium Delftia acidovorans, formerly Comamonas acidovorans, are determined by the particularly narrow channel constriction and the electrostatic field inside and outside the pore. A cluster of arginines (Arg 38, Arg 75, and Arg 133) determines the electrostatic field close to the constriction zone. Stacked amino acids carrying charges are prone to drastic pK(a) shifts. However, optimized calculations of the titration behavior of charged groups, based on the finite-difference Poisson-Boltzmann technique, suggest that all the arginines are charged at physiological pH. Protonation of the clustered arginines is stabilized by one buried glutamate residue (Glu 58), which is strongly interacting with Arg 75 and Arg 38. This functional arrangement of three charged amino acid residues is of general significance because it is found in the constriction zones of all known 16-stranded porins from the alpha-, beta-, and gamma-proteobacteria.

Continuum and atomistic modeling of ion partitioning into a peptide nanotube

Continuum and atomistic descriptions of the partitioning of ions into a self-assembled (D,L)-octapeptide nanotube, cyclo[-(L-Ala-D-Ala)(4)-], are presented. Perturbation free energy calculations, including Ewald electrostatics, are used to estimate the electrostatic component of the excess free energy of charging Li(+), Na(+), Rb(+), and Cl(minus sign) ions inside the nanotube. The radial density and orientational distribution of water around the ion is calculated for the ion at two different positions inside the tube; it is seen that the calculated distributions are sensitive to the location of the ions. Two different continuum electrostatic models are formulated to describe the ion solvation inside the nanotube. When enhanced orientational structuring of water dipoles is evidenced, explicitly including the first solvation shell as part of the low dielectric nanotube environment provides good agreement with molecular dynamics simulations. When water orientational structuring is as in the reference bulk solvent, we find that treating the first shell water explicitly or as a high dielectric continuum leads to similar results. These results are discussed, and their importance for continuum electrostatic modeling of ion channels are highlighted.

Brownian dynamics simulation of ion flow through porin channels

Bacterial porins, which allow the passage of solutes across the outer bacterial membrane, are structurally well characterized. They therefore lend themselves to detailed studies of the determinants of ion flow through transmembraneous channels. In a comparative study, we have performed Brownian dynamics simulations to obtain statistically significant transfer efficiencies for cations and anions through matrix porin OmpF, osmoporin OmpK36, phosphoporin PhoE and two OmpF charge mutants. The simulations show that the electrostatic potential at the highly charged channel constriction serves to enhance ion permeability of either cations or anions, dependent on the type of porin. At the same time translocation of counterions is not severely impeded. At the constriction, cations and anions follow distinct trajectories, due to the segregation of basic and acidic protein residues. Simulated ion selectivity and relative conductance agree well with experimental values, and are dependent crucially on the charge constellation at the pore constriction. The experimentally observed decrease in ion selectivity and single channel conductance with increasing ionic strength is well reproduced and can be attributed to electrostatic shielding of the pore lining.

Molecular electroporation: a unifying concept for the description of membrane pore formation by antibacterial peptides, exemplified with NK-lysin

The antibacterial activity of many small, positively charged peptides and proteins is based on pore formation in lipid bilayers. It is here proposed to arise from an electroporation effect. This hypothesis is supported by calculations of the electrostatic potential of NK-lysin associated to a membrane. For a significant area of the protein-membrane interface, the electrostatic potential is found to be above the minimum threshold for electroporation. A single highly charged alpha-helical segment of NK-lysin is mainly responsible for this effect. It is experimentally demonstrated that a peptide comprising this helix has antibacterial activity. We propose that superficial association to membranes suffices to trigger electroporation, provided the peptide is sufficiently charged. The effect is referred to as molecular electroporation.

