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.     

An ion''s view of the potassium channel. The structure of the permeation pathway as sensed by a variety of blocking ions

We have studied the block of potassium channels in voltage-clamped squid giant axons by nine organic and alkali cations, in order to learn how the channel selects among entering ions. When added to the internal solution, all of the ions blocked the channels, with inside-positive voltages enhancing the block. Cesium blocked the channels from the outside as well, with inside-negative voltages favoring block. We compared the depths to which different ions entered the channel by estimating the "apparent electrical distance" to the blocking site. Simulations with a three-barrier, double-occupancy model showed that the "apparent electrical distance," expressed as a fraction of the total transmembrane voltage, appears to be less than the actual value if the blocking ion can pass completely through the channel. These calculations strengthen our conclusion that sodium and cesium block at sites further into the channel than those occupied by lithium and the organic blockers. Our results, considered together with earlier work, demonstrate that the depth to which an ion can readily penetrate into the potassium channel depends both on its size and on the specific chemical groups on its molecular surface. The addition of hydroxyl groups to alkyl chains on a quaternary ammonium ion can both decrease the strength of binding and allow deeper penetration into the channel. For alkali cations, the degree of hydration is probably crucial in determining how far an ion penetrates. Lithium, the most strongly hydrated, appeared not to penetrate as far as sodium and cesium. Our data suggest that there are, minimally, four ion binding sites in the permeation pathway of the potassium channel, with simultaneous occupancy of at least two.     

Ligand binding to the voltage-gated Kv1.5 potassium channel in the open state--docking and computer simulations of a homology model

The binding of blockers to the human voltage-gated Kv1.5 potassium ion channel is investigated using a three-step procedure consisting of homology modeling, automated docking, and binding free energy calculations from molecular dynamics simulations, in combination with the linear interaction energy method. A reliable homology model of Kv1.5 is constructed using the recently published crystal structure of the Kv1.2 channel as a template. This model is expected to be significantly more accurate than earlier ones based on less similar templates. Using the three-dimensional homology model, a series of blockers with known affinities are docked into the cavity of the ion channel and their free energies of binding are calculated. The predicted binding free energies are in very good agreement with experimental data and the binding is predicted to be mainly achieved through nonpolar interactions, whereas the relatively small differences in the polar contribution determine the specificity. Apart from confirming the importance of residues V505, I508, V512, and V516 for ligand binding in the cavity, the results also show that A509 and P513 contribute significantly to the nonpolar binding interactions. Furthermore, we find that pharmacophore models based only on optimized free ligand conformations may not necessarily capture the geometric features of ligands bound to the channel cavity. The calculations herein give a detailed structural and energetic picture of blocker binding to Kv1.5 and this model should thus be useful for further ligand design efforts.     

Bufo marinus oocytes as a model for ion channel protein expression and functional characterization for electrophysiological studies.

Oocytes from Xenopus laevis are commonly used as an expression system for ion channel proteins. The aim of this study was to determine whether oocytes from the Colombian native toad, Bufo marinus, could be used as an alternative expression system for ion channel protein expression and functional characterization using the two-microelectrode voltage clamp method. B. marinus oocytes and X. laevis were isolated and cultured in similar conditions. The mean resting membrane potential of B. marinus oocytes was similar to that of X. laevis oocytes as well as the whole-cell basal currents. The potassium ion channel Kv1.1 was successfully expressed in B. marinus oocytes and showed a typical outward rectifying current. Potassium channel blockers reduced these currents. The similarities on electrical properties and expression of ion channel proteins show that B. marinus oocytes can be used effectively to express these proteins, making these cells a viable heterologous system for the expression of ion channel proteins and their electrophysiological characterization.     

Quantum calculations on water in the KcsA channel cavity with permeant and non-permeant ions

Different ions in the pore of the KcsA channel behave differently, and we relate this to their solvation. We show that the selectivity is dependent, in part, on the solvation in the cavity (sometimes referred to as the vestibule, it is the region containing water molecules between the intracellular gate and the selectivity filter at the extracellular end of the pore). We have shown earlier that potassium is more dependent at the upper end of the cavity region on solvation by the threonines there, while sodium ion has more water molecules as ligands. In addition, sodium ion is placed asymmetrically, while potassium is nearly exactly symmetric with respect to the four-fold symmetry of the channel. We have now extended these calculations to rubidium and cesium ions, and find that rubidium solvation resembles that of potassium (and both are permeant ions), while cesium resembles sodium (and both are non-permeant), in terms of the geometry of up to eight hydrating, and four non-hydrating, water molecules. In each case, a maximum of 12 water molecules are relevant to the calculation. The placement of the water molecules in the two cases is essentially the same as found from the electron density in the X-ray structure of Zhou and MacKinnon. For Na⁺ and K⁺, we show that energy decreases from bulk to the cavity to the lowest position in the selectivity filter (accurate energy could not be calculated for the heavier ions). A separate calculation shows that fixing the Na⁺ ion at the position of the K⁺ minimum, followed by re-optimization produced a significantly modified system, not something that could be produced by thermal fluctuations. Moving the K⁺ into the Na⁺ position in the upper cavity led to a small increase in energy, ≈ 3 k_BT, but was accompanied by large shifts in the positions of hydrating waters, which would create a major kinetic barrier. Therefore, thermal fluctuations could not invalidate the conclusions of the main calculations.     

