Shaker potassium channel gating. III: Evaluation of kinetic models for activation

Predictions of different classes of gating models involving identical conformational changes in each of four subunits were compared to the gating behavior of Shaker potassium channels without N-type inactivation. Each model was tested to see if it could simulate the voltage dependence of the steady state open probability, and the kinetics of the single-channel currents, macroscopic ionic currents and macroscopic gating currents using a single set of parameters. Activation schemes based upon four identical single-step activation processes were found to be incompatible with the experimental results, as were those involving a concerted, opening transition. A model where the opening of the channel requires two conformational changes in each of the four subunits can adequately account for the steady state and kinetic behavior of the channel. In this model, the gating in each subunit is independent except for a stabilization of the open state when all four subunits are activated, and an unstable closed conformation that the channel enters after opening. A small amount of negative cooperativity between the subunits must be added to account quantitatively for the dependence of the activation time course on holding voltage.     

Glutamate receptor-channel gating. Maximum likelihood analysis of gigaohm seal recordings from locust muscle.

Gigaohm recordings have been made from glutamate receptor channels in excised, outside-out patches of collagenase-treated locust muscle membrane. The channels in the excised patches exhibit the kinetic state switching first seen in megaohm recordings from intact muscle fibers. Analysis of channel dwell time distributions reveals that the gating mechanism contains at least four open states and at least four closed states. Dwell time autocorrelation function analysis shows that there are at least three gateways linking the open states of the channel with the closed states. A maximum likelihood procedure has been used to fit six different gating models to the single channel data. Of these models, a cooperative model yields the best fit, and accurately predicts most features of the observed channel gating kinetics.     

Transfer of beta subunit regulation from high to low voltage-gated Ca2+ channels

High voltage-activated Ca(2+) channel expression and gating is controlled by their beta subunits. Although the sites of interaction are known at the atomic level, how beta modulates gating remains to be determined. Using a chimeric approach, beta subunit regulation was conferred to a low voltage-activated channel. Regulation was dependent on a rigid linker connecting the alpha(1) interaction domain to IS6. Chimeric channels also revealed a role for IS6 in channel gating. Taken together, these results support a direct coupling model where beta subunits alter movements in IS6 that occur as the channel transits between closed, open, and inactivated states.     

Kinetic model of the gating system of the sodium channel in a Ranvier node membrane

A kinetic model of the sodium channel gating system consisting of four subunits with three states--closed (X), open (Y) and inactivated (Z)--is proposed. For the channel to conduct, all the four subunits must be in the open state. The transitions between states X and Y are independent, while those between states X and Z are coupled, so that for the particle considered transition of one of two neighbouring particles into state Z increases the activation energy of the step by kT. The model fits rather well to the experimental data.     

Cooperative nature of gating transitions in K+ channels as seen from dynamic importance sampling calculations

The growing dataset of K⁺ channel x‐ray structures provides an excellent opportunity to begin a detailed molecular understanding of voltage‐dependent gating. These structures, while differing in sequence, represent either a stable open or closed state. However, an understanding of the molecular details of gating will require models for the transitions and experimentally testable predictions for the gating transition. To explore these ideas, we apply dynamic importance sampling to a set of homology models for the molecular conformations of K⁺ channels for four different sets of sequences and eight different states. In our results, we highlight the importance of particular residues upstream from the Pro‐Val‐Pro (PVP) region to the gating transition. This supports growing evidence that the PVP region is important for influencing the flexibility of the S6 helix and thus the opening of the gating domain. The results further suggest how gating on the molecular level depends on intra‐subunit motions to influence the cooperative behavior of all four subunits of the K⁺ channel. We hypothesize that the gating process occurs in steps: first sidechain movement, then inter‐S5‐S6 subunit motions, and lastly the large‐scale domain rearrangements. Proteins 2010. © 2009 Wiley‐Liss, Inc.     

