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.     

Free energy of a potassium ion in a model of the channel formed by an amphipathic leucine-serine peptide

We use molecular dynamics simulations to investigate the position-dependent free energy of a potassium ion in a model of an ion channel formed by the synthetic amphipathic leucine-serine peptide, LS3. The channel model is a parallel bundle of six LS3 helices around which are packed 146 methane-like spheres in order to mimic a membrane. At either end of and within the channel are 1051 water molecules, plus four ions (two potassium and two chloride). The free energy of a potassium ion in the channel was estimated using the weighted histogram analysis (WHAM) method. This is the first time to our knowledge that such a calculation has been carried out as a function of the position of an ion in three dimensions within a channel. The results indicate that for this channel, which is lined by hydrophilic serine sidechains, there is a relatively weak dependence of the free energy on the axial/off-axial position of the ion. There are some off-axis local minima, especially in the C-terminal half of the channel. Using the free energy results, a single channel current-voltage curve was estimated using a one-dimensional Nernst-Planck equation. Although reasonable agreement with experiment is achieved for K(+) ions flowing from the N-terminal to the C-terminal mouth, in the opposite direction the current is underestimated. This underestimation may be a consequence of under-sampling of the conformational dynamics of the channel. We suggest that our simulations may have captured, for example, a sub-conductance level (i.e. an incompletely open state) of the LS3 channel.     

Molecular dynamics simulations of gramicidin A in a lipid bilayer: from structure-function relations to force fields

Molecular dynamics simulations of membrane proteins have become a popular tool for studying their dynamic features, which are not easily accessible by experiments. Whether the force fields developed for globular proteins are adequate this purpose is an important question that is often glossed over. Here we determine the permeation properties of potassium ions in the gramicidin A channel in a lipid bilayer from free energy simulations, and compare the results to experimental data. In particular, we check the dependence of the free energy barriers ions face at the channel center on the membrane size. The results indicate that there is a serious problem with the current rigid force fields independent of the membrane size, and new, possibly polarizable, force fields need to be developed to resolve this problem.     

Permeation of ions across the potassium channel: brownian dynamics studies

The physical mechanisms underlying the transport of ions across a model potassium channel are described. The shape of the model channel corresponds closely to that deduced from crystallography. From electrostatic calculations, we show that an ion permeating the channel, in the absence of any residual charges, encounters an insurmountable energy barrier arising from induced surface charges. Carbonyl groups along the selectivity filter, helix dipoles near the oval chamber, and mouth dipoles near the channel entrances together transform the energy barrier into a deep energy well. Two ions are attracted to this well, and their presence in the channel permits ions to diffuse across it under the influence of an electric field. Using Brownian dynamics simulations, we determine the magnitude of currents flowing across the channel under various conditions. The conductance increases with increasing dipole strength and reaches its maximum rapidly; a further increase in dipole strength causes a steady decrease in the channel conductance. The current also decreases systematically when the effective dielectric constant of the channel is lowered. The conductance with the optimal choice of dipoles reproduces the experimental value when the dielectric constant of the channel is assumed to be 60. The current-voltage relationship obtained with symmetrical solutions is linear when the applied potential is less than approximately 100 mV but deviates from Ohm's law at a higher applied potential. The reversal potentials obtained with asymmetrical solutions are in agreement with those predicted by the Nernst equation. The conductance exhibits the saturation property observed experimentally. We discuss the implications of these findings for the transport of ions across the potassium channels and membrane channels in general.     

Water and potassium dynamics inside the KcsA K(+) channel

Molecular dynamics simulations and electrostatic modeling are used to investigate structural and dynamical properties of the potassium ions and of water molecules inside the KcsA channel immersed in a membrane-mimetic environment. Two potassium ions, initially located in the selectivity filter binding sites, maintain their position during 2 ns of dynamics. A third potassium ion is very mobile in the water-filled cavity. The protein appears engineered so as to polarize water molecules inside the channel cavity. The resulting water induced dipole and the positively charged potassium ion within the cavity are the key ingredients for stabilizing the two K(+) ions in the binding sites. These two ions experience single file movements upon removal of the potassium in the cavity, confirming the role of the latter in ion transport through the channel.     

Energy distribution and ion selectivity of the bacterial potassium channel

The ion selectivity of the bacterial potassium channel K_CSA is explained upon comparing the energy characteristics of the interaction of cations (Li⁺, Na⁺, K⁺) with atoms of the selectivity filter of the protein pore. Quantum-chemical calculations reveal a deeper potential well for potassium ions, which accounts for preferred K⁺ permeation. It is shown that the conventional methods with AMBER, CHARMM, OPLS force fields in standard parametrization as well as partial re-parametrization give incorrect estimates of ion energy distribution in the channel.     

