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.     

Mutations in the S4 region isolate the final voltage-dependent cooperative step in potassium channel activation

Charged residues in the S4 transmembrane segment play a key role in determining the sensitivity of voltage-gated ion channels to changes in voltage across the cell membrane. However, cooperative interactions between subunits also affect the voltage dependence of channel opening, and these interactions can be altered by making substitutions at uncharged residues in the S4 region. We have studied the activation of two mutant Shaker channels that have different S4 amino acid sequences, ILT (V369I, I372L, and S376T) and Shaw S4 (the S4 of Drosophila Shaw substituted into Shaker), and yet have very similar ionic current properties. Both mutations affect cooperativity, making a cooperative transition in the activation pathway rate limiting and shifting it to very positive voltages, but analysis of gating and ionic current recordings reveals that the ILT and Shaw S4 mutant channels have different activation pathways. Analysis of gating currents suggests that the dominant effect of the ILT mutation is to make the final cooperative transition to the open state of the channel rate limiting in an activation pathway that otherwise resembles that of Shaker. The charge movement associated with the final gating transition in ILT activation can be measured as an isolated component of charge movement in the voltage range of channel opening and accounts for 13% ( approximately 1.8 e0) of the total charge moved in the ILT activation pathway. The remainder of the ILT gating charge (87%) moves at negative voltages, where channels do not open, and confirms the presence of Shaker-like conformational changes between closed states in the activation pathway. In contrast to ILT, the activation pathway of Shaw S4 seems to involve a single cooperative charge-moving step between a closed and an open state. We cannot detect any voltage-dependent transitions between closed states for Shaw S4. Restoring basic residues that are missing in Shaw S4 (R1, R2, and K7) rescues charge movement between closed states in the activation pathway, but does not alter the voltage dependence of the rate-limiting transition in activation.     

Sequence of Gating Charge Movement and Pore Gating in hERG Activation and Deactivation Pathways

K_V11.1 voltage-gated K⁺ channels are noted for unusually slow activation, fast inactivation, and slow deactivation kinetics, which tune channel activity to provide vital repolarizing current during later stages of the cardiac action potential. The bulk of charge movement in human ether-a-go-go-related gene (hERG) is slow, as is return of charge upon repolarization, suggesting that the rates of hERG channel opening and, critically, that of deactivation might be determined by slow voltage sensor movement, and also by a mode-shift after activation. To test these ideas, we compared the kinetics and voltage dependence of ionic activation and deactivation with gating charge movement. At 0 mV, gating charge moved ∼threefold faster than ionic current, which suggests the presence of additional slow transitions downstream of charge movement in the physiological activation pathway. A significant voltage sensor mode-shift was apparent by 24 ms at +60 mV in gating currents, and return of charge closely tracked pore closure after pulses of 100 and 300 ms duration. A deletion of the N-terminus PAS domain, mutation R4AR5A or the LQT2-causing mutation R56Q gave faster-deactivating channels that displayed an attenuated mode-shift of charge. This indicates that charge movement is perturbed by N- and C-terminus interactions, and that these domain interactions stabilize the open state and limit the rate of charge return. We conclude that slow on-gating charge movement can only partly account for slow hERG ionic activation, and that the rate of pore closure has a limiting role in the slow return of gating charges.     

Gating currents in Shaker K+ channels. Implications for activation and inactivation models.

We have studied ionic and gating currents in mutant and wild-type Shaker K+ channels to investigate the mechanisms of channel activation and the relationship between the voltage sensor of the channel and its inactivation particle. The turn on of the gating current shows a rising phase, indicating that the hypothetical identical activation subunits are not independent. Hyperpolarizing prepulses indicate that most of the voltage-dependence occurs in the transitions between closed states. The open-to-closed transition is voltage independent, as suggested by the presence of a rising phase in the off gating currents. In Shaker channels showing fast inactivation, the off gating charge is partially immobilized as a result of depolarizing pulses that elicit inactivation. In mutant channels lacking inactivation, the charge is recovered quickly at the end of the pulse. Internal TEA mimics the inactivation particle in its behavior but the charge immobilization is established faster and is complete. We conclude that the activation mechanism cannot be due to the movement of identical independent gating subunits, each undergoing first order transitions, and that the inactivation particle is responsible for charge immobilization in this channel.     

