A model of sodium channels

We have explored the permeation and blockage of ions in sodium channels, relating the channel structure to function using electrostatic profiles and Brownian dynamics simulations. The model used resembles the KcsA potassium channel with an added external vestibule and a shorter selectivity filter. The electrostatic energy landscape seen by permeating ions is determined by solving Poisson's equation. The two charged amino acid rings of Glu-Glu-Asp-Asp (EEDD) and Asp-Glu-Lys-Ala (DEKA) around the selectivity filter region are seen to play a crucial role in making the channel sodium selective, and strongly binding calcium ions such that they block the channel. Our model closely reproduces a range of experimental data including the current-voltage curves, current-concentration curves and blockage of monovalent ions by divalent ions.     

Mechanisms of permeation and selectivity in calcium channels

The mechanisms underlying ion transport and selectivity in calcium channels are examined using electrostatic calculations and Brownian dynamics simulations. We model the channel as a rigid structure with fixed charges in the walls, representing glutamate residues thought to be responsible for ion selectivity. Potential energy profiles obtained from multi-ion electrostatic calculations provide insights into ion permeation and many other observed features of L-type calcium channels. These qualitative explanations are confirmed by the results of Brownian dynamics simulations, which closely reproduce several experimental observations. These include the current-voltage curves, current-concentration relationship, block of monovalent currents by divalent ions, the anomalous mole fraction effect between sodium and calcium ions, attenuation of calcium current by external sodium ions, and the effects of mutating glutamate residues in the amino acid sequence.     

Current and selectivity in a model sodium channel under physiological conditions: Dynamic Monte Carlo simulations

A reduced model of a sodium channel is analyzed using Dynamic Monte Carlo simulations. These include the first simulations of ionic current under approximately physiological ionic conditions through a model sodium channel and an analysis of how mutations of the sodium channel's DEKA selectivity filter motif transform the channel from being Na(+) selective to being Ca(2+) selective. Even though the model of the pore, amino acids, and permeant ions is simplified, the model reproduces the fundamental properties of a sodium channel (e.g., 10 to 1 Na(+) over K(+) selectivity, Ca(2+) exclusion, and Ca(2+) selectivity after several point mutations). In this model pore, ions move through the pore one at a time by simple diffusion and Na(+) versus K(+) selectivity is due to both the larger K(+) not fitting well into the selectivity filter that contains amino acid terminal groups and K(+) moving more slowly (compared to Na(+)) when it is in the selectivity filter.     

Potassium and sodium ions in a potassium channel studied by molecular dynamics simulations

We have performed simulations of both a single potassium ion and a single sodium ion within the pore of the bacterial potassium channel KcsA. For both ions there is a dehydration energy barrier at the cytoplasmic mouth suggesting that the crystal structure is a closed conformation of the channel. There is a potential energy barrier for a sodium ion in the selectivity filter that is not seen for potassium. Radial distribution functions for both ions with the carbonyl oxygens of the selectivity filter indicate that sodium may interact more tightly with the filter than does potassium. This suggests that the key to the ion selectivity of KcsA is the greater dehydration energy of Na⁺ ions, and helps to explain the block of KcsA by internal Na⁺ ions.     

Molecular dynamics study of the KcsA potassium channel

The structural, dynamical, and thermodynamic properties of a model potassium channel are studied using molecular dynamics simulations. We use the recently unveiled protein structure for the KcsA potassium channel from Streptomyces lividans. Total and free energy profiles of potassium and sodium ions reveal a considerable preference for the larger potassium ions. The selectivity of the channel arises from its ability to completely solvate the potassium ions, but not the smaller sodium ions. Self-diffusion of water within the narrow selectivity filter is found to be reduced by an order of magnitude from bulk levels, whereas the wider hydrophobic section of the pore maintains near-bulk self-diffusion. Simulations examining multiple ion configurations suggest a two-ion channel. Ion diffusion is found to be reduced to approximately (1)/(3) of bulk diffusion within the selectivity filter. The reduced ion mobility does not hinder the passage of ions, as permeation appears to be driven by Coulomb repulsion within this multiple ion channel.     

