Gating kinetics of batrachotoxin-modified Na+ channels in the squid giant axon. Voltage and temperature effects.

The gating kinetics of batrachotoxin-modified Na+ channels were studied in outside-out patches of axolemma from the squid giant axon by means of the cut-open axon technique. Single channel kinetics were characterized at different membrane voltages and temperatures. The probability of channel opening (Po) as a function of voltage was well described by a Boltzmann distribution with an equivalent number of gating particles of 3.58. The voltage at which the channel was open 50% of the time was a function of [Na+] and temperature. A decrease in the internal [Na+] induced a shift to the right of the Po vs. V curve, suggesting the presence of an integral negative fixed charge near the activation gate. An increase in temperature decreased Po, indicating a stabilization of the closed configuration of the channel and also a decrease in entropy upon channel opening. Probability density analysis of dwell times in the closed and open states of the channel at 0 degrees C revealed the presence of three closed and three open states. The slowest open kinetic component constituted only a small fraction of the total number of transitions and became negligible at voltages greater than -65 mV. Adjacent interval analysis showed that there is no correlation in the duration of successive open and closed events. Consistent with this analysis, maximum likelihood estimation of the rate constants for nine different single-channel models produced a preferred model (model 1) having a linear sequence of closed states and two open states emerging from the last closed state. The effect of temperature on the rate constants of model 1 was studied. An increase in temperature increased all rate constants; the shift in Po would be the result of an increase in the closing rates predominant over the change in the opening rates. The temperature study also provided the basis for building an energy diagram for the transitions between channel states.     

Molecular coupling between voltage sensor and pore opening in the Arabidopsis inward rectifier K+ channel KAT1

Animal and plant voltage-gated ion channels share a common architecture. They are made up of four subunits and the positive charges on helical S4 segments of the protein in animal K+ channels are the main voltage-sensing elements. The KAT1 channel cloned from Arabidopsis thaliana, despite its structural similarity to animal outward rectifier K+ channels is, however, an inward rectifier. Here we detected KAT1-gating currents due to the existence of an intrinsic voltage sensor in this channel. The measured gating currents evoked in response to hyperpolarizing voltage steps consist of a very fast (tau = 318 +/- 34 micros at -180 mV) and a slower component (4.5 +/- 0.5 ms at -180 mV) representing charge moved when most channels are closed. The observed gating currents precede in time the ionic currents and they are measurable at voltages (less than or equal to -60) at which the channel open probability is negligible ( approximately 10-4). These two observations, together with the fact that there is a delay in the onset of the ionic currents, indicate that gating charge transits between several closed states before the KAT1 channel opens. To gain insight into the molecular mechanisms that give rise to the gating currents and lead to channel opening, we probed external accessibility of S4 domain residues to methanethiosulfonate-ethyltrimethylammonium (MTSET) in both closed and open cysteine-substituted KAT1 channels. The results demonstrate that the putative voltage-sensing charges of S4 move inward when the KAT1 channels open.     

Coordinated Movement of Cytoplasmic and Transmembrane Domains of RyR1 upon Gating

Ryanodine receptor type 1 (RyR1) produces spatially and temporally defined Ca²⁺ signals in several cell types. How signals received in the cytoplasmic domain are transmitted to the ion gate and how the channel gates are unknown. We used EGTA or neuroactive PCB 95 to stabilize the full closed or open states of RyR1. Single-channel measurements in the presence of FKBP12 indicate that PCB 95 inverts the thermodynamic stability of RyR1 and locks it in a long-lived open state whose unitary current is indistinguishable from the native open state. We analyzed two datasets of 15,625 and 18,527 frozen-hydrated RyR1-FKBP12 particles in the closed and open conformations, respectively, by cryo-electron microscopy. Their corresponding three-dimensional structures at 10.2 Å resolution refine the structure surrounding the ion pathway previously identified in the closed conformation: two right-handed bundles emerging from the putative ion gate (the cytoplasmic “inner branches” and the transmembrane “inner helices”). Furthermore, six of the identifiable transmembrane segments of RyR1 have similar organization to those of the mammalian Kv1.2 potassium channel. Upon gating, the distal cytoplasmic domains move towards the transmembrane domain while the central cytoplasmic domains move away from it, and also away from the 4-fold axis. Along the ion pathway, precise relocation of the inner helices and inner branches results in an approximately 4 Å diameter increase of the ion gate. Whereas the inner helices of the K⁺ channels and of the RyR1 channel cross-correlate best with their corresponding open/closed states, the cytoplasmic inner branches, which are not observed in the K⁺ channels, appear to have at least as important a role as the inner helices for RyR1 gating. We propose a theoretical model whereby the inner helices, the inner branches, and the h1 densities together create an efficient novel gating mechanism for channel opening by relaxing two right-handed bundle structures along a common 4-fold axis.     

