Shaker potassium channel gating. II: Transitions in the activation pathway

Voltage-dependent gating behavior of Shaker potassium channels without N-type inactivation (ShB delta 6-46) expressed in Xenopus oocytes was studied. The voltage dependence of the steady-state open probability indicated that the activation process involves the movement of the equivalent of 12-16 electronic charges across the membrane. The sigmoidal kinetics of the activation process, which is maintained at depolarized voltages up to at least +100 mV indicate the presence of at least five sequential conformational changes before opening. The voltage dependence of the gating charge movement suggested that each elementary transition involves 3.5 electronic charges. The voltage dependence of the forward opening rate, as estimated by the single- channel first latency distribution, the final phase of the macroscopic ionic current activation, the ionic current reactivation and the ON gating current time course, showed movement of the equivalent of 0.3 to 0.5 electronic charges were associated with a large number of the activation transitions. The equivalent charge movement of 1.1 electronic charges was associated with the closing conformational change. The results were generally consistent with models involving a number of independent and identical transitions with a major exception that the first closing transition is slower than expected as indicated by tail current and OFF gating charge measurements.     

Voltage-dependent Gating of Single Wild-Type and S4 Mutant KAT1 Inward Rectifier Potassium Channels

The voltage-dependent gating mechanism of KAT1 inward rectifier potassium channels was studied using single channel current recordings from Xenopus oocytes injected with KAT1 mRNA. The inward rectification properties of KAT1 result from an intrinsic gating mechanism in the KAT1 channel protein, not from pore block by an extrinsic cation species. KAT1 channels activate with hyperpolarizing potentials from −110 through −190 mV with a slow voltage-dependent time course. Transitions before first opening are voltage dependent and account for much of the voltage dependence of activation, while transitions after first opening are only slightly voltage dependent. Using burst analysis, transitions near the open state were analyzed in detail. A kinetic model with multiple closed states before first opening, a single open state, a single closed state after first opening, and a closed-state inactivation pathway accurately describes the single channel and macroscopic data. Two mutations neutralizing charged residues in the S4 region (R177Q and R176L) were introduced, and their effects on single channel gating properties were examined. Both mutations resulted in depolarizing shifts in the steady state conductance–voltage relationship, shortened first latencies to opening, decreased probability of terminating bursts, and increased burst durations. These effects on gating were well described by changes in the rate constants in the kinetic model describing KAT1 channel gating. All transitions before the open state were affected by the mutations, while the transitions after the open state were unaffected, implying that the S4 region contributes to the early steps in gating for KAT1 channels.     

Determinants of voltage-dependent gating and open-state stability in the S5 segment of Shaker potassium channels.

The best-known Shaker allele of Drosophila with a novel gating phenotype, Sh(5), differs from the wild-type potassium channel by a point mutation in the fifth membrane-spanning segment (S5) (Gautam, M., and M.A. Tanouye. 1990. Neuron. 5:67-73; Lichtinghagen, R., M. Stocker, R. Wittka, G. Boheim, W. Stühmer, A. Ferrus, and O. Pongs. 1990. EMBO [Eur. Mol. Biol. Organ.] J. 9:4399-4407) and causes a decrease in the apparent voltage dependence of opening. A kinetic study of Sh(5) revealed that changes in the deactivation rate could account for the altered gating behavior (Zagotta, W.N., and R.W. Aldrich. 1990. J. Neurosci. 10:1799-1810), but the presence of intact fast inactivation precluded observation of the closing kinetics and steady state activation. We studied the Sh(5) mutation (F401I) in ShB channels in which fast N-type inactivation was removed, directly confirming this conclusion. Replacement of other phenylalanines in S5 did not result in substantial alterations in voltage-dependent gating. At position 401, valine and alanine substitutions, like F401I, produce currents with decreased apparent voltage dependence of the open probability and of the deactivation rates, as well as accelerated kinetics of opening and closing. A leucine residue is the exception among aliphatic mutants, with the F401L channels having a steep voltage dependence of opening and slow closing kinetics. The analysis of sigmoidal delay in channel opening, and of gating current kinetics, indicates that wild-type and F401L mutant channels possess a form of cooperativity in the gating mechanism that the F401A channels lack. The wild-type and F401L channels' entering the open state gives rise to slow decay of the OFF gating current. In F401A, rapid gating charge return persists after channels open, confirming that this mutation disrupts stabilization of the open state. We present a kinetic model that can account for these properties by postulating that the four subunits independently undergo two sequential voltage-sensitive transitions each, followed by a final concerted opening step. These channels differ primarily in the final concerted transition, which is biased in favor of the open state in F401L and the wild type, and in the opposite direction in F401A. These results are consistent with an activation scheme whereby bulky aromatic or aliphatic side chains at position 401 in S5 cooperatively stabilize the open state, possibly by interacting with residues in other helices.     

