Dynamics of K+ ion conduction through Kv1.2

Modeling the binding of three toxins to the voltage-gated potassium channel (Kv1.3)

The conduction properties of the voltage-gated potassium channel Kv1.3 and its modes of interaction with several polypeptide venoms are examined using Brownian dynamics simulations and molecular dynamics calculations. Employing an open-state homology model of Kv1.3, we first determine current-voltage and current-concentration curves and ascertain that simulated results accord with experimental measurements. We then investigate, using a molecular docking method and molecular dynamics simulations, the complexes formed between the Kv1.3 channel and several Kv-specific polypeptide toxins that are known to interfere with the conducting mechanisms of several classes of voltage-gated K(+) channels. The depths of potential of mean force encountered by charybdotoxin, α-KTx3.7 (also known as OSK1) and ShK are, respectively, -19, -27, and -25 kT. The dissociation constants calculated from the profiles of potential of mean force correspond closely to the experimentally determined values. We pinpoint the residues in the toxins and the channel that are critical for the formation of the stable venom-channel complexes.

Computer Simulations of Voltage-Gated Cation Channels

The relentless growth in computational power has seen increasing applications of molecular dynamics (MD) simulation to the study of membrane proteins in realistic membrane environments, which include explicit membrane lipids, water and ions. The concomitant increasing availability of membrane protein structures for ion channels, and transporters -- to name just two examples -- has stimulated many of these MD studies. In the case of voltage-gated cation channels (VGCCs) recent computational works have focused on ion-conduction and gating mechanisms, along with their regulation by agonist/antagonist ligands. The information garnered from these computational studies is largely inaccessible to experiment and is crucial for understanding the interplay between the structure and function as well as providing new directions for experiments. This article highlights recent advances in probing the structure and function of potassium channels and offers a perspective on the challenges likely to arise in making analogous progress in characterizing sodium channels.

Theory and simulation of ion conduction in the pentameric GLIC channel

GLIC is a bacterial member of the large family of pentameric ligand-gated ion channels. To study ion conduction through GLIC and other membrane channels, we combine the one-dimensional potential of mean force for ion passage with a Smoluchowski diffusion model, making it possible to calculate single-channel conductance in the regime of low ion concentrations from all-atom molecular dynamics (MD) simulations. We then perform MD simulations to examine sodium ion conduction through the GLIC transmembrane pore in two systems with different bulk ion concentrations. The ion potentials of mean force, calculated from umbrella sampling simulations with Hamiltonian replica exchange, reveal a major barrier at the hydrophobic constriction of the pore. The relevance of this barrier for ion transport is confirmed by a committor function that rises sharply in the barrier region. From the free evolution of Na(+) ions starting at the barrier top, we estimate the effective diffusion coefficient in the barrier region, and subsequently calculate the conductance of the pore. The resulting diffusivity compares well with the position-dependent ion diffusion coefficient obtained from restrained simulations. The ion conductance obtained from the diffusion model agrees with the value determined via a reactive-flux rate calculation. Our results show that the conformation in the GLIC crystal structure, with an estimated conductance of ~1 picosiemens at 140 mM ion concentration, is consistent with a physiologically open state of the channel.

Molecular dynamics simulations of the TrkH membrane protein

TrkH is a transmembrane protein that mediates uptake of K(+) through the cell membrane. Despite the recent determination of its crystallographic structure, the nature of the permeation mechanism is still unknown, that is, whether K(+) ions move across TrkH by active transport or passive diffusion. Here, molecular dynamics simulations and the umbrella sampling technique have been employed to shed light on this question. The existence of binding site S3 and two alternative binding sites have been characterized. Analysis of the coordination number renders values that are almost constant, with a full contribution from the carbonyls of the protein only at S3. This observation contrasts with observations of K(+) channels, where the contribution of the protein to the coordination number is roughly constant in all four binding sites. An intramembrane loop is found immediately after the selectivity filter at the intracellular side of the protein, which obstructs the permeation pathway, and this is reflected in the magnitude of the energy barriers.