Stochastic Model of Gap Junctions Exhibiting Rectification and Multiple Closed States of Slow Gates

Gap-junction (GJ) channels formed from connexin (Cx) proteins provide direct pathways for electrical and metabolic cell-cell communication. Earlier, we developed a stochastic 16-state model (S16SM) of voltage gating of the GJ channel containing two pairs of fast and slow gates, each operating between open (o) and closed (c) states. However, experimental data suggest that gates may in fact contain two or more closed states. We developed a model in which the slow gate operates according to a linear reaction scheme, o↔c₁↔c₂, where c₁ and c₂ are initial-closed and deep-closed states that both close the channel fully, whereas the fast gate operates between the open state and the closed state and exhibits a residual conductance. Thus, we developed a stochastic 36-state model (S36SM) of GJ channel gating that is sensitive to transjunctional voltage (V_j). To accelerate simulation and eliminate noise in simulated junctional conductance (g_j) records, we transformed an S36SM into a Markov chain 36-state model (MC36SM) of GJ channel gating. This model provides an explanation for well-established experimental data, such as delayed g_j recovery after V_j gating, hysteresis of g_j-V_j dependence, and the low ratio of functional channels to the total number of GJ channels clustered in junctional plaques, and it has the potential to describe chemically mediated gating, which cannot be reflected using an S16SM. The MC36SM, when combined with global optimization algorithms, can be used for automated estimation of gating parameters including probabilities of c₁↔c₂ transitions from experimental g_j-time and g_j-V_j dependencies.     

Patch clamp study of the voltage-dependent anion channel in the thylakoid membrane

Measurements of single channel currents were performed on isolated membrane patches from osmotically swollen thylakoids of the Charophyte alga Nitellopsis obtusa. A channel with a high selectivity for anions over cations and a conductance of 100 to 110 pS (114 mM Cl–) was revealed. The channel has a bells-haped voltage-dependence of the open probability, with a maximum at about 0 mV. This dependence was explained by two gating processes, one causing channel closure at positive and one at negative potentials. The steepness of the voltage-dependence corresponded to approximately 2 elementary charges to be transferred across the entire membrane in each of the two gating processes. The analysis of the anion channel kinetics in the millisecond time domain revealed an e-fold increase of mean open and decrease of mean closed times when the membrane voltage was made more positive by 20 and 36 mV, respectively. Concert transitions of two identical anion channels between open and long inactivated states were observed, while the millisecond closed-open transitions of the two channels within a burst of activity were kinetically independent.This work was financially supported by the Deutsche Forschungsgemeinschaft (SFB 176 TP B11) and by a research fellowship from the Alexander von Humboldt Foundation to I.I. Pottosin.     

Gating kinetics of four classes of voltage-dependent K+ channels in pheochromocytoma cells

