The role of loop 5 in acetylcholine receptor channel gating

Nicotinic acetylcholine receptor channel (AChR) gating is an organized sequence of molecular motions that couples a change in the affinity for ligands at the two transmitter binding sites with a change in the ionic conductance of the pore. Loop 5 (L5) is a nine-residue segment (mouse alpha-subunit 92-100) that links the beta4 and beta5 strands of the extracellular domain and that (in the alpha-subunit) contains binding segment A. Based on the structure of the acetylcholine binding protein, we speculate that in AChRs L5 projects from the transmitter binding site toward the membrane along a subunit interface. We used single-channel kinetics to quantify the effects of mutations to alphaD97 and other L5 residues with respect to agonist binding (to both open and closed AChRs), channel gating (for both unliganded and fully-liganded AChRs), and desensitization. Most alphaD97 mutations increase gating (up to 168-fold) but have little or no effect on ligand binding or desensitization. Rate-equilibrium free energy relationship analysis indicates that alphaD97 moves early in the gating reaction, in synchrony with the movement of the transmitter binding site (Phi = 0.93, which implies an open-like character at the transition state). alphaD97 mutations in the two alpha-subunits have unequal energetic consequences for gating, but their contributions are independent. We conclude that the key, underlying functional consequence of alphaD97 perturbations is to increase the unliganded gating equilibrium constant. L5 emerges as an important and early link in the AChR gating reaction which, in the absence of agonist, serves to increase the relative stability of the closed conformation of the protein.     

Probing the Transition State of the Allosteric Pathway of the Shaker Kv Channel Pore by Linear Free-Energy Relations

Long-range coupling between distant functional elements of proteins may rely on allosteric communication trajectories lying along the protein structure, as described in the case of the Shaker voltage-activated potassium (Kv) channel model allosteric system. Communication between the distant Kv channel activation and slow inactivation pore gates was suggested to be mediated by a network of local pairwise and higher-order interactions among the functionally unique residues that constitute the allosteric trajectory. The mechanism by which conformational changes propagate along the Kv channel allosteric trajectory to achieve pore opening, however, remains unclear. Such conformational changes may propagate in either a concerted or a sequential manner during the reaction coordinate of channel opening. Residue-level structural information on the transition state of channel gating is required to discriminate between these possibilities. Here, we combine patch-clamp electrophysiology recordings of Kv channel gating and analysis using linear free-energy relations, focusing on a select set of residues spanning the allosteric trajectory of the Kv channel pore. We show that all allosteric trajectory residues tested exhibit an open-like conformation in the transition state of channel opening, implying that coupling interactions occur along the trajectory break in a concerted manner upon moving from the closed to the open state. Energetic coupling between the Kv channel gates thus occurs in a concerted fashion in both the spatial and the temporal dimensions, strengthening the notion that such trajectories correspond to pathways of mechanical deformation along which conformational changes propagate.     

Linear Free-Energy Relationships and the Dynamics of Gating in the Acetylcholine Receptor Channel

The muscle acetylcholine receptor channel (AChR) is a large (M_r 290K) transmembrane protein that mediates synaptic transmission. Theactivation of this ion channel can be understood in the framework of athermodynamic cycle with spontaneous gating (i.e., the closed open reaction) and ligand-binding events as the elementary steps. Becauseagonists bind more tightly to the open than to the closed state, gating ofliganded receptors is more favorable than that of unliganded receptors.Accordingly, channel opening must involve two major conformationalchanges: the ACh-binding sites switch from a low-affinity to a high-affinityform, and the pore (located 45 Å away from the binding sites)switches from an ion-impermeable to an ion-permeable conformation. Togain insight into the reaction mechanism of fully-liganded gating, wecharacterized the corresponding transition state in the context of the `linearfree-energy relationships' of physical organic chemistry (-valueanalysis). Gating of fully-liganded AChRs was studied by recordingsingle-channel currents using the patch-clamp technique. Perturbations tothe wild-type receptor were either series of different mutations at individualpositions or series of different agonists. Based on the obtained `snapshot'of the gating reaction at the transition state, and aware of the lack ofinformation about the rest of the energy profile, the most parsimoniousmechanism seems to be one where opening proceeds asynchronously, withthe low-to-high affinity change at the binding sites preceding the completeopening of the distant pore.     