Selectivity sequences in a model calcium channel: role of electrostatic field strength

The energetics that give rise to selectivity sequences of ionic binding selectivity of Li⁺, Na⁺, K⁺, Rb⁺, and Cs⁺ in a model of a calcium channel are considered. This work generalizes Eisenman’s classic treatment (Biophys J 2(Suppl. 2):259, 1962) by including multiple, mobile binding site oxygens that coordinate many permeating ions (all modeled as charged, hard spheres). The selectivity filter of the model calcium channel allows the carboxyl terminal groups of glutamate and aspartate side chains to directly interact with and coordinate the permeating ions. Ion dehydration effects are represented with a Born energy between the dielectric coefficients of the selectivity filter and the bath. High oxygen concentration creates a high field strength site that prefers small ions, as in Eisenman’s model. On the other hand, a low filter dielectric constant also creates a high field strength site, but this site prefers large ions, contrary to Eisenman’s model. These results indicate that field strength does not have a unique effect on ionic binding selectivity sequences once entropic, electrostatic, and dehydration forces are included in the model. Thus, Eisenman’s classic relationship between field strength and selectivity sequences must be supplemented with additional information about selectivity filters such as the calcium channel that has amino acid side chains mixing with ions to make a crowded permeation pathway.     

Modeling of the outer vestibule and selectivity filter of the L-type Ca2+ channel

Using the KcsA bacterial K+ channel crystal structure [Doyle, D. A., et al. (1998) Science 280, 69-74] and the model of the outer vestibule of the Na+ channel [Lipkind, G. M., and Fozzard, H. A. (2000) Biochemistry 39, 8161-8170] as structural templates, we propose a structural model of the outer vestibule and selectivity filter of the pore of the Ca2+ channel (alpha1C or Ca(v)1.2). The Ca2+ channel P loops were modeled by alpha-helix-turn-beta-strand motifs, with the glutamate residues of the EEEE motif located in the turns. P loops were docked in the extracellular part of the inverted teepee structure formed by S5 and S6 alpha-helices with backbone coordinates from the M1 and M2 helices of the KcsA crystal structure. This construction results in a conical outer vestibule that tapers to the selectivity filter at the bottom. The modeled selectivity ring forms a wide open pore ( approximately 6 A) in the absence of Ca2+. When Ca2+ is present ( approximately 1 microM), all four glutamate side chains move to the center and form a cage around the dehydrated Ca2+ ion, blocking the pore. In the millimolar concentration range, Ca2+ also interacts with two low-affinity sites located externally and internally, which were modeled by the same carboxylate groups of the selectivity filter. Calculation of the resulting electrostatic potentials show that the single Ca2+ ion is located in an electrostatic trap. Only when three Ca2+ ions are bound simultaneously in the high- and low-affinity sites of the selectivity filter is Ca2+ able to overcome electrostatic attraction, permitting Ca2+ flux.     

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.     

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.     

Electrostatic calculations for an ion channel. II. Kinetic behavior of the gramicidin A channel.

A theoretical model of the gramicidin A channel is presented and the kinetic behavior of the model is derived and compared with previous experimental results. The major assumption of the model is that the only interaction between ions in a multiply-occupied channel is electrostatic. The electrostatic calculations indicate in a multiply-occupied channel is electrostatic. The electrostatic calculations indicate that there will be potential wells at each end of the channel and, at high concentrations, that both wells can be occupied. The kinetics are based on two reaction steps: movement of the ion from the bulk solution to the well and movement between the two wells. The kinetics for this reaction rate approach are identical to those based on the Nernst-Planck equation in the limit where the movement between the two wells is rate limiting. The experimental results for sodium and potassium are consistent with a maximum of two ions per channel. To explain the thallium results it is necessary to allow three ions per channel. It is shown that this case is compatible with the electrostatic calculations if the presence of an anion is included. The theoretical kinetics are in reasonable quantitative agreement with the following experimental measurements: single channel conductance of sodium, potassium, and thallium; bi-ionic potential and permeability ratio between sodium-potassium and potassium-thallium; the limiting conductance of potassium and thallium at high applied voltages; current-voltage curves for sodium and potassium at low (but not high) concentrations; and the inhibition of sodium conductance by thallium. The results suggest that the potential well is located close to the channel mouth and that the conductance is partially limited by the rate going from the bulk solution to the well. For thallium, this entrance rate is probably diffusion limited.     

