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 model of sodium channels

We have explored the permeation and blockage of ions in sodium channels, relating the channel structure to function using electrostatic profiles and Brownian dynamics simulations. The model used resembles the KcsA potassium channel with an added external vestibule and a shorter selectivity filter. The electrostatic energy landscape seen by permeating ions is determined by solving Poisson's equation. The two charged amino acid rings of Glu-Glu-Asp-Asp (EEDD) and Asp-Glu-Lys-Ala (DEKA) around the selectivity filter region are seen to play a crucial role in making the channel sodium selective, and strongly binding calcium ions such that they block the channel. Our model closely reproduces a range of experimental data including the current-voltage curves, current-concentration curves and blockage of monovalent ions by divalent ions.     

A model of sodium channels

We have explored the permeation and blockage of ions in sodium channels, relating the channel structure to function using electrostatic profiles and Brownian dynamics simulations. The model used resembles the KcsA potassium channel with an added external vestibule and a shorter selectivity filter. The electrostatic energy landscape seen by permeating ions is determined by solving Poisson's equation. The two charged amino acid rings of Glu-Glu-Asp-Asp (EEDD) and Asp-Glu-Lys-Ala (DEKA) around the selectivity filter region are seen to play a crucial role in making the channel sodium selective, and strongly binding calcium ions such that they block the channel. Our model closely reproduces a range of experimental data including the current-voltage curves, current-concentration curves and blockage of monovalent ions by divalent ions.     

Preparation and properties of asymmetric large unilamellar vesicles: interleaflet coupling in asymmetric vesicles is dependent on temperature but not curvature

Using both Brownian and molecular dynamics, we replicate many of the salient features of Kv1.2, including the current-voltage-concentration profiles and the binding affinity and binding mechanisms of charybdotoxin, a scorpion venom. We also elucidate how structural differences in the inner vestibule can give rise to significant differences in its permeation characteristics. Current-voltage-concentration profiles are constructed using Brownian dynamics simulations, based on the crystal structure 2A79. The results are compatible with experimental data, showing similar conductance, rectification, and saturation with current. Unlike KcsA, for example, the inner pore of Kv1.2 is mainly hydrophobic and neutral, and to explore the consequences of this, we investigate the effect of mutating neutral proline residues at the mouth of the inner vestibule to charged aspartate residues. We find an increased conductance, less inward rectification, and quicker saturation of the current-voltage profile. Our simulations use modifications to our Brownian dynamics program that extend the range of channels that can be usefully modeled. Using molecular dynamics, we investigate the binding of the charybdotoxin scorpion venom to the outer vestibule of the channel. A potential of mean force is derived using umbrella sampling, giving a dissociation constant within a factor of ∼2 to experimentally derived constants. The residues involved in the toxin binding are in agreement with experimental mutagenesis studies. We thus show that the experimental observations on the voltage-gated channel, including the toxin-channel interaction, can reliably be replicated by using the two widely used computational tools.     

K(+) versus Na(+) ions in a K channel selectivity filter: a simulation study

Molecular dynamics simulations of a bacterial potassium channel (KcsA) embedded in a phospholipid bilayer reveal significant differences in interactions of the selectivity filter with K(+) compared with Na(+) ions. K(+) ions and water molecules within the filter undergo concerted single-file motion in which they translocate between adjacent sites within the filter on a nanosecond timescale. In contrast, Na(+) ions remain bound to sites within the filter and do not exhibit translocation on a nanosecond timescale. Furthermore, entry of a K(+) ion into the filter from the extracellular mouth is observed, whereas this does not occur for a Na(+) ion. Whereas K(+) ions prefer to sit within a cage of eight oxygen atoms of the filter, Na(+) ions prefer to interact with a ring of four oxygen atoms plus two water molecules. These differences in interactions in the selectivity filter may contribute to the selectivity of KcsA for K(+) ions (in addition to the differences in dehydration energy between K(+) and Na(+)) and the block of KcsA by internal Na(+) ions. In our simulations the selectivity filter exhibits significant flexibility in response to changes in ion/protein interactions, with a somewhat greater distortion induced by Na(+) than by K(+) ions.     