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.     

Gating Transition of Pentameric Ligand-Gated Ion Channels

Pentameric ligand-gated ion channels are an important family of membrane proteins and play key roles in physiological processes, including signal transduction at chemical synapses. Here, we study the conformational changes associated with the opening and closing of the channel pore. Based on recent crystal structures of two prokaryotic members of the family in open and closed states, respectively, mixed elastic network models are constructed for the transmembrane domain. To explore the conformational changes in the gating transition, a coarse-grained transition path is computed that smoothly connects the closed and open conformations of the channel. We find that the conformational transition involves no major rotations of the transmembrane helices, and is instead characterized by a concerted tilting of helices M2 and M3. In addition, helix M2 changes its bending state, which results in an early closure of the pore during the open-to-closed transition.     

Charged residues in the beta2 subunit involved in GABAA receptor activation

Fast synaptic inhibition in the mammalian central nervous system is mediated primarily via activation of the gamma-aminobutyric acid type A receptor (GABAA-R). Upon agonist binding, the receptor undergoes a structural transition from the closed to the open state. This transition, known as gating, is thought to be associated with a sequence of conformational changes originating at the agonist-binding site, ultimately resulting in opening of the channel. Using site-directed mutagenesis and several different GABAA-R agonists, we identified a number of highly conserved charged residues in the GABAA-R beta2 subunit that appear to be involved in receptor activation. We then used charge reversal double mutants and disulfide trapping to investigate the interactions between these flexible loops within the beta2 subunit. The results suggest that interactions between an acidic residue in loop 7 (Asp146) and a basic residue in pre-transmembrane domain-1 (Lys215) are involved in coupling agonist binding to channel gating.     

Mixed modes in opening of KcsA potassium channel from a targeted molecular dynamics simulation

Potassium channels conduct K⁺ flow selectively across the membrane through a central pore. During a process called gating, the potassium channels undergo a conformational change that opens or closes the ion-conducting pore. The potassium channel KcsA has been structurally determined in its closed state. However, the dynamic mechanism of the gating transition of the KcsA channel is still being investigated. Here, a targeted molecular dynamics simulation up to 150 ns is performed to investigate the detailed opening process of the KcsA channel with an open Kv1.2 structure serving as the target. The channel arrived at a self-determined quasi-stable state within 60 ns. The rigid-body and hinge-bending modes are observed mixed together in the remaining 90 ns long quasi-stable state. The mixed-mode movement seems come from the competition between the helix rigidity and the biased-applied gating force.     

Toward elucidating the heat activation mechanism of the TRPV1 channel gating by molecular dynamics simulation

As a key cellular sensor, the TRPV1 cation channel undergoes a gating transition from a closed state to an open state in response to various physical and chemical stimuli including noxious heat. Despite years of study, the heat activation mechanism of TRPV1 gating remains enigmatic at the molecular level. Toward elucidating the structural and energetic basis of TRPV1 gating, we have performed molecular dynamics (MD) simulations (with cumulative simulation time of 3 μs), starting from the high‐resolution closed and open structures of TRPV1 solved by cryo‐electron microscopy. In the closed‐state simulations at 30°C, we observed a stably closed channel constricted at the lower gate (near residue I679), while the upper gate (near residues G643 and M644) is dynamic and undergoes flickery opening/closing. In the open‐state simulations at 60°C, we found higher conformational variation consistent with a large entropy increase required for the heat activation, and both the lower and upper gates are dynamic with transient opening/closing. Through ensemble‐based structural analyses of the closed state versus the open state, we revealed pronounced closed‐to‐open conformational changes involving the membrane proximal domain (MPD) linker, the outer pore, and the TRP helix, which are accompanied by breaking/forming of a network of closed/open‐state specific hydrogen bonds. By comparing the closed‐state simulations at 30°C and 60°C, we observed heat‐activated conformational changes in the MPD linker, the outer pore, and the TRP helix that resemble the closed‐to‐open conformational changes, along with partial formation of the open‐state specific hydrogen bonds. Some of the residues involved in the above key hydrogen bonds were validated by previous mutational studies. Taken together, our MD simulations have offered rich structural and dynamic details beyond the static structures of TRPV1, and promising targets for future mutagenesis and functional studies of the TRPV1 channel. Proteins 2016; 84:1938–1949. © 2016 Wiley Periodicals, Inc.     

