Quantum mechanical calculations on selectivity in the KcsA channel: the role of the aqueous cavity

We have carried out quantum calculations on selected residues at the intracellular side of the selectivity filter of the KcsA potassium channel, using the published X-ray coordinates as starting points. The calculations involved primarily the side chains of residues lining the aqueous cavity on the intracellular side of the selectivity filter, in addition to water molecules, plus a K+ or Na+ ion. The results showed unambiguously that Na+ significantly distorts the symmetry of the channel at the entrance to the selectivity filter (at the residue T75), while K+ does so to a much smaller extent. In all, three ion positions have been calculated: the S4 (lowest) position at the bottom of the selectivity filter, the top of the cavity, and the midpoint of the cavity; Na+ is trapped at the cavity top, while K+ is cosolvated by the selectivity filter carbonyl groups plus threonine hydroxyl groups so that it can traverse the filter. Only one water molecule remains in the K+ solvation shell at the upper position in the cavity; this solvation shell also contains four threonine (T75) hydroxyl oxygens and two backbone carbonyls, while Na+ is solvated by five molecules of water and one oxygen from threonine hydroxyls. T75 at the entrance to the selectivity filter has a key role in recognition of the alkali ion, and T74 has secondary importance. The energetic basis for the preferential bonding of potassium by these residues is briefly discussed, based on additional calculations. Taken together, the results suggest that Na+ would have difficulty entering the cavity, and if it did, it would not be able to enter the selectivity filter.     

Incidence of partial charges on ion selectivity in potassium channels

Potassium channels are membrane proteins known to select potassium over sodium ions at a high diffusion rate. We conducted ab initio calculations on a filter model of KcsA of about 300 atoms at the Hartree-Fock level of theory. Partial charges were derived from the quantum mechanically determined electrostatic potential either with Merz-Kollman or Hinsen-Roux schemes. Large polarization and/or charge transfer occur on potassium ions located in the filter, while the charges on sodium ions remain closer to unity. As a result, a weaker binding is obtained for K(+) ions. Using a simplified version of a permeation model based on the concerted-motion mechanism for ion translocation within the single-file ion channel [P. H. Nelson, J. Chem. Phys. 117, 11396 (2002)], we discuss how differences in polarization effects in the adducts with K(+) and Na(+) can play a role as for ionic selectivity and conductance.     

Kinetic lattice grand canonical Monte Carlo simulation for ion current calculations in a model ion channel system

An algorithm in which kinetic lattice grand canonical Monte Carlo simulations are combined with mean field theory (KLGCMC/MF) is presented to calculate ion currents in a model ion channel system. In this simulation, the relevant region of the system is treated by KLGCMC simulations, while the rest of the system is described by modified Poisson-Boltzmann mean field theory. Calculation of reaction field due to induced charges on the channel/water and membrane/water boundaries is carried out using a basis-set expansion method [Im and Roux, J. Chem. Phys. 115, 4850 (2001)]. Calculation of ion currents, electrostatic potentials, and ion concentrations, as obtained from the KLGCMC/MF simulations, shows good agreement with Poisson-Nernst-Planck (PNP) theory predictions when the channel and membrane have the same dielectric constant as water. If the channel and membrane have a lower dielectric constant than water, however, there is a considerable difference between the KLGCMC/MF and PNP predictions. This difference is attributed to the reaction field, which is missing in PNP theory. It is demonstrated that the reaction field as well as fixed charges in the channel play key roles in selective ion transport. Limitations and further development of the current KLGCMC/MF approach are also discussed.     