Mechanism of ion permeation and selectivity in a voltage gated sodium channel

The rapid and selective transport of Na(+) through sodium channels is essential for initiating action potentials within excitable cells. However, an understanding of how these channels discriminate between different ion types and how ions permeate the pore has remained elusive. Using the recently published crystal structure of a prokaryotic sodium channel from Arcobacter butzleri, we are able to determine the steps involved in ion transport and to pinpoint the location and likely mechanism used to discriminate between Na(+) and K(+). Na(+) conduction is shown to involve the loosely coupled "knock-on" movement of two solvated ions. Selectivity arises due to the inability of K(+) to fit between a plane of glutamate residues with the preferred solvation geometry that involves water molecules bridging between the ion and carboxylate groups. These mechanisms are different to those described for K(+) channels, highlighting the importance of developing a separate mechanistic understanding of Na(+) and Ca(2+) channels.

Counting ion and water molecules in a streaming file through the open-filter structure of the K channel

The mechanisms underlying the selective permeation of ions through channel molecules are a fundamental issue related to understanding how neurons exert their functions. The "knock-on" mechanism, in which multiple ions in the selectivity filter are hit by an incoming ion, is one of the leading concepts. This mechanism has been supported by crystallographic studies that demonstrated ion distribution in the structure of the Streptomyces lividans (KcsA) potassium channel. These still pictures under equilibrium conditions, however, do not provide a snapshot of the actual, ongoing permeation processes. To understand the dynamics of permeation, we determined the ratio of the ion and water flow [the water-ion coupling ratio (CR(w-i))] through the KcsA channel by measuring the streaming potential (V(stream)) electrophysiologically. The V(stream) value was converted to the CR(w-i) value, which reveals how individual ion and water molecules are queued in the narrow and short filter during permeation. At high K(+) concentrations, the CR(w-i) value was 1.0, indicating that turnover between the alternating ion and water arrays occurs in a single-file manner. At low K(+), the CR(w-i) value was increased to a point over 2.2, suggesting that the filter contained mostly one ion at a time. These average behaviors of permeation were kinetically analyzed for a more detailed understanding of the permeation process. Here, we envisioned the permeation as queues of ion and water molecules and sequential transitions between different patterns of arrays. Under physiological conditions, we predicted that the knock-on mechanism may not be predominant.

On the selective ion binding hypothesis for potassium channels

The mechanism by which K(+) channels select for K(+) over Na(+) ions has been debated for the better part of a century. The prevailing view is that K(+) channels contain highly conserved sites that selectively bind K(+) over Na(+) ions through optimal coordination. We demonstrate that a series of alternating sites within the KcsA channel selectivity filter exists, which are thermodynamically selective for either K(+) (cage made from two planes of oxygen atoms) or Na(+) ions (a single plane of four oxygen atoms). By combining Bennett free energy perturbation calculations with umbrella sampling, we show that when K(+) and Na(+) are both permitted to move into their preferred positions, the thermodynamic preference for K(+) over Na(+) is significantly reduced throughout the entire selectivity filter. We offer a rationale for experimental measures of thermodynamic preference for K(+) over Na(+) from Ba(2+) blocking data, by demonstrating that the presence of Ba(2+) ions exaggerates K(+) over Na(+) thermodynamic stability due to the different binding locations of these ions. These studies reveal that K(+) channel selectivity may not be associated with the thermodynamics of ions in crystallographic K(+) binding sites, but requires consideration of the kinetic barriers associated with the different multi-ion permeation mechanisms.

Constant electric field simulations of the membrane potential illustrated with simple systems

Advances in modern computational methods and technology make it possible to carry out extensive molecular dynamics simulations of complex membrane proteins based on detailed atomic models. The ultimate goal of such detailed simulations is to produce trajectories in which the behavior of the system is as realistic as possible. A critical aspect that requires consideration in the case of biological membrane systems is the existence of a net electric potential difference across the membrane. For meaningful computations, it is important to have well validated methodologies for incorporating the latter in molecular dynamics simulations. A widely used treatment of the membrane potential in molecular dynamics consists of applying an external uniform electric field E perpendicular to the membrane. The field acts on all charged particles throughout the simulated system, and the resulting applied membrane potential V is equal to the applied electric field times the length of the periodic cell in the direction perpendicular to the membrane. A series of test simulations based on simple membrane-slab models are carried out to clarify the consequences of the applied field. These illustrative tests demonstrate that the constant-field method is a simple and valid approach for accounting for the membrane potential in molecular dynamics studies of biomolecular systems. This article is part of a Special Issue entitled: Membrane protein structure and function.