Altered sodium and gating current kinetics in frog skeletal muscle caused by low external pH

The effect of low pH on the kinetics of Na channel ionic and gating currents was studied in frog skeletal muscle fibers. Lowering external pH from 7.4 to 5.0 slows the time course of Na current consistent with about a +25-mV shift in the voltage dependence of activation and inactivation time constants. Similar shifts in voltage dependence adequately describe the effects of low pH on the tail current time constant (+23.3 mV) and the gating charge vs. voltage relationship (+22.1 mV). A significantly smaller shift of +13.3 mV described the effect of pH 5.0 solution on the voltage dependence of steady state inactivation. Changes in the time course of gating current at low pH were complex and could not be described as a shift in voltage dependence. tau g, the time constant that describes the time course of the major component of gating charge movement, was slowed in pH 5.0 solution by a factor of approximately 3.5 for potentials from -60 to +45 mV. We conclude that the effects of low pH on Na channel gating cannot be attributed simply to a change in surface potential. Therefore, although it may be appropriate to describe the effect of low pH on some Na channel kinetic properties as a "shift" in voltage dependence, it is not appropriate to interpret such shifts as a measure of changes in surface potential. The maximum gating charge elicited from a holding potential of -150 mV was little affected by low pH.(ABSTRACT TRUNCATED AT 250 WORDS)     

Open-State Occupancy Prevents Gating Charge Relaxation of N-type (CaV2.2) Calcium Channels

N-type and L-type channels have significant gating differences, and we wondered whether some of these differences are linked to the relationship between charge movement and channel opening. The time constants for N-channel closing (τ_Deact) and Off-gating charge movement (τQ_Off) were compared over a range of voltages. τQ_Off was significantly larger than τ_Deact at voltages < −10 mV, and the voltage dependence of the τQ_Off was less steep than that for τ_Deact, which suggests that gating charge relaxation does not limit channel closing. Roscovitine, a drug that slows N-channel closing by holding the channel in a high open-probability state, was found to slow both τQ_Off and τ_Deact, and thus the time courses of channel closing and gating charge relaxation were similar. Our gating current results were reproduced with the addition of a voltage-independent, closed-closed transition to our previously published two-open-state N-channel model. This work suggests that, like L-type channels, there is a voltage-independent transition along the N-channel activation/deactivation pathway, but this transition occurs between closed states instead of the closed-open states of the L-channel. Also unlike L-type channels, the gating charge appears to be locked into the activated position by the N-channel open state.     

Integrated allosteric model of voltage gating of HCN channels

Hyperpolarization-activated (pacemaker) channels are dually gated by negative voltage and intracellular cAMP. Kinetics of native cardiac f-channels are not compatible with HH gating, and require closed/open multistate models. We verified that members of the HCN channel family (mHCN1, hHCN2, hHCN4) also have properties not complying with HH gating, such as sigmoidal activation and deactivation, activation deviating from fixed power of an exponential, removal of activation "delay" by preconditioning hyperpolarization. Previous work on native channels has indicated that the shifting action of cAMP on the open probability (Po) curve can be accounted for by an allosteric model, whereby cAMP binds more favorably to open than closed channels. We therefore asked whether not only cAMP-dependent, but also voltage-dependent gating of hyperpolarization-activated channels could be explained by an allosteric model. We hypothesized that HCN channels are tetramers and that each subunit comprises a voltage sensor moving between "reluctant" and "willing" states, whereas voltage sensors are independently gated by voltage, channel closed/open transitions occur allosterically. These hypotheses led to a multistate scheme comprising five open and five closed channel states. We estimated model rate constants by fitting first activation delay curves and single exponential time constant curves, and then individual activation/deactivation traces. By simply using different sets of rate constants, the model accounts for qualitative and quantitative aspects of voltage gating of all three HCN isoforms investigated, and allows an interpretation of the different kinetic properties of different isoforms. For example, faster kinetics of HCN1 relative to HCN2/HCN4 are attributable to higher HCN1 voltage sensors' rates and looser voltage-independent interactions between subunits in closed/open transitions. It also accounts for experimental evidence that reduction of sensors' positive charge leads to negative voltage shifts of Po curve, with little change of curve slope. HCN voltage gating thus involves two processes: voltage sensor gating and allosteric opening/closing.     

