Ion permeation through a narrow channel: using gramicidin to ascertain all-atom molecular dynamics potential of mean force methodology and biomolecular force fields

We investigate methods for extracting the potential of mean force (PMF) governing ion permeation from molecular dynamics simulations (MD) using gramicidin A as a prototypical narrow ion channel. It is possible to obtain well-converged meaningful PMFs using all-atom MD, which predict experimental observables within order-of-magnitude agreement with experimental results. This was possible by careful attention to issues of statistical convergence of the PMF, finite size effects, and lipid hydrocarbon chain polarizability. When comparing the modern all-atom force fields of CHARMM27 and AMBER94, we found that a fairly consistent picture emerges, and that both AMBER94 and CHARMM27 predict observables that are in semiquantitative agreement with both the experimental conductance and dissociation coefficient. Even small changes in the force field, however, result in significant changes in permeation energetics. Furthermore, the full two-dimensional free-energy surface describing permeation reveals the location and magnitude of the central barrier and the location of two binding sites for K(+) ion permeation near the channel entrance--i.e., an inner site on-axis and an outer site off-axis. We conclude that the MD-PMF approach is a powerful tool for understanding and predicting the function of narrow ion channels in a manner that is consistent with the atomic and thermally fluctuating nature of proteins.     

Gating of Connexin Channels by transjunctional-voltage: Conformations and models of open and closed states

Voltage is an important physiologic regulator of channels formed by the connexin gene family. Connexins are unique among ion channels in that both plasma membrane inserted hemichannels (undocked hemichannels) and intercellular channels (aggregates of which form gap junctions) have important physiological roles. The hemichannel is the fundamental unit of gap junction voltage-gating. Each hemichannel displays two distinct voltage-gating mechanisms that are primarily sensitive to a voltage gradient formed along the length of the channel pore (the transjunctional voltage) rather than sensitivity to the absolute membrane potential (V_m or V_i-o). These transjunctional voltage dependent processes have been termed V_j- or fast-gating and loop- or slow-gating. Understanding the mechanism of voltage-gating, defined as the sequence of voltage-driven transitions that connect open and closed states, first and foremost requires atomic resolution models of the end states. Although ion channels formed by connexins were among the first to be characterized structurally by electron microscopy and x-ray diffraction in the early 1980′s, subsequent progress has been slow. Much of the current understanding of the structure-function relations of connexin channels is based on two crystal structures of Cx26 gap junction channels. Refinement of crystal structure by all-atom molecular dynamics and incorporation of charge changing protein modifications has resulted in an atomic model of the open state that arguably corresponds to the physiologic open state. Obtaining validated atomic models of voltage-dependent closed states is more challenging, as there are currently no methods to solve protein structure while a stable voltage gradient is applied across the length of an oriented channel. It is widely believed that the best approach to solve the atomic structure of a voltage-gated closed ion channel is to apply different but complementary experimental and computational methods and to use the resulting information to derive a consensus atomic structure that is then subjected to rigorous validation. In this paper, we summarize our efforts to obtain and validate atomic models of the open and voltage-driven closed states of undocked connexin hemichannels.This article is part of a Special Issue entitled: Gap Junction Proteins edited by Jean Claude Herve.     

Permeation Models and Structure-Function Relationships in Ion Channels

Recent determination of the molecular structures of potassium andmechanosensitive channels from x-ray crystallography has led to arenewed interest in ion channels. The challenge for permeation modelsis to understand the functional properties of channels from the availablestructural information. Here we give a critical review of the three maincontenders, namely, continuum theories, Brownian dynamics and moleculardynamics. Continuum theories are shown to be invalid in a narrow channel environment because they ignore the self-energy of ions arising from theinduced charges on the dielectric boundary. Brownian and moleculardynamics are thus the only physically valid methods for studying thestructure-function relations in ion channels. Applications of thesemethods to potassium and calcium channels are presented, which illustratethe multi-ion nature of the permeation mechanism in selective biologicalchannels.     

