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

Electrostatic field-exposed water in nanotube at constant axial pressure

Water confined within nanoscale geometries under external field has many interesting properties which is very important for its application in biological processes and engineering. Using molecular dynamics simulations, we investigate the effect of external fields on polarization and structure as well as phase transformations of water confined within carbon nanotubes. We find that dipoles of water molecules tend to align along external field in nanoscale cylindrical confinement. Such alignment directly leads to the longitudinal electrostriction and cross-sectional dilation of water in nanotube. It also influences the stability of ice structures. As the electrostatic field strengthens, the confined water undergoes phase transitions from a prism structure to a helical one to a single chain as the electrostatic field strengthens. These results imply a rich phase diagram of the confined water due to the presence of external electriostatic field, which can be of importance for the industrial applications in nanopores.

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.

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 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.

Hierarchical approach to predicting permeation in ion channels

A hierarchical computational strategy combining molecular modeling, electrostatics calculations, molecular dynamics, and Brownian dynamics simulations is developed and implemented to compute electrophysiologically measurable properties of the KcsA potassium channel. Models for a series of channels with different pore sizes are developed from the known x-ray structure, using insights into the gating conformational changes as suggested by a variety of published experiments. Information on the pH dependence of the channel gating is incorporated into the calculation of potential profiles for K(+) ions inside the channel, which are then combined with K(+) ion mobilities inside the channel, as computed by molecular dynamics simulations, to provide inputs into Brownian dynamics simulations for computing ion fluxes. The open model structure has a conductance of approximately 110 pS under symmetric 250 mM K(+) conditions, in reasonable agreement with experiments for the largest conducting substate. The dimensions of this channel are consistent with electrophysiologically determined size dependence of quaternary ammonium ion blocking from the intracellular end of this channel as well as with direct structural evidence that tetrabutylammonium ions can enter into the interior cavity of the channel. Realistic values of Ussing flux ratio exponents, distribution of ions within the channel, and shapes of the current-voltage and current-concentration curves are obtained. The Brownian dynamics calculations suggest passage of ions through the selectivity filter proceeds by a "knock-off" mechanism involving three ions, as has been previously inferred from functional and structural studies of barium ion blocking. These results suggest that the present calculations capture the essential nature of K(+) ion permeation in the KcsA channel and provide a proof-of-concept for the integrated microscopic/mesoscopic multitiered approach for predicting ion channel function from structure, which can be applied to other channel structures.

Electronic excitation as a mechanism of the ion selectivity filter

A correlation between the character of pharmacological activity and the energies of electronic transitions in some biologically active molecules, affecting the nervous system, has been found. In order to explain the correlation, a new principle of the membrane ion selectivity filter has been suggested. The principle is based on the recombination process of a metal cation, passing through the filter, with an electron, when the energy quantum (equal to the metal ionization energy) is emitted. The amino acid residue group, performing the function of the channel filter, absorbs this quantum, transits itself into an electronically excited state, changes its conformation and lets, as a result, the cation pass. The process is possible only in that case when the amino acid residue group has a transition of the same energy, therefore not all of metals can pass through the filter. From the viewpoint of this conception, an active molecule acts because of its transition into an electronically excited state of the same energy and interfering, thereby, with the natural processes.

Effective diffusion coefficients of K+ and Cl- ions in ion channel models

We have used molecular dynamics simulations, corresponding to a total simulation time of 11 ns, to investigate the effective short-time local diffusion coefficient of potassium and chloride ions in a series of model ion channels. These models, which include channels formed by the fungal peptide alamethicin, by a synthetic leucine-serine peptide, and by the pore-lining M2 helix bundle of the nicotinic acetylcholine receptor, have a range of different secondary structures, diameters and hydrophobicities. We find that the diffusion coefficients of both ions are appreciably reduced in the narrower channels, the extent of the reduction being similar for both the anionic and cationic species. This suggests that a difference in mobility cannot be the source of the ion selectivity exhibited by some of the channels (for example, the leucine-serine peptide). We find no evidence for a reduction in mobility of either ion in the nAChR model. These results are broadly in line with a previous similar study of Na+ ions, and may be useful in Poisson-Nernst-Planck, Eyring rate theory or Brownian dynamics calculations of channel conductance.

CFTR: mechanism of anion conduction

CFTR: Mechanism of Anion Conduction. Physiol. Rev. 79, Suppl.: S47-S75, 1999. - The purpose of this review is to collect together the results of recent investigations of anion conductance by the cystic fibrosis transmembrane conductance regulator along with some of the basic background that is a prerequisite for developing some physical picture of the conduction process. The review begins with an introduction to the concepts of permeability and conductance and the Nernst-Planck and rate theory models that are used to interpret these parameters. Some of the physical forces that impinge on anion conductance are considered in the context of permeability selectivity and anion binding to proteins. Probes of the conduction process are considered, particularly permeant anions that bind tightly within the pore and block anion flow. Finally, structure-function studies are reviewed in the context of some predictions for the origin of pore properties.