Kinetic modeling of ion conduction in KcsA potassium channel

KcsA constitutes a potassium channel of known structure that shows both high conduction rates and selectivity among monovalent cations. A kinetic model for ion conduction through this channel that assumes rapid ion transport within the filter has recently been presented by Nelson. In a recent, brief communication, we used the model to provide preliminary explanations to the experimental current-voltage J-V and conductance-concentration g-S curves obtained for a series of monovalent ions (K(+),Tl(+), and Rb(+)). We did not assume rapid ion transport in the calculations, since ion transport within the selectivity filter could be rate limiting for ions other than native K(+). This previous work is now significantly extended to the following experimental problems. First, the outward rectification of the J-V curves in K(+) symmetrical solutions is analyzed using a generalized kinetic model. Second, the J-V and g-S curves for NH(4) (+) are obtained and compared with those of other ions (the NH(4) (+) J-V curve is qualitatively different from those of Rb(+) and Tl(+)). Third, the effects of Na(+) block on K(+) and Rb(+) currents through single KcsA channels are studied and the different blocking behavior is related to the values of the translocation rate constants characteristic of ion transport within the filter. Finally, the significantly decreased K(+) conductance caused by mutation of the wild-type channel is also explained in terms of this rate constant. In order to keep the number of model parameters to a minimum, we do not allow the electrical distance (an empirical parameter of kinetic models that controls the exponential voltage dependence of the dissociation rate) to vary with the ionic species. Without introducing the relatively high number of adjustable parameters of more comprehensive site-based models, we show that ion association to the filter is rate controlling at low concentrations, but ion dissociation from the filter and ion transport within the filter could limit conduction at high concentration. Although some experimental data from other authors were included to allow qualitative comparison with model calculations, the absolute values of the effective rate constants obtained are only tentative. However, the relative changes in these constants needed to explain qualitatively the experiments should be of significance.     

Molecular dynamics simulation links conformation of a pore-flanking region to hyperekplexia-related dysfunction of the inhibitory glycine receptor

Inhibitory glycine receptors mediate rapid synaptic inhibition in mammalian spinal cord and brainstem. The previously identified hyperekplexia mutation GLRA1(P250T), located within the intracellular TM1-2 loop of the GlyR alpha1 subunit, results in altered receptor activation and desensitization. Here, elementary steps of ion channel function of alpha1(250) mutants were resolved and shown to correlate with hydropathy and molar volume of residue alpha1(250). Single-channel recordings and rapid activation kinetic studies using laser pulse photolysis showed reduced conductance but similar open probability of alpha1(P250T) mutant channels. Molecular dynamics simulation of a helix-turn-helix motif representing the intracellular TM1-2 domain revealed alterations in backbone conformation, indicating an increased flexibility in these mutants that paralleled changes in elementary steps of channel function. Thus, the architecture of the TM1-2 loop is a critical determinant of ion channel conductance and receptor desensitization.     

The role of spatial dispersion of the dielectric constant of spherical water cavity in the lowering of the free energy of ion transfer to the cavity

Simple analytical expression is derived for the changes in the ion solvation energy W _NE upon its transfer to the center of water cavity with radius R _Cav, surrounded by protein substance with dielectric constant ?_p. In the derivation, nonlocal-electrostatic Poisson equation for the water cavity was solved by using Hildebrandt method called in literature “New Formulation of Nonlocal Electrostatics.” It was shown that for potassium channel with the most open conformation KcsA, at R _Cav = 1.6 nm and the water correlation length Λ = 0.8 nm, the energy W _NE is by 1.25 k _B T less that the resolvation energy calculated by the classical theory with the cavity’s dielectric constant ?_Cav = 78.5. Therefore, the nonlocal-electrostatic effects in the water cavity of the potassium channel facilitate K⁺ transfer over the potential barrier in the channel’s cavity. The lowering of the cavity radius results in the K⁺ sucking up into the channel cavity; the effect is missed in the classical electrostatics.     

Cooperative transport in a potassium ion channel

Our current understanding of ion permeation through the selectivity filter of the KcsA potassium channel is based on the concept of a multi-ion transport mechanism. The details of this concerted movement, however, are not well understood. In the present paper we report on molecular dynamics simulations which provides new insights. It is shown that ion translocation is based on the collective hopping of ions and water molecules which is mediated by the flexible charged carbonyl groups lining the backbone of the pore. In particular, there is strong evidence for pairwise translocations where one ion and one water molecule form a bound state. We suggest a physical explanation of the observed phenomena employing a simple lattice model. It is argued that the water molecules can act as rectifiers during the hopping of ion-water pairs.     