Activation of Shaker Potassium Channels : III. An Activation Gating Model for Wild-Type and V2 Mutant Channels

A functional kinetic model is developed to describe the activation gating process of the Shaker potassium channel. The modeling in this paper is constrained by measurements described in the preceding two papers, including macroscopic ionic and gating currents and single channel ionic currents. These data were obtained from the normally activating wild-type channel as well as a mutant channel V2, in which the leucine at position 382 has been mutated to a valine. Different classes of models that incorporate Shaker''s symmetrical tetrameric structure are systematically examined. Many simple gating models are clearly inadequate, but a model that can account for all of the qualitative features of the data has the channel open after its four subunits undergo three transitions in sequence, and two final transitions that reflect the concerted action of the four subunits. In this model, which we call Scheme 3+2′, the channel can also close to several states that are not part of the activation path. Channel opening involves a large total charge movement (10.8 e₀), which is distributed among a large number of small steps each with rather small charge movements (between 0.6 and 1.05 e₀). The final two transitions are different from earlier steps by having slow backward rates. These steps confer a cooperative mechanism of channel opening at Shaker''s activation voltages. In the context of Scheme 3+2′, significant effects of the V2 mutation are limited to the backward rates of the final two transitions, implying that L382 plays an important role in the conformational stability of the final two states.     

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.     

Gating of Shaker K+ channels: II. The components of gating currents and a model of channel activation.

Steady-state and kinetic properties of gating currents of the Shaker K+ channels were studied in channels expressed in Xenopus oocytes and recorded with the cut-open oocyte voltage clamp. The charge versus potential (Q-V) curve reveals at least two components of charge, the first moving in the hyperpolarized region (V1/2 = -63 mV) and the second, with a larger apparent valence, moving in the more depolarized region (V1/2 = -44 mV). The kinetic analysis of gating currents revealed also two exponential decaying components that corresponded in their voltage dependence with the charge components described in the steady-state. The first component was found to correlate with the effects of prepulses that produce the Cole-Moore shift of the ionic and gating currents and seems to be occurring completely within closed conformations of the channel. The second component seems to be related to the events occurring between the closed states just preceding, but not including, the transition to the open state. The ON and OFF gating currents exhibit a pronounced rising phase at potentials at which the second component becomes important, and this region corresponds to the potential range where the channel opens. The results could not be explained with simple parallel models, but the data can be fitted to a sequential model that could be related to a first rearrangement of the putative four subunits in cooperative fashion, followed by a concerted charge movement that leads to the open channel. The first series of charge movements are produced by transitions between several closed states carrying less than two electronic charges per step, while a step carrying about 3.5 electronic charges can explain the second component. This step is followed by the transition to the open state carrying less than 0.5 electronic charges. This model is able to reproduce all the kinetic and steady-state properties of the gating currents and predicts many of the properties of the ionic currents.     

Mechanistic contributions of residues in the M1 transmembrane domain of the nicotinic receptor to channel gating

The nicotinic receptor (AChR) is a pentamer of homologous subunits with an alpha(2)betaepsilondelta composition in adult muscle. Each subunit contains four transmembrane domains (M1-M4). Position 15' of the M1 domain is phenylalanine in alpha subunits while it is isoleucine in non-alpha subunits. Given this peculiar conservation pattern, we studied its contribution to muscle AChR activation by combining mutagenesis with single-channel kinetic analysis. AChRs containing the mutant alpha subunit (alphaF15'I) as well as those containing the reverse mutations in the non-alpha subunits (betaI15'F, deltaI15'F, and epsilonI15'F) show prolonged lifetimes of the diliganded open channel resulting from a slower closing rate with respect to wild-type AChRs. The kinetic changes are not equivalent among subunits, the beta subunit, being the one that produces the most significant stabilization of the open state. Kinetic analysis of betaI15'F of AChR channels activated by the low-efficacious agonist choline revealed a 10-fold decrease in the closing rate, a 2.5-fold increase in the opening rate, a 28-fold increase in the gating equilibrium constant in the diliganded receptor, and a significant increase opening in the absence of agonist. Mutations at betaI15' showed that the structural bases of its contribution to gating is complex. Rate-equilibrium linear free-energy relationships suggest an approximately 70% closed-state-like environment for the beta15' position at the transition state of gating. The overall results identify position 15' as a subunit-selective determinant of channel gating and add new experimental evidence that gives support to the involvement of the M1 domain in the operation of the channel gating apparatus.     