The pore helix dipole has a minor role in inward rectifier channel function

Ion channels lower the energetic barrier for ion passage across cell membranes and enable the generation of bioelectricity. Electrostatic interactions between permeant ions and channel pore helix dipoles have been proposed as a general mechanism for facilitating ion passage. Here, using genetic selections to probe interactions of an exemplar potassium channel blocker, barium, with the inward rectifier Kir2.1, we identify mutants bearing positively charged residues in the potassium channel signature sequence at the pore helix C terminus. We show that these channels are functional, selective, resistant to barium block, and have minimally altered conductance properties. Both the experimental data and model calculations indicate that barium resistance originates from electrostatics. We demonstrate that potassium channel function is remarkably unperturbed when positive charges occur near the permeant ions at a location that should counteract pore helix electrostatic effects. Thus, contrary to accepted models, the pore helix dipole seems to be a minor factor in potassium channel permeation.     

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.     

Simulation of voltage-driven hydrated cation transport through narrow transmembrane channels.

Molecular dynamics studies for the voltage-driven transport of the alkali metal ions lithium, sodium, and potassium through gramicidin A-type channels filled with water molecules are presented. The number of water molecules in the channel is obtained from a previous study (Skerra, A., and J. Brickmann, 1987, Biophys. J., 51:969-976). It is shown that the selectivity of the intrachannel ion diffusion through our model pore conforms to the experimentally observed selectivity of the gramicidin A channel. It is demonstrated that the number of water molecules in the channel plays a key role for the selectivity.     

Gramicidin channel selectivity. Molecular mechanics calculations for formamidinium, guanidinium, and acetamidinium.

Empirical energy function calculations were used to evaluate the effects of minimization on the structure of a gramicidin A channel and to analyze the energies of interaction between three cations (guanidinium, acetamidinium, formamidinium) and the channel as a function of position along the channel axis. The energy minimized model of the gramicidin channel, which was based on the results of Venkatachalam and Urry (1983), has a constriction at the channel entrance. If the channel is not allowed to relax in the presence of the ions (rigid model), there is a large potential energy barrier for all three cations. The barrier varies with cation size and is due to high van der Waals and ion deformation energies. If the channel is minimized in the presence of the ions, the potential energy barrier to formamidinium entry is almost eliminated, but a residual barrier remains for guanidinium and acetamidinium. The residual barrier is primarily due, not to the expansion of the helix, but, to the disruption of hydrogen bonds between the terminal ethanoloamine and the next turn of the helix which occurs when the carbonyls of the outer turn of the helix librate inward toward the ion as it enters the channel. The residual potential energy barriers could be a possible explanation for the measured selectivity of gramicidin for formamidinium over guanidinium. The results of this full-atomic model address the applicability of the size-exclusion concept for the selectivity of the gramicidin channel.     

Exploring blocker binding to a homology model of the open hERG K+ channel using docking and molecular dynamics methods

Binding of blockers to the human voltage-gated hERG potassium channel is studied using a combination of homology modelling, automated docking calculations and molecular dynamics simulations, where binding affinities are evaluated using the linear interaction energy method. A homology model was constructed based on the available crystal structure of the bacterial KvAP channel and the affinities of a series of sertindole analogues predicted using this model. The calculations reproduce the relative binding affinities of these compounds very well and indicate that both polar interactions near the intracellular opening of the selectivity filter as well as hydrophobic complementarity in the region around F656 are important for blocker binding. These results are consistent with recent alanine scanning mutation experiments on the blocking of the hERG channel by other compounds.     

A new pH-sensitive rectifying potassium channel in mitochondria from the embryonic rat hippocampus

Patch-clamp single-channel studies on mitochondria isolated from embryonic rat hippocampus revealed the presence of two different potassium ion channels: a large-conductance (288±4pS) calcium-activated potassium channel and second potassium channel with outwardly rectifying activity under symmetric conditions (150/150mM KCl). At positive voltages, this channel displayed a conductance of 67.84pS and a strong voltage dependence at holding potentials from -80mV to +80mV. The open probability was higher at positive than at negative voltages. Patch-clamp studies at the mitoplast-attached mode showed that the channel was not sensitive to activators and inhibitors of mitochondrial potassium channels but was regulated by pH. Moreover, we demonstrated that the channel activity was not affected by the application of lidocaine, an inhibitor of two-pore domain potassium channels, or by tertiapin, an inhibitor of inwardly rectifying potassium channels. In summary, based on the single-channel recordings, we characterised for the first time mitochondrial pH-sensitive ion channel that is selective for cations, permeable to potassium ions, displays voltage sensitivity and does not correspond to any previously described potassium ion channels in the inner mitochondrial membrane. This article is part of a Special Issue entitled: 17th European Bioenergetics Conference (EBEC 2012).     