A permeation theory for single-file ion channels: one- and two-step models

How many steps are required to model permeation through ion channels? This question is investigated by comparing one- and two-step models of permeation with experiment and MD simulation for the first time. In recent MD simulations, the observed permeation mechanism was identified as resembling a Hodgkin and Keynes knock-on mechanism with one voltage-dependent rate-determining step [Jensen et al., PNAS 107, 5833 (2010)]. These previously published simulation data are fitted to a one-step knock-on model that successfully explains the highly non-Ohmic current-voltage curve observed in the simulation. However, these predictions (and the simulations upon which they are based) are not representative of real channel behavior, which is typically Ohmic at low voltages. A two-step association/dissociation (A/D) model is then compared with experiment for the first time. This two-parameter model is shown to be remarkably consistent with previously published permeation experiments through the MaxiK potassium channel over a wide range of concentrations and positive voltages. The A/D model also provides a first-order explanation of permeation through the Shaker potassium channel, but it does not explain the asymmetry observed experimentally. To address this, a new asymmetric variant of the A/D model is developed using the present theoretical framework. It includes a third parameter that represents the value of the "permeation coordinate" (fractional electric potential energy) corresponding to the triply occupied state n of the channel. This asymmetric A/D model is fitted to published permeation data through the Shaker potassium channel at physiological concentrations, and it successfully predicts qualitative changes in the negative current-voltage data (including a transition to super-Ohmic behavior) based solely on a fit to positive-voltage data (that appear linear). The A/D model appears to be qualitatively consistent with a large group of published MD simulations, but no quantitative comparison has yet been made. The A/D model makes a network of predictions for how the elementary steps and the channel occupancy vary with both concentration and voltage. In addition, the proposed theoretical framework suggests a new way of plotting the energetics of the simulated system using a one-dimensional permeation coordinate that uses electric potential energy as a metric for the net fractional progress through the permeation mechanism. This approach has the potential to provide a quantitative connection between atomistic simulations and permeation experiments for the first time.

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.

Energetics of double-ion occupancy in the gramicidin A channel

To understand the energetics of double-ion occupancy in gramicidin A (gA) channels, the 2D potential of mean force (PMF) is calculated for two ions at different positions along the channel axis. The cross sections of this 2D PMF are compared with available one-ion PMFs to highlight the effect of one ion on the permeation dynamics of the other. It is found that, if the first ion stays on one side in the channel, the second ion has to pass over an additional barrier to move into the outer binding site. At the same time, both outer and inner binding sites for the second ion become shallower than those in the one-ion PMF. The calculated ion-ion repulsion for a doubly occupied channel is about 2 kcal/mol, in good agreement with previous experimental estimates. The number of water molecules inside the channel and their dipole moment are calculated to interpret the energetics of double-ion occupancy. As the first ion moves into the outer binding site and then further into the channel, the oxygen atoms of the single-file water column in the channel are oriented to point toward the ion. The observed dipole moment distribution of a singly occupied channel has only one sharp peak, and the water alignment is essentially perfect once the ion is in the inner binding site. For this reason, there is an energy penalty to accommodate a second ion at the opposite end of the channel.