Dynamic properties of Na+ ions in models of ion channels: a molecular dynamics study

We present simulation results for the effective diffusion coefficients of a sodium ion in a series of model ion channels of different diameters and hydrophobicities, including models of alamethicin, a leucine-serine peptide, and the M2 helix bundle of the nicotinic acetylcholine receptor. The diffusion coefficient, which in the simulations has a value of 0.15(2) A2ps-1 in bulk water, is found to be reduced to as little as 0.02(1) A2ps-1 in the narrower channels, and to about 0.10(5) A2ps-1 in wider channels such as the nicotinic acetylcholine receptor. It is anticipated that this work will be useful in connection with calculations of channel conductivity using such techniques as the Poisson-Nernst-Planck equation, Eyring rate theory, or Brownian dynamics.

Modelling and simulation of ion channels: applications to the nicotinic acetylcholine receptor

Molecular dynamics simulations with experimentally derived restraints have been used to develop atomic models of M2 helix bundles forming the pore-lining domains of the nicotinic acetylcholine receptor and related ligand-gated ion channels. M2 helix bundles have been used in microscopic simulations of the dynamics and energetics of water and ions within an ion channel. Translational and rotational motion of water are restricted within the pore, and water dipoles are aligned relative to the pore axis by the surrounding helix dipoles. Potential energy profiles for translation of a Na+ ion along the pore suggest that the protein and water components of the interaction energy exert an opposing effect on the ion, resulting in a relatively flat profile which favors cation permeation. Empirical conductance calculations based on a pore radius profile suggest that the M2 helix model is consistent with a single channel conductance of ca. 50 pS. Continuum electrostatics calculations indicate that a ring of glutamate residues at the cytoplasmic mouth of the alpha 7 nicotinic receptor M2 helix bundle may not be fully ionized. A simplified model of the remainder of the channel protein when added to the M2 helix bundle plays a significant role in enhancing the ion selectivity of the channel.

Function of the N-acetyl-L-histidine system in the vertebrate eye. Evidence in support of a role as a molecular water pump

N-acetyl-L-histidine (NAH) is a major constituent of poikilotherm brain, eye, heart, and muscle, but for which there is no known function. NAH is characterized by high tissue concentrations, a high tissue/extracellular fluid (ECF) gradient, and by a continuous selective and regulated efflux into ECF. In the eye, there is a complete compartmentalization of the synthetic and hydrolytic enzymes, with synthesis of NAH from AcCoA and L-histidine (His) occurring in the lens, and its hydrolysis to acetate and His restricted to surrounding ocular fluids. Using 14C-isotopes, the cycling of NAH between lens and ocular fluids in a simple support medium consisting of NaCl (0.9%), Ca2+ (4 mEq/L) and D-glucose (5 mM) at pH 7.4 has previously been observed. In the present study, using the isolated lens of the goldfish eye, each of the components of that support medium has been individually varied in order to determine its effect on NAH release down its intercompartmental gradient. As a result of these and related studies, it is suggested that NAH may function as a metabolically recyclable gradient-driven molecular water pump. It is proposed that water influx or generation of metabolic water serves as the trigger mechanism to open a Ca-dependent gate for the release of NAH down its gradient, along with its associated water. Preliminary analyses suggest that in addition to its potential for multiple daily cycles, a strongly ionized hydrophilic molecule, such as NAH, may include a large power function as a result of its attraction to water, and it has been calculated that an aqua complex of each NAH molecule may have 33 dipole-dipole-associated water molecules as it passes into ECF. It is this unique combination of a capacity for multiple cycles per day, coupled with a large power function, that may allow for such an intracellular osmolyte to be present in relatively low concentration in comparison to total cellular osmolality, and yet to perform a large and important task with little expenditure of energy. With each NAH molecule recycled up to 10 times/d, and a power factor of 33, there could be 330 mmol of water transported/mmol of NAH each day. With typical NAH concentrations in brains of poikilothermic vertebrates of 5-10 mmol/kg, there is the potential for up to 3.3 mol (60 mL) of water to be removed each day/kg of brain, a value that represents about 8% of total brain water content. Dewatering of the released osmolyte would occur in two additional steps, consisting of its hydrolysis and the subsequent active uptake of its metabolites. It is also suggested that NAH is the archetype of several metabolically and structurally related cellular osmolytes found in both poikilotherms and homeotherms, for which there is similarly no known function, and these may form a family of cycling hydrophilic osmolytes that serve as molecular water pumps in a variety of tissues. These include the basic His containing derivatives: NAH, carnosine, anserine, ophidine, and homocarnosine, and the acidic aspartate derivatives: N-acetyl-L-aspartate (NAA) and N-acetyl-L-aspartylglutamate (NAAG). In each of these cases, the high intracellular/extracellular osmolyte gradient appears to be maintained by combining a hydrophilic protein amino acid with a nonprotein moiety to block its use in other intracellular metabolic pathways, and by blocking catabolism of the derivative by maintaining its hydrolytic enzyme in an extracytosolic membrane or extracellular compartment. Unlike other known water-regulating mechanisms, the proposed cellular system is unique in that as a water pump, it can function as a water regulator independently of extracellular solute composition or osmolality. Finally, based on the hypothesis developed, the NAH system would represent the first cellular water pump to be identified.

