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Rate-equilibrium free energy relationship (REFER) analysis provides information on transition-state structures and has been applied to reveal the temporal sequence in which the different regions of an ion channel protein move during a closed–open conformational transition. To date, the theory used to interpret REFER relationships has been developed only for equilibrium mechanisms. Gating of most ion channels is an equilibrium process, but recently several ion channels have been identified to have retained nonequilibrium traits in their gating cycles, inherited from transporter-like ancestors. So far it has not been examined to what extent REFER analysis is applicable to such systems. By deriving the REFER relationships for a simple nonequilibrium mechanism, this paper addresses whether an equilibrium mechanism can be distinguished from a nonequilibrium one by the characteristics of their REFER plots, and whether information on the transition-state structures can be obtained from REFER plots for gating mechanisms that are known to be nonequilibrium cycles. The results show that REFER plots do not carry information on the equilibrium nature of the underlying gating mechanism. Both equilibrium and nonequilibrium mechanisms can result in linear or nonlinear REFER plots, and complementarity of REFER slopes for opening and closing transitions is a trivial feature true for any mechanism. Additionally, REFER analysis provides limited information about the transition-state structures for gating schemes that are known to be nonequilibrium cycles.     

Free-energy landscapes of ion-channel gating are malleable: changes in the number of bound ligands are accompanied by changes in the location of the transition state in acetylcholine-receptor channels

Acetylcholine-receptor channels (AChRs) are allosteric membrane proteins that mediate synaptic transmission by alternatively opening and closing ("gating") a cation-selective transmembrane pore. Although ligand binding is not required for the channel to open, the binding of agonists (for example, acetylcholine) increases the closed right harpoon over left harpoon open equilibrium constant because the ion-impermeable --> ion-permeable transition of the ion pathway is accompanied by a low-affinity --> high-affinity change at the agonist-binding sites. The fact that the gating conformational change of muscle AChRs can be kinetically modeled as a two-state reaction has paved the way to the experimental characterization of the corresponding transition state, which represents a snapshot of the continuous sequence of molecular events separating the closed and open states. Previous studies of fully (di) liganded AChRs, combining single-channel kinetic measurements, site-directed mutagenesis, and data analysis in the framework of the linear free-energy relationships of physical organic chemistry, have suggested a transition-state structure that is consistent with channel opening being an asynchronous conformational change that starts at the extracellular agonist-binding sites and propagates toward the intracellular end of the pore. In this paper, I characterize the gating transition state of unliganded AChRs, and report a remarkable difference: unlike that of diliganded gating, the unliganded transition state is not a hybrid of the closed- and open-state structures but, rather, is almost indistinguishable from the open state itself. This displacement of the transition state along the reaction coordinate obscures the mechanism underlying the unliganded closed right harpoon over left harpoon open reaction but brings to light the malleable nature of free-energy landscapes of ion-channel gating.     

Transition-state ensemble in enzyme catalysis: possibility, reality, or necessity?

Proteins are not rigid structures; they are dynamic entities, with numerous conformational isomers (substates). The dynamic nature of protein structures amplifies the structural variation of the transition state for chemical reactions performed by proteins. This suggests that utilizing a transition state ensemble to describe chemical reactions involving proteins may be a useful representation. Here we re-examine the nature of the transition state of protein chemical reactions (enzyme catalysis), considering both recent developments in chemical reaction theory (Marcus theory for SN2 reactions), and protein dynamics effects. The classical theory of chemical reactions relies on the assumption that a reaction must pass through an obligatory transition-state structure. The widely accepted view of enzymatic catalysis holds that there is tight binding of the substrate to the transition-state structure, lowering the activation energy. This picture, may, however, be oversimplified. The real meaning of a transition state is a surface, not a single saddle point on the potential energy surface. In a reaction with a "loose" transition-state structure, the entire transition-state region, rather than a single saddle point, contributes to reaction kinetics. Consequently, here we explore the validity of such a model, namely, the enzymatic modulation of the transition-state surface. We examine its utility in explaining enzyme catalysis. We analyse the possibility that instead of optimizing binding to a well-defined transition-state structure, enzymes are optimized by evolution to bind efficiently with a transition-state ensemble, with a broad range of activated conformations. For enzyme catalysis, the key issue is still transition state (ensemble) stabilization. The source of the catalytic power is the modulation of the transition state. However, our definition of the transition state is the entire transition-state surface rather just than a single well-defined structure. This view of the transition-state ensemble is consistent with the nature of the protein molecule, as embodied and depicted in the protein energy landscape of folding, and binding, funnels.     