A functional model for G protein activation of the muscarinic K+ channel in guinea pig atrial myocytes. Spectral analysis of the effect of GTP on single-channel kinetics

To elucidate the functional interaction between the active G protein subunit (GK*) and the cardiac muscarinic K+ (KACh) channel, the effect of intracellular GTP on the channel current fluctuation in the presence of 0.5 microM extracellular acetylcholine was examined in inside-out patches from guinea pig atrial myocytes using spectral analysis technique. The power density spectra of current fluctuations induced at various concentrations of GTP ([GTP]) were well fitted by the sum of two Lorentzian functions. Because the channel has one open state, the open-close transitions of the channel gate represented by the spectra could be described as C2<-->C1<-->O. As [GTP] was raised, the channel activity increased in a positive cooperative manner. The powers of the two Lorentzian components concomitantly increased, while the corner frequencies and the ratio of the powers at 0 Hz remained almost constant. This indicates that G protein activation did not affect the gating of each channel but mainly increased the number of functionally active channels in the patch to enhance the channel activity. Regulation of the number of functionally active channels could be described by a slow transition of the channel states, U (unavailable)<-- >A (available), which is independent of the gating. The equilibrium of this slow transition was shifted by GTP from U to A. Monod-Wyman- Changeux's allosteric model for the channel state transition(U<-->A) could well describe the positive cooperative increase in the channel availability by GTP, assuming that, in the presence of saturating concentrations of ACh, [GK*] linearly increased as [GTP] was raised in our experimental range. The model indicates that the cardiac KACh channel could be described as a multimer composed of four or more functionally identical subunits, to each of which one GK* binds.     

KCNQ1 Channels Do Not Undergo Concerted but Sequential Gating Transitions in Both the Absence and the Presence of KCNE1 Protein

The co-assembly of KCNQ1 with KCNE1 produces I_KS, a K⁺ current, crucial for the repolarization of the cardiac action potential. Mutations in these channel subunits lead to life-threatening cardiac arrhythmias. However, very little is known about the gating mechanisms underlying KCNQ1 channel activation. Shaker channels have provided a powerful tool to establish the basic gating mechanisms of voltage-dependent K⁺ channels, implying prior independent movement of all four voltage sensor domains (VSDs) followed by channel opening via a last concerted cooperative transition. To determine the nature of KCNQ1 channel gating, we performed a thermodynamic mutant cycle analysis by constructing a concatenated tetrameric KCNQ1 channel and by introducing separately a gain and a loss of function mutation, R231W and R243W, respectively, into the S4 helix of the VSD of one, two, three, and four subunits. The R231W mutation destabilizes channel closure and produces constitutively open channels, whereas the R243W mutation disrupts channel opening solely in the presence of KCNE1 by right-shifting the voltage dependence of activation. The linearity of the relationship between the shift in the voltage dependence of activation and the number of mutated subunits points to an independence of VSD movements, with each subunit incrementally contributing to channel gating. Contrary to Shaker channels, our work indicates that KCNQ1 channels do not experience a late cooperative concerted opening transition. Our data suggest that KCNQ1 channels in both the absence and the presence of KCNE1 undergo sequential gating transitions leading to channel opening even before all VSDs have moved.     

K channel subconductance levels result from heteromeric pore conformations

Voltage-gated K channels assemble from four identical subunits symmetrically arranged around a central permeation pathway. Each subunit harbors a voltage-sensing domain. The sigmoidal nature of the activation kinetics suggests that multiple sensors need to undergo a conformational change before the channel can open. Following activation, individual K channels alternate stochastically between two main permeation states, open and closed. This binary character of single channel behavior suggests the presence of a structure in the permeation pathway that can exist in only two conformations. However, single channel analysis of drk1 (K(v)2.1) K channels demonstrated the existence of four additional, intermediate conductance levels. These short-lived subconductance levels are visited when the channel gate moves between the closed and fully open state. We have proposed that these sublevels arise from transient heteromeric pore conformations, in which some, but not all, subunits are in the "open" state. A minimal model based on this hypothesis relates specific subconductance states with the number of activated subunits (Chapman et al., 1997). To stringently test this hypothesis, we constructed a tandem dimer that links two K channel subunits with different activation thresholds. Activation of this dimer by strong depolarizations resulted in the characteristic binary open-close behavior. However, depolarizations to membrane potentials in between the activation thresholds of the two parents elicited highly unusual single channel gating, displaying frequent visits to two subconductance levels. The voltage dependence and kinetics of the small and large sublevels associate them with the activation of one and two subunits, respectively. The data therefore support the hypothesis that subconductance levels result from heteromeric pore conformations. In this model, both sensor movement and channel opening have a subunit basis and these processes are allosterically coupled.     

