Computing transient gating charge movement of voltage-dependent ion channels

The opening of voltage-gated sodium, potassium, and calcium ion channels has a steep relationship with voltage. In response to changes in the transmembrane voltage, structural movements of an ion channel that precede channel opening generate a capacitative gating current. The net gating charge displacement due to membrane depolarization is an index of the voltage sensitivity of the ion channel activation process. Understanding the molecular basis of voltage-dependent gating of ion channels requires the measurement and computation of the gating charge, Q. We derive a simple and accurate semianalytic approach to computing the voltage dependence of transient gating charge movement (Q–V relationship) of discrete Markov state models of ion channels using matrix methods. This approach allows rapid computation of Q–V curves for finite and infinite length step depolarizations and is consistent with experimentally measured transient gating charge. This computational approach was applied to Shaker potassium channel gating, including the impact of inactivating particles on potassium channel gating currents.     

Gating current noise produced by Brownian models of a voltage sensor

The activation of voltage-dependent ion channels is associated with the movement of gating charges, which give rise to gating currents. Although gating currents from a single channel are too small to be detected, analysis of the fluctuations of macroscopic gating currents from a population of channels allows a good guess of their magnitude. The analysis of experimental gating current fluctuations, when interpreted in terms of a rate model of channel activation and assuming sufficiently high bandwidth, is in accordance with the presence of a main step along the activation pathway carrying a charge of 2.3–2.4 e₀. To give a physical interpretation to these results and to relate them to the known atomic structure of the voltage sensor domain, we used a Brownian model of voltage-dependent gating based on atomic detail structure, that follows the laws of electrodynamics. The model predicts gating currents and gating current fluctuations essentially similar to those experimentally observed. The detailed study of the model output, also performed by making several simplifications aimed at understanding the basic dependencies of the gating current fluctuations, suggests that in real channels the voltage sensor moves along a sequence of intermediate states separated by relatively low (<5 kT) energy barriers. As a consequence, crossings of successive gating charges through the gating pore become very frequent, and the corresponding current shots are often seen to overlap because of the relatively high filtering. Notably, this limited bandwidth effect is at the origin of the relatively high single-step charge experimentally detected.     

Modification of a voltage-gated K+ channel from sarcoplasmic reticulum by a pronase-derived specific endopeptidase

AK+ -selective membrane conductance channel from rabbit sarcoplasmic reticulum (SR) is studied in an artificial planar phospholipid bilayer. Membranes containing many such channels display voltage-dependent conductance, which is well described by a two-state conformational equilibrium with a free energy term linearly dependent on applied voltage. Pronase-derived alkaline proteinase b (APb), when added to the side of the membrane opposite to the SR vesicles (trans side), reduces the voltage dependence of the K+ conductance. Single-channel fluctuation experiments show that after APb treatment, the channel is still able to undergo transitions between its open and closed states, but that the probability of forming the open state is only slightly voltage-dependent. In terms of the conformational model, the enzyme's primary effect is to reduce the effective gating charge of the opening process by over 80%; a second effect of APb is to reduce the internal free energy of opening from +1.2 to +0.4 kcal/mol. The kinetics of APb action are strongly voltage-dependent, so as to indicate that the enzyme can react only with the channel's open state. The results imply that the channel contains a highly charged polypeptide region which moves in the direction perpendicular to the membrane plane when transitions between the open and closed states occur. A lysine or arginine residue in this region becomes exposed to the trans aqueous solution when the channel is in its open conformation.     

A common pathway for charge transport through voltage-sensing domains

Voltage-gated ion channels derive their voltage sensitivity from the movement of specific charged residues in response to a change in transmembrane potential. Several studies on mechanisms of voltage sensing in ion channels support the idea that these gating charges move through a well-defined permeation pathway. This gating pathway in a voltage-gated ion channel can also be mutated to transport free cations, including protons. The recent discovery of proton channels with sequence homology to the voltage-sensing domains suggests that evolution has perhaps exploited the same gating pathway to generate a bona fide voltage-dependent proton transporter. Here we will discuss implications of these findings on the mechanisms underlying charge (and ion) transport by voltage-sensing domains.     

Removal of the outermost arginine in IVS4 segment of the Ca(V)3.1 channel affects amplitude but not voltage dependence of gating current

Positively charged amino acids in S4 segments of voltage-dependent Ca(V)3.1 channel form putative voltage sensor. Previously we have shown that exchange of uppermost positively charged arginine in IVS4 segment for cysteine (mutation R1717C) affected deactivation and inactivation, but not activation of macroscopic current. Now we compared gating currents from both channels. Maximal amplitude of charge movement in R1717C channel decreased but voltage-dependent characteristics of charge movement were not significantly altered. We concluded that mutation of R1717C affects the coupling between S4 activation and pore opening, but not the S4 activation itself.     

