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.     

Mixed modes in opening of KcsA potassium channel from a targeted molecular dynamics simulation

Potassium channels conduct K⁺ flow selectively across the membrane through a central pore. During a process called gating, the potassium channels undergo a conformational change that opens or closes the ion-conducting pore. The potassium channel KcsA has been structurally determined in its closed state. However, the dynamic mechanism of the gating transition of the KcsA channel is still being investigated. Here, a targeted molecular dynamics simulation up to 150 ns is performed to investigate the detailed opening process of the KcsA channel with an open Kv1.2 structure serving as the target. The channel arrived at a self-determined quasi-stable state within 60 ns. The rigid-body and hinge-bending modes are observed mixed together in the remaining 90 ns long quasi-stable state. The mixed-mode movement seems come from the competition between the helix rigidity and the biased-applied gating force.     

Modelling the effect of a GHz electric field on the dynamics of K+ ions in KcsA potassium channel

The dynamics of potassium ions in a KcsA channel, located within a stochastically fluctuating medium, is modelled via the application of the molecular dynamics simulation method. We investigate the effect of presence and absence of an applied electric field, either constant or periodic, on the dynamics of the channel. It is found that the ions undergo a hopping motion when the channel is exposed to a constant electric field of strength 0.03 V/nm. Furthermore, an alternating electric field in the GHz range, normally present in the daily environment and encountered by most biological systems, is applied to the channel, showing that in this frequency range, the rigidity of the atomic bonds of the filter is increased, which in turn disturbs the ionic passage rate through the filter. Consequently, in this frequency range, the application of electric fields may affect the function of such channels.     

Electrostatic state of the cytoplasmic domain influences inactivation at the selectivity filter of the KcsA potassium channel

KcsA is a proton-activated K⁺ channel that is regulated at two gates: an activation gate located in the inner entrance of the pore and an inactivation gate at the selectivity filter. Previously, we revealed that the cytoplasmic domain (CPD) of KcsA senses proton and that electrostatic changes of the CPD influences the opening and closing of the activation gate. However, our previous studies did not reveal the effect of CPD on the inactivation gate because we used a non-inactivating mutant (E71A). In the present study, we used mutants that did not harbor the E71A mutation, and showed that the electrostatic state of the CPD influences the inactivation gate. Three novel CPD mutants were generated in which some negatively charged amino acids were replaced with neutral amino acids. These CPD mutants conducted K⁺, but showed various inactivation properties. Mutants carrying the D149N mutation showed high open probability and slow inactivation, whereas those without the D149N mutation showed low open probability and fast inactivation, similar to wild-type KcsA. In addition, mutants with D149N showed poor K⁺ selectivity, and permitted Na⁺ to flow. These results indicated that electrostatic changes in the CPD by D149N mutation triggered the loss of fast inactivation and changes in the conformation of selectivity filter. Additionally, the loss of fast inactivation induced by D149N was reversed by R153A mutation, suggesting that not only the electrostatic state of D149, but also that of R153 affects inactivation.     

TETRAETHYLAMMONIUM BINDING TO THE OUTER MOUTH OF THE KcsA POTASSIUM CHANNEL: IMPLICATIONS FOR ION PERMEATION

ABSTRACT

Extracellular tetraethylammonium (TEA⁺) inhibits the current carried out by K⁺ ions in potassium channels. Structural models of wild-type (WT) and Y82C KcsA K⁺ channel/TEA⁺ complexes are here built using docking procedures, electrostatics calculations and molecular dynamics simulations. The calculations are based on the structure determined by Doyle et al.¹¹Our calculations suggest that in WT, the TEA⁺ cation turns binds at the outer mouth of the selectivity filter, stabilized by electrostatic and hydrophobic interactions with the four Tyr⁸² side chains. Replacement of Tyr⁸² with Cys causes a decrease of the affinity of the cation for the channel, consistently with the available site-directed mutagenesis data¹⁶. An MD simulation in which K⁺ replaces TEA⁺ provides evidence that TEA⁺ binding site can accommodate a potassium ion, in agreement with the high-resolution structure recently reported by Zhou et al.²⁰     