Inter-Subunit Interactions across the Upper Voltage Sensing-Pore Domain Interface Contribute to the Concerted Pore Opening Transition of Kv Channels

The tight electro-mechanical coupling between the voltage-sensing and pore domains of Kv channels lies at the heart of their fundamental roles in electrical signaling. Structural data have identified two voltage sensor pore inter-domain interaction surfaces, thus providing a framework to explain the molecular basis for the tight coupling of these domains. While the contribution of the intra-subunit lower domain interface to the electro-mechanical coupling that underlies channel opening is relatively well understood, the contribution of the inter-subunit upper interface to channel gating is not yet clear. Relying on energy perturbation and thermodynamic coupling analyses of tandem-dimeric Shaker Kv channels, we show that mutation of upper interface residues from both sides of the voltage sensor-pore domain interface stabilizes the closed channel state. These mutations, however, do not affect slow inactivation gating. We, moreover, find that upper interface residues form a network of state-dependent interactions that stabilize the open channel state. Finally, we note that the observed residue interaction network does not change during slow inactivation gating. The upper voltage sensing-pore interaction surface thus only undergoes conformational rearrangements during channel activation gating. We suggest that inter-subunit interactions across the upper domain interface mediate allosteric communication between channel subunits that contributes to the concerted nature of the late pore opening transition of Kv channels.     

Structure of the transition state of gating in the acetylcholine receptor channel pore: a phi-value analysis

The gating mechanism of the acetylcholine receptor channel (AChR) was investigated by using rate equilibrium linear free energy relationships (LFERs) to probe the transition state between the closed and open conformations. The properties of the transition state of gating in the second transmembrane segment (M2) of the delta subunit, one of the five homologous pore-lining segments, was measured on a residue-by-residue basis. Series of point mutations were engineered at individual positions of this domain, and the corresponding constructs were characterized electrophysiologically, at the single-channel level. Fully liganded AChR opening and closing rate constants were estimated, and Phi-values (which are a measure of the extent of the conformational change realized at the transition state) were calculated for each reaction series as the slope of the Br?nsted relationship (log rate constant versus log equilibrium constant). Our results indicate that, at the transition state of gating, the extracellular half of deltaM2 partly resembles the open state (Phi-values between 0.24 and 0.38) while the intracellular half completely resembles the closed state (Phi-values between -0.18 and 0.03), with a break point near the middle of the M2 segment. This suggests that during gating the two halves of deltaM2 move asynchronously, with the rearrangement of the extracellular portion preceding (following) that of the intracellular part of deltaM2 during opening (closing). This particular sequence of molecular events indicates that the gating conformational change, which starts at the extracellular acetylcholine-binding sites (when opening), does not propagate exclusively along the primary sequence of the protein. In addition, our data are consistent with the deltaM2 segment bending or swiveling around its central residues during gating. We also elaborate on unsettled aspects of the analysis such as the accuracy of two-point LFERs, the physical interpretation of fractional Phi-values, and the existence of single versus parallel transition states for the gating reaction.     