The peptaibol antiamoebin as a model ion channel: similarities to bacterial potassium channels.

Antiamoebin (AAM) is a polypeptide antibiotic that is capable of forming ion channels in phospholipid membranes: planar bilayer studies have suggested the channels are octamers. The crystal structure of a monomeric form of AAM has provided the basis for molecular modelling of an octameric helical bundle channel. The channel model is funnel-shaped due to a substantial bend in the middle of the polypeptide chain caused by the presence of several imino acids. Inter-monomer hydrogen bonds orientate a ring of glutamine side chains to form a constriction in the pore lumen. The channel lumen is lined both by side chains of Gln11 and by polypeptide backbone carbonyl groups. Electrostatic calculations on the model are compatible with a channel that transports cations across membranes. The AAM channel model is compared with the crystal structures of two bacterial (KcsA andMthK) potassium channels. AAM and the potassium channels exhibit common functional features, such as cation-selectivity and similar single channel conductances. Common structural features include being multimers, each formed from a bundle of eight transmembrane helices, with lengths roughly comparable to the thickness of lipid bilayers. In addition, they all have aromatic amino acids that lie at the bilayer interfaces and which may aid in the stabilization of the transmembrane helices, as well as narrower constrictions that define the ion binding sites or selectivity filters in the pore lumen. The commonality of structural and functional features in these channels thus suggests that antiamoebin is a good, simple model for more complex bacterial and eukaryotic ion channels, capable of providing insight into details of the mechanisms of ion transport and multimeric channel stability.     

A physical model of potassium channel activation: from energy landscape to gating kinetics

We have developed a method for rapidly computing gating currents from a multiparticle ion channel model. Our approach is appropriate for energy landscapes that can be characterized by a network of well-defined activation pathways with barriers. To illustrate, we represented the gating apparatus of a channel subunit by an interacting pair of charged gating particles. Each particle underwent spatial diffusion along a bistable potential of mean force, with electrostatic forces coupling the two trajectories. After a step in membrane potential, relaxation of the smaller barrier charge led to a time-dependent reduction in the activation barrier of the principal gate charge. The resulting gating current exhibited a rising phase similar to that measured in voltage-dependent ion channels. Reduction of the two-dimensional diffusion landscape to a circular Markov model with four states accurately preserved the time course of gating currents on the slow timescale. A composite system containing four subunits leading to a concerted opening transition was used to fit a series of gating currents from the Shaker potassium channel. We end with a critique of the model with regard to current views on potassium channel structure.     

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.     

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.     

ATP-sensitive potassium channel in mitochondria of the eukaryotic microorganism Acanthamoeba castellanii

We describe the existence of a potassium ion transport mechanism in the mitochondrial inner membrane of a lower eukaryotic organism, Acanthamoeba castellanii. We found that substances known to modulate potassium channel activity influenced the bioenergetics of A. castellanii mitochondria. In isolated mitochondria, the rate of resting respiration is increased by about 10% in response to potassium channel openers, i.e. diazoxide and BMS-191095, during succinate-, malate-, or NADH-sustained respiration. This effect is strictly dependent on the presence of potassium ions in an incubation medium and is reversed by glibenclamide (a potassium channel blocker). Diazoxide and BMS-191095 also caused a slight but statistically significant depolarization of mitochondrial membrane potential (measured with a TPP(+)-specific electrode), regardless of the respiratory substrate used. The resulting steady state value of membrane potential was restored after treatment with glibenclamide or 1 mM ATP. Additionally, the electrophysiological properties of potassium channels present in the A. castellanii inner mitochondrial membrane are described in the reconstituted system, using black lipid membranes. Conductance from 90 +/- 7 to 166 +/- 10 picosiemens, inhibition by 1 mM ATP/Mg(2+) or glibenclamide, and activation by diazoxide were observed. These results suggest that an ATP-sensitive potassium channel similar to that of mammalian mitochondria is present in A. castellanii mitochondria.     

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.     

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.     

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.     

Model of adaptation of the nerve fiber ranvier node membrane to the action of a steady current as the result of sodium channel inactivation

The effect of the second-order kinetics of the sodium channel inactivation system on spike activity was studied on a modified Hodgkin-Huxley model of the amphibian Ranvier node (Dodge model). The results of calculations based on the experimental data of Chiu, Kniffki, et al. suggest that the cause of adaptation of the amphibian nerve fiber membrane may be the second-order kinetics of the sodium channel inactivation system. Unlike the potassium mechanism of adaptation, the sodium mechanism is associated with constancy or a progressive decline of response amplitudes.