Charge movement in gating-locked HCN channels reveals weak coupling of voltage sensors and gate

HCN (hyperpolarization-activated cyclic nucleotide gated) pacemaker channels have an architecture similar to that of voltage-gated K⁺ channels, but they open with the opposite voltage dependence. HCN channels use essentially the same positively charged voltage sensors and intracellular activation gates as K⁺ channels, but apparently these two components are coupled differently. In this study, we examine the energetics of coupling between the voltage sensor and the pore by using cysteine mutant channels for which low concentrations of Cd²⁺ ions freeze the open–closed gating machinery but still allow the sensors to move. We were able to lock mutant channels either into open or into closed states by the application of Cd²⁺ and measure the effect on voltage sensor movement. Cd²⁺ did not immobilize the gating charge, as expected for strict coupling, but rather it produced shifts in the voltage dependence of voltage sensor charge movement, consistent with its effect of confining transitions to either closed or open states. From the magnitude of the Cd²⁺-induced shifts, we estimate that each voltage sensor produces a roughly three- to sevenfold effect on the open–closed equilibrium, corresponding to a coupling energy of ∼1.3–2 kT per sensor. Such coupling is not only opposite in sign to the coupling in K⁺ channels, but also much weaker.     

Activation of squid axon K+ channels. Ionic and gating current studies

We have used data obtained from measurements of ionic and gating currents to study the process of K+ channel activation in squid giant axons. A marked improvement in the recording of K+ channel gating currents (IKg) was obtained by total replacement of Cl- in the external solution by NO-3, which eliminates approximately 50% of the Na+ channel gating current with no effect on IKg. The midpoint of the steady state charge-voltage (Qrel - V) relationship is approximately 40 mV hyperpolarized to that of the steady state activation (fo - V) curve, which is an indication that the channel has many nonconducting states. Ionic and gating currents have similar time constants for both ON and OFF pulses. This eliminates any Hodgkin-Huxley nx scheme for K+ channel activation. An interrupted pulse paradigm shows that the last step in the activation process is not rate limiting. IKg shows a nonartifactual rising phase, which indicates that the first step is either the slowest step in the activation sequence or is voltage independent. These data are consistent with the following general scheme for K+ channel activation: (formula; see text)     

Estimating the voltage-dependent free energy change of ion channels using the median voltage for activation

Voltage-gated ion channels are crucial for electrical activity and chemical signaling in a variety of cell types. Structure-activity studies involving electrophysiological characterization of mutants are widely used and allow us to quickly realize the energetic effects of a mutation by measuring macroscopic currents and fitting the observed voltage dependence of conductance to a Boltzmann equation. However, such an approach is somewhat limiting, principally because of the inherent assumption that the channel activation is a two-state process. In this analysis, we show that the area delineated by the gating charge displacement curve and its ordinate axis is related to the free energy of activation of a voltage-gated ion channel. We derive a parameter, the median voltage of charge transfer (V(m)), which is proportional to this area, and prove that the chemical component of free energy change of a system can be obtained from the knowledge of V(m) and the maximum number of charges transferred. Our method is not constrained by the number or connectivity of intermediate states and is applicable to instances in which the observed responses show a multiphasic behavior. We consider various models of ion channel gating with voltage-dependent steps, latent charge movement, inactivation, etc. and discuss the applicability of this approach in each case. Notably, our method estimates a net free energy change of approximately -14 kcal/mol associated with the full-scale activation of the Shaker potassium channel, in contrast to -2 to -3 kcal/mol estimated from a single Boltzmann fit. Our estimate of the net free energy change in the system is consistent with those derived from detailed kinetic models (Zagotta et al. 1994. J. Gen. Physiol. doi:10.1085/jgp.103.2.321). The median voltage method can reliably quantify the magnitude of free energy change associated with activation of a voltage-dependent system from macroscopic equilibrium measurements. This will be particularly useful in scanning mutagenesis experiments.     