Brownian dynamics simulations of ion transport through the VDAC

It is important to gain a physical understanding of ion transport through the voltage-dependent anion channel (VDAC) because this channel provides primary permeation pathways for metabolites and electrolytes between the cytosol and mitochondria. We performed grand canonical Monte Carlo/Brownian dynamics (GCMC/BD) simulations to explore the ion transport properties of human VDAC isoform 1 (hVDAC1; PDB:2K4T) embedded in an implicit membrane. When the MD-derived, space-dependent diffusion constant was used in the GCMC/BD simulations, the current-voltage characteristics and ion number profiles inside the pore showed excellent agreement with those calculated from all-atom molecular-dynamics (MD) simulations, thereby validating the GCMC/BD approach. Of the 20 NMR models of hVDAC1 currently available, the third one (NMR03) best reproduces both experimental single-channel conductance and ion selectivity (i.e., the reversal potential). In addition, detailed analyses of the ion trajectories, one-dimensional multi-ion potential of mean force, and protein charge distribution reveal that electrostatic interactions play an important role in the channel structure and ion transport relationship. Finally, the GCMC/BD simulations of various mutants based on NMR03 show good agreement with experimental ion selectivity. The difference in ion selectivity between the wild-type and the mutants is the result of altered potential of mean force profiles that are dominated by the electrostatic interactions.     

Molecular dynamics simulations of the Cx26 hemichannel: evaluation of structural models with Brownian dynamics

The recently published crystal structure of the Cx26 gap junction channel provides a unique opportunity for elucidation of the structure of the conductive connexin pore and the molecular determinants of its ion permeation properties (conductance, current-voltage [I-V] relations, and charge selectivity). However, the crystal structure was incomplete, most notably lacking the coordinates of the N-terminal methionine residue, which resides within the pore, and also lacking two cytosolic domains. To allow computational studies for comparison with the known channel properties, we completed the structure. Grand canonical Monte Carlo Brownian dynamics (GCMC/BD) simulations of the completed and the published Cx26 hemichannel crystal structure indicate that the pore is too narrow to permit significant ion flux. The GCMC/BD simulations predict marked inward current rectification and almost perfect anion selectivity, both inconsistent with known channel properties. The completed structure was refined by all-atom molecular dynamics (MD) simulations (220 ns total) in an explicit solvent and POPC membrane system. These MD simulations produced an equilibrated structure with a larger minimal pore diameter, which decreased the height of the permeation barrier formed by the N terminus. GCMC/BD simulations of the MD-equilibrated structure yielded more appropriate single-channel conductance and less anion/cation selectivity. However, the simulations much more closely matched experimentally determined I-V relations when the charge effects of specific co- and posttranslational modifications of Cx26 previously identified by mass spectrometry were incorporated. We conclude that the average equilibrated structure obtained after MD simulations more closely represents the open Cx26 hemichannel structure than does the crystal structure, and that co- and posttranslational modifications of Cx26 hemichannels are likely to play an important physiological role by defining the conductance and ion selectivity of Cx26 channels. Furthermore, the simulations and data suggest that experimentally observed heterogeneity in Cx26 I-V relations can be accounted for by variation in co- and posttranslational modifications.     

Molecular dynamics - potential of mean force calculations as a tool for understanding ion permeation and selectivity in narrow channels