Binding and selectivity in L-type calcium channels: a mean spherical approximation

L-type calcium channels are Ca(2+) binding proteins of great biological importance. They generate an essential intracellular signal of living cells by allowing Ca(2+) ions to move across the lipid membrane into the cell, thereby selecting an ion that is in low extracellular abundance. Their mechanism of selection involves four carboxylate groups, containing eight oxygen ions, that belong to the side chains of the "EEEE" locus of the channel protein, a setting similar to that found in many Ca(2+)-chelating molecules. This study examines the hypothesis that selectivity in this locus is determined by mutual electrostatic screening and volume exclusion between ions and carboxylate oxygens of finite diameters. In this model, the eight half-charged oxygens of the tethered carboxylate groups of the protein are confined to a subvolume of the pore (the "filter"), but interact spontaneously with their mobile counterions as ions interact in concentrated bulk solutions. The mean spherical approximation (MSA) is used to predict ion-specific excess chemical potentials in the filter and baths. The theory is calibrated using a single experimental observation, concerning the apparent dissociation constant of Ca(2+) in the presence of a physiological concentration of NaCl. When ions are assigned their independently known crystal diameters and the carboxylate oxygens are constrained, e.g., to a volume of 0.375 nm(3) in an environment with an effective dielectric coefficient of 63.5, the hypothesized selectivity filter produces the shape of the calcium binding curves observed in experiment, and it predicts Ba(2+)/Ca(2+) and Na(+)/Li(+) competition, and Cl(-) exclusion as observed. The selectivities for Na(+), Ca(2+), Ba(2+), other alkali metal ions, and Cl(-) thus can be predicted by volume exclusion and electrostatic screening alone. Spontaneous coordination of ions and carboxylates can produce a wide range of Ca(2+) selectivities, depending on the volume density of carboxylate groups and the permittivity in the locus. A specific three-dimensional structure of atoms at the binding site is not needed to explain Ca(2+) selectivity.     

Energetics of divalent selectivity in a calcium channel: the ryanodine receptor case study

A model of the ryanodine receptor (RyR) calcium channel is used to study the energetics of binding selectivity of Ca²⁺ versus monovalent cations. RyR is a calcium-selective channel with a DDDD locus in the selectivity filter, similar to the EEEE locus of the L-type calcium channel. While the affinity of RyR for Ca²⁺ is in the millimolar range (as opposed to the micromolar range of the L-type channel), the ease of single-channel measurements compared to L-type and its similar selectivity filter make RyR an excellent candidate for studying calcium selectivity. A Poisson-Nernst-Planck/density functional theory model of RyR is used to calculate the energetics of selectivity. Ca²⁺ versus monovalent selectivity is driven by the charge/space competition mechanism in which selectivity arises from a balance of electrostatics and the excluded volume of ions in the crowded selectivity filter. While electrostatic terms dominate the selectivity, the much smaller excluded-volume term also plays a substantial role. In the D4899N and D4938N mutations of RyR that are analyzed, substantial changes in specific components of the chemical potential profiles are found far from the mutation site. These changes result in the significant reduction of Ca²⁺ selectivity found in both theory and experiments.     

Sodium channel activators: model of binding inside the pore and a possible mechanism of action

Sodium channel activators, batrachotoxin and veratridine, cause sodium channels to activate easier and stay open longer than normal channels. Traditionally, this was explained by an allosteric mechanism. However, increasing evidence suggests that activators can bind inside the pore. Here, we model the open sodium channel with activators and propose a novel mechanism of their action. The activator-bound channel retains a hydrophilic pathway for ions between the ligand and conserved asparagine in segment S6 of repeat II. One end of the activator approaches the selectivity filter, decreasing the channel conductance and selectivity. The opposite end reaches the gate stabilizing it in the open state.     

Trimethyloxonium modification of batrachotoxin-activated Na channels alters functionally important protein residues.

The extracellular side of single batrachotoxin-activated voltage-dependent Na channels isolated from rat skeletal muscle membranes incorporated into neutral planar lipid bilayers were treated in situ with the carboxyl methylating reagent, trimethyloxonium (TMO). These experiments were designed to determine whether TMO alters Na channel function by a general through-space electrostatic mechanism or by methylating specific carboxyl groups essential to channel function. TMO modification reduced single-channel conductance by decreasing the maximal turnover rate. Modification increased channel selectivity for sodium ions relative to potassium ions as measured under biionic conditions. TMO modification increased the mu-conotoxin (muCTX) off-rate by three orders of magnitude. Modification did not alter the muCTX on-rate at low ionic strength or Na channel voltage-dependent gating characteristics. These data demonstrate that TMO does not act via a general electrostatic mechanism. Instead, TMO targets protein residues specifically involved in ion conduction, ion selectivity, and muCTX binding. These data support the hypothesis that muCTX blocks open-channel current by physically obstructing the ion channel pore.     