Role of water molecules in the KcsA protein channel by molecular dynamics calculations

Molecular dynamics simulations supported by electrostatic calculations have been conducted on the KcsA channel to determine the role of water molecules in the pore. Starting from the X-ray structure of the KcsA channel in its closed state at 2.0 angstroms resolution, the opening of the pore towards a conformation built on the basis of EPR results is studied. We show that water molecules act as a structural element for the K+ ions inside the filter and the hydrophobic cavity of the channel. In the filter, water tends to enhance the depth of the wells occupied by the K+ ions, while in the cavity there is a strong correlation between the water molecules and the cavity ion. As a consequence, the protein remains very stable in the presence of three K+ ions in the selectivity filter and one in the cavity. The analysis of the dynamics of water molecules in the cavity reveals preferred orientations of the dipoles along the pore axis, and a correlated behavior between this dipole orientation and the displacement of the K+ ion during the gating process.     

Molecular dynamics and continuum electrostatics studies of inactivation in the HERG potassium channel

Fast inactivation of the HERG potassium channel plays a critical role in normal cardiac function. Malfunction of these channels due to either genetic mutations or blockade by drugs leads to cardiac arrhythmias. An unusually long S5-P linker in the outer mouth of HERG is implicated in the fast inactivation mechanism. To examine the role of the S5-P linker in this inactivation mechanism, we study the permeation properties of the open and inactive states of a recent homology model of HERG. This model was constructed using the KcsA potassium channel as a template and contains specific conformations of the S5-P linker in the open and inactive states. We perform molecular dynamics simulations on the HERG model, followed by free energy, structural, and continuum electrostatics calculations. Our free energy calculations lead to selectivity results of the model channel (K+ over Na+) that are different in some respects from those of other potassium channels but consistent with experimental observations. Our structural results show that, in the inactive state, the S5-P linkers move closer to the channel axis, possibly causing a steric hindrance to permeating K+ ions. Our electrostatics calculations reveal, in the inactive state, an electrostatic potential energy barrier of approximately 14 kT at the extracellular pore entrance, again sufficient to stop K+ ion permeation through the pore. These results suggest that a steric and/or electrostatic plug mechanism contributes to inactivation in the HERG homology model.     

Controlled delivery of proteins into bilayer lipid membranes on chip

The study and the exploitation of membrane proteins for drug screening applications requires a controllable and reliable method for their delivery into an artificial suspended membrane platform based on lab-on-a-chip technology. In this work, a polymeric device for forming lipid bilayers suitable for electrophysiology studies and biosensor applications is presented. The chip supports a single bilayer and is configured for controlled protein delivery through on-chip microfluidics. In order to demonstrate the principle of protein delivery, the potassium channel KcsA was reconstituted into proteoliposomes, which were then fused with the suspended bilayer on-chip. Fusion of single proteoliposomes with the membrane was identified electrically. Single channel conductance measurements of KcsA in the on-chip bilayer were recorded and these were compared to previously published data obtained with a conventional planar bilayer system.     

Functional dynamics of ion channels: modulation of proton movement by conformational switches

Detailed comparative studies of proton relay in native and chemically modified gramicidin channels provide a unique opportunity to uncover the structural basis of biological proton transport. The function of ion channels hinges on their ability to provide surrogate solvation in narrow pore filters so as to overcome the dielectric barrier presented by biological membranes. In the potassium channel KcsA and in the cation channel gramicidin, permeant selectivity and mobility are determined by the proteinaceous matrix via hydrogen bonding, charge-dipole, and dipole-dipole interactions. In particular, main-chain carbonyl groups in these pore interiors play an essential role in the solvation of alkali ions and of protons. In this study, molecular dynamics simulations reveal how the translocation of H(+) is controlled by nanosecond conformational transitions exchanging distorted states of the peptidic backbone in the single-file region of a dioxolane-linked analogue of the gramicidin dimer. These results underline the functional role of channel dynamics and provide a mechanism for the modulation of proton currents by fluctuating dipoles.     

