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.     

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.     

Conducting-state properties of the KcsA potassium channel from molecular and Brownian dynamics simulations.

The mechanisms underlying transport of ions across the potassium channel are examined using electrostatic calculations and three-dimensional Brownian dynamics simulations. We first build open-state configurations of the channel with molecular dynamics simulations, by pulling the transmembrane helices outward until the channel attains the desired interior radius. To gain insights into ion permeation, we construct potential energy profiles experienced by an ion traversing the channel in the presence of other resident ions. These profiles reveal that in the absence of an applied field the channel accommodates three potassium ions in a stable equilibrium, two in the selectivity filter and one in the central cavity. In the presence of a driving potential, this three-ion state becomes unstable, and ion permeation across the channel is observed. These qualitative explanations are confirmed by the results of three-dimensional Brownian dynamics simulations. We find that the channel conducts when the ionizable residues near the extracellular entrance are fully charged and those near the intracellular side are partially charged. The conductance increases steeply as the radius of the intracellular mouth of the channel is increased from 2 A to 5 A. Our simulation results reproduce several experimental observations, including the current-voltage curves, conductance-concentration relationships, and outward rectification of currents.     

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.     

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.     

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.     

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.     

The fast gating mechanism in ClC-0 channels

We investigate and then modify the hypothesis that a glutamate side chain acts as the fast gate in ClC-0 channels. We first create a putative open-state configuration of the prokaryotic ClC Cl- channel using its crystallographic structure as a basis. Then, retaining the same pore shape, the prokaryotic ClC channel is converted to ClC-0 by replacing all the nonconserved polar and charged residues. Using this open-state channel model, we carry out molecular dynamics simulations to study how the glutamate side chain can move between open and closed configurations. When the side chain extends toward the extracellular end of the channel, it presents an electrostatic barrier to Cl- conduction. However, external Cl- ions can push the side chain into a more central position where, pressed against the channel wall, it does not impede the motion of Cl- ions. Additionally, a proton from a low-pH external solution can neutralize the extended glutamate side chain, which also removes the barrier to conduction. Finally, we use Brownian dynamics simulations to demonstrate the influence of membrane potential and external Cl- concentration on channel open probability.     

Conduction of Na+ and K+ through the NaK channel: molecular and Brownian dynamics studies

Conduction of ions through the NaK channel, with M0 helix removed, was studied using both Brownian dynamics and molecular dynamics. Brownian dynamics simulations predict that the truncated NaK has approximately a third of the conductance of the related KcsA K⁺ channel, is outwardly rectifying, and has a Michaelis-Menten current-concentration relationship. Current magnitude increases when the glutamine residue located near the intracellular gate is replaced with a glutamate residue. The channel is blocked by extracellular Ca²⁺. Molecular dynamics simulations show that, under the influence of a strong applied potential, both Na⁺ and K⁺ move across the selectivity filter, although conduction rates for Na⁺ ions are somewhat lower. The mechanism of conduction of Na⁺ differs significantly from that of K⁺ in that Na⁺ is preferentially coordinated by single planes of pore-lining carbonyl oxygens, instead of two planes as in the usual K⁺ binding sites. The water-containing filter pocket resulting from a single change in the selectivity filter sequence (compared to potassium channels) disrupts several of the planes of carbonyl oxygens, and thus reduces the filter's ability to discriminate against sodium.     

Role of acetylcholine receptor domains in ion selectivity

The nicotinic acetylcholine receptor (nAChR) is a ligand gated ion channel protein, composed of three domains: a transmembrane domain (TM-domain), extracellular domain (EC-domain), and intracellular domain (IC-domain). Due to its biological importance, much experimental and theoretical research has been carried out to explore its mechanisms of gating and selectivity, but there are still many unresolved issues, especially on the ion selectivity. Moreover, most of the previous theoretical work has concentrated on the TM-domain or EC-domain of nAChR, which may be insufficient to understand the entire structure–function relation. In this work, we perform molecular dynamics, Brownian dynamics simulations and continuum electrostatic calculations to investigate the role of different nAChR domains in ion conduction and selectivity. The results show that although both the EC and IC domains contain strong negative charges that create large cation concentrations at either end of the pore, this alone is not sufficient to create the observed cation selectivity and may play a greater role in determining the channel conductance. The presence of cations in the wide regions of the pore can screen out the protein charge allowing anions to enter, meaning that local regions of the TM-domain are most likely responsible for discriminating between ions. These new results complement our understanding about the ion conduction and selectivity mechanism of nAChR.     

