The sliding-helix voltage sensor: mesoscale views of a robust structure-function relationship

The 70-year search for the voltage sensing mechanism of ion channels

This retrospective on the voltage‐sensing mechanisms and gating models of ion channels begins in 1952 with the charged gating particles postulated by Hodgkin and Huxley, viewed as charges moving across the membrane and controlling its permeability to Na⁺ and K⁺ ions. Hodgkin and Huxley postulated that their movement should generate small and fast capacitive currents, which were recorded 20 years later as gating currents. In the early 1980s, several voltage‐dependent channels were cloned and found to share a common architecture: four homologous domains or subunits, each displaying six transmembrane α‐helical segments, with the fourth segment (S4) displaying four to seven positive charges invariably separated by two non‐charged residues. This immediately suggested that this segment was serving as the voltage sensor of the channel (the molecular counterpart of the charged gating particle postulated by Hodgkin and Huxley) and led to the development of the sliding helix model. Twenty years later, the X‐ray crystallographic structures of many voltage‐dependent channels allowed investigation of their gating by molecular dynamics. Further understanding of how channels gate will benefit greatly from the acquisition of high‐resolution structures of each of their relevant functional or structural states. This will allow the application of molecular dynamics and other approaches. It will also be key to investigate the energetics of channel gating, permitting an understanding of the physical and molecular determinants of gating. The use of multiscale hierarchical approaches might finally prove to be a rewarding strategy to overcome the limits of the various single approaches to the study of channel gating.

Multiscale modeling shows that dielectric differences make NaV channels faster than KV channels

The generation of action potentials in excitable cells requires different activation kinetics of voltage-gated Na (Na_V) and K (K_V) channels. Na_V channels activate much faster and allow the initial Na⁺ influx that generates the depolarizing phase and propagates the signal. Recent experimental results suggest that the molecular basis for this kinetic difference is an amino acid side chain located in the gating pore of the voltage sensor domain, which is a highly conserved isoleucine in K_V channels but an equally highly conserved threonine in Na_V channels. Mutagenesis suggests that the hydrophobicity of this side chain in Shaker K_V channels regulates the energetic barrier that gating charges cross as they move through the gating pore and control the rate of channel opening. We use a multiscale modeling approach to test this hypothesis. We use high-resolution molecular dynamics to study the effect of the mutation on polarization charge within the gating pore. We then incorporate these results in a lower-resolution model of voltage gating to predict the effect of the mutation on the movement of gating charges. The predictions of our hierarchical model are fully consistent with the tested hypothesis, thus suggesting that the faster activation kinetics of Na_V channels comes from a stronger dielectric polarization by threonine (Na_V channel) produced as the first gating charge enters the gating pore compared with isoleucine (K_V channel).

Voltage-dependent gating in K channels: experimental results and quantitative models

Voltage-dependent K channels open and close in response to voltage changes across the cell membrane. This voltage dependence was postulated to depend on the presence of charged particles moving through the membrane in response to voltage changes. Recording of gating currents originating from the movement of these particles fully confirmed this hypothesis, and gave substantial experimental clues useful for the detailed understanding of the process. In the absence of structural information, the voltage-dependent gating was initially investigated using discrete Markov models, an approach only capable of providing a kinetic and thermodynamic comprehension of the process. The elucidation of the crystal structure of the first voltage-dependent channel brought in a dramatic change of pace in the understanding of channel gating, and in modeling the underlying processes. It was now possible to construct quantitative models using molecular dynamics, where all the interactions of each individual atom with the surroundings were taken into account, and its motion predicted by Newton's laws. Unfortunately, this modeling is computationally very demanding, and in spite of the advances in simulation procedures and computer technology, it is still limited in its predictive ability. To overcome these limitations, several groups have developed more macroscopic voltage gating models. Their approaches understandably require a number of approximations, which must however be physically well justified. One of these models, based on the description of the voltage sensor as a Brownian particle, that we have recently developed, is able to simultaneously describe the behavior of a single voltage sensor and to predict the macroscopic gating current originating from a population of sensors. The basics of this model are here described, and a typical application using the Kv1.2/2.1 chimera channel structure is also presented.

Simulation of Gating Currents of the Shaker K Channel Using a Brownian Model of the Voltage Sensor

The physical mechanism underlying the voltage-dependent gating of K channels is usually addressed theoretically using molecular dynamics simulations. However, besides being computationally very expensive, this approach is presently unable to fully predict the behavior of fundamental variables of channel gating such as the macroscopic gating current, and hence, it is presently unable to validate the model. To fill this gap, here we propose a voltage-gating model that treats the S4 segment as a Brownian particle moving through a gating channel pore and adjacent internal and external vestibules. In our model, charges on the S4 segment are screened by charged residues localized on neighboring segments of the channel protein and by ions present in the vestibules, whose dynamics are assessed using a flux conservation equation. The electrostatic voltage spatial profile is consistently assessed by applying the Poisson equation to all the charges present in the system. The treatment of the S4 segment as a Brownian particle allows description of the dynamics of a single S4 segment using the Langevin stochastic differential equation or the behavior of a population of S4 segments-useful for assessing the macroscopic gating current-using the Fokker-Planck equation. The proposed model confirms the gating charge transfer hypothesis with the movement of the S4 segment among five different stable positions where the gating charges interact in succession with the negatively charged residues on the channel protein. This behavior produces macroscopic gating currents quite similar to those experimentally found.