Effects of external cesium and rubidium on outward potassium currents in squid axons

We have studied the effects of external cesium and rubidium on potassium conductance of voltage clamped squid axons over a broad range of concentrations of these ions relative to the external potassium concentration. Our primary novel finding concerning cesium is that relatively large concentrations of this ion are able to block a small, but statistically significant fraction of outward potassium current for potentials less than approximately 50 mV positive to reversal potential. This effect is relieved at more positive potentials. We have also found that external rubidium blocks outward current with a qualitatively similar voltage dependence. This effect is more readily apparent than the cesium blockade, occurring even for concentrations less than that of external potassium. Rubidium also has a blocking effect on inward current, which is relieved for potentials more than 20-40 mV negative to reversal, thereby allowing both potassium and rubidium ions to cross the membrane. We have described these results with a single-file diffusion model of ion permeation through potassium channels. The model analysis suggests that both rubidium and cesium ions exert their blocking effects at the innermost site of a two-site channel, and that rubidium competes with potassium ions for entry into the channel more effectively than does cesium under comparable conditions.     

Influence of interionic interactions on functional state and blocker binding of voltage-gated potassium channels

A mechanism of ion conduction of a voltage-gated potassium channel KcsA was investigated in full-atomic approximation at a trajectory length of 100 ns using the Lomonosov supercomputer. Methods of molecular dynamics were employed. A structure of the KcsA channel in the open state obtained by X-ray structure analysis (PDB ID 3fb7) was used. Free energy profiles of the KcsA pore occupied with either one or three potassium ions were calculated. It was shown that, under physiological conditions, ions pass through the channel pore cooperatively and the mechanism most probably includes three ions permeating in concert. Interactions of the mammalian voltage-gated channel Kv1.2 with neurotoxin were investigated. It was demonstrated that the effect of interionic interactions on binding of a blocker is rather insufficient.     

Transportation behavior of alkali ions through a cell membrane ion channel. A quantum chemical description of a simplified isolated model

Quantum chemical model calculations were carried out for modeling the ion transport through an isolated ion channel of a cell membrane. An isolated part of a natural ion channel was modeled. The model channel was a calixarene derivative, hydrated sodium and potassium ions were the models of the transported ion. The electrostatic potential of the channel and the energy of the channel-ion system were calculated as a function of the alkali ion position. Both attractive and repulsive ion-channel interactions were found. The calculations - namely the dependence of the system energy and the atomic charges of the water molecules with respect to the position of the alkali ion in the channel - revealed the molecular-structural background of the potassium selectivity of this artificial ion channel. It was concluded that the studied ion channel mimics real biological ion channel quite well.     

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.     

Comparative study of the energetics of ion permeation in Kv1.2 and KcsA potassium channels

Biological ion channels rely on a multi-ion transport mechanism for fast yet selective permeation of ions. The crystal structure of the KcsA potassium channel provided the first microscopic picture of this process. A similar mechanism is assumed to operate in all potassium channels, but the validity of this assumption has not been well investigated. Here, we examine the energetics of ion permeation in Shaker Kv1.2 and KcsA channels, which exemplify the six-transmembrane voltage-gated and two-transmembrane inward-rectifier channels. We study the feasibility of binding a third ion to the filter and the concerted motion of ions in the channel by constructing the potential of mean force for K⁺ ions in various configurations. For both channels, we find that a pair of K⁺ ions can move almost freely within the filter, but a relatively large free-energy barrier hinders the K⁺ ion from stepping outside the filter. We discuss the effect of the CMAP dihedral energy correction that was recently incorporated into the CHARMM force field on ion permeation dynamics.     

Inactivation of potassium current in squid axon by a variety of quaternary ammonium ions

The characteristics of potassium channel block by a diverse group of quaternary ammonium (QA) ions was examined in squid axons. Altering the size and nature of the head and/or tail groups of the QA ions applied internally produced only quantitative differences in the potassium current block. Although their entry rate is diminished, compounds with head groups as large as 11 X 12 A are capable of occluding the channel, whereas the smallest QA ions, with head groups approximately 5 X 6 A, are not potent blockers. When one or three terminal hydrogens of the head group were replaced by hydroxyl moieties, the compound's blocking ability was diminished, suggesting that QA binding is not improved by hydrogen bonding at these positions. QA ions bound to their site within the potassium channel with 1:1 stoichiometry, and the site is perhaps 20% or more of the distance through the membrane electric field. Raising external potassium concentration did not alter the steady-state or kinetic features of the QA block of outward potassium currents; however, increasing temperature or adding Ba2+ internally increased the rate of decay of the QA-blocked currents. From the structure-function analysis of the QA ions, projections concerning both the architecture of the potassium channel's inner mouth and the significance of various chemical constituents of the ions were made. The potassium channel may now be pictured as having a wider mouth (up to 11 X 12 A) extending to the QA binding site and then narrowing quickly to the region of channel selectivity. Important alterations that improve the blocking ability of the compounds include: (a) lengthening the alkyl hydrocarbon tail group (up to 10 carbon), (b) lengthening a second hydrocarbon chain of the head group (e.g., decyldimethylphenylammonium bromide [C10DM phi]), and (c) adding a carbonyl moiety to the tail (e.g., ambutonium).     