Structural dynamics of the M4 transmembrane segment during acetylcholine receptor gating

The transition state structures that link the stable end states of allosteric proteins are largely unresolved. We used single-molecule kinetic analysis to probe the dynamics of the M4 transmembrane segments during the closed<==>open isomerization of the neuromuscular acetylcholine receptor ion channel (AChR). We measured the slopes (phi) of the free energy relationships for 87 mutants, which reveal the open- versus closed-like characters of the mutated residues at the transition state and hence the sequence and organization of gating molecular motions. phi was constant throughout the length of the alpha subunit M4 segment with an average value of 0.54, suggesting that this domain moves as a unit, approximately midway through the reaction. Analysis of a hybrid construct indicates that the two alpha subunits move synchronously. Between subunits, the sequence of M4 motions is alpha-epsilon-beta. The AChR ion channel emerges as a dynamic nanomachine with many moving parts.     

Does the Na channel conduct ions through a water-filled pore or a condensed-state pathway?

Many investigators assert that the ion-conducting pathway of the Na channel is a water-filled pore. This assertion must be reevaluated to clear the way for more productive approaches to channel gating. The hypothesis of an aqueous pore leaves the questions of voltage-dependent gating and ion selectivity unexplained because a column of water can neither serve as a switch nor provide the necessary selectivity. The price of believing in an aqueous pore therefore is a futile search for separate ad hoc mechanisms for gating and selectivity. The fallacy is to assume that only water is available to carry ions rapidly, ignoring the role of the glycoprotein, which can form an elastomeric phase with water. The elastomer is a state of matter, neither liquid nor solid, in which the molecules of a liquid are threaded together with cross-linked polymer chains; it supports fast ion motion (Owen, 1989). An alternative hypothesis for channel gating, based on condensed-state materials science, already exists (Leuchtag, 1988, 1991a). The ferroelectric-superionic transition hypothesis (FESITH) postulates that the Na channel exists in a metastable ordered (closed) state at resting potential and, on threshold depolarization, undergoes a reversible order-disorder phase transition to a less-ordered, ion-conducting (open) state. The ordered state is ferroelectric; the disordered state is a fast ion conductor selective for Li+ and Na+. The basis of the voltage dependence is elevation of transition temperature with electric field, well established in ferroelectrics. FESITH is consistent with single-channel transitions, gating currents, heat and cold block, and other phenomena observed at channel or membrane level.(ABSTRACT TRUNCATED AT 250 WORDS)     

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.     

A physical model of potassium channel activation: from energy landscape to gating kinetics

We have developed a method for rapidly computing gating currents from a multiparticle ion channel model. Our approach is appropriate for energy landscapes that can be characterized by a network of well-defined activation pathways with barriers. To illustrate, we represented the gating apparatus of a channel subunit by an interacting pair of charged gating particles. Each particle underwent spatial diffusion along a bistable potential of mean force, with electrostatic forces coupling the two trajectories. After a step in membrane potential, relaxation of the smaller barrier charge led to a time-dependent reduction in the activation barrier of the principal gate charge. The resulting gating current exhibited a rising phase similar to that measured in voltage-dependent ion channels. Reduction of the two-dimensional diffusion landscape to a circular Markov model with four states accurately preserved the time course of gating currents on the slow timescale. A composite system containing four subunits leading to a concerted opening transition was used to fit a series of gating currents from the Shaker potassium channel. We end with a critique of the model with regard to current views on potassium channel structure.     

Ion channels for the mechano-electrical transduction and efferent synapse of the hair cell

Auditory and vestibular information is applied to the hair cell hair bundle as mechanical energy, and is transduced into electrical energy by gating ion channels. The m-e.t. channel has a unitary conductance of 50 pS and a broad selectivity to monovalent cations and to divalent cations. Ca ions are the most permeable through the channel. The angular displacement of the hair bundle is the primary gating factor. Circumstantial evidence indicates the possibility of the direct gating of channels by the membrane deformation itself. The transduction potential activates voltage gated Ca channel and leads to the release of neurotransmitters which activate afferent neurones. Cholinergic muscarinic receptors likely mediate the inhibitory efferent innervation to the hair cell.     