Concerted gating mechanism underlying KATP channel inhibition by ATP

KATP channels assemble from four regulatory SUR1 and four pore-forming Kir6.2 subunits. At the single-channel current level, ATP-dependent gating transitions between the active burst and the inactive interburst conformations underlie inhibition of the KATP channel by intracellular ATP. Previously, we identified a slow gating mutation, T171A in the Kir6.2 subunit, which dramatically reduces rates of burst to interburst transitions in Kir6.2DeltaC26 channels without SUR1 in the absence of ATP. Here, we constructed all possible mutations at position 171 in Kir6.2DeltaC26 channels without SUR1. Only four substitutions, 171A, 171F, 171H, and 171S, gave rise to functional channels, each increasing Ki,ATP for ATP inhibition by >55-fold and slowing gating to the interburst by >35-fold. Moreover, we investigated the role of individual Kir6.2 subunits in the gating by comparing burst to interburst transition rates of channels constructed from different combinations of slow 171A and fast T171 "wild-type" subunits. The relationship between gating transition rate and number of slow subunits is exponential, which excludes independent gating models where any one subunit is sufficient for inhibition gating. Rather, our results support mechanisms where four ATP sites independently can control a single gate formed by the concerted action of all four Kir6.2 subunit inner helices of the KATP channel.     

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.     

A Modeling Study of T-Type Ca Channel Gating and Modulation by L-Cysteine in Rat Nociceptors

L-cysteine (L-cys) increases the amplitude of T-type Ca²⁺ currents in rat T-rich nociceptor-like dorsal root ganglia neurons. The modulation of T-type Ca²⁺ channel gating by L-cys was studied by fitting Markov state models to whole-cell currents recorded from T-rich neurons. The best fitting model tested included three resting states and inactivation from the second resting state and the open state. Inactivation and the final opening step were voltage-independent, whereas transitions between the resting states and deactivation were voltage-dependent. The transition rates between the first two resting states were an order of magnitude faster than those between the second and third resting states, and the voltage-dependency of forward transitions through resting states was two to three times greater than for analogous backward transitions. Analysis with the best fitting model suggested that L-cys increases current amplitude mainly by increasing the transition rate from resting to open and decreasing the transition rate from open to inactivated. An additional model was developed that could account for the bi-exponential time course of recovery from inactivation of the currents and the high frequency of blank sweeps in single channel recordings. This model detected basically the same effects of L-cys on channel gating as the best fitting model.     

Models of HERG gating

HERG (Kv11.1, KCNH2) is a voltage-gated potassium channel with unique gating characteristics. HERG has fast voltage-dependent inactivation, relatively slow deactivation, and fast recovery from inactivation. This combination of gating kinetics makes study of HERG difficult without using mathematical models. Several HERG models have been developed, with fundamentally different organization. HERG is the molecular basis of I_Kr, which plays a critical role in repolarization. We programmed and compared five distinct HERG models. HERG gating cannot be adequately replicated using Hodgkin-Huxley type formulation. Using Markov models, a five-state model is required with three closed, one open, and one inactivated state, and a voltage-independent step between some of the closed states. A fundamental difference between models is the presence/absence of a transition directly from the proximal closed state to the inactivated state. The only models that effectively reproduce HERG data have no direct closed-inactivated transition, or have a closed-inactivated transition that is effectively zero compared to the closed-open transition, rendering the closed-inactivation transition superfluous. Our single-channel model demonstrates that channels can inactivate without conducting with a flickering or bursting open-state. The various models have qualitative and quantitative differences that are critical to accurate predictions of HERG behavior during repolarization, tachycardia, and premature depolarizations.     

An extracellular domain of the accessory β1 subunit is required for modulating BK channel voltage sensor and gate

A family of tissue-specific auxiliary β subunits modulates large conductance voltage- and calcium-activated potassium (BK) channel gating properties to suit their diverse functions. Paradoxically, β subunits both promote BK channel activation through a stabilization of voltage sensor activation and reduce BK channel openings through an increased energetic barrier of the closed-to-open transition. The molecular determinants underlying β subunit function, including the dual gating effects, remain unknown. In this study, we report the first identification of a β1 functional domain consisting of Y74, S104, Y105, and I106 residues located in the extracellular loop of β1. These amino acids reside within two regions of highest conservation among related β1, β2, and β4 subunits. Analysis in the context of the Horrigan-Aldrich gating model revealed that this domain functions to both promote voltage sensor activation and also reduce intrinsic gating. Free energy calculations suggest that the dual effects of the β1 Y74 and S104-I106 domains can be largely accounted for by a relative destabilization of channels in open states that have few voltage sensors activated. These results suggest a unique and novel mechanism for β subunit modulation of voltage-gated potassium channels wherein interactions between extracellular β subunit residues with the external portions of the gate and voltage sensor regulate channel opening.     