Ion channels catalyze the permeation of charged molecules across cell membranes and are essential for many vital physiological functions, including nerve and muscle activity. To understand better the mechanisms underlying ion conduction and valence selectivity of narrow ion channels, we have employed free energy techniques to calculate the potential of mean force (PMF) for ion movement through the prototypical gramicidin A channel. Employing modern all-atom molecular dynamics (MD) force fields with umbrella sampling methods that incorporate one hundred 1-2 ns trajectories, we find that it is possible to achieve semi-quantitative agreement with experimental binding and conductance measurements. We also examine the sensitivity of the MD-PMF results to the choice of MD force field and compare PMFs for potassium, calcium and chloride ions to explore the basis for the valence selectivity of this narrow and uncharged ion channel. A large central barrier is observed for both anions and divalent ions, consistent with lack of experimental conductance. Neither anion or divalent cation is seen to be stabilized inside the channel relative to the bulk electrolyte and each leads to large disruptions to the protein and membrane structure when held deep inside the channel. Weak binding of calcium ions outside the channel corresponds to a free energy well that is too shallow to demonstrate channel blocking. Our findings emphasize the success of the MD-PMF approach and the sensitivity of ion energetics to the choice of biomolecular force field.     

Probing structural features of Alzheimer's amyloid-β pores in bilayers using site-specific amino acid substitutions

A current hypothesis for the pathology of Alzheimer's disease (AD) proposes that amyloid-β (Aβ) peptides induce uncontrolled, neurotoxic ion flux across cellular membranes. The mechanism of ion flux is not fully understood because no experiment-based Aβ channel structures at atomic resolution are currently available (only a few polymorphic states have been predicted by computational models). Structural models and experimental evidence lend support to the view that the Aβ channel is an assembly of loosely associated mobile β-sheet subunits. Here, using planar lipid bilayers and molecular dynamics (MD) simulations, we show that amino acid substitutions can be used to infer which residues are essential for channel structure. We created two Aβ(1-42) peptides with point mutations: F19P and F20C. The substitution of Phe19 with Pro inhibited channel conductance. MD simulation suggests a collapsed pore of F19P channels at the lower bilayer leaflet. The kinks at the Pro residues in the pore-lining β-strands induce blockage of the solvated pore by the N-termini of the chains. The cysteine mutant is capable of forming channels, and the conductance behavior of F20C channels is similar to that of the wild type. Overall, the mutational analysis of the channel activity performed in this work tests the proposition that the channels consist of a β-sheet rich organization, with the charged/polar central strand containing the mutation sites lining the pore, and the C-terminal strands facing the hydrophobic lipid tails. A detailed understanding of channel formation and its structure should aid studies of drug design aiming to control unregulated Aβ-dependent ion fluxes.     

Nonindependent K+ Movement through the Pore in IRK1 Potassium Channels

We measured unidirectional K⁺ in- and efflux through an inward rectifier K channel (IRK1) expressed in Xenopus oocytes. The ratio of these unidirectional fluxes differed significantly from expectations based on independent ion movement. In an extracellular solution with a K⁺ concentration of 25 mM, the data were described by a Ussing flux-ratio exponent, n′, of ∼2.2 and was constant over a voltage range from −50 to −25 mV. This result indicates that the pore of IRK1 channels may be simultaneously occupied by at least three ions. The IRK1 n′ value of 2.2 is significantly smaller than the value of 3.5 obtained for Shaker K channels under identical conditions. To determine if other permeation properties that reflect multi-ion behavior differed between these two channel types, we measured the conductance (at 0 mV) of single IRK1 channels as a function of symmetrical K⁺ concentration. The conductance could be fit by a saturating hyperbola with a half-saturation K⁺ activity of 40 mM, substantially less than the reported value of 300 mM for Shaker K channels. We investigated the ability of simple permeation models based on absolute reaction rate theory to simulate IRK1 current–voltage, conductance, and flux-ratio data. Certain classes of four-barrier, three-site permeation models are inconsistent with the data, but models with high lateral barriers and a deep central well were able to account for the flux-ratio and single channel data. We conclude that while the pore in IRK1 and Shaker channels share important similarities, including K⁺ selectivity and multi-ion occupancy, they differ in other properties, including the sensitivity of pore conductance to K⁺ concentration, and may differ in the number of K⁺ ions that can simultaneously occupy the pore: IRK1 channels may contain three ions, but the pore in Shaker channels can accommodate four or more ions.     