Ion current calculations based on three dimensional Poisson-Nernst-Planck theory for a cyclic peptide nanotube

Ion current calculations based on Poisson-Nernst-Planck (PNP) theory are performed for a synthetic cyclic peptide nanotube that consists of eight or ten cyclo[(-L-Trp-D-Leu-)4] embedded in a lipid bilayer membrane to investigate the ion transport properties of the nanotube. To explore systems with arbitrary geometries, three-dimensional PNP theory is implemented using a finite difference method. The influence of dipolar lipid molecules on the ion currents is also examined by turning on or off the charges of the lipid dipoles in dipalmitoylphosphatidylcholine (DPPC). Comparisons between the calculated and experimentally measured ion currents show that the PNP approach agrees well with the measurements at low ion concentrations but overestimates the currents at higher concentrations. Concentration profiles reveal the selectivity of the peptide nanotube to cations, which is attributed to the negatively charged carbonyl oxygens inside the nanotube. The dominant cation and the minimum anion concentrations inside the cyclic peptide nanotube suggest that these cyclic peptide nanotubes can be employed as ion sensors. In the case of the polar DPPC bilayer, smaller currents are obtained in the calculation. The variation of current with polarity of the lipids implies that both polar and nonpolar lipid bilayer membranes can be utilized to regulate ion currents in the peptide nanotube and other ion channels. Strengths and limitations of the PNP theory are also discussed.     

A parallel finite element simulator for ion transport through three‐dimensional ion channel systems

A parallel finite element simulator, ichannel, is developed for ion transport through three‐dimensional ion channel systems that consist of protein and membrane. The coordinates of heavy atoms of the protein are taken from the Protein Data Bank and the membrane is represented as a slab. The simulator contains two components: a parallel adaptive finite element solver for a set of Poisson–Nernst–Planck (PNP) equations that describe the electrodiffusion process of ion transport, and a mesh generation tool chain for ion channel systems, which is an essential component for the finite element computations. The finite element method has advantages in modeling irregular geometries and complex boundary conditions. We have built a tool chain to get the surface and volume mesh for ion channel systems, which consists of a set of mesh generation tools. The adaptive finite element solver in our simulator is implemented using the parallel adaptive finite element package Parallel Hierarchical Grid (PHG) developed by one of the authors, which provides the capability of doing large scale parallel computations with high parallel efficiency and the flexibility of choosing high order elements to achieve high order accuracy. The simulator is applied to a real transmembrane protein, the gramicidin A (gA) channel protein, to calculate the electrostatic potential, ion concentrations and I – V curve, with which both primitive and transformed PNP equations are studied and their numerical performances are compared. To further validate the method, we also apply the simulator to two other ion channel systems, the voltage dependent anion channel (VDAC) and α‐Hemolysin (α‐HL). The simulation results agree well with Brownian dynamics (BD) simulation results and experimental results. Moreover, because ionic finite size effects can be included in PNP model now, we also perform simulations using a size‐modified PNP (SMPNP) model on VDAC and α‐HL. It is shown that the size effects in SMPNP can effectively lead to reduced current in the channel, and the results are closer to BD simulation results. © 2013 Wiley Periodicals, Inc.     