A sodium channel gating model based on single channel, macroscopic ionic, and gating currents in the squid giant axon.

Sodium channel gating behavior was modeled with Markovian models fitted to currents from the cut-open squid giant axon in the absence of divalent cations. Optimum models were selected with maximum likelihood criteria using single-channel data, then models were refined and extended by simultaneous fitting of macroscopic ionic currents, ON and OFF gating currents, and single-channel first latency densities over a wide voltage range. Best models have five closed states before channel opening, with inactivation from at least one closed state as well as the open state. Forward activation rate constants increase with depolarization, and deactivation rate constants increase with hyperpolarization. Rates of inactivation from the open or closed states are generally slower than activation or deactivation rates and show little or no voltage dependence. Channels tend to reopen several times before inactivating. Macroscopic rates of activation and inactivation result from a combination of closed, open and inactivated state transitions. At negative potentials the time to first opening dominates the macroscopic current due to slow activation rates compared with deactivation rates: channels tend to reopen rarely, and often inactivate from closed states before they reopen. At more positive potentials, the time to first opening and burst duration together produce the macroscopic current.     

Relationship between pore occupancy and gating in BK potassium channels

Permeant ions can have significant effects on ion channel conformational changes. To further understand the relationship between ion occupancy and gating conformational changes, we have studied macroscopic and single-channel gating of BK potassium channels with different permeant monovalent cations. While the slopes of the conductance-voltage curve were reduced with respect to potassium for all permeant ions, BK channels required stronger depolarization to open only when thallium was the permeant ion. Thallium also slowed the activation and deactivation kinetics. Both the change in kinetics and the shift in the GV curve were dependent on the thallium passing through the permeation pathway, as well as on the concentration of thallium. There was a decrease in the mean open time and an increase in the number of short flicker closing events with thallium as the permeating ion. Mean closed durations were unaffected. Application of previously established allosteric gating models indicated that thallium specifically alters the opening and closing transition of the channel and does not alter the calcium activation or voltage activation pathways. Addition of a closed flicker state into the allosteric model can account for the effect of thallium on gating. Consideration of the thallium concentration dependence of the gating effects suggests that the flicker state may correspond to the collapsed selectivity filter seen in crystal structures of the KcsA potassium channel under the condition of low permeant ion concentration.     

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.     

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.     

Binding of a gating modifier toxin induces intersubunit cooperativity early in the Shaker K channel's activation pathway

Potassium currents from voltage-gated Shaker K channels activate with a sigmoid rise. The degree of sigmoidicity in channel opening kinetics confirms that each subunit of the homotetrameric Shaker channel undergoes more than one conformational change before the channel opens. We have examined effects of two externally applied gating modifiers that reduce the sigmoidicity of channel opening. A toxin from gastropod mucus, 6-bromo-2-mercaptotryptamine (BrMT), and divalent zinc are both found to slow the same conformational changes early in Shaker's activation pathway. Sigmoidicity measurements suggest that zinc slows a conformational change independently in each channel subunit. Analysis of activation in BrMT reveals cooperativity among subunits during these same early steps. A lack of competition with either agitoxin or tetraethylammonium indicates that BrMT binds channel subunits outside of the external pore region in an allosterically cooperative fashion. Simulations including negatively cooperative BrMT binding account for its ability to induce gating cooperativity during activation. We conclude that cooperativity among K channel subunits can be greatly altered by experimental conditions.     

The voltage-activated hydrogen ion conductance in rat alveolar epithelial cells is determined by the pH gradient