Transfer of twelve charges is needed to open skeletal muscle Na+ channels

Voltage-dependent Na+ channels are thought to sense membrane potential with fixed charges located within the membrane's electrical field. Measurement of open probability (Po) as a function of membrane potential gives a quantitative indication of the number of such charges that move through the field in opening the channel. We have used single- channel recording to measure skeletal muscle Na+ channel open probability at its most negative extreme, where channels may open as seldom as once per minute. To prevent fast inactivation from masking the voltage dependence of Po, we have generated a clone of the rat skeletal muscle Na+ channel that is lacking in fast inactivation (IFM1303QQQ). Using this mutant channel expressed in Xenopus oocytes, and the extra resolution afforded by single-channel analysis, we have extended the resolution of the hyperpolarized tail of the Po curve by four orders of magnitude. We show that previous measurements, which indicated a minimum of six effective gating charges, may have been made in a range of Po values that had not yet arrived at its limiting slope. In our preparation, a minimum of 12 charges must function in the activation gating of the channel. Our results will require reevaluation of kinetic models based on six charges, and they have major implications for the interpretation of S4 mutagenesis studies and structure/function models of the Na+ channel.     

Non-Native R1 Substitution in the S4 Domain Uniquely Alters Kv4.3 Channel Gating

The S4 transmembrane domain in Shaker (Kv1) voltage-sensitive potassium channels has four basic residues (R1–R4) that are responsible for carrying the majority of gating charge. In Kv4 channels, however, R1 is replaced by a neutral valine at position 287. Among other differences, Kv4 channels display prominent closed state inactivation, a mechanism which is minimal in Shaker. To determine if the absence of R1 is responsible for important variation in gating characteristics between the two channel types, we introduced the V287R mutant into Kv4.3 and analyzed its effects on several voltage sensitive gating transitions. We found that the mutant increased the voltage sensitivity of steady-state activation and altered the kinetics of activation and deactivation processes. Although the kinetics of macroscopic inactivation were minimally affected, the characteristics of closed-state inactivation and recovery from open and closed inactivated states were significantly altered. The absence of R1 can only partially account for differences in the effective voltage sensitivity of gating between Shaker and Kv4.3. These results suggest that the S4 domain serves an important functional role in Kv4 channel activation and deactivation processes, and also those of closed-state inactivation and recovery.     

Regulation of K+ flow by a ring of negative charges in the outer pore of BKCa channels. Part II: Neutralization of aspartate 292 reduces long channel openings and gating current slow component

Neutralization of the aspartate near the selectivity filter in the GYGD pore sequence (D292N) of the voltage- and Ca(2+)-activated K+ channel (MaxiK, BKCa) does not prevent conduction like the corresponding mutation in Shaker channel, but profoundly affects major biophysical properties of the channel (Haug, T., D. Sigg, S. Ciani, L. Toro, E. Stefani, and R. Olcese. 2004. J. Gen. Physiol. 124:173-184). Upon depolarizations, the D292N mutant elicited mostly gating current, followed by small or no ionic current, at voltages where the wild-type hSlo channel displayed robust ionic current. In fact, while the voltage dependence of the gating current was not significantly affected by the mutation, the overall activation curve was shifted by approximately 20 mV toward more depolarized potentials. Several lines of evidence suggest that the mutation prevents population of certain open states that in the wild type lead to high open probability. The activation curves of WT and D292N can both be fitted to the sum of two Boltzmann distributions with identical slope factors and half activation potentials, just by changing their relative amplitudes. The steeper and more negative component of the activation curve was drastically reduced by the D292N mutation (from 0.65 to 0.30), suggesting that the population of open states that occurs early in the activation pathway is reduced. Furthermore, the slow component of the gating current, which has been suggested to reflect transitions from closed to open states, was greatly reduced in D292N channels. The D292N mutation also affected the limiting open probability: at 0 mV, the limiting open probability dropped from approximately 0.5 for the wild-type channel to 0.06 in D292N (in 1 mM [Ca2+]i). In addition to these effects on gating charge and open probability, as already described in Part I, the D292N mutation introduces a approximately 40% reduction of outward single channel conductance, as well as a strong outward rectification.     