Phosphorylation shifts the time-dependence of cardiac Ca++ channel gating currents.

A general mechanism for the physiological regulation of the activity of voltage-dependent Na+, Ca++, K+, and Cl channels by neurotransmitters in a variety of excitable cell types may involve a final common pathway of a cyclic AMP-dependent phosphorylation of the channel protein. The functional correlates of channel phosphorylation are known to involve a change in the probability of opening, and a negative or positive shift in the voltage dependence for activation of the conductance. The voltage dependence for activation appears to be governed by the properties of the charge movement of the voltage-sensing moiety of the channel. This study of the gating charge movement of cardiac Ca++ channels has revealed that isoproterenol or cAMP (via a presumed phosphorylation of the channel) speeds the kinetics of the Ca++ channel gating charge movement. These results suggest that the changes in the kinetics and voltage dependence of the cardiac calcium currents produced by beta-adrenergic stimulation are initiated, in part, by parallel changes in the gating charge movement.     

Nucleotides provide a voltage-sensitive gate for the rapid anion channel of arabidopsis hypocotyl cells

The rapid anion channel of Arabidopsis hypocotyl cells is highly voltage-dependent. At hyperpolarized potentials, the channel is closed, and membrane depolarization is required for channel activation. We have previously shown that channel gating is regulated by intracellular nucleotides. In the present study, we further analyze the channel gating, and we propose a mechanism to explain its regulation by voltage. In the absence of intracellular nucleotides, closure at hyperpolarized voltages is abolished. Structure-function studies of adenyl nucleotides show that the apparent gating charge of the current increases with the negative charge carried by nucleotides. We propose that the fast anion channel is gated by the voltage-dependent entry of free nucleotides into the pore, leading to a voltage-dependent block at hyperpolarized potentials. In agreement with this mechanism in which intracellular nucleotides need to be recruited to the channel pore, kinetic analyses of whole-cell and single-channel currents show that the rate of closure is faster when intracellular nucleotide concentration is increased, whereas the rate of channel activation is unchanged. Furthermore, decreasing the concentration of extracellular chloride enhances the intracellular nucleotide block. This result supports the hypothesis of a mechanism in which blocking nucleotides and permeant anions interact within the channel pore.     

Mutations within the S4-S5 linker alter voltage sensor constraints in hERG K+ channels

Human ether-a-go-go related gene (hERG) channel gating is associated with slow activation, yet the mechanistic basis for this is unclear. Here, we examine the effects of mutation of a unique glycine residue (G546) in the S4-S5 linker on voltage sensor movement and its coupling to pore gating. Substitution of G546 with residues possessing different physicochemical properties shifted activation gating by ∼−50 mV (with the exception of G546C). With the activation shift taken into account, the time constant of activation was also accelerated, suggesting a stabilization of the closed state by ∼1.6-4.3 kcal/mol (the energy equivalent of one to two hydrogen bonds). Predictions of the α-helical content of the S4-S5 linker suggest that the presence of G546 in wild-type hERG provides flexibility to the helix. Deactivation gating was affected differentially by the G546 substitutions. G546V induced a pronounced slow component of closing that was voltage-independent. Fluorescence measurements of voltage sensor movement in G546V revealed a slow component of voltage sensor return that was uncoupled from charge movement, suggesting a direct effect of the mutation on voltage sensor movement. These data suggest that G546 plays a critical role in channel gating and that hERG channel closing involves at least two independently modifiable reconfigurations of the voltage sensor.     

Membrane potential and time requirements for detection of weak signals by voltage‐gated ion channels

The question of minimum detection limits for biological processes sensitive to membrane potential perturbations has arisen in various contexts. Of special interest are the prediction of theoretical limits for sensory perception processes and for possible biological effects of environmental or therapeutic electric and magnetic fields. A new method is presented here, addressing the particular case in which perturbations of membrane potential affect the gating rate probability of voltage‐sensitive ion channels. Using a two‐state model for channel gating, the influence of the perturbing potential on the mean fraction of open channels is approximated by a Boltzmann distribution, and integrated over time to obtain a quantity proportional to the net change in expected charge transfer through the membrane. This change in net charge transfer (the signal, S) is compared to the expected root mean variance in charge transfer (the noise, N) due to random channel gating. Using a nominal criterion of S/N = 1, a model is developed for predicting the minimum time and number of ion channels necessary to detect a given membrane potential. Example calculations, carried out for a gating charge of 6, indicate that a 1 μV induced membrane potential can be detected after 10 ms by an ensemble of less than 10⁸ ion channels. Bioelectromagnetics 20:102–109, 1999. Published 1999 Wiley‐Liss, Inc.     