Conformational changes in the pore of CLC-0

The Torpedo Cl- channel, CLC-0, is inhibited by clofibric acid derivatives from the intracellular side. We used the slow gate-deficient mutant CLC-0C212S to investigate the mechanism of block by the clofibric acid-derivative p-chlorophenoxy-acetic acid (CPA). CPA blocks open channels with low affinity (KDO= 45 mM at 0 mV) and shows fast dissociation (koff = 490 s-1 at -140 mV). In contrast, the blocker binds to closed channels with higher affinity and with much slower kinetics. This state-dependent block coupled with the voltage dependence of the gating transitions results in a highly voltage-dependent inhibition of macroscopic currents (KD approximately 1 mM at -140 mV; KD approximately 65 mM at 60 mV). The large difference in CPA affinity of the open and closed state suggests that channel opening involves more than just a local conformational rearrangement. On the other hand, in a recent work (Dutzler, R., E.B. Campbell, and R. MacKinnon. 2003. Science. 300:108-112) it was proposed that the conformational change underlying channel opening is limited to a movement of a single side chain. A prediction of this latter model is that mutations that influence CPA binding to the channel should affect the affinities for an open and closed channel in a similar manner since the general structure of the pore remains largely unchanged. To test this hypothesis we introduced point mutations in four residues (S123, T471, Y512, and K519) that lie close to the intracellular pore mouth or to the putative selectivity filter. Mutation T471S alters CPA binding exclusively to closed channels. Pronounced effects on the open channel block are observed in three other mutants, S123T, Y512A, and K519Q. Together, these results collectively suggest that the structure of the CPA binding site is different in the open and closed state. Finally, replacement of Tyr 512, a residue directly coordinating the central Cl- ion in the crystal structure, with Phe or Ala has very little effect on single channel conductance and selectivity. These observations suggest that channel opening in CLC-0 consists in more than a movement of a side chain and that other parts of the channel and of the selectivity filter are probably involved.     

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.     

Kinetics of unliganded acetylcholine receptor channel gating.

Open- and closed-state lifetimes of unliganded acetylcholine receptor channel activity were analyzed by the method of likelihood maximazation. For both open times and closed times, the best-fitting density is most often a sum of two exponentials. These multiple open states cannot depend on the number of receptor binding sites occupied since they are observed in the absence of ligand. The rate of spontaneous opening and the faster decay constant of closing increased as the membrane was hyperpolarized. The voltage dependence of the rate of spontaneous opening is stronger than that for curare-liganded channels. Evidence that the acetylcholine receptor channel can open spontaneously in the absence of ligand has been presented previously (Sanchez et al, 1983; Brehm et al, 1984; Jackson, 1984). To add to this evidence, alpha-bungarotoxin was added to the patch electrode, causing the frequency of openings to decay with time. The rate constant determined from this decay is similar to rate constants reported for the binding of iodinated alpha-bungarotoxin to the acetylcholine receptor. The frequency of unliganded channel opening has been estimated as 2 X 10(-3) s-1 per receptor. A comparison of carbamylcholine-liganded and spontaneous gating transition rates suggests that ligand binding increases the rate of opening by a factor of 1.4 X 10(7). Carbamylcholine binding increases the mean open time by a factor of 5. Thus, a cholinergic agonist activates the acetylcholine receptor by destabilizing the closed state. The liganded and unliganded channel gating rates were used to analyze the energetics of ligand activation of the acetylcholine receptor channel, and to relate the open channel dissociation constant to the closed channel dissociation constant.     

Conserved gating hinge in ligand- and voltage-dependent K+ channels

Ion channels open and close their pore in a process called gating. On the basis of crystal structures of two voltage-independent K(+) channels, KcsA and MthK, a conformational change for gating has been proposed whereby the inner helix bends at a glycine hinge point (gating hinge) to open the pore and straightens to close it. Here we ask if a similar gating hinge conformational change underlies the mechanics of pore opening of two eukaryotic voltage-dependent K(+) channels, Shaker and BK channels. In the Shaker channel, substitution of the gating hinge glycine with alanine and several other amino acids prevents pore opening, but the ability to open is recovered if a secondary glycine is introduced at an adjacent position. A proline at the gating hinge favors the open state of the Shaker channel as if by preventing inner helix straightening. In BK channels, which have two adjacent glycine residues, opening is significantly hindered in a graded manner with single and double mutations to alanine. These results suggest that K(+) channels, whether ligand- or voltage-dependent, open when the inner helix bends at a conserved glycine gating hinge.     