Cycle flux algebra for ion and water flux through the KcsA channel single-file pore links microscopic trajectories and macroscopic observables

In narrow pore ion channels, ions and water molecules diffuse in a single-file manner and cannot pass each other. Under such constraints, ion and water fluxes are coupled, leading to experimentally observable phenomena such as the streaming potential. Analysis of this coupled flux would provide unprecedented insights into the mechanism of permeation. In this study, ion and water permeation through the KcsA potassium channel was the focus, for which an eight-state discrete-state Markov model has been proposed based on the crystal structure, exhibiting four ion-binding sites. Random transitions on the model lead to the generation of the net flux. Here we introduced the concept of cycle flux to derive exact solutions of experimental observables from the permeation model. There are multiple cyclic paths on the model, and random transitions complete the cycles. The rate of cycle completion is called the cycle flux. The net flux is generated by a combination of cyclic paths with their own cycle flux. T.L. Hill developed a graphical method of exact solutions for the cycle flux. This method was extended to calculate one-way cycle fluxes of the KcsA channel. By assigning the stoichiometric numbers for ion and water transfer to each cycle, we established a method to calculate the water-ion coupling ratio (CR(w-i)) through cycle flux algebra. These calculations predicted that CR(w-i) would increase at low potassium concentrations. One envisions an intuitive picture of permeation as random transitions among cyclic paths, and the relative contributions of the cycle fluxes afford experimental observables.

Structural models of TREK channels and their gating mechanism

Mechanosensitive TREK channels belong to the family of K2P channels, a family of widely distributed, well modulated channels that uniquely have two similar or identical subunits, each with two TM1-P-TM2 motifs. Our goal is to build viable structural models of TREK channels, as representatives of K2P channels family. The structures available to be used as templates belong to the 2TM channels superfamily. These have low sequence similarity and different structural features: four symmetrically arranged subunits, each having one TM1-P-TM2 motif. Our model building strategy used two subunits of the template (KcsA) to build one subunit of the target (TREK-1). Our models of the Closed channel were adjusted to differ substantially from those of the template, e.g., TM2 of the 2nd repeat is near the axis of the pore whereas TM2 of the 1st repeat is far from the axis. Segments linking the two repeats and immediately following the last TM segment were modeled ab initio as α-helices based on helical periodicities of hydrophobic and hydrophilic residues, highly conserved and poorly conserved residues, and statistically related positions from multiple sequence alignments. The models were further refined by two-fold symmetry-constrained MD simulations using a protocol we developed previously. We also built models of the Open state and suggest a possible tension-activated gating mechanism characterized by helical motion with two-fold symmetry. Our models are consistent with deletion/truncation mutagenesis and thermodynamic analysis of gating described in the accompanying paper.

Pore opening and closing of a pentameric ligand-gated ion channel

Nerve signaling in humans and chemical sensing in bacteria both rely on the controlled opening and closing of the ion-conducting pore in pentameric ligand-gated ion channels. With the help of a multiscale simulation approach that combines mixed elastic network model calculations with molecular dynamics simulations, we study the opening and closing of the pore in Gloeobacter violaceus channel GLIC at atomic resolution. In our simulations of the GLIC transmembrane domain, we first verify that the two endpoints of the transition are open and closed to sodium ion conduction, respectively. We then show that a two-stage tilting of the pore-lining helices induces cooperative drying and iris-like closing of the channel pore. From the free energy profile of the gating transition and from unrestrained simulations, we conclude that the pore of the isolated GLIC transmembrane domain closes spontaneously. The mechanical work of opening the pore is performed primarily on the M2-M3 loop. Strong interactions of this short and conserved loop with the extracellular domain are therefore crucial to couple ligand binding to channel opening.

Molecular control of ionic conduction in polymer nanopores

Polymeric nanopores show unique transport properties and have attracted a great deal of scientific interest as a test system to study ionic and molecular transport at the nanoscale. By means of all-atom molecular dynamics, we simulated the ion dynamics inside polymeric polyethylene terephthalate nanopores. For this purpose, we established a protocol to assemble atomic models of polymeric material into which we sculpted a nanopore model with the key features of experimental devices, namely a conical geometry and a negative surface charge density. Molecular dynamics simulations of ion currents through the pore show that the protonation state of the carboxyl group of exposed residues have a considerable effect on ion selectivity, by affecting ionic densities and electrostatic potentials inside the nanopores. The role of high concentrations of Ca2+ ions was investigated in detail.