Nonequilibrium gating and voltage dependence of the ClC-0 Cl- channel

The gating of ClC-0, the voltage-dependent Cl- channel from Torpedo electric organ, is strongly influenced by Cl- ions in the external solution. Raising external Cl- over the range 1-600 mM favors the fast- gating open state and disfavors the slow-gating inactivated state. Analysis of purified single ClC-0 channels reconstituted into planar lipid bilayers was used to identify the role of Cl- ions in the channel's fast voltage-dependent gating process. External, but not internal, Cl- had a major effect on the channel's opening rate constant. The closing rate was more sensitive to internal Cl- than to external Cl-. Both opening and closing rates varied with voltage. A model was derived that postulates (a) that in the channel's closed state, Cl- is accessible to a site located at the outer end of the conduction pore, where it binds in a voltage-independent fashion, (b) that this closed conformation can open, whether liganded by Cl- or not, in a weakly voltage-dependent fashion, (c) that the Cl(-)-liganded closed channel undergoes a conformational change to a different closed state, such that concomitant with this change, Cl- ion moves inward, conferring voltage-dependence to this step, and (d) that this new Cl(-)- liganded closed state opens with a very high rate. According to this picture, Cl- movement within the pre-open channel is the major source of voltage dependence, and charge movement intrinsic to the channel protein contributes very little to voltage-dependent gating of ClC-0. Moreover, since the Cl- activation site is probably located in the ion conduction pathway, the fast gating of ClC-0 is necessarily coupled to ion conduction, a nonequilibrium process.     

Temperature Dependence of Steady-State and Presteady-State Kinetics of a Type IIb Na+/Pi Cotransporter

The temperature dependence of the transport kinetics of flounder Na(+)-coupled inorganic phosphate (P(i)) cotransporters (NaPi-IIb) expressed in Xenopus oocytes was investigated using radiotracer and electrophysiological assays. (32)P(i) uptake was strongly temperature-dependent and decreased by approximately 80% at a temperature change from 25 degrees C to 5 degrees C. The corresponding activation energy (E (a)) was approximately 14 kcal mol(-1) for the cotransport mode. The temperature dependence of the cotransport and leak modes was determined from electrogenic responses to 1 mM P(i) and phosphonoformic acid (PFA), respectively, under voltage clamp. The magnitude of the P(i)- and PFA-induced changes in holding current decreased with temperature. E (a) at -100 mV for the cotransport and leak modes was approximately 16 kcal mol(-1) and approximately 11 kcal mol(-1), respectively, which suggested that the leak is mediated by a carrier, rather than a channel, mechanism. Moreover, E (a) for cotransport was voltage-independent, suggesting that a major conformational change in the transport cycle is electroneutral. To identify partial reactions that confer temperature dependence, we acquired presteady-state currents at different temperatures with 0 mM P(i) over a range of external Na(+). The relaxation time constants increased, and the peak time constant shifted toward more positive potentials with decreasing temperature. Likewise, there was a depolarizing shift of the charge distribution, whereas the total available charge and apparent valency predicted from single Boltzmann fits were temperature-independent. These effects were explained by an increased temperature sensitivity of the Na(+)-debinding rate compared with the other voltage-dependent rate constants.     

Intrinsic Voltage Dependence and Ca2+ Regulation of mslo Large Conductance Ca-activated K+ Channels