Ionic permeation and conduction properties of neuronal KCNQ2/KCNQ3 potassium channels

Heteromeric KCNQ2/3 potassium channels are thought to underlie the M-current, a subthreshold potassium current involved in the regulation of neuronal excitability. KCNQ channel subunits are structurally unique, but it is unknown whether these structural differences result in unique conduction properties. Heterologously expressed KCNQ2/3 channels showed a permeation sequence of while showing a conduction sequence of A differential contribution of component subunits to the properties of heteromeric KCNQ2/3 channels was demonstrated by studying homomeric KCNQ2 and KCNQ3 channels, which displayed contrasting ionic selectivities. KCNQ2/3 channels did not exhibit an anomalous mole-fraction effect in mixtures of K(+) and Rb(+). However, extreme voltage-dependence of block by external Cs(+) was indicative of multi-ion pore behavior. Block of KCNQ2/3 channels by external Ba(2+) ions was voltage-independent, demonstrating unusual ionic occupation of the outer pore. Selectivity properties and block of KCNQ2 were altered by mutation of outer pore residues in a manner consistent with the presence of multiple ion-binding sites. KCNQ2/3 channel deactivation kinetics were slowed exclusively by Rb(+), whereas activation of KCNQ2/3 channels was altered by a variety of external permeant ions. These data indicate that KCNQ2/3 channels are multi-ion pores which exhibit distinctive mechanisms of ion conduction and gating.     

Insights into the biophysical properties of GABA(A) ion channels: modulation of ion permeation by drugs and protein interactions

The fundamental properties of ion channels assure their selectivity for a particular ion, its rapid permeation through a central pore and that such electrical activity is modulated by factors that control the opening and closing (gating) of the channel. All cell types possess ion channels and their regulated flux of ions across the membrane play critical roles in all steps of life. An ion channel does not act alone to control cell excitability but rather forms part of larger protein complexes. The identification of protein interaction partners of ion channels and their influence on both the fundamental biophysical properties of the channel and its expression in the membrane are revealing the many ways in which electrical activity may be regulated. Highlighted here is the novel use of the patch clamp method to dissect out the influence of protein interactions on the activity of individual GABA(A) receptors. The studies demonstrate that ion conduction is a dynamic property of a channel and that protein interactions in a cytoplasmic domain underlie the channel's ability to alter ion permeation. A structural model describing a reorganisation of the conserved cytoplasmic gondola domain and the influence of drugs on this process are presented.     

短杆菌肽A-DMPC通道内离子输运的分子动力学模拟

用最近提出的构建膜体系初始构象的有效方法 ,构建了在DMPC脂膜环境下短杆菌肽A通道模型 (GA -DMPC)。通过对Na 、Ca2 、Cl-三种不同离子在GA -DMPC通道内不同位置的分子动力学模拟 ,研究离子在通道内输运过程中与通道及通道内水分子的相互作用 ,从分子动力学的角度阐明离子在通道内的输运机制。主要计算结果表明 :(1)离子在通道内的输运使GA的构象发生变化 ,GA的柔性是离子在通道内通透的重要因素 ;(2)Cl- 离子可扩大通道半径 ,Na 离子和Ca2 离子则减小通道半径。Cl-离子不能在GA通道内通透 ;(3)离子的出现使通道内水分子的偶极方向发生变化。上述结果均与实验相符。     

Sodium flux ratio in voltage-clamped squid giant axons

The sodium flux ratio across the axolemma of internally perfused, voltage-clamped giant axons of Loligo pealei has been measured at various membrane potentials. The flux ratio exponent obtained from these measurements was about unity and independent of membrane voltage over the 50 mV range from about -20 to l mV. These results, combined with previous measurements of ion permeation through sodium channels, show that the sodium channel behaves like a multi-ion pore with two ion binding sites that are rarely simultaneously occupied by sodium.     