Deciphering ionic current signatures of DNA transport through a nanopore

Within just a decade from the pioneering work demonstrating the utility of nanopores for molecular sensing, nanopores have emerged as versatile systems for single-molecule manipulation and analysis. In a typical setup, a gradient of the electrostatic potential captures charged solutes from the solution and forces them to move through a single nanopore, across an otherwise impermeable membrane. The ionic current blockades resulting from the presence of a solute in a nanopore can reveal the type of the solute, for example, the nucleotide makeup of a DNA strand. Despite great success, the microscopic mechanisms underlying the functionality of such stochastic sensors remain largely unknown, as it is not currently possible to characterize the microscopic conformations of single biomolecules directly in a nanopore and thereby unequivocally establish the causal relationship between the observables and the microscopic events. Such a relationship can be determined using molecular dynamics-a computational method that can accurately predict the time evolution of a molecular system starting from a given microscopic state. This article describes recent applications of this method to the process of DNA transport through biological and synthetic nanopores.

Principles of conduction and hydrophobic gating in K+ channels

We present the first atomic-resolution observations of permeation and gating in a K(+) channel, based on molecular dynamics simulations of the Kv1.2 pore domain. Analysis of hundreds of simulated permeation events revealed a detailed conduction mechanism, resembling the Hodgkin-Keynes "knock-on" model, in which translocation of two selectivity filter-bound ions is driven by a third ion; formation of this knock-on intermediate is rate determining. In addition, at reverse or zero voltages, we observed pore closure by a novel "hydrophobic gating" mechanism: A dewetting transition of the hydrophobic pore cavity-fastest when K(+) was not bound in selectivity filter sites nearest the cavity-caused the open, conducting pore to collapse into a closed, nonconducting conformation. Such pore closure corroborates the idea that voltage sensors can act to prevent pore collapse into the intrinsically more stable, closed conformation, and it further suggests that molecular-scale dewetting facilitates a specific biological function: K(+) channel gating. Existing experimental data support our hypothesis that hydrophobic gating may be a fundamental principle underlying the gating of voltage-sensitive K(+) channels. We suggest that hydrophobic gating explains, in part, why diverse ion channels conserve hydrophobic pore cavities, and we speculate that modulation of cavity hydration could enable structural determination of both open and closed channels.

Symmetry-restrained molecular dynamics simulations improve homology models of potassium channels

Most crystallized homo-oligomeric ion channels are highly symmetric, which dramatically decreases conformational space and facilitates building homology models (HMs). However, in molecular dynamics (MD) simulations channels deviate from ideal symmetry and accumulate thermal defects, which complicate the refinement of HMs using MD. In this work we evaluate the ability of symmetry constrained MD simulations to improve HMs accuracy, using an approach conceptually similar to Critical Assessment of techniques for protein Structure Prediction (CASP) competition: build HMs of channels with known structure and evaluate the efficiency of proposed methods in improving HMs accuracy (measured as deviation from experimental structure). Results indicate that unrestrained MD does not improve the accuracy of HMs, instantaneous symmetrization improves accuracy but not stability of HMs during subsequent unrestrained MD, while gradually imposing symmetry constraints improves both accuracy (by 5-50%) and stability of HMs. Moreover, accuracy and stability are strongly correlated, making stability a reliable criterion in predicting the accuracy of new HMs. Proteins 2010. (c) 2009 Wiley-Liss, Inc.

Importance of the peptide backbone description in modeling the selectivity filter in potassium channels

A dihedral energy correction (CMAP) term has been recently included in the CHARMM force field to obtain a more accurate description of the peptide backbone. Its importance in improving dynamical properties of proteins and preserving their stability in long molecular-dynamics simulations has been established for several globular proteins. Here we investigate its role in maintaining the structure and function of two potassium channels, Shaker K(v)1.2 and KcsA, by performing molecular-dynamics simulations with and without the CMAP correction in otherwise identical systems. We show that without CMAP, it is not possible to maintain the experimentally observed orientations of the carbonyl groups in the selectivity filter in Shaker, and the channel loses its selectivity property. In the case of KcsA, the channel retains some selectivity even without CMAP because the carbonyl orientations are relatively better preserved compared to Shaker.