A gate mechanism indicated in the selectivity filter of the potassium channel KscA

Classical molecular dynamics (MD) and non-equilibrium steered molecular dynamics (SMD) simulations were performed on the molecular structure of the potassium channel KcsA using the GROMOS 87 force fields. Our simulations focused on mechanistic and dynamic properties of the permeation of potassium ions through the selectivity filter of the channel. According to the SMD simulations a concerted movement of ions inside the selectivity filter from the cavity to extracellular side depends on the conformation of the peptide linkage between Val76 and Gly77 residues in one subunit of the channel. In SMD simulations, if the carbonyl oxygen of Val76 is positioned toward the ion bound at the S3 site (gate-opened conformation) the net flux of ions through the filter is observed. When the carbonyl oxygen leaped out from the filter (gate-closed conformation), ions were blocked at the S3 site and no flux occurred. A reorientation of the Thr75-Val76 linkage indicated by the CHARMM-based MD simulations performed Berneche and Roux [(2005) Structure 13:591–600; (2000) Biophys J 78:2900–2917] as a concomitant process of the Val76-Gly77 conformational interconversion was not observed in our GROMOS-based MD simulations.     

Steered molecular dynamics simulations of Na+ permeation across the gramicidin A channel

The potential of mean forces (PMF) governing Na+ permeation through gramicidin A (gA) channels with explicit water and membrane was characterized using steered molecular dynamics (SMD) simulations. Constant-force SMD with a steering force parallel to the channel axis revealed at least seven energy wells in each monomer of the channel dimer. Except at the channel dimer interface, each energy well is associated with at least three and at most four backbone carbonyl oxygens and two water oxygens in a pseudo-hexahedral or pseudo-octahedral coordination with the Na+ ion. Repeated constant-velocity SMD by dragging a Na+ ion from each energy well in opposite directions parallel to the channel axis allowed the computation of the PMF across the gA channel, revealing a global minimum corresponding to Na+ binding sites near the entrance of gA at +/-9.3 A from the geometric center of the channel. The effect of volatile anesthetics on the PMF was also analyzed in the presence of halothane molecules. Although the accuracy of the current PMF calculation from SMD simulations is not yet sufficient to quantify the PMF difference with and without anesthetics, the comparison of the overall PMF profiles nevertheless confirms that the anesthetics cause insignificant changes to the structural makeup of the free energy wells along the channel and the overall permeation barrier. On average, the PMF appears less rugged in the outer part of the channel in the presence of anesthetics, consistent with our earlier finding that halothane interaction with anchoring residues makes the gA channel more dynamic. A causal relationship was observed between the reorientation of the coordinating backbone carbonyl oxygen and Na+ transit from one energy well to another, suggesting the possibility that even minute changes in the conformation of pore-lining residues due to dynamic motion could be sufficient to trigger the ion permeation. Because some of the carbonyl oxygens contribute to Na+ coordination in two adjacent energy wells, our SMD results reveal that the atomic picture of ion "hopping" through a gA channel actually involves a Na+ ion being carried in a relay by the coordinating oxygens from one energy well to the next. Steered molecular dynamics complements other computational approaches as an attractive means for the atomistic interpretation of experimental permeation studies.     

Effect of Protein Dimerization on Ion Conductivity of Gramicidin A Channel Studied Using Polarizable Force Field

In studies of ion channel systems, due to the huge computational cost of polarizable force fields, classical force fields remain the most widely used for a long time. In this work, we used the AMOEBA polarizable atomic multipole force field in enhanced sampling simulations of single-channel gramicidin A (gA) and double-channel gA systems and investigated its reliability in characterizing ion-transport properties of the gA ion channel under dimerization. The influence of gA dimerization on the permeation of potassium and sodium ions through the channel was described in terms of conductance, diffusion coefficient, and free energy profile. Results from the polarizable force field simulations show that the conductance of potassium and sodium ions passing through the single- and double-channel agrees well with experimental values. Further data analysis reveals that the molecular mechanism of protein dimerization affects the ion-transport properties of gA channels, i.e., protein dimerization accelerates the permeation of potassium and sodium ions passing through the double-channel by adjusting the environment around gA protein (the distribution of phospholipid head groups, ions outside the channel, and bulk water), rather than directly adjusting the conformation of gA protein.     