Voltage-activated H+ currents were studied in rat alveolar epithelial cells using tight-seal whole-cell voltage clamp recording and highly buffered, EGTA-containing solutions. Under these conditions, the tail current reversal potential, Vrev, was close to the Nernst potential, EH, varying 52 mV/U pH over four delta pH units (delta pH = pHo - pHi). This result indicates that H+ channels are extremely selective, PH/PTMA > 10(7), and that both internal and external pH, pHi, and pHo, were well controlled. The H+ current amplitude was practically constant at any fixed delta pH, in spite of up to 100-fold symmetrical changes in H+ concentration. Thus, the rate-limiting step in H+ permeation is pH independent, must be localized to the channel (entry, permeation, or exit), and is not bulk diffusion limitation. The instantaneous current- voltage relationship exhibited distinct outward rectification at symmetrical pH, suggesting asymmetry in the permeation pathway. Sigmoid activation kinetics and biexponential decay of tail currents near threshold potentials indicate that H+ channels pass through at least two closed states before opening. The steady state H+ conductance, gH, as well as activation and deactivation kinetic parameters were all shifted along the voltage axis by approximately 40 mV/U pH by changes in pHi or pHo, with the exception of the fast component of tail currents which was shifted less if at all. The threshold potential at which H+ currents were detectably activated can be described empirically as approximately 20-40(pHo-pHi) mV. If internal and external protons regulate the voltage dependence of gH gating at separate sites, then they must be equally effective. A simpler interpretation is that gating is controlled by the pH gradient, delta pH. We propose a simple general model to account for the observed delta pH dependence. Protonation at an externally accessible site stabilizes the closed channel conformation. Deprotonation of this site permits a conformational change resulting in the appearance of a protonation site, possibly the same one, which is accessible via the internal solution. Protonation of the internal site stabilizes the open conformation of the channel. In summary, within the physiological range of pH, the voltage dependence of H+ channel gating depends on delta pH and not on the absolute pH.     

Slo3 K+ channels: voltage and pH dependence of macroscopic currents

The mouse Slo3 gene (KCNMA3) encodes a K(+) channel that is regulated by changes in cytosolic pH. Like Slo1 subunits responsible for the Ca(2+) and voltage-activated BK-type channel, the Slo3 alpha subunit contains a pore module with homology to voltage-gated K(+) channels and also an extensive cytosolic C terminus thought to be responsible for ligand dependence. For the Slo3 K(+) channel, increases in cytosolic pH promote channel activation, but very little is known about many fundamental properties of Slo3 currents. Here we define the dependence of macroscopic conductance on voltage and pH and, in particular, examine Slo3 conductance activated at negative potentials. Using this information, the ability of a Horrigan-Aldrich-type of general allosteric model to account for Slo3 gating is examined. Finally, the pH and voltage dependence of Slo3 activation and deactivation kinetics is reported. The results indicate that Slo3 differs from Slo1 in several important ways. The limiting conductance activated at the most positive potentials exhibits a pH-dependent maximum, suggesting differences in the limiting open probability at different pH. Furthermore, over a 600 mV range of voltages (-300 to +300 mV), Slo3 conductance shifts only about two to three orders of magnitude, and the limiting conductance at negative potentials is relatively voltage independent compared to Slo1. Within the context of the Horrigan-Aldrich model, these results indicate that the intrinsic voltage dependence (z(L)) of the Slo3 closed-open equilibrium and the coupling (D) between voltage sensor movement are less than in Slo1. The kinetic behavior of Slo3 currents also differs markedly from Slo1. Both activation and deactivation are best described by two exponential components, both of which are only weakly voltage dependent. Qualitatively, the properties of the two kinetic components in the activation time course suggest that increases in pH increase the fraction of more rapidly opening channels.     

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.     

Voltage-dependent gating of Shaker A-type potassium channels in Drosophila muscle

The voltage-dependent gating mechanism of A1-type potassium channels coded for by the Shaker locus of Drosophila was studied using macroscopic and single-channel recording techniques on embryonic myotubes in primary culture. From a kinetic analysis of data from single A1 channels, we have concluded that all of the molecular transitions after first opening, including the inactivation transition, are voltage independent and therefore not associated with charge movement through the membrane. In contrast, at least some of the activation transitions leading to first opening are considerably voltage dependent and account for all of the voltage dependence seen in the macroscopic currents. This mechanism is similar in many ways to that of vertebrate neuronal voltage-sensitive sodium channels, and together with the sequence similarities in the S4 region suggests a conserved mechanism for voltage-dependent gating among channels with different selectivities. By testing independent and coupled models for activation and inactivation we have determined that the final opening transition and inactivation are not likely to arise from the independent action of multiple subunits, each with simple gating transitions, but rather come about through their aggregate properties. A partially coupled model accurately reproduces all of the single-channel and macroscopic data. This model will provide a framework on which to organize and understand alterations in gating that occur in Shaker variants and mutants.     

Calcium currents in the A7r5 smooth muscle-derived cell line. An allosteric model for calcium channel activation and dihydropyridine agonist action

We have investigated the gating kinetics of calcium channels in the A7r5 cell line at the level of single channels and whole cell currents, in the absence and presence of dihydropyridine (DHP) calcium channel agonists. Although latencies to first opening and macroscopic currents are strongly voltage dependent, analysis of amplitude histograms indicates that the primary open-closed transition is voltage independent. This suggests that the molecular mechanisms for voltage sensing and channel opening are distinct, but coupled. We propose a modified Monod-Wyman-Changeux (MWC) model for channel activation, where movement of a voltage sensor is analogous to ligand binding, and the closed and open channels correspond to inactive (T) and active (R) states. This model can account for the activation kinetics of the calcium channel, and is consistent with the existence of four homologous domains in the main subunit of the calcium channel protein. DHP agonists slow deactivation kinetics, shift the activation curve to more negative potentials with an increase in slope, induce intermingled fast and slow channel openings, and reduce the latency to first opening. These effects are predicted by the MWC model if we make the simple assumption that DHP agonists act as allosteric effectors to stabilize the open states of the channel.     