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.

Ion-water and water-water interactions in a gramicidinlike channel: effects due to group polarizability and backbone flexibility

In the gramicidin channel, ionic transport and water transport occur simultaneously. Gramicidin's transport properties are influenced by ionic interactions with both the polypeptide and the channel waters. We present results of molecular dynamics studies on a series of alkali metal ions interacting with a water-filled gramicidinlike channel (a configurationally constrained polyglycine analog) at the dimer junction, in mid-monomer, and near the channel entrance. We investigate details of both short and long range ion-water and water-water correlation; these are notably dependent on the explicit consideration of polarizability and the degree of backbone flexibility. The nature of ion-water and water-water correlations changes as ionic size decreases and these changes may be augmented or attenuated by manipulation of the two parameters under study. Incorporating polarizability generally shortens ion-water distances and enhances ion-induced electrostriction (decreased water-water separations), while simultaneously reducing the long range orientational correlation of the single filing waters within the channel. Increasing flexibility predictably results in a broadening of the distribution of water-water and ion-water separations and contributes to the loss of long range orientational correlations. Both effects are ion specific; Cs+ and Na+ interact with the channel in distinctly different ways, while K+ represents an intermediate case more closely resembling Cs+. Our results demonstrate that incorporation of polarizability in the potential function has significant effects on the properties of channel water and, consequently, on the ionic transport process. While ion-water and water-water distances are decreased due to this feature, thereby fostering longer ranged correlations within the channel, enhanced interactions between water molecules and peptide groups tend to mitigate this effect. Possible implications for the multiple occupancy states of gramicidin and long range information transfer via a single file water chain are considered.

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.

Molecular dynamics simulations of water within models of ion channels

The transbilayer pores formed by ion channel proteins contain extended columns of water molecules. The dynamic properties of such waters have been suggested to differ from those of water in its bulk state. Molecular dynamics simulations of ion channel models solvated within and at the mouths of their pores are used to investigate the dynamics and structure of intra-pore water. Three classes of channel model are investigated: a) parallel bundles of hydrophobic (Ala20) alpha-helices; b) eight-stranded hydrophobic (Ala10) antiparallel beta-barrels; and c) parallel bundles of amphipathic alpha-helices (namely, delta-toxin, alamethicin, and nicotinic acetylcholine receptor M2 helix). The self-diffusion coefficients of water molecules within the pores are reduced significantly relative to bulk water in all of the models. Water rotational reorientation rates are also reduced within the pores, particularly in those pores formed by alpha-helix bundles. In the narrowest pore (that of the Ala20 pentameric helix bundle) self-diffusion coefficients and reorientation rates of intra-pore waters are reduced by approximately an order of magnitude relative to bulk solvent. In Ala20 helix bundles the water dipoles orient antiparallel to the helix dipoles. Such dipole/dipole interaction between water and pore may explain how water-filled ion channels may be formed by hydrophobic helices. In the bundles of amphipathic helices the orientation of water dipoles is modulated by the presence of charged side chains. No preferential orientation of water dipoles relative to the pore axis is observed in the hydrophobic beta-barrel models.

Water in channel-like cavities: structure and dynamics

Ion channels contain narrow columns of water molecules. It is of interest to compare the structure and dynamics of such intrapore water with those of the bulk solvent. Molecular dynamics simulations of modified TIP3P water molecules confined within channel-like cavities have been performed and the orientation and dynamics of the water molecules analyzed. Channels were modeled as cylindrical cavities with lengths ranging from 15 to 60 A and radii from 3 to 12 A. At the end of the molecular dynamics simulations water molecules were observed to be ordered into approximately concentric cylindrical shells. The waters of the outermost shell were oriented such that their dipoles were on average perpendicular to the normal of the wall of the cavity. Water dynamics were analyzed in terms of self-diffusion coefficients and rotational reorientation rates. For cavities of radii 3 and 6 A, water mobility was reduced relative to that of simulated bulk water. For 9- and 12-A radii confined water molecules exhibited mobilities comparable with that of the bulk solvent. If water molecules were confined within an hourglass-shaped cavity (with a central radius of 3 A increasing to 12 A at either end) a gradient of water mobility was observed along the cavity axis. Thus, water within simple models of transbilayer channels exhibits perturbations of structure and dynamics relative to bulk water. In particular the reduction of rotational reorientation rate is expected to alter the local dielectric constant within a transbilayer pore.

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.