Effect of channel block on the collective spiking activity of coupled stochastic Hodgkin-Huxley neurons

Toxins, such as tetraethylammonium (TEA) and tetrodotoxin (TTX), can make potassium or sodium ion channels poisoned, respectively, and hence reduce the number of working ion channels and lead to the diminishment of conductance. In this paper, we have studied by numerical simulations the effects of sodium and potassium ion channel poisoning on the collective spiking activity of an array of coupled stochastic Hodgkin-Huxley (HH) neurons. It is found for a given number of neurons sodium or potas- sium ion channel block can either enhance or reduce the collective spiking regularity, depending on the membrane patch size. For a given smaller or larger patch size, potassium and sodium ion channel block can reduce or enhance the collective spiking regularity, but they have different patch size ranges for the transformation. This result shows that sodium or potassium ion channel block might have dif- ferent effects on the collective spiking activity in coupled HH neurons from the effects for a single neuron, which represents the interplay among the diminishment of maximal conductance and the in- crease of channel noise strength due to the channel blocks, as well as the bi-directional coupling be- tween the neurons.     

Excluded volume effect for large and small solutes in water

The cavitation effect, i.e., the process of the creation of a void of excluded volume in bulk solvent (a cavity), is considered. The cavitation free energy is treated in terms of the information theory (IT) approach [Hummer, G.; Garde, S.; Garcia, A. E.; Paulaitis, M. E.; Pratt, L. R. J. Phys. Chem. B 1998, 102, 10469]. The binomial cell model suggested earlier is applied as the IT default distribution p(m) for the number m of solute (water) particles occupying a cavity of given size and shape. In the present work, this model is extended to cover the entire range of cavity size between small ordinary molecular solutes and bulky biomolecular structures. The resulting distribution consists of two binomial peaks responsible for producing the free energy contributions, which are proportional respectively to the volume and to the surface area of a cavity. The surface peak dominates in the large cavity limit, when the two peaks are well separated. The volume effects become decisive in the opposite limit of small cavities, when the two peaks reduce to a single-peak distribution as considered in our earlier work. With a proper interpolation procedure connecting these two regimes, the MC simulation results for model spherical solutes with radii increasing up to R = 10 A [Huang, D. H.; Geissler, P. L.; Chandler, D. J. Phys. Chem. B 2001, 105, 6704] are well reproduced. The large cavity limit conforms to macroscopic properties of bulk water solvent, such as surface tension, isothermal compressibility and Tolman length. The computations are extended to include nonspherical solutes (hydrocarbons C1-C6).     

Charge density distributions derived from smoothed electrostatic potential functions: design of protein reduced point charge models

To generate reduced point charge models of proteins, we developed an original approach to hierarchically locate extrema in charge density distribution functions built from the Poisson equation applied to smoothed molecular electrostatic potential (MEP) functions. A charge fitting program was used to assign charge values to the so-obtained reduced representations. In continuation to a previous work, the Amber99 force field was selected. To easily generate reduced point charge models for protein structures, a library of amino acid templates was designed. Applications to four small peptides, a set of 53 protein structures, and four KcsA ion channel models, are presented. Electrostatic potential and solvation free energy values generated by the reduced models are compared with the corresponding values obtained using the original set of atomic charges. Results are in closer agreement with the original all-atom electrostatic properties than those obtained with a previous reduced model that was directly built from the smoothed MEP functions [Leherte and Vercauteren in J Chem Theory Comput 5:3279–3298, 2009].     

Solid-state NMR spectroscopy applied to a chimeric potassium channel in lipid bilayers

We show that solid-state NMR can be used to investigate the structure and dynamics of a chimeric potassium channel, KcsA-Kv1.3, in lipid bilayers. Sequential resonance assignments were obtained using a combination of (15)N- (13)C and (13)C- (13)C correlation experiments conducted on fully labeled and reverse-labeled as well as C-terminally truncated samples. Comparison of our results with those from X-ray crystallography and solution-state NMR in micelles on the closely related KcsA K (+) channel provides insight into the mechanism of ion channel selectivity and underlines the important role of the lipid environment for membrane protein structure and function.