Ionic interactions in multiply occupied channels

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

Electrostatics and the ion selectivity of ligand-gated channels

The nicotinic acetylcholine receptor (nAChR) is a cation-selective ion channel that opens in response to acetylcholine binding. The related glycine receptor (GlyR) is anion selective. The pore-lining domain of each protein may be modeled as a bundle of five parallel M2 helices. Models of the pore-lining domains of homopentameric nAChR and GlyR have been used in continuum electrostatics calculations to probe the origins of ion selectivity. Calculated pKA values suggest that "rings" of acidic or basic side chains at the mouths of the nAChR or GlyR M2 helix bundles, respectively, may not be fully ionized. In particular, for the nAChR the ring of glutamate side chains at the extracellular mouth of the pore is predicted to be largely protonated at neutral pH, whereas those glutamate side chains in the intracellular and intermediate rings (at the opposite mouth of the pore) are predicted to be fully ionized. Inclusion of the other domains of each protein represented as an irregular cylindrical tube in which the M2 bundles are embedded suggests that both the M2 helices and the extramembrane domains play significant roles in determining ion selectivity.

Ion regulation of the kinetics of potential-dependent potassium channels

We apply a theoretical approach developed earlier. The interaction ofions that permeate a channel with slowly relaxing charged channel-forminggroups (ion-conformational interaction - ICI) is addressed by thisapproach. One can describe the ion concentration influence (ion regulation)on channel functioning in this manner. A patch-clamp method in a'whole-cell' configuration is used to study the ICI. For this purpose theinfluence of an external concentration of potassium ions on thepotential-dependent potassium current (I(A)) in the externalmembrane of GH(3) cells was studied. The increase of[K(+) (out)] from 5 mM to 100 mM causes anon-monotonous shift of current-voltage dependencies. The dependence of bothan activation time constant tgr(n) and a steady-state activation(n(∞)) on [K(+)](out) have a minimum andmaximum respectively. The analysis of the results suggests that the observedeffects are caused by ICI. A physical model is developed to describe thedependence of the potassium channel kinetics on the external concentrationof the ions and the membrane potential. The 'deformation' of the closedstate of the gate and the corresponding energy shifts cause the observednon-monotonous dependencies due to ICI. Thus, the general theoreticalapproach has an experimental confirmation and is applied to concreteexamples. Formulas for concentrational dependencies of the channel kineticsare given for practical uses.

The dielectric properties of water within model transbilayer pores

Ion channels contain extended columns of water molecules within their transbilayer pores. The dynamic properties of such intrapore water have been shown to differ from those of water in its bulk state. In previous molecular dynamics simulations of two classes of model pore (parallel bundles of Ala20 alpha-helices and antiparallel barrels of Ala10 beta-strands), a substantially reduced translational and rotational mobility of waters was observed within the pore relative to bulk water. Molecular dynamics simulations in the presence of a transpore electrostatic field (i.e., a voltage drop along the pore axis) have been used to estimate the resultant polarization (due to reorientation) of the intrapore water, and hence to determine the local dielectric behavior within the pore. It is shown that the local dielectric constant of water within a pore is reduced for models formed by parallel alpha-helix bundles, but not by those formed by beta-barrels. This result is discussed in the context of electrostatics calculations of ion permeation through channels, and the effect of the local dielectric of water within a helix bundle pore is illustrated with a simple Poisson-Boltzmann calculation.

Electrostatics of a simple membrane model using Green's functions formalism

The electrostatics of a simple membrane model picturing a lipid bilayer as a low dielectric constant slab immersed in a homogeneous medium of high dielectric constant (water) can be accurately computed using the exact Green's functions obtainable for this geometry. We present an extensive discussion of the analysis and numerical aspects of the problem and apply the formalism and algorithms developed to the computation of the energy profiles of a test charge (e.g., ion) across the bilayer and a molecular model of the acetylcholine receptor channel embedded in it. The Green's function approach is a very convenient tool for the computer simulation of ionic transport across membrane channels and other membrane problems where a good and computationally efficient first-order treatment of dielectric polarization effects is crucial.