Continuum Gating Current Models Computed with Consistent Interactions

The action potential of nerve and muscle is produced by voltage-sensitive channels that include a specialized device to sense voltage. The voltage sensor depends on the movement of charges in the changing electric field as suggested by Hodgkin and Huxley. Gating currents of the voltage sensor are now known to depend on the movements of positively charged arginines through the hydrophobic plug of a voltage sensor domain. Transient movements of these permanently charged arginines, caused by the change of transmembrane potential V, further drag the S4 segment and induce opening/closing of the ion conduction pore by moving the S4-S5 linker. This moving permanent charge induces capacitive current flow everywhere. Everything interacts with everything else in the voltage sensor and protein, and so it must also happen in its mathematical model. A Poisson-Nernst-Planck (PNP)-steric model of arginines and a mechanical model for the S4 segment are combined using energy variational methods in which all densities and movements of charge satisfy conservation laws, which are expressed as partial differential equations in space and time. The model computes gating current flowing in the baths produced by arginines moving in the voltage sensor. The model also captures the capacitive pile up of ions in the vestibules that link the bulk solution to the hydrophobic plug. Our model reproduces the signature properties of gating current: 1) equality of ON and OFF charge Q in integrals of gating current, 2) saturating voltage dependence in the Q(charge)-voltage curve, and 3) many (but not all) details of the shape of gating current as a function of voltage. Our results agree qualitatively with experiments and can be improved by adding more details of the structure and its correlated movements. The proposed continuum model is a promising tool to explore the dynamics and mechanism of the voltage sensor.

Bubble gating in biological ion channels: A density functional theory study

We study the behavior of a waterlike liquid inside the gate of a biological ion channel following the basic geometry of the well studied potassium channel KcsA. We calculate the three-dimensional density distribution ρ(r) of the liquid within the framework of classical density functional theory and observe the formation of a low density region (bubble) when the gate is narrow. This observation corresponds to a finite-size form of capillary evaporation and supports the so-called bubble-gate theory. From the density profile we also compute the energy landscape of the gate and the energy required to change the gate from a closed (narrow) to an open (wide) state and vice versa.

Cation Selectivity in Biological Cation Channels Using Experimental Structural Information and Statistical Mechanical Simulation

Cation selective channels constitute the gate for ion currents through the cell membrane. Here we present an improved statistical mechanical model based on atomistic structural information, cation hydration state and without tuned parameters that reproduces the selectivity of biological Na+ and Ca2+ ion channels. The importance of the inclusion of step-wise cation hydration in these results confirms the essential role partial dehydration plays in the bacterial Na+ channels. The model, proven reliable against experimental data, could be straightforwardly used for designing Na+ and Ca2+ selective nanopores.

Domain and interdomain energetics underlying gating in Shaker-type Kv channels

To understand gating events with a time-base many orders-of-magnitude slower than that of atomic motion in voltage-gated ion channels such as the Shaker-type KV channels, a multiscale physical model is constructed from the experimentally well-characterized voltage-sensor (VS) domains coupled to a hydrophobic gate. The four VS domains are described by a continuum electrostatic model under voltage-clamp conditions, the control of ion flow by the gate domain is described by a vapor-lock mechanism, and the simple coupling principle is informed by known experimental results and trial-and-error. The configurational energy computed for each element is used to produce a total Hamiltonian that is a function of applied voltage, VS positions, and gate radius. We compute statistical-mechanical expectation values of macroscopic laboratory observables. This approach stands in contrast with molecular-dynamic models which are challenged by increasing scale, and kinetic models which assume a probability distribution rather than derive it from the underlying physics. This generic model predicts well the Shaker charge/voltage and conductance/voltage relations; the tight constraints underlying these results allow us to quantitatively assess the underlying physical mechanisms. The total electrical work picked up by the VS domains is an order-of-magnitude larger than the work required to actuate the gate itself, suggesting an energetic basis for the evolutionary flexibility of the voltage-gating mechanism. The cooperative slide-and-interlock behavior of the VS domains described by the VS-gate coupling relation leads to the experimentally observed bistable gating. This engineering approach should prove useful in the investigation of various elements underlying gating characteristics and degraded behavior due to mutation.

Caution is required in interpretation of mutations in the voltage sensing domain of voltage gated channels as evidence for gating mechanisms

The gating mechanism of voltage sensitive ion channels is generally considered to be the motion of the S4 transmembrane segment of the voltage sensing domains (VSD). The primary supporting evidence came from R→C mutations on the S4 transmembrane segment of the VSD, followed by reaction with a methanethiosulfonate (MTS) reagent. The cys side chain is –SH (reactive form –S⁻); the arginine side chain is much larger, leaving space big enough to accommodate the MTS sulfonate head group. The cavity created by the mutation has space for up to seven more water molecules than were present in wild type, which could be displaced irreversibly by the MTS reagent. Our quantum calculations show there is major reorientation of three aromatic residues that face into the cavity in response to proton displacement within the VSD. Two phenylalanines reorient sufficiently to shield/unshield the cysteine from the intracellular and extracellular ends, depending on the proton positions, and a tyrosine forms a hydrogen bond to the cysteine sulfur with its side chain –OH. These could produce the results of the experiments that have been interpreted as evidence for physical motion of the S4 segment, without physical motion of the S4 backbone. The computations strongly suggest that the interpretation of cysteine substitution reaction experiments be re-examined in the light of these considerations.

Effects of electrical polarization on the opening rate constant of a voltage-gated ion channel

Ion channel gating kinetics can be described using Kramers' diffusion theory of reaction rates between several closed and open states, where transition rates between states depend exponentially on the membrane potential V. It has been suggested that transition rates have a more complex dependence on V at voltage extremes, but this has never been quantified. We measured the rate constant of the last closed to open transition in a voltage-gated ion channel and show that it does not depend exponentially on membrane potential at values of V greater than ≈150 mV. To explain this behavior, we estimate the effects of electrical polarization of the water contained in crevices within the channel protein, using an electrostatic model of the approximate three-dimensional geometry and the nonlinear effects of charges on the polarization of water.