beta-Scorpion toxin modifies gating transitions in all four voltage sensors of the sodium channel

Several naturally occurring polypeptide neurotoxins target specific sites on the voltage-gated sodium channels. Of these, the gating modifier toxins alter the behavior of the sodium channels by stabilizing transient intermediate states in the channel gating pathway. Here we have used an integrated approach that combines electrophysiological and spectroscopic measurements to determine the structural rearrangements modified by the beta-scorpion toxin Ts1. Our data indicate that toxin binding to the channel is restricted to a single binding site on domain II voltage sensor. Analysis of Cole-Moore shifts suggests that the number of closed states in the activation sequence prior to channel opening is reduced in the presence of toxin. Measurements of charge-voltage relationships show that a fraction of the gating charge is immobilized in Ts1-modified channels. Interestingly, the charge-voltage relationship also shows an additional component at hyperpolarized potentials. Site-specific fluorescence measurements indicate that in presence of the toxin the voltage sensor of domain II remains trapped in the activated state. Furthermore, the binding of the toxin potentiates the activation of the other three voltage sensors of the sodium channel to more hyperpolarized potentials. These findings reveal how the binding of beta-scorpion toxin modifies channel function and provides insight into early gating transitions of sodium channels.     

Charge displacements in a single potassium ion channel macromolecule during gating.

Single ion channel currents can only provide indirect information on channel molecular events (except for timing). In contrast, the electric displacement currents associated with channel gating, termed gating currents, can provide direct information regarding the channel molecule's conformational changes. However, thus far gating currents have been measured only from ensembles of numerous stochastically activated channels and therefore the information they provide is limited. This work presents, for the first time, measurements of gating currents from a single channel molecule. Averaging close to 8000 pre-open currents, aligned to the single channel opening time, enabled the detection of single channel gating currents with a resolution of 2 electron charges. The measured charge displacements show: 1) a slow component, approximately 2 fA above baseline level, assumed to represent stochastic conformational changes, and 2) transients, the most significant of which occur 1.1 and 0.3 ms before channel opening. The transients most likely represent apparent deterministic stages in the gating process. The largest transient current peak was 5.1 +/- 1.6 fA and the total equivalent charge transported across the membrane was 4.7 +/- 2.5 electron charges. This data is unique also in that it presents monitoring of the behavior of a single, well-defined macromolecule.     

Hill coefficient for estimating the magnitude of cooperativity in gating transitions of voltage-dependent ion channels

A frequently used measure for the extent of cooperativity in ligand binding by an allosteric protein is the Hill coefficient, obtained by fitting data of initial reaction velocity (or fractional binding saturation) as a function of substrate concentration to the Hill equation. Here, it is demonstrated that the simple two-state Boltzmann equation that is widely used to fit voltage-activation data of voltage-dependent ion channels is analogous to the Hill equation. A general empiric definition for a Hill coefficient (n(H)) for channel gating transitions that is analogous to the logarithmic potential sensitivity function of Almers is derived. This definition provides a novel framework for interpreting the meaning of the Hill coefficient. In considering three particular and simple gating schemes for a voltage-activated cation channel, the relation of the Hill coefficient to the magnitude and nature of cooperative interactions along the reaction coordinate of channel gating is demonstrated. A possible functional explanation for the low value of the Hill coefficient for gating transitions of the Shaker voltage-activated K(+) channel is suggested. The analogy between the Hill coefficients for ligand binding and for channel gating transitions further points to a unified conceptual framework in analyzing enzymes and channels behavior.     