Clonal pheochromocytoma (PC-12) cells have four different types of voltage-dependent K+ channels whose activation does not require high concentrations of Ca++ on the cytoplasmic side of the membrane (Hoshi, T., and R. W. Aldrich, 1988, Journal of General Physiology, 91:73-106). The durations of open and closed events of these four different types of voltage-dependent K+ channels were measured using the excised configuration of the patch-clamp method. The open durations of a class of K+ channels termed the Kz channel, which activates rapidly and inactivates slowly in response to depolarizing pulses, had two exponential components. The closed durations of the Kz channel had at least four exponential components. The time constants of the fastest of the two exponential components in the closed durations were very similar to those of the two exponential components present in the first-latency distribution. The first latencies of the Kz channel decreased steeply with depolarization, contributing to the increased probability of the channel being open with depolarization. The Kz channel also had a very slow gating process that resulted in a clustering of blank sweeps. A gating scheme containing two open states and five closed states is consistent with the observations. The Ky channel had one exponential component in the open durations and three exponential components in the closed durations. The first latencies varied greatly depending on the prepulse voltage and duration. The results were consistent with a sequential model with a large number of closed states and one open state. The Kx channel, which required large hyperpolarizing prepulses to remove steady state inactivation and did not show inactivation with maintained depolarization, had two exponential components in the open durations and three exponential components in the closed durations. The burst behavior of the Kx channel involved many more than two states. The transient Kw channel had one exponential component in the open durations and the mean open time increased with depolarization. The first latencies of the Kw channel were steeply dependent on the voltage, decreasing with depolarization.     

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.     

Effect of ATP concentration on CFTR Cl- channels: a kinetic analysis of channel regulation.

Phosphorylated cystic fibrosis transmembrane conductance regulator (CFTR) Cl- channels require nucleoside triphosphates, such as ATP, to open. As the concentration of intracellular ATP increases, the probability of the channel being open (Po) increases. To better understand how ATP regulates the channel, we studied excised inside-out membrane patches that contained single, phosphorylated CFTR Cl- channels and examined the kinetics of gating at different concentrations of ATP. As the ATP concentration increased from 0.1 to 3 mM the mean closed time decreased, but mean open time did not change. Analysis of the data using histograms of open- and closed-state durations, the maximum likelihood method, and the log-likelihood ratio test suggested that channel behavior could be described by a model containing one open and two closed states (C1<==>C2<==>O). ATP regulated phosphorylated channels at the transition between the closed states C1 and C2: as the concentration of ATP increased, the rate of transition from C1 to C2 (C1-->C2) increased. In contrast, transitions from C2 to C1 and between C2 and the open state (O) were not significantly altered by ATP. Addition of ADP in the presence of ATP decreased the transition rate from C1 to C2 without affecting other transition rates. These data suggest that ATP regulates CFTR Cl- channels through an interaction that increases the rate of transition from the closed state to a bursting state in which the channel flickers back and forth between an open and a closed state (C2). This transition may reflect ATP binding or perhaps a step subsequent to binding.     

The molecular mechanism by which PIP(2) opens the intracellular G-loop gate of a Kir3.1 channel

Inwardly rectifying potassium (Kir) channels are characterized by a long pore comprised of continuous transmembrane and cytosolic portions. A high-resolution structure of a Kir3.1 chimera revealed the presence of the cytosolic (G-loop) gate captured in the closed or open conformations. Here, we conducted molecular-dynamics simulations of these two channel states in the presence and absence of phosphatidylinositol bisphosphate (PIP(2)), a phospholipid that is known to gate Kir channels. Simulations of the closed state with PIP(2) revealed an intermediate state between the closed and open conformations involving direct transient interactions with PIP(2), as well as a network of transitional inter- and intrasubunit interactions. Key elements in the G-loop gating transition involved a PIP(2)-driven movement of the N-terminus and C-linker that removed constraining intermolecular interactions and led to CD-loop stabilization of the G-loop gate in the open state. To our knowledge, this is the first dynamic molecular view of PIP(2)-induced channel gating that is consistent with existing experimental data.     

A data-driven model of a modal gated ion channel: The inositol 1,4,5-trisphosphate receptor in insect Sf9 cells