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

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

Modeling diverse range of potassium channels with Brownian dynamics

Using the experimentally determined KcsA structure as a template, we propose a plausible explanation for the diversity of potassium channels seen in nature. A simplified model of KcsA is constructed from its atomic resolution structure by smoothing out the protein-water boundary and representing the atoms forming the channel protein as a homogeneous, low dielectric medium. The properties of the simplified and atomic-detail models, deduced from electrostatic calculations and Brownian dynamics simulations, are shown to be qualitatively similar. We then study how the current flowing across the simplified model channel changes as the shape of the intrapore region is modified. This is achieved by increasing the radius of the intracellular pore systematically from 1.5 to 5 A while leaving the dimensions of the selectivity filter and inner chamber unaltered. The strengths of the dipoles located near the entrances of the channel, the carbonyl groups lining the selectivity filter, and the helix macrodipoles are kept constant. The channel conductance increases steadily as the radius of the intracellular pore is increased. The rate-limiting step for both the outward and inward current is the time it takes for an ion to cross the residual energy barrier located in the intrapore region. The current-voltage relationship obtained with symmetrical solutions is linear when the applied potential is less than approximately 100 mV but deviates slightly from Ohm's law at higher applied potentials. The nonlinearity in the current-voltage curve becomes less pronounced as the radius of the intracellular pore is increased. When the strengths of the dipoles near the intracellular entrance are reduced, the channel shows a pronounced inward rectification. Finally, the conductance exhibits the saturation property observed experimentally. We discuss the implications of these findings on the transport of ions across the potassium channels and membrane channels in general.     

Mechanisms of tetraethylammonium ion block in the KcsA potassium channel

We report results from automated docking and microscopic molecular dynamics simulations of the tetraethylammonium (TEA) complexes with KcsA. Binding modes and energies for TEA binding at the external and internal sides of the channel pore are examined utilising the linear interaction energy method. Effects of the channel ion occupancy (based on our previous results for the ion permeation mechanisms) on the binding energies are considered. Calculations show that TEA forms stable complexes at both the external and internal entrances of the selectivity filter. Furthermore, the effects of the Y82V mutation are evaluated and the results show, in agreement with experimental data, that the mutant has a significantly reduced binding affinity for TEA at the external binding site, which is attributed to stabilising hydrophobic interactions between the ligand and the tyrosines.     

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.     

Extracellular blockade of K(+) channels by TEA: results from molecular dynamics simulations of the KcsA channel

TEA is a classical blocker of K(+) channels. From mutagenesis studies, it has been shown that external blockade by TEA is strongly dependent upon the presence of aromatic residue at Shaker position 449 which is located near the extracellular entrance to the pore (Heginbotham, L., and R. MacKinnon. 1992. Neuron. 8:483-491). The data suggest that TEA interacts simultaneously with the aromatic residues of the four monomers. The determination of the 3-D structure of the KcsA channel using X-ray crystallography (Doyle, D.A., J.M. Cabral, R.A. Pfuetzner, A. Kuo, J.M. Gulbis, S.L. Cohen, B.T. Chait, and R. MacKinnon. 1998. Science. 280:69-77) has raised some issues that remain currently unresolved concerning the interpretation of these observations. In particular, the center of the Tyr82 side chains in KcsA (corresponding to position 449 in Shaker) forms a square of 11.8-A side, a distance which is too large to allow simultaneous interactions of a TEA molecule with the four aromatic side chains. In this paper, the external blockade by TEA is explored by molecular dynamics simulations of an atomic model of KcsA in an explicit phospholipid bilayer with aqueous salt solution. It is observed, in qualitative accord with the experimental results, that TEA is stable when bound to the external side of the wild-type KcsA channel (with Tyr82), but is unstable when bound to a mutant channel in which the tyrosine residue has been substituted by a threonine. The free energy profile of TEA relative to the pore is calculated using umbrella sampling simulations to characterize quantitatively the extracellular blockade. It is found, in remarkable agreement with the experiment, that the TEA is more stably bound by 2.3 kcal/mol to the channel with four tyrosine residues. In the case of the wild-type KcsA channel, TEA (which has the shape of a flattened oblate spheroid) acts as an ideal plug blocking the pore. In contrast, it is considerably more off-centered and tilted in the case of the mutant channel. The enhanced stability conferred by the tyrosine residues does not arise from Pi-cation interactions, but appears to be due to differences in the hydration structure of the TEA. Finally, it is shown that the experimentally observed voltage dependence of TEA block, which is traditionally interpreted in terms of the physical position of the TEA along the axis of the pore, must arise indirectly via coupling with the ions in the pore.     