Shape of the free energy barriers for protein folding probed by multiple perturbation analysis

The characterization of the free energy barriers has been a major goal in studies on the mechanism of protein folding. Testing the effect of mutations or denaturants on protein folding reactions revealed that transition state movement is rare, suggesting that folding barriers are robust and narrow maxima on the free energy landscape. Here we demonstrate that the application of multiple perturbations allows the observation of small transition state movements that escape detection in single perturbation experiments. We used tendamistat as a model protein to test the broadness of the free energy barriers. Tendamistat folds over two consecutive transition states and through a high-energy intermediate. Measuring the combined effect of temperature and denaturant on the position of the transition state in the wild-type protein and in several mutants revealed that the early transition state shows significant transition state movement. Its accessible surface area state becomes more native-like with destabilization of the native state by temperature. To the same extent, the entropy of the early transition state becomes more native-like with increasing denaturant concentration, in accordance with Hammond behavior. The position of the late transition state, in contrast, is much less sensitive to the applied perturbations. These results suggest that the barriers in protein folding become increasingly narrow as the folding polypeptide chain approaches the native state.     

Open state destabilization by ATP occupancy is mechanism speeding burst exit underlying KATP channel inhibition by ATP.

The ATP-sensitive potassium (K(ATP)) channel is named after its characteristic inhibition by intracellular ATP. The inhibition is a centerpiece of how the K(ATP) channel sets electrical signaling to the energy state of the cell. In the beta cell of the endocrine pancreas, for example, ATP inhibition results from high blood glucose levels and turns on electrical activity leading to insulin release. The underlying gating mechanism (ATP inhibition gating) includes ATP stabilization of closed states, but the action of ATP on the open state of the channel is disputed. The original models of ATP inhibition gating proposed that ATP directly binds the open state, whereas recent models indicate a prerequisite transition from the open to a closed state before ATP binds and inhibits activity. We tested these two classes of models by using kinetic analysis of single-channel currents from the cloned mouse pancreatic K(ATP) channel expressed in Xenopus oocytes. In particular, we combined gating models based on fundamental rate law and burst gating kinetic considerations. The results demonstrate open-state ATP dependence as the major mechanism by which ATP speeds exit from the active burst state underlying inhibition of the K(ATP) channel by ATP.     

Understanding Voltage Gating of Providencia stuartii Porins at Atomic Level

Bacterial porins are water-filled β-barrel channels that allow translocation of solutes across the outer membrane. They feature a constriction zone, contributed by the plunging of extracellular loop 3 (L3) into the channel lumen. Porins are generally in the open state, but undergo gating in response to external voltages. To date the underlying mechanism is unclear. Here we report results from molecular dynamics simulations on the two porins of Providenica stuartii, Omp-Pst1 and Omp-Pst2, which display distinct voltage sensitivities. Voltage gating was observed in Omp-Pst2, where the binding of cations in-between L3 and the barrel wall results in exposing a conserved aromatic residue in the channel lumen, thereby halting ion permeation. Comparison of Omp-Pst1 and Omp-Pst2 structures and trajectories suggests that their sensitivity to voltage is encoded in the hydrogen-bonding network anchoring L3 onto the barrel wall, as we observed that it is the strength of this network that governs the probability of cations binding behind L3. That Omp-Pst2 gating is observed only when ions flow against the electrostatic potential gradient of the channel furthermore suggests a possible role for this porin in the regulation of charge distribution across the outer membrane and bacterial homeostasis.     