Salt bridges in the miniature viral channel Kcv are important for function

The viral potassium channel Kcv comprises only 94 amino acids, which represent the pore module of more complex K(+) channels. As for Kir-type channels, Kcv also has a short N-terminal helix exposed to the cytoplasm, upstream of the first transmembrane domain. Here we show that this helix is relevant for Kcv function. The presence of charged amino acids, which form dynamic inter- and intra-subunit salt bridges is crucial. Electrophysiological measurements, yeast rescue experiments and molecular dynamics simulations show that mutants in which the critical salt bridge formation is impaired have no or reduced channel activity. We conclude that these salt bridges destabilise the complexation of K(+) ions by negative charges on the inner transmembrane domain at the entrance into the cavity. This feature facilitates a continuous and coordinated transfer of ions between the cavity and the cytoplasm for channels without the canonical bundle crossing.

Dynamics, energetics, and selectivity of the low-K+ KcsA channel structure

Potassium channels are a diverse family of integral membrane proteins through which K(+) can pass selectively. There is ongoing debate about the nature of conformational changes associated with the opening/closing and conductive/nonconductive states of potassium channels. The channels partly exert their function by varying their conductance through a mechanism known as C-type inactivation. Shortly after the activation of K(+) channels, their selectivity filter stops conducting ions at a rate that depends on various stimuli. The molecular mechanism of C-type inactivation has not been fully understood yet. However, the X-ray structure of the KcsA channel obtained in the presence of low K(+) concentration is thought to be representative of a K(+) channel in the C-type inactivated state. Here, extensive, fully atomistic molecular dynamics and free-energy simulations of the low-K(+) KcsA structure in an explicit lipid bilayer are performed to evaluate the stability of this structure and the selectivity of its binding sites. We find that the low-K(+) KcsA structure is stable on the timescale of the molecular dynamics simulations performed, and that ions preferably remain in S1 and S4. In the absence of ions, the selectivity filter evolves toward an asymmetric architecture, as already observed in other computations of the high-K(+) structure of KcsA and KirBac. The low-K(+) KcsA structure is not permeable by Na(+), K(+), or Rb(+), and the selectivity of its binding sites is different from that of the high-K(+) structure.

Model development for the viral Kcv potassium channel

A computational model for the open state of the short viral Kcv potassium channel was created and tested based on homology modeling and extensive molecular-dynamics simulation in a membrane environment. Particular attention was paid to the structure of the highly flexible N-terminal region and to the protonation state of membrane-exposed lysine residues. Data from various experimental sources, NMR spectroscopy, and electrophysiology, as well as results from three-dimensional reference interaction site model integral equation theory were taken into account to select the most reasonable model among possible variants. The final model exhibits spontaneous ion transitions across the complete pore, with and without application of an external field. The nonequilibrium transport events could be induced reproducibly without abnormally large driving potential and without the need to place ions artificially at certain key positions along the transition path. The transport mechanism through the filter region corresponds to the classic view of single-file motion, which in our case is coupled to frequent exchange of ions between the innermost filter position and the cavity.

Intrinsic Free Energy of the Conformational Transition of the KcsA Signature Peptide from Conducting to Nonconducting State

We explore a conformational transition of the TATTVGYG signature peptide of the KcsA ion selectivity filter and its GYG to AYA mutant from the conducting α-strand state into the nonconducting pII-like state using a novel technique for multidimensional optimization of transition path ensembles and free energy calculations. We find that the wild type peptide, unlike the mutant, intrinsically favors the conducting state due to G77 backbone propensities and additional hydrophobic interaction between the V76 and Y78 side chains in water. The molecular mechanical free energy profiles in explicit water are in very good agreement with the corresponding adiabatic energies from the Generalized Born Molecular Volume (GBMV) implicit solvent model. However comparisons of the energies to higher level B3LYP/6-31G(d) Density Functional Theory calculations with Polarizable Continuum Model (PCM) suggest that the nonconducting state might be more favorable than predicted by molecular mechanics simulations. By extrapolating the single peptide results to the tetrameric channel, we propose a novel hypothesis for the ion selectivity mechanism.