Estimating the dielectric constant of the channel protein and pore

When modelling biological ion channels using Brownian dynamics (BD) or Poisson–Nernst–Planck theory, the force encountered by permeant ions is calculated by solving Poisson’s equation. Two free parameters needed to solve this equation are the dielectric constant of water in the pore and the dielectric constant of the protein forming the channel. Although these values can in theory be deduced by various methods, they do not give a reliable answer when applied to channel-like geometries that contain charged particles. To determine the appropriate values of the dielectric constants, here we solve the inverse problem. Given the structure of the MthK channel, we attempt to determine the values of the protein and pore dielectric constants that minimize the discrepancies between the experimentally-determined current–voltage curve and the curve obtained from BD simulations. Two different methods have been applied to determine these values. First, we use all possible pairs of the pore dielectric constant of water, ranging from 20 to 80 in steps of 10, and the protein dielectric constant of 2–10 in steps of 2, and compare the simulated results with the experimental values. We find that the best agreement is obtained with experiment when a protein dielectric constant of 2 and a pore water dielectric constant of 60 is used. Second, we employ a learning-based stochastic optimization algorithm to pick out the optimum combination of the two dielectric constants. From the algorithm we obtain an optimum value of 2 for the protein dielectric constant and 64 for the pore dielectric constant.     

Brownian dynamics investigation into the conductance state of the MscS channel crystal structure

We suggest that the crystal structure of the mechanosensitive channel of small conductance is in a minimally conductive state rather than being fully activated. Performing Brownian dynamics simulations on the crystal structure show that no ions pass through it. When simulations are conducted on just the transmembrane domain (excluding the cytoplasmic residues 128 to 280) ions are seen to pass through the channel, but the conductance of ∼ 30 pS is well below experimentally measured values. The mutation L109S that replaces a pore lining hydrophobic residue with a polar one is found to have little effect on the conductance of the channel. Widening the hydrophobic region of the pore by 2.5 Å however, increases the channel conductance to over 200 pS suggesting that only a minimal conformational change is required to gate the pore.     

Brownian dynamics theory for predicting internal and external blockages of tetraethylammonium in the KcsA potassium channel

The theory of Brownian dynamics is used to model permeation and the blocking of KcsA potassium channels by tetraethylammonium (TEA). A novel Brownian dynamics simulation algorithm is implemented that comprises two free energy profiles; one profile is seen by the potassium ions and the other by the TEA molecules whose shape is approximated by a sphere. Our simulations reveal that internally applied TEA blocks the passage of K⁺ ions by physically occluding the pore. A TEA molecule in the external reservoir encounters an attractive energy-well created by four tyrosine residues at position 82, in addition to all other attractive and repulsive forces impinging on it. Using Brownian dynamics, we investigate how deep the energy-well needs to be to reproduce the experimentally determined inhibitory constant k_i for the TEA blockade of KcsA or the mutant Shaker T449Y. The one-dimensional free energy profile obtained from molecular dynamics is first converted into a one-dimensional potential energy profile, and is then transformed into a three-dimensional free energy profile in Brownian dynamics by adding the short-range potential from the channel walls. When converted, the free energy profile calculated from molecular dynamics gives a well-depth of ∼10 kT. We systematically alter the depths of the profiles, and then use Brownian dynamics simulations to numerically determine the current versus TEA-concentration curves. We show that the sequence of binding and unbinding events of the TEA molecule to the binding pocket can be modeled by a first-order Markov process. The Brownian dynamics simulations also reveal that the probability of a TEA molecule binding to the binding pocket in KcsA potassium channels increases exponentially with TEA concentration and depends also on the applied potential and the K⁺ concentration in the simulation assembly.     

A comparison between two prokaryotic potassium channels (KirBac1.1 and KcsA) in a molecular dynamics (MD) simulation study

The two potassium ion channels KirBac1.1 and KcsA are compared in a Molecular Dynamics (MD) simulation study. The location and motion of the potassium ions observed in the simulations are compared to those in the X-ray structures and previous simulations. In our simulations several of the crystallography resolved ion sites in KirBac1.1 are occupied by ions. In addition to this, two in KirBac1.1 unresolved sites where occupied by ions at sites that are in close correspondence to sites found in KcsA. There is every reason to believe that the conserved alignment of the selectivity filter in the potassium ion channel family corresponds to a very similar mechanism for ion transport across the filter. The gate residues, Phe146 in KirBac1.1 and Ala111 in KcsA acted in the simulations as effective barriers which never were passed by ions nor water molecules.     