Molecular basis of ion permeability in a voltage‐gated sodium channel

Voltage‐gated sodium channels are essential for electrical signalling across cell membranes. They exhibit strong selectivities for sodium ions over other cations, enabling the finely tuned cascade of events associated with action potentials. This paper describes the ion permeability characteristics and the crystal structure of a prokaryotic sodium channel, showing for the first time the detailed locations of sodium ions in the selectivity filter of a sodium channel. Electrostatic calculations based on the structure are consistent with the relative cation permeability ratios (Na⁺ ≈ Li⁺ ≫ K⁺, Ca²⁺, Mg²⁺) measured for these channels. In an E178D selectivity filter mutant constructed to have altered ion selectivities, the sodium ion binding site nearest the extracellular side is missing. Unlike potassium ions in potassium channels, the sodium ions in these channels appear to be hydrated and are associated with side chains of the selectivity filter residues, rather than polypeptide backbones.     

Identification of a novel pharmacophore for peptide toxins interacting with K+ channels

KappaM-conotoxin RIIIK blocks TSha1 K+ channels from trout with high affinity by interacting with the ion channel pore. As opposed to many other peptides targeting K+ channels, kappaM-RIIIK does not possess a functional dyad. In this study we combine thermodynamic mutant cycle analysis and docking calculations to derive the binding mode of kappaM-conotoxin RIIIK to the TSha1 channel. The final model reveals a novel pharmacophore, where no positively charged side chain occludes the channel pore. Instead the positive-charged residues of the toxin form a basic ring; kappaM-RIIIK is anchored to the K+ channel via electrostatic interactions of this basic ring with the loop and pore helix residues of the channel. The channel amino acid Glu-354 is likely to be a fundamental determinant of the selectivity of kappaM-RIIIK for the TSha1 channel. The Cgamma-OH of Hyp-15 is in contact with the carbonyls of the selectivity filter, disturbing the charge distribution pattern necessary for the coordination of K+ ions. This novel, experimentally based pharmacophore model proves the existence of diverse binding modes of peptidic toxins to K+ channels and underlines the role of intermolecular electrostatic interactions involving channel loop side chains in determining the selectivity of toxins for specific K+ channel types.     

Block of CaV1.2 channels by Gd3+ reveals preopening transitions in the selectivity filter

Using the lanthanide gadolinium (Gd(3+)) as a Ca(2+) replacing probe, we investigated the voltage dependence of pore blockage of Ca(V)1.2 channels. Gd(+3) reduces peak currents (tonic block) and accelerates decay of ionic current during depolarization (use-dependent block). Because diffusion of Gd(3+) at concentrations used (<1 microM) is much slower than activation of the channel, the tonic effect is likely to be due to the blockage that occurred in closed channels before depolarization. We found that the dose-response curves for the two blocking effects of Gd(3+) shifted in parallel for Ba(2+), Sr(2+), and Ca(2+) currents through the wild-type channel, and for Ca(2+) currents through the selectivity filter mutation EEQE that lowers the blocking potency of Gd(3+). The correlation indicates that Gd(3+) binding to the same site causes both tonic and use-dependent blocking effects. The apparent on-rate for the tonic block increases with the prepulse voltage in the range -60 to -45 mV, where significant gating current but no ionic current occurs. When plotted together against voltage, the on-rates of tonic block (-100 to -45 mV) and of use-dependent block (-40 to 40 mV) fall on a single sigmoid that parallels the voltage dependence of the gating charge. The on-rate of tonic block by Gd(3+) decreases with concentration of Ba(2+), indicating that the apparent affinity of the site to permeant ions is about 1 mM in closed channels. Therefore, we propose that at submicromolar concentrations, Gd(3+) binds at the entry to the selectivity locus and that the affinity of the site for permeant ions decreases during preopening transitions of the channel.     

Modeling of ion permeation in calcium and sodium channel selectivity filters

Structure-function studies have shown that it is possible to convert a sodium channel to a calcium-selective channel by a single amino acid substitution in the selectivity filter locus. Ion permeation through the "model selectivity filter" was modeled with a reduced set of functional groups representative of the constituent amino acid side chains. Force-field minimizations were conducted to obtain the energy profile of the cations as they get desolvated and bind to the "model selectivity filter." The calculations suggest that the ion selectivity in the calcium channel is due to preferential binding, whereas in the sodium channel it is due to exclusion. Energetics of displacement of a bound cation from the calcium "model selectivity filter" by another cation suggest that "multi-ion mechanism" reduces the activation barrier for ion permeation. Thus, the simple model captures qualitatively most of the conduction characteristics of sodium and calcium channels. However, the computed barriers for permeation are fairly large, suggesting that ion interaction with additional residues along the transport path may be essential to effect desolvation.     

Voltage profile along the permeation pathway of an open channel

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