Simulations of ion current in realistic models of ion channels: the KcsA potassium channel

Realistic studies of ion current in biologic channels present a major challenge for computer simulation approaches. All-atom molecular dynamics simulations involve serious time limitations that prevent their use in direct evaluation of ion current in channels with significant barriers. The alternative use of Brownian dynamics (BD) simulations can provide the current for simplified macroscopic models. However, the time needed for accurate calculations of electrostatic energies can make BD simulations of ion current expensive. The present work develops an approach that overcomes some of the above challenges and allows one to simulate ion currents in models of biologic channels. Our method provides a fast and reliable estimate of the energetics of the system by combining semimacroscopic calculations of the self-energy of each ion and an implicit treatment of the interactions between the ions, as well as the interactions between the ions and the protein-ionizable groups. This treatment involves the use of the semimacroscopic version of the protein dipole Langevin dipole (PDLD/S) model in its linear response approximation (LRA) implementation, which reduces the uncertainties about the value of the protein "dielectric constant." The resulting free energy surface is used to generate the forces for on-the-fly BD simulations of the corresponding ion currents. Our model is examined in a preliminary simulation of the ion current in the KcsA potassium channel. The complete free energy profile for a single ion transport reflects reasonable energetics and captures the effect of the protein-ionized groups. This calculated profile indicates that we are dealing with the channel in its closed state. Reducing the barrier at the gate region allows us to simulate the ion current in a reasonable computational time. Several limiting cases are examined, including those that reproduce the observed current, and the nature of the productive trajectories is considered. The ability to simulate the current in realistic models of ion channels should provide a powerful tool for studies of the biologic function of such systems, including the analysis of the effect of mutations, pH, and electric potentials.     

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.     

An energy-efficient gating mechanism in the acetylcholine receptor channel suggested by molecular and Brownian dynamics

Acetylcholine receptors mediate electrical signaling between nerve and muscle by opening and closing a transmembrane ion conductive pore. Molecular and Brownian dynamics simulations are used to shed light on the location and mechanism of the channel gate. Four separate 5 ns molecular dynamics simulations are carried out on the imaged structure of the channel, a hypothetical open structure with a slightly wider pore and a mutant structure in which a central ring of hydrophobic residues is replaced by polar groups. Water is found to partially evacuate the pore during molecular simulations of the imaged structure, whereas ions face a large energy barrier and do not conduct through the channel in Brownian dynamics simulations. The pore appears to be in a closed configuration despite containing an unobstructed pathway across the membrane as a series of hydrophobic residues in the center of the channel provide an unfavorable home to water and ions. When the channel is widened slightly, water floods into the channel and ions conduct at a rate comparable to the currents measured experimentally in open channels. The pore remains permeable to ions provided the extracellular end of the pore-lining helix is restrained near the putative open configuration to mimic the presence of the ligand binding domain. Replacing some of the hydrophobic residues with polar ones decreases the barrier for ion permeation but does not result in significant currents. The channel is posited to utilize an energy efficient gating mechanism in which only minor conformational changes of the hydrophobic region of the pore are required to create macroscopic changes in conductance.     

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.     

Position of the third Na+ site in the aspartate transporter GltPh and the human glutamate transporter, EAAT1

Glutamate transport via the human excitatory amino acid transporters is coupled to the co-transport of three Na(+) ions, one H(+) and the counter-transport of one K(+) ion. Transport by an archaeal homologue of the human glutamate transporters, Glt(Ph), whose three dimensional structure is known is also coupled to three Na(+) ions but only two Na(+) ion binding sites have been observed in the crystal structure of Glt(Ph). In order to fully utilize the Glt(Ph) structure in functional studies of the human glutamate transporters, it is essential to understand the transport mechanism of Glt(Ph) and accurately determine the number and location of Na(+) ions coupled to transport. Several sites have been proposed for the binding of a third Na(+) ion from electrostatic calculations and molecular dynamics simulations. In this study, we have performed detailed free energy simulations for Glt(Ph) and reveal a new site for the third Na(+) ion involving the side chains of Threonine 92, Serine 93, Asparagine 310, Aspartate 312, and the backbone of Tyrosine 89. We have also studied the transport properties of alanine mutants of the coordinating residues Threonine 92 and Serine 93 in Glt(Ph), and the corresponding residues in a human glutamate transporter, EAAT1. The mutant transporters have reduced affinity for Na(+) compared to their wild type counterparts. These results confirm that Threonine 92 and Serine 93 are involved in the coordination of the third Na(+) ion in Glt(Ph) and EAAT1.     