Functional evidence for a supramolecular structure for the Streptomyces lividans potassium channel KcsA

Here we present functional evidence for involvement of poly-(R)-3-hydroxybutyrate (PHB) and inorganic polyphosphate (polyP) in ion conduction and selection at the intracellular side of the Streptomyces lividans potassium channel, KcsA. At < or = 25 degrees C, KcsA forms channels in planar bilayers that display signal characteristics of PHB/polyP channels at the intracellular side; i.e., a preference for divalent Mg(2+) cations at pH 7.2, and a preference for monovalent K+ cations at pH 6.8. Between 25 and 26 degrees C, KcsA undergoes a transition to a new conformation in which the channel exhibits high selectivity for K+, regardless of solution pH. This suggests that basic residues of the C-terminal polypeptides have moved closer to the polyP end unit, reducing its negative charge. The data support a supramolecular structure for KcsA in which influx of ions is prevented by the selectivity pore, whereas efflux of K+ is governed by a conductive core of PHB/polyP in partnership with the C-terminal polypeptide strands.     

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

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

Using mutagenesis to study potassium channel mechanisms

The voltage-activated K⁺ channels are members of an ion channel family that includes the voltage-activated Na⁺ and Ca²⁺ channels. These ion channels mediate the transmembrane ionic currents that are responsible for the electrical signals produced by cells. The recent cloning of numerous voltage-activated K⁺ channels has made it possible to combine molecular-genetic and biophysical methods to study K⁺ channel mechanisms. These mutagenesis-function studies are beginning to provide new information about the architecture of K⁺ channel proteins and how they form a voltage-gated, K⁺-selective pore.     

Brownian dynamics study of flux ratios in sodium channels

Measurements of unidirectional fluxes in ion channels provide one of the experimental methods for studying the steps involved in ion permeation in biological pores. Conventionally, the number of ions in the pore is inferred by fitting the ratio of inward and outward currents to an exponential function with an adjustable parameter known as the flux ratio exponent. Here we investigate the relationship between the number of ions in the pore and the flux ratio exponent in a model sodium channel under a range of conditions. Brownian dynamics simulations enable us to count the precise number of ions in the channel and at the same time measure the currents flowing across the pore in both directions. We show here that the values of the flux ratio exponent n′ ranges between 1 and 3 and is highly dependent on the ionic concentrations in which measurements are made. This is a consequence of the fact that both inward and outward currents are susceptible to saturation with increasing concentration. These results indicate that measurements of the flux ratio exponent cannot be directly related to the number of ions in the pore and that interpretation of such experimental measurements requires careful consideration of the conditions in which the study is made.     

KcsA closed and open: modelling and simulation studies

Bacterial homologues of mammalian potassium channels provide structures of two states of a gated K channel. Thus, the crystal structure of KcsA represents a closed state whilst that of MthK represents an open state. Using homology modelling and molecular dynamics simulations we have built a model of the transmembrane domain of KcsA in an open state and have compared its conformational stability with that of the same domain of KcsA in a closed state. Approximate Born energy calculations of monovalent cations within the two KcsA channel states suggest that the intracellular hydrophobic gate in the closed state provides a barrier of height ~5 kT to ion permeation, whilst in the open state the barrier is absent. Simulations (10 ns duration) in an octane slab (a simple membrane mimetic) suggest that closed- and open-state models are of comparable conformational stability, both exhibiting conformational drifts of ~3.3 Å C RMSD relative to the respective starting models. Substantial conformational fluctuations are observed in the intracellular gate region during both simulations (closed state and open state). In the simulation of open-state KcsA, rapid (<5 ns) exit of all three K⁺ ions occurs through the intracellular mouth of the channel. Helix kink and swivel motion is observed at the molecular hinge formed by residue G99 of the M2 helix. This motion is more substantial for the open- than for the closed-state model of the channel.     