The kinetic and steady-state properties of macroscopic mslo Ca-activated K⁺ currents were studied in excised patches from Xenopus oocytes. In response to voltage steps, the timecourse of both activation and deactivation, but for a brief delay in activation, could be approximated by a single exponential function over a wide range of voltages and internal Ca²⁺ concentrations ([Ca]_i). Activation rates increased with voltage and with [Ca]_i, and approached saturation at high [Ca]_i. Deactivation rates generally decreased with [Ca]_i and voltage, and approached saturation at high [Ca]_i. Plots of the macroscopic conductance as a function of voltage (G-V) and the time constant of activation and deactivation shifted leftward along the voltage axis with increasing [Ca]_i. G-V relations could be approximated by a Boltzmann function with an equivalent gating charge which ranged between 1.1 and 1.8 e as [Ca]_i varied between 0.84 and 1,000 μM. Hill analysis indicates that at least three Ca²⁺ binding sites can contribute to channel activation. Three lines of evidence indicate that there is at least one voltage-dependent unimolecular conformational change associated with mslo gating that is separate from Ca²⁺ binding. (a) The position of the mslo G-V relation does not vary logarithmically with [Ca]_i. (b) The macroscopic rate constant of activation approaches saturation at high [Ca]_i but remains voltage dependent. (c) With strong depolarizations mslo currents can be nearly maximally activated without binding Ca²⁺. These results can be understood in terms of a channel which must undergo a central voltage-dependent rate limiting conformational change in order to move from closed to open, with rapid Ca²⁺ binding to both open and closed states modulating this central step.     

Kinetic and Energetic Analysis of Thermally Activated TRPV1 Channels

Thermal TRP channels are important for thermal sensation and nociception, but their gating mechanisms have remained elusive. With optically generated submillisecond temperature steps from 22°C to >60°C, we have directly measured the activation and deactivation kinetics of TRPV1 channels, and from the measurements we determined the energetics of thermal gating. We show that activation by temperature follows single exponential time courses. It occurs in a few milliseconds and is significantly faster than activation by agonists. The gating has characteristics of a melting process involving large compensatory enthalpy (>100 kcal/mol) and entropy changes with little free energy change. The reaction path is asymmetrical with temperature mainly driving the opening while the closing has nominal but negative temperature dependence (i.e., sensitivity to cold). Both voltage and agonists alter the slope of the temperature-dependent gating curve as well as shifting the midpoint. However, compared to the energetic effect of temperature on gating, the effect of voltage is small. Our data on the interdependence between voltage and direct temperature responses are not fit to a model involving independent stimuli but instead support a temperature-sensing mechanism that is coupled to charge movement or agonist binding.     

Exploring voltage-dependent ion channels in silico by hysteretic conductance

Kinetic models of voltage-dependent ion channels are normally inferred from time records of macroscopic current relaxation or microscopic single channel data. A complementary explorative approach is outlined. Hysteretic conductance refers to conductance delays in response to voltage changes, delays at either macroscopic or microscopic levels of observation. It enables complementary assessments of model assumptions and gating schemes of voltage-dependent channels, e.g. independent versus cooperative gating, and multiple gating modes. Under the Hodgkin-Huxley condition of independent gating, and under ideal measurement conditions, hysteretic conductance makes it also possible to estimate voltage-dependent rate functions. The argument is mainly theoretical, based on experimental observations, and illustrated by simulations of Markov kinetic models.     

A self-consistent approach for determining pairwise interactions that underlie channel activation

Signaling proteins such as ion channels largely exist in two functional forms, corresponding to the active and resting states, connected by multiple intermediates. Multiparametric kinetic models based on sophisticated electrophysiological experiments have been devised to identify molecular interactions of these conformational transitions. However, this approach is arduous and is not suitable for large-scale perturbation analysis of interaction pathways. Recently, we described a model-free method to obtain the net free energy of activation in voltage- and ligand-activated ion channels. Here we extend this approach to estimate pairwise interaction energies of side chains that contribute to gating transitions. Our approach, which we call generalized interaction-energy analysis (GIA), combines median voltage estimates obtained from charge-voltage curves with mutant cycle analysis to ascertain the strengths of pairwise interactions. We show that, for a system with an arbitrary gating scheme, the nonadditive contributions of amino acid pairs to the net free energy of activation can be computed in a self-consistent manner. Numerical analyses of sequential and allosteric models of channel activation also show that this approach can measure energetic nonadditivities even when perturbations affect multiple transitions. To demonstrate the experimental application of this method, we reevaluated the interaction energies of six previously described long-range interactors in the Shaker potassium channel. Our approach offers the ability to generate detailed interaction energy maps in voltage- and ligand-activated ion channels and can be extended to any force-driven system as long as associated “displacement” can be measured.     