Ion selectivity mechanism in a bacterial pentameric ligand-gated ion channel

The proton-gated ion channel from Gloeobacter violaceus (GLIC) is a prokaryotic homolog of the eukaryotic nicotinic acetylcholine receptor that responds to the binding of neurotransmitter acetylcholine and mediates fast signal transmission. Recent emergence of a high-resolution crystal structure of GLIC captured in a potentially open state allowed detailed, atomic-level insight into ion conduction and selectivity mechanisms in these channels. Herein, we have examined the barriers to ion conduction and origins of ion selectivity in the GLIC channel by the construction of potential-of-mean-force profiles for sodium and chloride ions inside the transmembrane region. Our calculations reveal that the GLIC channel is open for a sodium ion to transport, but presents a ∼11 kcal/mol free energy barrier for a chloride ion. Our collective findings identify three distinct contributions to the observed preference for the permeant ions. First, there is a substantial contribution due to a ring of negatively charged glutamate residues (E-2′) at the narrow intracellular end of the channel. The negative electrostatics of this region and the ability of the glutamate side chains to directly bind cations would strongly favor the passage of sodium ions while hindering translocation of chloride ions. Second, our results imply a significant hydrophobic contribution to selectivity linked to differences in the desolvation penalty for the sodium versus chloride ions in the central hydrophobic region of the pore. This hydrophobic contribution is evidenced by the large free energy barriers experienced by Cl⁻ in the middle of the pore for both GLIC and the E-2′A mutant. Finally, there is a distinct contribution arising from the overall negative electrostatics of the channel.     

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.     

Glutamate substitution in repeat IV alters divalent and monovalent cation permeation in the heart Ca2+ channel.

In voltage-gated ion channels, residues responsible for ion selectivity were identified in the pore-lining SS1-SS2 segments. Negatively charged glutamate residues (E393, E736, E1145, and E1446) found in each of the four repeats of the alpha 1C subunit were identified as the major determinant of selectivity in Ca2+ channels. Neutralization of glutamate residues by glutamine in repeat I (E393Q), repeat III (E1145Q), and repeat IV (E1446Q) decreased the channel affinity for calcium ions 10-fold from the wild-type channel. In contrast, neutralization of glutamate residues in repeat II failed to significantly alter Ca2+ affinity. Likewise, mutation of neighboring residues in E1149K and D1450N did not affect the channel affinity, further supporting the unique role of glutamate residues E1145 in repeat III and E1446 in repeat IV in determining Ca2+ selectivity. Conservative mutations E1145D and E1446D preserved high-affinity Ca2+ binding, which suggests that the interaction between Ca2+ and the pore ligand sites is predominantly electrostatic and involves charge neutralization. Mutational analysis of E1446 showed additionally that polar residues could achieve higher Ca2+ affinity than small hydrophobic residues could. The role of high-affinity calcium binding sites in channel permeation was investigated at the single-channel level. Neutralization of glutamate residue in repeats I, II, and III did not affect single-channel properties measured with 115 mM BaCl2. However, mutation of the high-affinity binding site E1446 was found to significantly affect the single-channel conductance for Ba2+ and Li+, providing strong evidence that E1446 is located in the narrow region of the channel outer mouth. Side-chain substitutions at 1446 in repeat IV were used to probe the nature of divalent cation-ligand interaction and monovalent cation-ligand interaction in the calcium channel pore. Monovalent permeation was found to be inversely proportional to the volume of the side chain at position 1446, with small neutral residues such as alanine and glycine producing higher Li+ currents than the wild-type channel. This suggests that steric hindrance is a major determinant for monovalent cation conductance. Divalent permeation was more complex. Ba2+ single-channel conductance decreased when small neutral residues such as glycine were replaced by bulkier ones such as glutamine. However, negatively charged amino acids produced single-channel conductance higher than predicted from the size of their side chain. Hence, negatively charged residues at position 1446 in repeat IV are required for divalent cation permeation.