Gating characteristics of a steeply voltage-dependent gap junction channel in rat Schwann cells

The gating properties of macroscopic and microscopic gap junctional currents were compared by applying the dual whole cell patch clamp technique to pairs of neonatal rat Schwann cells. In response to transjunctional voltage pulses (Vj), macroscopic gap junctional currents decayed exponentially with time constants ranging from < 1 to < 10 s before reaching steady-state levels. The relationship between normalized steady-state junctional conductance (Gss) and (Vj) was well described by a Boltzmann relationship with e-fold decay per 10.4 mV, representing an equivalent gating charge of 2.4. At Vj > 60 mV, Gss was virtually zero, a property that is unique among the gap junctions characterized to date. Determination of opening and closing rate constants for this process indicated that the voltage dependence of macroscopic conductance was governed predominantly by the closing rate constant. In 78% of the experiments, a single population of unitary junctional currents was detected corresponding to an unitary channel conductance of approximately 40 pS. The presence of only a limited number of junctional channels with identical unitary conductances made it possible to analyze their kinetics at the single channel level. Gating at the single channel level was further studied using a stochastic model to determine the open probability (Po) of individual channels in a multiple channel preparation. Po decreased with increasing Vj following a Boltzmann relationship similar to that describing the macroscopic Gss voltage dependence. These results indicate that, for Vj of a single polarity, the gating of the 40 pS gap junction channels expressed by Schwann cells can be described by a first order kinetic model of channel transitions between open and closed states.     

FPL 64176 modification of Ca(V)1.2 L-type calcium channels: dissociation of effects on ionic current and gating current

FPL 64176 (FPL) is a nondihydropyridine compound that dramatically increases macroscopic inward current through L-type calcium channels and slows activation and deactivation. To understand the mechanism by which channel behavior is altered, we compared the effects of the drug on the kinetics and voltage dependence of ionic currents and gating currents. Currents from a homogeneous population of channels were obtained using cloned rabbit Ca(V)1.2 (alpha1C, cardiac L-type) channels stably expressed in baby hamster kidney cells together with beta1a and alpha2delta1 subunits. We found a striking dissociation between effects of FPL on ionic currents, which were modified strongly, and on gating currents, which were not detectably altered. Inward ionic currents were enhanced approximately 5-fold for a voltage step from -90 mV to +10 mV. Kinetics of activation and deactivation were slowed dramatically at most voltages. Curiously, however, at very hyperpolarized voltages (< -250 mV), deactivation was actually faster in FPL than in control. Gating currents were measured using a variety of inorganic ions to block ionic current and also without blockers, by recording gating current at the reversal potential for ionic current (+50 mV). Despite the slowed kinetics of ionic currents, FPL had no discernible effect on the fundamental movements of gating charge that drive channel gating. Instead, FPL somehow affects the coupling of charge movement to opening and closing of the pore. An intriguing possibility is that the drug causes an inactivated state to become conducting without otherwise affecting gating transitions.     

Inactivation viewed through single sodium channels

Recordings of the sodium current in tissue-cultured GH3 cells show that the rate of inactivation in whole cell and averaged single channel records is voltage dependent: tau h varied e-fold/approximately 26 mV. The source of this voltage dependence was investigated by examining the voltage dependence of individual rate constants, estimated by maximum likelihood analysis of single channel records, in a five-state kinetic model. The rate constant for inactivating from the open state, rather than closing, increased with depolarization, as did the probability that an open channel inactivates. The rate constant for closing from the open state had the opposite voltage dependence. Both rate constants contributed to the mean open time, which was not very voltage dependent. Both open time and burst duration were less than tau h for voltages up to -20 mV. The slowest time constant of activation, tau m, was measured from whole cell records, by fitting a single exponential either to tail currents or to activating currents in trypsin-treated cells, in which the inactivation was abolished. tau m was a bell-shaped function of voltage and had a voltage dependence similar to tau h at voltages more positive than -35 mV, but was smaller than tau h. At potentials more negative than about -10 mV, individual channels may open and close several times before inactivating. Therefore, averaged single channel records, which correspond with macroscopic current elicited by a depolarization, are best described by a convolution of the first latency density with the autocorrelation function rather than with 1 - (channel open time distribution). The voltage dependence of inactivation from the open state, in addition to that of the activation process, is a significant factor in determining the voltage dependence of macroscopic inactivation. Although the rates of activation and inactivation overlapped greatly, independent and coupled inactivation could not be statistically distinguished for two models examined. Although rates of activation affect the observed rate of inactivation at intermediate voltages, extrapolation of our estimates of rate constants suggests that at very depolarized voltages the activation process is so fast that it is an insignificant factor in the time course of inactivation. Prediction of gating currents shows that an inherently voltage-dependent inactivation process need not produce a conspicuous component in the gating current.     