Inactivation gating of Kv7.1 channels does not involve concerted cooperative subunit interactions

Inactivation is an intrinsic property of numerous voltage-gated K⁺ (Kv) channels and can occur by N-type or/and C-type mechanisms. N-type inactivation is a fast, voltage independent process, coupled to activation, with each inactivation particle of a tetrameric channel acting independently. In N-type inactivation, a single inactivation particle is necessary and sufficient to occlude the pore. C-type inactivation is a slower process, involving the outermost region of the pore and is mediated by a concerted, highly cooperative interaction between all four subunits. Inactivation of Kv7.1 channels does not exhibit the hallmarks of N- and C-type inactivation. Inactivation of WT Kv7.1 channels can be revealed by hooked tail currents that reflects the recovery from a fast and voltage-independent inactivation process. However, several Kv7.1 mutants such as the pore mutant L273F generate an additional voltage-dependent slow inactivation. The subunit interactions during this slow inactivation gating remain unexplored. The goal of the present study was to study the nature of subunit interactions along Kv7.1 inactivation gating, using concatenated tetrameric Kv7.1 channel and introducing sequentially into each of the four subunits the slow inactivating pore mutation L273F. Incorporating an incremental number of inactivating mutant subunits did not affect the inactivation kinetics but slowed down the recovery kinetics from inactivation. Results indicate that Kv7.1 inactivation gating is not compatible with a concerted cooperative process. Instead, adding an inactivating subunit L273F into the Kv7.1 tetramer incrementally stabilizes the inactivated state, which suggests that like for activation gating, Kv7.1 slow inactivation gating is not a concerted process.     

C-type inactivation of a voltage-gated K+ channel occurs by a cooperative mechanism.

The lymphocyte voltage-gated K+ channel, Kv1.3, inactivates by a C-type process. We have elucidated the molecular basis for this process using a kinetic analysis of wild-type and mutant (A413V) Kv1.3 homo- and heteromultimeric currents in a mammalian lymphoid expression system. The medians of the measured inactivation time constants for wild-type and A413V homotetrameric currents are 204 and 4 ms, respectively. Co-expression of these subunits produces heteromultimeric channels manifesting inactivation kinetics intermediate between those of wild-type and A413V homomultimers. We have considered several models in which each subunit acts either independently or cooperatively to produce the observed inactivation kinetics. The cooperative model gives excellent fits to the data for any heteromultimeric composition of subunits, clearly distinguishing it from the independent models. In the cooperative model, the difference in free energy between the open and inactivated states of the channel is invariant with subunit composition and equals approximately 1.5 kcal/mol. Each subunit contributes equally to the activation free energy for transitions between open and inactivated states, with an A413V subunit decreasing the free energy barrier for inactivation (and for recovery from inactivation) by approximately 0.6 kcal/mol. Our results are consistent with a physical model in which the outer mouth of the channel constricts during C-type inactivation (G. Yellen, D. Sodickson, T. Chen, and M.E. Jurman, 1994, Biophys. J. 66:1068-1075).     

Two-dimensional kinetic analysis suggests nonsequential gating of mechanosensitive channels in Xenopus oocytes

Xenopus oocytes express mechanosensitive (MS(XO)) channels that can be studied in excised patches of membrane with the patch-clamp technique. This study examines the steady-state kinetic gating properties of MS(XO) channels using detailed single-channel analysis. The open and closed one-dimensional dwell-time distributions were described by the sums of 2-3 open and 5-7 closed exponential components, respectively, indicating that the channels enter at least 2-3 open and 5-7 closed kinetic states during gating. Dependency plots revealed that the durations of adjacent open and closed intervals were correlated, indicating two or more gateway states in the gating mechanism for MS channels. Maximum likelihood fitting of two-dimensional dwell-time distributions to both generic and specific models was used to examine gating mechanism and rank models. A kinetic scheme with five closed and five open states, in which each closed state could make a direct transition to an open state (two-tiered model) could account for the major features of the single-channel data. Two-tiered models that allowed direct transitions to subconductance open states in addition to the fully open state were also consistent with multiple gateway states. Thus, the gating mechanism of MS(XO) channels differs from the sequential (linear) gating mechanisms considered for MS channels in bacteria, chick skeletal muscle, and Necturus proximal tubule.