The inositol 1,4,5-trisphosphate (IP(3)) receptor (IP(3)R) channel is crucial for the generation and modulation of intracellular Ca(2+) signals in animal cells. To gain insight into the complicated ligand regulation of this ubiquitous channel, we constructed a simple quantitative continuous-time Markov-chain model from the data. Our model accounts for most experimentally observed gating behaviors of single native IP(3)R channels from insect Sf9 cells. Ligand (Ca(2+) and IP(3)) dependencies of channel activity established six main ligand-bound channel complexes, where a complex consists of one or more states with the same ligand stoichiometry and open or closed conformation. Channel gating in three distinct modes added one complex and indicated that three complexes gate in multiple modes. This also restricted the connectivity between channel complexes. Finally, latencies of channel responses to abrupt ligand concentration changes defined a model with specific network topology between 9 closed and 3 open states. The model with 28 parameters can closely reproduce the equilibrium gating statistics for all three gating modes over a broad range of ligand concentrations. It also captures the major features of channel response latency distributions. The model can generate falsifiable predictions of IP(3)R channel gating behaviors and provide insights to both guide future experiment development and improve IP(3)R channel gating analysis. Maximum likelihood estimates of the model parameters and of the parameters in the De Young-Keizer model yield strong statistical evidence in favor of our model. Our method is simple and easily applicable to the dynamics of other ion channels and molecules.     

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.     

Two-dimensional probability density analysis of single channel currents from reconstituted acetylcholine receptors and sodium channels

Two-dimensional probability density analysis of single channel current recordings was applied to two purified channel proteins reconstituted in planar lipid bilayers: Torpedo acetylcholine receptors and voltage-sensitive sodium channels from rat brain. The information contained in the dynamic history of the gating process, i.e., the time sequence of opening and closing events was extracted from two-dimensional distributions of transitions between identifiable states. This approach allows one to identify kinetic models consistent with the observables. Gating of acetylcholine receptors expresses "memory" of the transition history: the receptor has two channel open (O) states; the residence time in each of them strongly depends on both the preceding open time and the intervening closed interval. Correspondingly, the residence time in the closed (C) states depends on both the preceding open time and the preceding closed time. This result confirms the scheme that considers, at least, two transition pathways between the open and closed states and extends the details of the model in that it defines that the short-lived open state is primarily entered from long-lived closed states while the long-lived open state is accessed mainly through short-lived closed states. Since ligand binding to the acetylcholine-binding sites is a reaction with channel closed states, we infer that the longest closed state (approximately 19 ms) is unliganded, the intermediate closed state (approximately 2 ms) is singly liganded and makes transitions to the short open state (approximately 0.5 ms) and the shortest closed state (approximately 0.4 ms) is doubly liganded and isomerizes to long open states (approximately 5 ms). This is the simplest interpretation consistent with available data. In contrast, sodium channels modified with batrachotoxin to eliminate inactivation show no correlation in the sequence of channel opening and closing events, i.e., have no memory of the transition history. This result is, therefore, consistent with any kinetic scheme that considers a single transition pathway between open and closed states, and confirms the C-C-O model previously inferred from one-dimensional distribution analysis. The strategy described should be of general validity in the analysis of single channel events from channel proteins in both natural and reconstituted membranes.     

Stochastic description of sodium channel gating

A stochastic model of the sodium channel is proposed. Transitions from the resting to the open state of the channel is described by the gamma distribution. The open state is temporary with an average open time T, and the channel proceeds to the inactivated state. The channel can be represented by two identical control molecules which undergo conformation transitions under changes of the electrical field. The gating of the channel is analyzed and its relation to the gating current is proposed. The movements of the control molecules are not identical with the charge movements. Charged parts of control molecules move in the electrical field of the membrane and make their conformation energetically possible. The model is represented by a set of differential equations, and explicit solutions for long depolarizing voltage steps are found. Parameters are determined to fit literary experimental data.     

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.     

Conformational changes in S6 coupled to the opening of cyclic nucleotide-gated channels.

In cyclic nucleotide-gated channels (CNG), direct binding of cyclic nucleotides in the carboxy-terminal region is allosterically coupled to opening of the pore. A CNG1 channel pore was probed using site-directed cysteine substitution to elucidate conformational changes associated with channel opening. The effects of cysteine modification on permeation suggest a structural homology between CNG and KcsA pores. We found that intersubunit disulfide bonds form spontaneously between S399C residues in the helix bundle when channels are in the closed but not in the open state. While MTSET modification of pore-lining residues was state dependent, Ag(+) modification of V391C, in the inner vestibule, occurred at the same diffusion-limited rate in both open and closed states. Our results suggest that the helix bundle undergoes a conformational change associated with gating but is not the activation gate for CNG channels.     