The membrane potential and its representation by a constant electric field in computer simulations

A theoretical framework is elaborated to account for the effect of a transmembrane potential in computer simulations. It is shown that a simulation with a constant external electric field applied in the direction normal to the membrane is equivalent to the influence of surrounding infinite baths maintained to a voltage difference via ion-exchanging electrodes connected to an electromotive force. It is also shown that the linearly-weighted displacement charge within the simulation system tracks the net flow of charge through the external circuit comprising the electromotive force and the electrodes. Using a statistical mechanical reduction of the degrees of freedom of the external system, three distinct theoretical routes are formulated and examined for the purpose of characterizing the free energy of a protein embedded in a membrane that is submitted to a voltage difference. The W-route is constructed from the variations in the voltage-dependent potential of mean force along a reaction path connecting two conformations of the protein. The Q-route is based on the average displacement charge as a function of the conformation of the protein. Finally, the G-route considers the relative charging free energy of specific residues, with and without applied membrane potentials. The theoretical formulation is illustrated with a simple model of an ion crossing a vacuum slab surrounded by two aqueous bulk phases and with a fragment of the voltage-sensor of the KvAP potassium channel.

Conformational changes in the selectivity filter of the open-state KcsA channel: an energy minimization study

Potassium channels switch between closed and open conformations and selectively conduct K(+) ions. There are at least two gates. The TM2 bundle at the intracellular site is the primary gate of KcsA, and rearrangements at the selectivity filter (SF) act as the second gate. The SF blocks ion flow via an inactivation process similar to C-type inactivation of voltage-gated K(+) channels. We recently generated the open-state conformation of the KcsA channel. We found no major, possibly inactivating, structural changes in the SF associated with this massive inner-pore rearrangement, which suggests that the gates might act independently. Here we energy-minimize the open state of wild-type and mutant KcsA, validating in silico structures of energy-minimized SFs by comparison with crystallographic structures, and use these data to gain insight into how mutation, ion depletion, and K(+) to Na(+) substitution influence SF conformation. Both E71 or D80 protonations/mutations and the presence/absence of protein-buried water molecule(s) modify the H-bonding network stabilizing the P-loops, spawning numerous SF conformations. We find that the inactivated state corresponds to conformations with a partially unoccupied or an entirely empty SF. These structures, involving modifications in all four P-loops, are stabilized by H-bonds between amide H and carbonyl O atoms from adjacent P-loops, which block ion passage. The inner portions of the P-loops are more rigid than the outer parts. Changes are localized to the outer binding sites, with innermost site S4 persisting in the inactivated state. Strong binding by Na(+) locally contracts the SF around Na(+), releasing ligands that do not participate in Na(+) coordination, and occluding the permeation pathway. K(+) selectivity primarily appears to arise from the inability of the SF to completely dehydrate Na(+) ions due to basic structural differences between liquid water and the "quasi-liquid" SF matrix.

Double bilayers and transmembrane gradients: a molecular dynamics study of a highly charged peptide

The position and extent of movement of a charged peptide within a membrane bilayer provides much controversy. In our study, we have examined the nature of the highly charged helix-turn-helix motif (S3b and S4) to address how a highly charged peptide is stabilized within a bilayer in the presence of various transmembrane electrical potentials. Our double-bilayer simulation results show how the variation of the salt concentrations between the inner and outer bath establishes a transmembrane potential. Our results also show that important features of the peptide affected by changes in electrical potential are the center of mass depth, the swivel/kink degrees of conformation, and the hydrogen-bonding patterns. As the voltage gradient across the bilayer increased, the center of mass of the peptide shifted in a direction toward the outer bath. The peptide also has a higher percent helical content and the swivel/kink conformation is more rigid for nonpolarized systems where no voltage drop occurred between salt baths. Our results also provide some suggestions for how this domain may be affected by environmental changes as part of the voltage sensor in a K-channel.

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.