Ion channels activated by light in Limulus ventral photoreceptors

The light-activated conductance of Limulus ventral photoreceptors was studied using the patch-clamp technique. Channels (40 pS) were observed whose probability of opening was greatly increased by light. In some cells the latency of channel activation was nearly the same as that of the macroscopic response, while in other cells the channel latency was much greater. Like the macroscopic conductance, channel activity was reduced by light adaptation but enhanced by the intracellular injection of the calcium chelator EGTA. The latter observation indicates that channel activation was not a secondary result of the light-induced rise in intracellular calcium. A two-microelectrode voltage-clamp method was used to measure the voltage dependence of the light-activated macroscopic conductance. It was found that this conductance is constant over a wide voltage range more negative than zero, but it increases markedly at positive voltages. The single channel currents measured over this same voltage range show that the single channel conductance is independent of voltage, but that channel gating properties are dependent on voltage. Both the mean channel open time and the opening rate increase at positive voltages. These properties change in a manner consistent with the voltage dependence of the macroscopic conductance. The broad range of similarities between the macroscopic and single channel currents supports the conclusion that the 40-pS channel that we have observed is the principal channel underlying the response to light in these photoreceptors.     

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.     

A kinetic model of single and clustered IP3 receptors in the absence of Ca2+ feedback

Ca2+ liberation through inositol 1,4,5-trisphosphate receptor (IP3R) channels generates complex patterns of spatiotemporal cellular Ca2+ signals owing to the biphasic modulation of channel gating by Ca2+ itself. These processes have been extensively studied in Xenopus oocytes, where imaging studies have revealed local Ca2+ signals ("puffs") arising from clusters of IP3R, and patch-clamp studies on isolated oocyte nuclei have yielded extensive data on IP3R gating kinetics. To bridge these two levels of experimental data, we developed an IP3R model and applied stochastic simulation and transition matrix theory to predict the behavior of individual and clustered IP3R channels. The channel model consists of four identical, independent subunits, each of which has an IP3-binding site together with one activating and one inactivating Ca2+-binding site. The channel opens when at least three subunits undergo a conformational change to an "active" state after binding IP3 and Ca2+. The model successfully reproduces patch-clamp data; including the dependence of open probability, mean open duration, and mean closed duration on [IP3] and [Ca2+]. Notably, the biexponential distribution of open-time duration and the dependence of mean open time on [Ca2+] are explained by populations of openings involving either three or four active subunits. As a first step toward applying the single IP3R model to describe cellular responses, we then simulated measurements of puff latency after step increases of [IP3]. Assuming that stochastic opening of a single IP3R at basal cytosolic [Ca2+] and any given [IP3] has a high probability of rapidly triggering neighboring channels by calcium-induced calcium release to evoke a puff, optimal correspondence with experimental data of puff latencies after photorelease of IP3 was obtained when the cluster contained a total of 40-70 IP3Rs.     

Modeling subunit cooperativity in opening of tetrameric ion channels

Most potassium channels are tetramers of four homologous polypeptides (subunits). During channel gating, each subunit undergoes several conformational changes independent of the state of other subunits before reaching a permissive state, from which the channel can open. However, transition from the permissive states to the open state involves a concerted movement of all subunits. This cooperative transition must be included in Markov models of channel gating. Previously, it was implemented by considering all possible combinations of four subunit states in a much larger expanded model of channel states (e.g., 27,405 channel states versus 64 subunit states), which complicates modeling and is computationally intense, especially when accurate modeling requires a large number of subunit states. To overcome these complexities and retain the tetrameric molecular structure, a modeling approach was developed to incorporate the cooperative transition directly from the subunit models. In this approach, the open state is separated from the subunit models and represented by the net flux between the open state and the permissive states. Dynamic variations of the probability of state residencies computed using this direct approach and the expanded model were identical. Implementation of the direct approach is simple and its computational time is orders-of-magnitude shorter than the equivalent expanded model.