Modeling of the outer vestibule and selectivity filter of the L-type Ca2+ channel

Using the KcsA bacterial K+ channel crystal structure [Doyle, D. A., et al. (1998) Science 280, 69-74] and the model of the outer vestibule of the Na+ channel [Lipkind, G. M., and Fozzard, H. A. (2000) Biochemistry 39, 8161-8170] as structural templates, we propose a structural model of the outer vestibule and selectivity filter of the pore of the Ca2+ channel (alpha1C or Ca(v)1.2). The Ca2+ channel P loops were modeled by alpha-helix-turn-beta-strand motifs, with the glutamate residues of the EEEE motif located in the turns. P loops were docked in the extracellular part of the inverted teepee structure formed by S5 and S6 alpha-helices with backbone coordinates from the M1 and M2 helices of the KcsA crystal structure. This construction results in a conical outer vestibule that tapers to the selectivity filter at the bottom. The modeled selectivity ring forms a wide open pore ( approximately 6 A) in the absence of Ca2+. When Ca2+ is present ( approximately 1 microM), all four glutamate side chains move to the center and form a cage around the dehydrated Ca2+ ion, blocking the pore. In the millimolar concentration range, Ca2+ also interacts with two low-affinity sites located externally and internally, which were modeled by the same carboxylate groups of the selectivity filter. Calculation of the resulting electrostatic potentials show that the single Ca2+ ion is located in an electrostatic trap. Only when three Ca2+ ions are bound simultaneously in the high- and low-affinity sites of the selectivity filter is Ca2+ able to overcome electrostatic attraction, permitting Ca2+ flux.     

An electrostatic interaction between TEA and an introduced pore aromatic drives spring-in-the-door inactivation in Shaker potassium channels

Slow inactivation of Kv1 channels involves conformational changes near the selectivity filter. We examine such changes in Shaker channels lacking fast inactivation by considering the consequences of mutating two residues, T449 just external to the selectivity filter and V438 in the pore helix near the bottom of the selectivity filter. Single mutant T449F channels with the native V438 inactivate very slowly, and the canonical foot-in-the-door effect of extracellular tetraethylammonium (TEA) is not only absent, but the time course of slow inactivation is accelerated by TEA. The V438A mutation dramatically speeds inactivation in T449F channels, and TEA slows inactivation exactly as predicted by the foot-in-the-door model. We propose that TEA has this effect on V438A/T449F channels because the V438A mutation produces allosteric consequences within the selectivity filter and may reorient the aromatic ring at position 449. We investigated the possibility that the blocker promotes the collapse of the outer vestibule (spring-in-the-door) in single mutant T449F channels by an electrostatic attraction between a cationic TEA and the quadrupole moments of the four aromatic rings. To test this idea, we used in vivo nonsense suppression to serially fluorinate the introduced aromatic ring at the 449 position, a manipulation that withdraws electrons from the aromatic face with little effect on the shape, net charge, or hydrophobicity of the aromatic ring. Progressive fluorination causes monotonically enhanced rates of inactivation. In further agreement with our working hypothesis, increasing fluorination of the aromatic gradually transforms the TEA effect from spring-in-the-door to foot-in-the-door. We further substantiate our electrostatic hypothesis by quantum mechanical calculations.     

The protonation state of the Glu-71/Asp-80 residues in the KcsA potassium channel: a first-principles QM/MM molecular dynamics study

Although a few x-ray structures of the KcsA K(+) channel have been crystallized several issues concerning the mechanisms of the ionic permeation and the protonation state of the selectivity filter ionizable side chains are still open. Using a first-principles quantum mechanical/molecular mechanical simulation approach, we have investigated the protonation state of Glu-71 and Asp-80, two important residues located in the vicinity of the selectivity filter. Results from the dynamics show that a proton is shared between the two residues, with a slight preference for Glu-71. The proton is found to exchange on the picosecond timescale, an interesting phenomenon that cannot be observed in classical molecular dynamics. Simulations of different ionic loading states of the filter show that the probability for the proton transfer is correlated with the filter occupancy. In addition, the Glu-71/Asp-80 pair is able to modulate the potential energy profile experienced by a K(+) ion as it translates along the pore axis. These theoretical predictions, along with recent experimental results, suggest that changes of the filter structure could be associated with a shift in the Glu-Asp protonation state, which in turn would influence the ion translocation.     

The aromatic binding site for tetraethylammonium ion on potassium channels.

K+ channels are quite variable in their sensitivity to the pore-blocking agent tetraethylammonium ion (TEA) when it is applied to the extracellular side of the membrane. A Shaker K+ channel can be made highly sensitive by introducing a tyrosine (or phenylalanine) at residue 449 in each of the four subunits. A shift in the voltage dependence of blockade indicates that TEA senses a smaller fraction of the transmembrane electric field in the highly sensitive channels. There is a linear relationship between the free energy for TEA blockade and the number of subunits (zero, two, or four) containing tyrosine at 449, as if these four residues interact simultaneously with a TEA molecule to produce a high affinity binding site. The temperature dependence of blockade suggests that the interaction is not purely hydrophobic. These findings are consistent with a TEA-binding site formed by a bracelet of pore-lining aromatic residues. The center of the bracelet could bind a TEA molecule through a cation-pi orbital interaction.     