Theoretical studies of the M2 transmembrane segment of the glycine receptor: models of the open pore structure and current-voltage characteristics

The pentameric glycine receptor (GlyR), a member of the nicotinicoid superfamily of ligand-gated ion channels, is an inhibitory Cl(-) channel that is gated by glycine. Using recently published NMR data of the second transmembrane segment (M2) of the human alpha1 GlyR, structural models of pentameric assemblies embedded in a lipid bilayer were constructed using a combination of experimentally determined constraints coupled with all-atom energy minimization. Based on this structure of the pentameric M2 "pore", Brownian dynamics simulations of ion permeation through this putative conducting open state of the channel were carried out. Simulated I-V curves were in good agreement with published experimental current-voltage curves and the anion/cation permeability ratio, suggesting that our open-state model may be representative of the conducting channel of the full-length receptor. These studies also predicted regions of chloride occupancy and suggested residues critical to anion permeation. Calculations of the conductance of the cation-selective mutant A251E channel are also consistent with experimental data. In addition, both rotation and untilting of the pore helices of our model were found to be broadly consistent with closing of the channel, albeit at distinct regions that may reflect alternate gates of the receptor.     

CHAP: A Versatile Tool for the Structural and Functional Annotation of Ion Channel Pores

The control of ion channel permeation requires the modulation of energetic barriers or “gates” within their pores. However, such barriers are often simply identified from the physical dimensions of the pore. Such approaches have worked well in the past, but there is now evidence that the unusual behavior of water within narrow hydrophobic pores can produce an energetic barrier to permeation without requiring steric occlusion of the pathway. Many different ion channels have now been shown to exploit “hydrophobic gating” to regulate ion flow, and it is clear that new tools are required for more accurate functional annotation of the increasing number of ion channel structures becoming available. We have previously shown how molecular dynamics simulations of water can be used as a proxy to predict hydrophobic gates, and we now present a new and highly versatile computational tool, the Channel Annotation Package (CHAP) that implements this methodology.     

Ion solvation and structural stability in a sodium channel investigated by molecular dynamics calculations

The stability and ion binding properties of the homo-tetrameric pore domain of a prokaryotic, voltage-gated sodium channel are studied by extensive all-atom molecular dynamics simulations, with the channel protein being embedded in a fully hydrated lipid bilayer. It is found that Na(+) ion presents in a mostly hydrated state inside the wide pore of the selectivity filter of the sodium channel, in sharp contrast to the nearly fully dehydrated state for K(+) ions in potassium channels. Our results also indicate that Na(+) ions make contact with only one or two out of the four polypeptide chains forming the selectivity filter, and surprisingly, the selectivity filter exhibits robust stability for various initial ion configurations even in the absence of ions. These findings are quite different from those in potassium channels. Furthermore, an electric field above 0.5V/nm is suggested to be able to induce Na(+) permeation through the selectivity filter.     

Ion permeation in normal and batrachotoxin-modified Na+ channels in the squid giant axon

Na+ permeation through normal and batrachotoxin (BTX)-modified squid axon Na+ channels was characterized. Unmodified and toxin-modified Na+ channels were studied simultaneously in outside-out membrane patches using the cut-open axon technique. Current-voltage relations for both normal and BTX-modified channels were measured over a wide range of Na+ concentrations and voltages. Channel conductance as a function of Na+ concentration curves showed that within the range 0.015-1 M Na+ the normal channel conductance is 1.7-2.5-fold larger than the BTX-modified conductance. These relations cannot be fitted by a simple Langmuir isotherm. Channel conductance at low concentrations was larger than expected from a Michaelis-Menten behavior. The deviations from the simple case were accounted for by fixed negative charges located in the vicinity of the channel entrances. Fixed negative charges near the pore mouths would have the effect of increasing the local Na+ concentration. The results are discussed in terms of energy profiles with three barriers and two sites, taking into consideration the effect of the fixed negative charges. Either single- or multi-ion pore models can account for all the permeation data obtained in both symmetric and asymmetric conditions. In a temperature range of 5-15 degrees C, the estimated Q10 for the conductance of the BTX-modified Na+ channel was 1.53. BTX appears not to change the Na+ channel ion selectively (for the conditions used) or the surface charge located near the channel entrances.     