Two different conformational states of the KirBac3.1 potassium channel revealed by electron crystallography

Potassium channels allow the selective flow of K(+) ions across membranes. In response to external gating signals, the potassium channel can move reversibly through a series of structural conformations from a closed to an open state. 2D crystals of the inwardly rectifying K(+) channel KirBac3.1 from Magnetospirillum magnetotacticum have been captured in two distinct conformations, providing "snap shots" of the gating process. Analysis by electron cryomicroscopy of these KirBac3.1 crystals has resulted in reconstructed images in projection at 9 A resolution. Kir channels are tetramers of four subunits arranged as dimers of dimers. Each subunit has two transmembrane helices (inner and outer). In one crystal form, the pore is blocked; in the other crystal form, the pore appears open. Modeling based on the KirBac1.1 (closed) crystal structure shows that opening of the ion conduction pathway could be achieved by bending of the inner helices and significant movements of the outer helices.     

Ion channel gating: insights via molecular simulations

Ion channels are gated, i.e. they can switch conformation between a closed and an open state. Molecular dynamics simulations may be used to study the conformational dynamics of ion channels and of simple channel models. Simulations on model nanopores reveal that a narrow (<4 A) hydrophobic region can form a functionally closed gate in the channel and can be opened by either a small (approximately 1 A) increase in pore radius or an increase in polarity. Modelling and simulation studies confirm the importance of hydrophobic gating in K channels, and support a model in which hinge-bending of the pore-lining M2 (or S6 in Kv channels) helices underlies channel gating. Simulations of a simple outer membrane protein, OmpA, indicate that a gate may also be formed by interactions of charged side chains within a pore, as is also the case in ClC channels.     

Stoichiometry of Kir channels with phosphatidylinositol bisphosphate

Phosphatidylinositol bisphosphate (PIP(2)) is the most abundant phosphoinositide in the plasma membrane of cells and its interaction with many ion channel proteins has proven to be a critical factor enabling ion channel gating. All members of the inwardly rectifying potassium (Kir) channel family depend on PIP(2) for their activity, displaying distinct affinities and stereospecificities of interaction with the phosphoinositide. Here, we explored the stoichiometry of Kir channels with PIP(2). We first showed that PIP(2) regulated the activity of Kir3.4 channels mainly by altering their bursting behavior. Detailed burst analysis indicates that the channels assumed up to four open states and a connectivity of four between open and closed states depending on the available PIP(2) levels. Moreover, by controlling the number of PIP(2)-sensitive subunits in the stoichiometry of a tetrameric Kir2.1 channel, we showed that characteristic channel activity was obtained when at least two wild-type subunits were present. Our studies support a kinetic model for gating of Kir channels by PIP(2), where each of the four open states corresponds to the channel activated by one to four PIP(2) molecules.     

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.     

A physical model of sodium channel gating

Most current models of membrane ion channel gating are abstract compartmental models consisting of many undefined states connected by rate constants arbitrarily assigned to fit the known kinetics. In this paper is described a model with states that are defined in terms of physically plausible real systems which is capable of describing accurately most of the static and dynamic properties measured for the sodium channel of the squid axon. The model has two components. The Q-system consists of charges and dipoles that can move in response to an electric field applied across the membrane. It would contain and may compose the gating charge that is known to transfer prior to channel opening. The N-system consists of a charged group or dipole that is constrained to move only in the plane of the membrane and thus does not interact directly with the trans-membrane electric field but can interact electrostatically with the Q-system. The N-system has only two states, its resting state (channel closed) and its excited state (channel open) and its response time is very short in comparison with that of the Q-system. On depolarizing the membrane the the N-system will not make a transition to its open state until a critical amount of Q-charge transfer has occurred. Using only four adjustable parameters that are fully determined by fitting the equilibrium properties of the model to those of the sodium channel in the squid axon, the model is then able to describe with some accuracy the kinetics of channel opening and closing and includes the Cole and Moore delay. In addition to these predictions of the behaviour of assemblies of channels the model predicts some of the individual channel properties measured by patch clamp techniques.