Phosphorylation of K+ channels in the squid giant axon. A mechanistic analysis

Protein phosphorylation is an important mechanism in the modulation of voltage-dependent ionic channels. In squid giant axons, the potassium delayed rectifier channel is modulated by an ATP-mediated phosphorylation mechanism, producing important changes in amplitude and kinetics of the outward current. The characteristics and biophysical basis for the phosphorylation effects have been extensively studied in this preparation using macroscopic, single-channel and gating current experiments. Phosphorylation produces a shift in the voltage dependence of all voltage-dependent parameters including open probability, slow inactivation, first latency, and gating charge transferred. The locus of the effect seems to be located in a fast 20 pS channel, with characteristics of delayed rectifier, but at least another channel is phosphorylated under our experimental conditions. These results are interpreted quantitatively with a mechanistic model that explains all the data. In this model the shift in voltage dependence is produced by electrostatic interactions between the transferred phosphate and the voltage sensor of the channel.     

A physical model of potassium channel activation: from energy landscape to gating kinetics

We have developed a method for rapidly computing gating currents from a multiparticle ion channel model. Our approach is appropriate for energy landscapes that can be characterized by a network of well-defined activation pathways with barriers. To illustrate, we represented the gating apparatus of a channel subunit by an interacting pair of charged gating particles. Each particle underwent spatial diffusion along a bistable potential of mean force, with electrostatic forces coupling the two trajectories. After a step in membrane potential, relaxation of the smaller barrier charge led to a time-dependent reduction in the activation barrier of the principal gate charge. The resulting gating current exhibited a rising phase similar to that measured in voltage-dependent ion channels. Reduction of the two-dimensional diffusion landscape to a circular Markov model with four states accurately preserved the time course of gating currents on the slow timescale. A composite system containing four subunits leading to a concerted opening transition was used to fit a series of gating currents from the Shaker potassium channel. We end with a critique of the model with regard to current views on potassium channel structure.     

Role of charged residues in the S1-S4 voltage sensor of BK channels

The activation of large conductance Ca(2+)-activated (BK) potassium channels is weakly voltage dependent compared to Shaker and other voltage-gated K(+) (K(V)) channels. Yet BK and K(V) channels share many conserved charged residues in transmembrane segments S1-S4. We mutated these residues individually in mSlo1 BK channels to determine their role in voltage gating, and characterized the voltage dependence of steady-state activation (P(o)) and I(K) kinetics (tau(I(K))) over an extended voltage range in 0-50 microM [Ca(2+)](i). mSlo1 contains several positively charged arginines in S4, but only one (R213) together with residues in S2 (D153, R167) and S3 (D186) are potentially voltage sensing based on the ability of charge-altering mutations to reduce the maximal voltage dependence of P(O). The voltage dependence of P(O) and tau(I(K)) at extreme negative potentials was also reduced, implying that the closed-open conformational change and voltage sensor activation share a common source of gating charge. Although the position of charged residues in the BK and K(V) channel sequence appears conserved, the distribution of voltage-sensing residues is not. Thus the weak voltage dependence of BK channel activation does not merely reflect a lack of charge but likely differences with respect to K(V) channels in the position and movement of charged residues within the electric field. Although mutation of most sites in S1-S4 did not reduce gating charge, they often altered the equilibrium constant for voltage sensor activation. In particular, neutralization of R207 or R210 in S4 stabilizes the activated state by 3-7 kcal mol(-1), indicating a strong contribution of non-voltage-sensing residues to channel function, consistent with their participation in state-dependent salt bridge interactions. Mutations in S4 and S3 (R210E, D186A, and E180A) also unexpectedly weakened the allosteric coupling of voltage sensor activation to channel opening. The implications of our findings for BK channel voltage gating and general mechanisms of voltage sensor activation are discussed.     

Electrostatics explains the shift in VDAC gating with salt activity gradient

We have analyzed voltage-dependent anion-selective channel (VDAC) gating on the assumption that the states occupied by the channel are determined mainly by their electrostatic energy. The voltage dependence of VDAC gating both in the presence and in the absence of a salt activity gradient was explained just by invoking electrostatic interactions. A model describing this energy in the main VDAC states has been developed. On the basis of the model, we have considered how external factors cause the redistribution of the channels among their conformational states. We propose that there is a difference in the electrostatic interaction between the voltage sensor and fixed charge within the channel when the former is located in the cis side of membrane as opposed to the trans. This could be the main cause of the shift in the probability curve. The theory describes satisfactorily the experimental data (Zizi et al., Biophys. J. 1998. 75:704-713) and explains some peculiarities of VDAC gating. The asymmetry of the probability curve was related to the apparent location of the VDAC voltage sensor in the open state. By analyzing published experimental data, we concluded that this apparent location is influenced by the diffusion potential. Also discussed is the possibility that VDAC gating at high voltage may be better described by assuming that the mobile charge consists of two parts that have to overcome different energetic barriers in the channel-closing process.