Role of polyphosphate in regulation of the Streptomyces lividans KcsA channel

We examine the hypotheses that the Streptomyces lividans potassium channel KcsA is gated at neutral pH by the electrochemical potential, and that its selectivity and conductance are governed at the cytoplasmic face by interactions between the KcsA polypeptides and a core molecule of inorganic polyphosphate (polyP). The four polypeptides of KcsA are postulated to surround the end unit of the polyP molecule with a collar of eight arginines, thereby modulating the negative charge of the polyP end unit and increasing its preference for binding monovalent cations. Here we show that KcsA channels can be activated in planar lipid bilayers at pH 7.4 by the chemical potential alone. Moreover, one or both of the C-terminal arginines are replaced with residues of progressively lower basicity-lysine, histidine, valine, asparagine-and the effects of these mutations on conductance and selectivity for K⁺ over Mg²⁺ is tested in planar bilayers as a function of Mg²⁺ concentration and pH. As the basicity of the C-terminal residues decreases, Mg²⁺ block increases, and Mg²⁺ becomes permeant when medium pH is greater than the pI of the C-terminal residues. The results uphold the premise that polyP and the C-terminal arginines are decisive elements in KcsA channel regulation.     

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

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

A site accessible to extracellular TEA+ and K+ influences intracellular Mg2+ block of cloned potassium channels

The members of the RCK family of cloned voltage-dependent K⁺ channels are quite homologous in primary structure, but they are highly diverse in functional properties. RCK4 channels differ from RCK1 and RCK2 channels in inactivation and permeation properties, the sensitivity to external TEA, and to current modulation by external K⁺ ions. Here we show several other interesting differences: While RCK1 and RCK2 are blocked in a voltage and concentration dependent manner by internal Mg²⁺ ions, RCK4 is only weakly blocked at very high potentials. The single-channel current-voltage relations of RCK4 are rather linear while RCK2 exhibits an inwardly rectifying single-channel current in symmetrical K⁺ solutions. The deactivation of the channels, measured by tail current protocols, is faster in RCK4 by a factor of two compared with RCK2. In a search for the structural motif responsible for these differences, point mutants creating homology between RCK2 and RCK4 in the pore region were tested. The single-point mutant K533Y in the background of RCK4 conferred the properties of Mg²⁺ block, tail current kinetics, and inward ion permeation of RCK2 to RCK4. This mutant was previously shown to be responsible for the alterations in external TEA sensitivity and channel regulation by external K⁺ ions. Thus, this residue is expected to be located at the external side of the pore entrance. The data are consistent with the idea that the mutation alters the channel occupancy by K⁺ and thereby indirectly affects internal Mg²⁺ block and channel closing.Abbreviations TEA tetraethylammonium - EGTA Ethylene glycol-bis (-aminoethyl ether) N,N,N,N-tetraacetic acid - 2S3B model 2-site 3-barrier model Correspondence to: S. H. Heinemann     

Local and global structure of the monomeric subunit of the potassium channel KcsA probed by NMR

KcsA is a homotetrameric 68-kDa membrane-associated potassium channel which selectively gates the flux of potassium ions across the membrane. The channel is known to undergo a pH-dependent open-to-closed transition. Here we describe an NMR study of the monomeric subunit of the channel (KcsA^M), solubilized in SDS micelles. Chemical shift, solvent exchange, backbone ¹⁵N relaxation and residual dipolar coupling (RDC) data show the TM1 helix to remain intact, but the TM2 helix contains a distinct kink, which is subject to concentration-independent but pH-dependent conformational exchange on a microsecond time scale. The kink region, centered at G99, was previously implicated in the gating of the tetrameric KcsA channel. An RDC-based model of KcsA^M at acidic pH orients TM1 and the two helical segments of the kinked TM2 in a configuration reminiscent of the open conformation of the channel. Thus, the transition between states appears to be an inherent capability of the monomer, with the tetrameric assembly exerting a modulatory effect upon the transition which gives the channel its physiological gating profile.     

Kinetics of inward-rectifier K+ channel block by quaternary alkylammonium ions. dimension and properties of the inner pore

We examined block of two inward-rectifier K+ channels, IRK1 and ROMK1, by a series of intracellular symmetric quaternary alkylammonium ions (QAs) whose side chains contain one to five methylene groups. As shown previously, the ROMK1 channels bind larger QAs with higher affinity. In contrast, the IRK1 channels strongly select TEA over smaller or larger QAs. This remarkable difference in QA selectivity between the two channels results primarily from differing QA unbinding kinetics. The apparent rate constant for binding (kon) of all examined QAs is significantly smaller than expected for a diffusion-limited process. Furthermore, a large ( approximately 30-fold) drop in kon occurs when the number of methylene groups in QAs increases from three to four. These observations argue that between the intracellular solution and the QA-binding locus, there exists a constricted pathway, whose dimension ( approximately 9 A) is comparable to that of a K+ ion with a single H2O shell.