A semi-microscopic Monte Carlo study of permeation energetics in a gramicidin-like channel: the origin of cation selectivity

The influence of a gramicidin-like channel former on ion free energy barriers is studied using Monte Carlo simulation. The model explicitly describes the ion, the water dipoles, and the peptide carbonyls; the remaining degrees of freedom, bulk electrolyte, non-polar lipid and peptide regions, and electronic (high frequency) permittivity, are treated in continuum terms. Contributions of the channel waters and peptide COs are studied both separately and collectively. We found that if constrained to their original orientations, the COs substantially increase the cationic permeation free energy; with or without water present, CO reorientation is crucial for ion-CO interaction to lower cation free energy barriers; the translocation free energy profiles for potassium-, rubidium-, and cesium-like cations exhibit no broad barriers; the lipid-bound peptide interacts more effectively with anions than cations; anionic translocation free energy profiles exhibit well defined maxima. Using experimental data to estimate transfer free energies of ions and water from bulk electrolyte to a non-polar dielectric (continuum lipid), we found reasonable ion permeation profiles; cations bind and permeate, whereas anions cannot enter the channel. Cation selectivity arises because, for ions of the same size and charge, anions bind hydration water more strongly.

A universal steady state I-V relationship for membrane current

A purely electrical mechanism for the gating of membrane ionic channel gives rise to a simple I-V relationship for membrane current. Our approach is based on the known presence of gating charge, which is an established property of the membrane channel gating. The gating charge is systematically treated as a polarization of the channel protein which varies with the external electric field and modifies the effective potential through which the ions migrate in the channel. Two polarization effects have been considered: 1) the up or down shift of the whole potential function, and 2) the change in the effective electric field inside the channel which is due to familiar effect of the effective reduction of the electric field inside a dielectric body because of the presence of surface charges on its surface. Both effects are linear in the channel polarization. The ionic current is described by a steady state solution of the Nernst-Planck equation with the potential directly controlled by the gating charge system. The solution describes reasonably well the steady state and peak-current I-V relationships for different channels, and when applied adiabatically, explains the time lag between the gating charge current and the rise of the ionic current. The approach developed can be useful as an effective way to model the ionic currents in axons, cardiac cells and other excitable tissues.

Extended dipolar chain model for ion channels: electrostriction effects and the translocational energy barrier

We reinvestigate the dipolar chain model for an ion channel. Our goal is to account for the influence that ion-induced electrostriction of channel water has on the translocational energy barriers experienced by different ions in the channel. For this purpose, we refine our former model by relaxing the positional constraint on the ion and the water dipoles and by including Lennard-Jones contributions in addition to the electrostatic interactions. The positions of the ion and the waters are established by minimization of the free energy. As before, interaction with the external medium is described via the image forces. Application to alkali cations show that the short range interactions modulate the free energy profiles leading to a selectivity sequence for translocation. We study the influence of some structural parameters on this sequence and compare our theoretical predictions with observed results for gramicidin.

Influence of a channel-forming peptide on energy barriers to ion permeation, viewed from a continuum dielectric perspective

The continuum three-dielectric model for an aqueous ion channel pore-forming peptide-membrane system is extended to account for the finite length of the channel. We focus on the electrostatic influence that a channel-forming peptide may exert on energy barriers to ion permeation. The nonlinear dielectric behavior of channel water caused by dielectric saturation in the presence of an ion is explicitly modeled by assigning channel water a mean dielectric constant much less than that of bulk water. An exact solution of the continuum problem is formulated by approximating the dielectric behavior of bulk water, assigning it a dielectric constant of infinity. The validity of this approximation is verified by comparison with a Poisson-Boltzmann description of the electrolyte. The formal equivalence of high ionic strength and high electrolyte dielectric constant is demonstrated. We estimate limits on the reduction of the electrostatic free energy caused by ionic interaction with the channel-forming peptide. We find that even assigning this region an epsilon of 100, its influence is insufficient to lower permeation free energy barriers to values consistent with observed channel conductances. We provide estimates of the effective dielectric constant of this highly polarizable region, by comparing energy barriers computed using the continuum approach with those found from a semi-microscopic analysis of a simplified model of a gramicidin-like charge distribution. Possible ways of improving both models are discussed.