Conformational model for ion permeation in membrane channels: a comparison with multi-ion models and applications to calcium channel permeability.

The permeation properties of ion channels existing in several conductive states were analyzed. Each state was represented by the one-ion model. A special emphasis was placed on features, assumed to be indicative of a multi-ion mode of channel occupancy such as a deviation of concentration dependence of channel conductance from the Michaelis-Menten equation, an anomalous mole fraction effect, a strong voltage dependence of ion block and coupling of unidirectional fluxes (anomalous Ussing flux ratio). The conformational model was shown to have all these properties. The ion permeation through voltage-sensitive calcium channels fulfilled all the characteristics of the model proposed.     

Block of tetrodotoxin-resistant Na+ channel pore by multivalent cations: gating modification and Na+ flow dependence

Tetrodotoxin-resistant (TTX-R) Na(+) channels are much less susceptible to external TTX but more susceptible to external Cd(2+) block than tetrodotoxin-sensitive (TTX-S) Na(+) channels. Both TTX and Cd(2+) seem to block the channel near the "DEKA" ring, which is probably part of a multi-ion single-file region adjacent to the external pore mouth and is involved in the selectivity filter of the channel. In this study we demonstrate that other multivalent transitional metal ions such as La(3+), Zn(2+), Ni(2+), Co(2+), and Mn(2+) also block the TTX-R channels in dorsal root ganglion neurons. Just like Cd(2+), the blocking effect has little intrinsic voltage dependence, but is profoundly influenced by Na(+) flow. The apparent dissociation constants of the blocking ions are always significantly smaller in inward Na(+) currents than those in outward Na(+) current, signaling exit of the blocker along with the Na(+) flow and a high internal energy barrier for "permeation" of these multivalent blocking ions through the pore. Most interestingly, the activation and especially the inactivation kinetics are slowed by the blocking ions. Moreover, the gating changes induced by the same concentration of a blocking ion are evidently different in different directions of Na(+) current flow, but can always be correlated with the extent of pore block. Further quantitative analyses indicate that the apparent slowing of channel activation is chiefly ascribable to Na(+) flow-dependent unblocking of the bound La(3+) from the open Na(+) channel, whereas channel inactivation cannot happen with any discernible speed in the La(3+)-blocked channel. Thus, the selectivity filter of Na(+) channel is probably contiguous to a single-file multi-ion region at the external pore mouth, a region itself being nonselective in terms of significant binding of different multivalent cations. This region is "open" to the external solution even if the channel is "closed" ("deactivated"), but undergoes imperative conformational changes during the gating (especially the inactivation) process of the channel.     

Potassium channels as multi-ion single-file pores

A literature review reveals many lines of evidence that both delayed rectifier and inward rectifier potassium channels are multi-ion pores. These include unidirectional flux ratios given by the 2--2.5 power of the electrochemical activity ratio, very steeply voltage-dependent block with monovalent blocking ions, relief of block by permeant ions added to the side opposite from the blocking ion, rectification depending on E--EK, and a minimum in the reversal potential or conductance as external K+ ions are replaced by an equivalent concentration of T1+ ions. We consider a channel with a linear sequence of energy barriers and binding sites. The channel can be occupied by more than one ion at a time, and ions hop in single file into vacant sites with rate constants that depend on barrier heights, membrane potential, and interionic repulsion. Such multi-ion models reproduce qualitatively the special flux properties of potassium channels when the barriers for hopping out of the pore are larger than for hopping between sites within the pore and when there is repulsion between ions. These conditions also produce multiple maxima in the conductance-ion activity relationship. In agreement with Armstrong's hypothesis (1969. J. Gen. Physiol. 54:553--575), inward rectification may be understood in terms of block by an internal blocking cation. Potassium channels must have at least three sites and often contain at least two ions at a time.