Change of pore helix conformational state upon opening of cyclic nucleotide-gated channels

The structure of the pore region of the alpha subunit of the bovine rod cyclic nucleotide-gated channel was probed using cysteine-scanning mutagenesis and hydrophilic sulfhydryl-reactive methanethiosulfonate (MTS) reagents. A region homologous to the pore helix in the X-ray crystal structure of the KcsA K(+) channel showed a helical pattern of reactivity with externally applied MTS reagents. Surprisingly, three out of four of the reactive residues, all on one face of the pore helix, only reacted with MTS reagents in the closed state. A residue on the opposite face of the helix only reacted with MTS reagents in the open state. These results indicate that the pore helix (or its surroundings) undergoes a change in conformation, perhaps involving a rotation around its long axis, that opens a gate localized to the selectivity filter of the channel.     

Delineation of the clotrimazole/TRAM-34 binding site on the intermediate conductance calcium-activated potassium channel, IKCa1.

Selective and potent triarylmethane blockers of the intermediate conductance calcium-activated potassium channel, IKCa1, have therapeutic use in sickle cell disease and secretory diarrhea and as immunosuppressants. Clotrimazole, a membrane-permeant triarylmethane, blocked IKCa1 with equal affinity when applied externally or internally, whereas a membrane-impermeant derivative TRAM-30 blocked the channel only when applied to the cytoplasmic side, indicating an internal drug-binding site. Introduction of the S5-P-S6 region of the triarylmethane-insensitive small conductance calcium-activated potassium channel SKCa3 into IKCa1 rendered the channel resistant to triarylmethanes. Replacement of Thr(250) or Val(275) in IKCa1 with the corresponding SKCa3 residues selectively abolished triarylmethane sensitivity without affecting the affinity of the channel for tetraethylammonium, charybdotoxin, and nifedipine. Introduction of these two residues into SKCa3 rendered the channel sensitive to triarylmethanes. In a molecular model of IKCa1, Thr(250) and Val(275) line a water-filled cavity just below the selectivity filter. Structure-activity studies suggest that the side chain methyl groups of Thr(250) and Val(275) may lock the triarylmethanes in place via hydrophobic interactions with the pi-electron clouds of the phenyl rings. The heterocyclic moiety may project into the selectivity filter and obstruct the ion-conducting pathway from the inside.     

K(+)/Na(+) selectivity of the KcsA potassium channel from microscopic free energy perturbation calculations

Microscopic molecular dynamics free energy perturbation calculations of the K(+)/Na(+) selectivity in the KcsA potassium channel, based on its experimental three-dimensional structure, are reported. The relative binding free energies for K(+) and Na(+) in the most relevant ion occupancy states of the four-site selectivity filter are calculated. The previously proposed mechanism for ion permeation through the KcsA channel is predicted, in agreement with available experimental data, to have a significant selectivity for K(+) over Na(+). The calculations also show that the individual 'binding site' selectivities are generally not additive and the doubly loaded states of the filter thus display cooperative effects. The only site that is not K(+) selective is that which is located at the entrance to the internal water cavity, suggesting the possibility that internal Na(+) could block outward currents.     

A multipoint hydrogen-bond network underlying KcsA C-type inactivation

In the prokaryotic potassium channel KcsA activation gating at the inner bundle gate is followed by C-type inactivation at the selectivity filter. Entry into the C-type inactivated state has been directly linked to the strength of the H-bond interaction between residues Glu-71 and Asp-80 behind the filter, and is allosterically triggered by the rearrangement of the inner bundle gate. Here, we show that H-bond pairing between residues Trp-67 and Asp-80, conserved in most K⁺ channels, constitutes another critical interaction that determines the rate and extent of KcsA C-type inactivation. Disruption of the equivalent interaction in Shaker (Trp-434-Asp-447) and Kv1.2 (Trp-366-Asp-379) leads also to modulation of the inactivation process, suggesting that these residues also play an analogous role in the inactivation gating of Kv channels. The present results show that in KcsA C-type inactivation gating is governed by a multipoint hydrogen-bond network formed by the triad Trp-67-Glu71-Asp-80. This triad exerts a critical role in the dynamics and conformational stability of the selectivity filter and might serve as a general modulator of selectivity filter gating in other members of the K⁺ channel family.