Thermal stability of the K+ channel tetramer: cation interactions and the conserved threonine residue at the innermost site (S4) of the KcsA selectivity filter

The selectivity filter of most K+ channels contains a highly conserved Thr residue that uniquely forms the S4 binding site for K+ by dual coordination with the backbone carbonyl oxygen and side chain hydroxyl of the same residue. This study examines the effect of mutations of Thr75 in the S4 site of theKcsA K+ channel on the cation dependence of the thermal stability of the tetramer, a phenomenon that reflects the structural role of cations in the filter. Conservative mutations of Thr75 destabilize the tetramer and alter its temperature dependence. Replacement of Thr with Ala or Cys lowers the apparent affinity ofK+, Rb+, and Cs+ for tetramer stabilization by factors ranging from 4- to 14-fold. These same mutations lower the apparent affinity of Ba2+ by approximately 10(3)- or approximately 10(4)-fold for Ala and Cys substitution, respectively,consistent with the known preference of the S4 site for Ba2+. In contrast, substitution of Ala or Cys at T75 anomalously enhances the ability of Na+ to stabilize the tetramer, suggesting that the native Thr residue at S4 is important for ultrahigh K+/Na+ selectivity of K+ channel pores. Elevated temperature orCu2+ cation catalyzes formation of covalent dimers of the T75C mutant of KcsA via formation of disulfide bonds between Cys residues of adjacent subunits. Thiophilic cations such as Hg2+ and Ag+ specifically protect the T75C tetramer against heat-induced dimer formation, demonstrating the contribution of cation interactions to tetramer stability in a channel with a non-native S4 site engineered to bind foreign cations.

Saturation and microsecond gating of current indicate depletion-induced instability of the MaxiK selectivity filter

Patch clamp experiments on single MaxiK channels expressed in HEK293 cells were performed with a high temporal resolution (50-kHz filter) in symmetrical solutions with 50, 150, or 400 mM KCl and 2.5 mM CaCl(2) and 2.5 mM MgCl(2). At membrane potentials >+100 mV, the single-channel current showed a negative slope resistance, concomitantly with a flickery block, which was not influenced by Ca(2+) or Mg(2+). The analysis of the amplitude histograms by beta distributions revealed that current in this voltage range was reduced by two effects: rate limitation at the cytosolic side of the pore and gating with rate constants 10-20-fold higher than the cutoff frequency of the filter (i.e., dwell times in the microsecond range). The data were analyzed in terms of a model that postulates a coupling between both effects; if the voltage over the selectivity filter withdraws ions from the cavity at a higher rate than that of refilling from the cytosol, the selectivity filter becomes instable because of ion depletion, and current is interrupted by the resulting flickering. The fit of the IV curves revealed a characteristic voltage of 35 mV. In contrast, the voltage dependence of the gating factor R, i.e., the ratio between true and apparent single-channel current, could be fitted by exponentials with a characteristic voltage of 60 mV, suggesting that only part of the transmembrane potential is felt by the flux through the selectivity filter.

Conduction properties of KcsA measured using brownian dynamics with flexible carbonyl groups in the selectivity filter

In the narrow segment of an ion conducting pathway, it is likely that a permeating ion influences the positions of the nearby atoms that carry partial or full electronic charges. Here we introduce a method of incorporating the motion of charged atoms lining the pore into Brownian dynamics simulations of ion conduction. The movements of the carbonyl groups in the selectivity filter of the KcsA channel are calculated explicitly, allowing their bond lengths, bond angles, and dihedral angels to change in response to the forces acting upon them. By systematically changing the coefficients of bond stretching and of angle bending, the carbon and oxygen atoms can be made to fluctuate from their fixed positions by varying mean distances. We show that incorporating carbonyl motion in this way does not alter the mechanism of ion conduction and only has a small influence on the computed current. The slope conductance of the channel increases by approximately 25% when the root mean-square fluctuations of the carbonyl groups are increased from 0.01 to 0.61 A. The energy profiles and the number of resident ions in the channel remain unchanged. The method we utilized here can be extended to allow the movement of glutamate or aspartate side chains lining the selectivity filters of other ionic channels.