An S6 mutation in BK channels reveals beta1 subunit effects on intrinsic and voltage-dependent gating

Large conductance, Ca(2+)- and voltage-activated K(+) (BK) channels are exquisitely regulated to suit their diverse roles in a large variety of physiological processes. BK channels are composed of pore-forming alpha subunits and a family of tissue-specific accessory beta subunits. The smooth muscle-specific beta1 subunit has an essential role in regulating smooth muscle contraction and modulates BK channel steady-state open probability and gating kinetics. Effects of beta1 on channel's gating energetics are not completely understood. One of the difficulties is that it has not yet been possible to measure the effects of beta1 on channel's intrinsic closed-to-open transition (in the absence of voltage sensor activation and Ca(2+) binding) due to the very low open probability in the presence of beta1. In this study, we used a mutation of the alpha subunit (F315Y) that increases channel openings by greater than four orders of magnitude to directly compare channels' intrinsic open probabilities in the presence and absence of the beta1 subunit. Effects of beta1 on steady-state open probabilities of both wild-type alpha and the F315Y mutation were analyzed using the dual allosteric HA model. We found that mouse beta1 has two major effects on channel's gating energetics. beta1 reduces the intrinsic closed-to-open equilibrium that underlies the inhibition of BK channel opening seen in submicromolar Ca(2+). Further, P(O) measurements at limiting slope allow us to infer that beta1 shifts open channel voltage sensor activation to negative membrane potentials, which contributes to enhanced channel opening seen at micromolar Ca(2+) concentrations. Using the F315Y alpha subunit with deletion mutants of beta1, we also demonstrate that the small N- and C-terminal intracellular domains of beta1 play important roles in altering channel's intrinsic opening and voltage sensor activation. In summary, these results demonstrate that beta1 has distinct effects on BK channel intrinsic gating and voltage sensor activation that can be functionally uncoupled by mutations in the intracellular domains.     

Effects of glutaraldehyde on sodium channel activation and inactivation in frog nerve fiber

The effects of glutaraldehyde on sodium channel gating were investigated in the membrane of the node of Ranvier in frog nerve fiber. It was found that treating the membrane with glutaraldehyde slows the rate of inactivation, renders the inactivation curve considerably less steep, and leads to the appearance of a steady-state current component. It also decelerated the activation rate and reduced the slope of the central portion of the activation curve, which was shifted over to depolarization at the membrane. This produced no significant change in the effective charge in the effective charge of activation as determined from the limiting logarithmic slope of the activation curve. The mechanisms possibly underlying these changes in sodium channel gating are discussed.Institute of Cytology, Academy of Sciences of the USSR, Leningrad. Translated from Neirofiziologiya, Vol. 18, No. 5, pp. 579–586, September–October, 1986.     

Effects of chloramine-T on activation and inactivation of sodium channels in neuroblastoma cells

The effects of chloramine-T, a reagent specific to methionine residues, on sodium channel gating mechanisms was investigated in neuroblastoma cell membrane. Treating the membrane with chloramine was found to retard inactivation kinetics and considerably reduce the slope of the inactivation curve, while pushing the activation curve toward hyperpolarization ranges without changing the slope of the central portion perceptibly. Effective activation charge, as determined from the limiting logarithmic slope of activation, was reduced by a factor of 1.17. Possible reasons for the changes observed in sodium channel gating mechanisms are discussed.Institute of Cytology, Academy of Sciences of the USSR, Leningrad. Translated from Neirofiziologiya, Vol. 19, No. 6, pp. 789–795, November–December, 1987.     

The N-terminus of the K channel KAT1 controls its voltage-dependent gating by altering the membrane electric field.

Functional roles of different domains (pore region, S4 segment, N-terminus) of the KAT1 potassium channel in its voltage-dependent gating were electrophysiologically studied in Xenopus oocytes. The KAT1 properties did not depend on the extracellular K+ concentration or on residue H267, equivalent to one of the residues known to be important in C-type inactivation in Shaker channels, indicating that the hyperpolarization-induced KAT1 inward currents are related to the channel activation rather than to recovery from inactivation. Neutralization of a positively charged amino acid in the S4 domain (R176S) reduced the gating charge movement, suggesting that it acts as a voltage-sensing residue in KAT1. N-terminal deletions alone (e.g., delta20-34) did not affect the gating charge movement. However, the deletions paradoxically increased the voltage sensitivity of the R176S mutant channel, but not that of the wild-type channel. We propose a simple model in which the N-terminus determines the KAT1 voltage sensitivity by contributing to the electric field sensed by the voltage sensor.