Energetic and spatial parameters for gating of the bacterial large conductance mechanosensitive channel, MscL

MscL is multimeric protein that forms a large conductance mechanosensitive channel in the inner membrane of Escherichia coli. Since MscL is gated by tension transmitted through the lipid bilayer, we have been able to measure its gating parameters as a function of absolute tension. Using purified MscL reconstituted in liposomes, we recorded single channel currents and varied the pressure gradient (P) to vary the tension (T). The tension was calculated from P and the radius of curvature was obtained using video microscopy of the patch. The probability of being open (Po) has a steep sigmoidal dependence on T, with a midpoint (T1/2) of 11.8 dyn/cm. The maximal slope sensitivity of Po/Pc was 0.63 dyn/cm per e-fold. Assuming a Boltzmann distribution, the energy difference between the closed and fully open states in the unstressed membrane was DeltaE = 18.6 kBT. If the mechanosensitivity arises from tension acting on a change of in-plane area (DeltaA), the free energy, TDeltaA, would correspond to DeltaA = 6.5 nm2. MscL is not a binary channel, but has four conducting states and a closed state. Most transition rates are independent of tension, but the rate-limiting step to opening is the transition between the closed state and the lowest conductance substate. This transition thus involves the greatest DeltaA. When summed over all transitions, the in-plane area change from closed to fully open was 6 nm2, agreeing with the value obtained in the two-state analysis. Assuming a cylindrical channel, the dimensions of the (fully open) pore were comparable to DeltaA. Thus, the tension dependence of channel gating is primarily one of increasing the external channel area to accommodate the pore of the smallest conducting state. The higher conducting states appear to involve conformational changes internal to the channel that don't involve changes in area.     

Voltage-dependent conformational changes in connexin channels

Channels formed by connexins display two distinct types of voltage-dependent gating, termed V(j)- or fast-gating and loop- or slow-gating. Recent studies, using metal bridge formation and chemical cross-linking have identified a region within the channel pore that contributes to the formation of the loop-gate permeability barrier. The conformational changes are remarkably large, reducing the channel pore diameter from 15 to 20? to less than 4?. Surprisingly, the largest conformational change occurs in the most stable region of the channel pore, the 3(10) or parahelix formed by amino acids in the 42-51 segment. The data provide a set of positional constraints that can be used to model the structure of the loop-gate closed state. Less is known about the conformation of the V(j)-gate closed state. There appear to be two different mechanisms; one in which conformational changes in channel structure are linked to a voltage sensor contained in the N-terminus of Cx26 and Cx32 and a second in which the C-terminus of Cx43 and Cx40 may act either as a gating particle to block the channel pore or alternatively to stabilize the closed state. The later mechanism utilizes the same domains as implicated in effecting pH gating of Cx43 channels. It is unclear if the two V(j)-gating mechanisms are related or if they represent different gating mechanisms that operate separately in different subsets of connexin channels. A model of the V(j)-closed state of Cx26 hemichannel that is based on the X-ray structure of Cx26 and electron crystallographic structures of a Cx26 mutation suggests that the permeability barrier for V(j)-gating is formed exclusively by the N-terminus, but recent information suggests that this conformation may not represent a voltage-closed state. Closed state models are considered from a thermodynamic perspective based on information from the 3.5? Cx26 crystal structure and molecular dynamics (MD) simulations. The applications of computational and experimental methods to define the path of allosteric molecular transitions that link the open and closed states are discussed. This article is part of a Special Issue entitled: The Communicating junctions, composition, structure and characteristics.     

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

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

Open-state conformation of the KcsA K+ channel: Monte Carlo normal mode following simulations

Potassium channels fluctuate between closed and open states. The detailed mechanism of the conformational changes opening the intracellular pore in the K+ channel from Streptomyces lividans (KcsA) is unknown. Applying Monte Carlo normal mode following, we find that gating involves rotation and unwinding of the TM2 bundle, lateral movement of the TM2 helices away from the channel axis, and disappearance of the TM2 bundle. The open-state conformation of KcsA exhibits a very wide inner vestibule, with a radius approximately 5-7 A and inner helices bent at the A98-G99 hinge. Computed conformational changes demonstrate that spin labeling and X-ray experiments illuminate different stages in gating: transition begins with clockwise rotation of the TM2 helices ending at a final state with the TM2 bend hinged near residues A98-G99. The concordance between the computational and experimental results provides atomic-level insights into the structural rearrangements of the channel's inner pore.     

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.