Effect of external electric fields on the potential energy profile of K+ ions in selective filter of the KcsA potassium channel

In this study, the potential energy profile of potassium ions in the selective filter part of a KcsA channel was investigated via the application of the molecular simulation method. For this purpose, using the molecular dynamics simulation, the effect of an applied electric field, either constant or oscillating, was studied on the dynamics of K ions in the filter. It was found that when the channel is exposed to a constant electric field of strength 0.03 V/nm, the ions experience a hopping motion. Furthermore, it was shown that the application of oscillating electric fields of 1 and 2.5 GHz, can increase the rigidity of the filter atomic bonds. By computing the potential energy of K ion in the filter, it was shown that the depth of the potential wells, corresponding to the filter sites, increased when an alternative field was applied. Therefore, exposing the channel to the GHz oscillating electric field could disturb the passing rate of ions through the filter, which in turn may affect the operation of these kinds of channels.     

A computational study of ion binding and protonation states in the KcsA potassium channel

We report results from microscopic molecular dynamics and free energy perturbation simulations of the KcsA potassium channel based on its experimental atomic structure. Conformational properties of selected amino acid residues as well as equilibrium positions of K(+) ions inside the selectivity filter and the internal water cavity are examined. Positions three and four (counting from the extracellular site) in the experimental structure correspond to distinctly separate binding sites for K(+) ions inside the selectivity filter. The protonation states of Glu71 and Asp80, which are close to each other and to the selectivity filter, as well as K(+) binding energies are determined using free energy perturbation calculations. The Glu71 residue which is buried inside a protein cavity is found to be most stable in the neutral form while the solvent exposed Asp80 is ionized. The channel altogether exothermically binds up to three ions, where two of them are located inside the selectivity filter and one in the internal water cavity. Ion permeation mechanisms are discussed in relation to these results.     

Effects of channel blocking on information transmission and energy efficiency in squid giant axons

Action potentials are the information carriers of neural systems. The generation of action potentials involves the cooperative opening and closing of sodium and potassium channels. This process is metabolically expensive because the ions flowing through open channels need to be restored to maintain concentration gradients of these ions. Toxins like tetraethylammonium can block working ion channels, thus affecting the function and energy cost of neurons. In this paper, by computer simulation of the Hodgkin-Huxley neuron model, we studied the effects of channel blocking with toxins on the information transmission and energy efficiency in squid giant axons. We found that gradually blocking sodium channels will sequentially maximize the information transmission and energy efficiency of the axons, whereas moderate blocking of potassium channels will have little impact on the information transmission and will decrease the energy efficiency. Heavy blocking of potassium channels will cause self-sustained oscillation of membrane potentials. Simultaneously blocking sodium and potassium channels with the same ratio increases both information transmission and energy efficiency. Our results are in line with previous studies suggesting that information processing capacity and energy efficiency can be maximized by regulating the number of active ion channels, and this indicates a viable avenue for future experimentation.     

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.     

Tail end of the s6 segment: role in permeation in shaker potassium channels

The permeation pathway in voltage-gated potassium channels has narrow constrictions at both the extracellular and intracellular ends. These constrictions might limit the flux of cations from one side of the membrane to the other. The extracellular constriction is the selectivity filter, whereas the intracellular bundle crossing is proposed to act as the activation gate that opens in response to a depolarization. This four-helix bundle crossing is composed of S6 transmembrane segments, one contributed by each subunit. Here, we explore the cytoplasmic extension of the S6 transmembrane segment of Shaker potassium channels, just downstream from the bundle crossing. We substituted cysteine for each residue from N482 to T489 and determined the amplitudes of single channel currents and maximum open probability (P(o,max)) at depolarized voltages using nonstationary noise analysis. One mutant, F484C, significantly reduces P(o,max), whereas Y483C, F484C, and most notably Y485C, reduce single channel conductance (gamma). Mutations of residue Y485 have no effect on the Rb(+)/K(+) selectivity, suggesting a local effect on gamma rather than an allosteric effect on the selectivity filter. Y485 mutations also reduce pore block by tetrabutylammonium, apparently by increasing the energy barrier for blocker movement through the open activation gate. Replacing Rb(+) ions for K(+) ions reduces the amplitude of single channel currents and makes gamma insensitive to mutations of Y485. These results suggest that Rb(+) ions increase an extracellular energy barrier, presumably at the selectivity filter, thus making it rate limiting for flux of permeant ions. These results indicate that S6(T) residues have an influence on the conformation of the open activation gate, reflected in both the stability of the open state and the energy barriers it presents to ions.