Kinetic time constants independent of previous single-channel activity suggest Markov gating for a large conductance Ca-activated K channel

Models for the gating of ion channels usually assume that the rate constants for leaving any given kinetic state are independent of previous channel activity. Although such discrete Markov models have been successful in describing channel gating, there is little direct evidence for the Markov assumption of time-invariant rate constants for constant conditions. This paper tests the Markov assumption by determining whether the single-channel kinetics of the large conductance Ca-activated K channel in cultured rat skeletal muscle are independent of previous single-channel activity. The experimental approach is to examine dwell-time distributions conditional on adjacent interval durations. The time constants of the exponential components describing the distributions are found to be independent of adjacent interval duration, and hence, previous channel activity. In contrast, the areas of the different components can change. Since the observed time constants are a function of the underlying rate constants for transitions among the kinetic states, the observation of time constants independent of previous channel activity suggests that the rate constants are also independent of previous channel activity. Thus, the channel kinetics are consistent with Markov gating. An observed dependent (inverse) relationship between durations of adjacent open and shut intervals together with Markov gating indicates that there are two or more independent transition pathways connecting open and shut states. Finally, no evidence is found to suggest that gating is not at thermodynamic equilibrium: the inverse relationship was independent of the time direction of analysis.     

Biophysics of mechanoreception

Several types of cells' skeletal, muscle, nerve, epithelia, and heart have been shown to contain ion channels which are sensitive to membrane tension. In chick skeletal muscle, the transduction persists in excised patches and involves no chemical messengers. Quantitative analysis of single channel records reveals that the sensitivity to stretch can be described by a linear four state model with three closed (C) and one open (O) state: (Formula: see text). Only the rate constant k12 is sensitive to tension (and membrane potential) following the law: k12 = kO12 exp/(theta T2 + alpha V) where theta is a constant describing the sensitivity to tension, T, and alpha is a constant describing the sensitivity to voltage, V, and kO12 is a constant. The form of the tension sensitivity can be accounted for by a model in which strain energy is used to gate the channel. Analysis of strain sensitivity, theta, indicates that the channel must concentrate energy from a large (ca. 500-nm diameter) area of membrane which suggests that the channel is in series with a component of the cytoskeleton. Treatment with cytochalasins suggests that actin is mechanically in parallel with the channel. When a channel with the above properties is incorporated into a simple model of mechanical transduction in hair cells, the resulting model is capable of explaining the kinetic features and the sensitivity found in the cochlear-vestibular system. The proposed gating mechanism of mechanical transduction appears to be general and can account for existing data on a variety of systems.     

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.     

Catalyst-like modulation of transition states for CFTR channel opening and closing: New stimulation strategy exploits nonequilibrium gating

Cystic fibrosis transmembrane conductance regulator (CFTR) is the chloride ion channel mutated in cystic fibrosis (CF) patients. It is an ATP-binding cassette protein, and its resulting cyclic nonequilibrium gating mechanism sets it apart from most other ion channels. The most common CF mutation (ΔF508) impairs folding of CFTR but also channel gating, reducing open probability (P_o). This gating defect must be addressed to effectively treat CF. Combining single-channel and macroscopic current measurements in inside-out patches, we show here that the two effects of 5-nitro-2-(3-phenylpropylamino)benzoate (NPPB) on CFTR, pore block and gating stimulation, are independent, suggesting action at distinct sites. Furthermore, detailed kinetic analysis revealed that NPPB potently increases P_o, also of ΔF508 CFTR, by affecting the stability of gating transition states. This finding is unexpected, because for most ion channels, which gate at equilibrium, altering transition-state stabilities has no effect on P_o; rather, agonists usually stimulate by stabilizing open states. Our results highlight how for CFTR, because of its unique cyclic mechanism, gating transition states determine P_o and offer strategic targets for potentiator compounds to achieve maximal efficacy.     

TRPM8 voltage sensor mutants reveal a mechanism for integrating thermal and chemical stimuli

TRPM8, a member of the transient receptor potential (TRP) channel superfamily, is expressed in thermosensitive neurons, in which it functions as a cold and menthol sensor. TRPM8 and most other temperature-sensitive TRP channels (thermoTRPs) are voltage gated; temperature and ligands regulate channel opening by shifting the voltage dependence of activation. The mechanisms and structures underlying gating of thermoTRPs are currently poorly understood. Here we show that charge-neutralizing mutations in transmembrane segment 4 (S4) and the S4-S5 linker of human TRPM8 reduce the channel's gating charge, which indicates that this region is part of the voltage sensor. Mutagenesis-induced changes in voltage sensitivity translated into altered thermal sensitivity, thereby establishing the strict coupling between voltage and temperature sensing. Specific mutations in this region also affected menthol affinity, which indicates a direct interaction between menthol and the TRPM8 voltage sensor. Based on these findings, we present a Monod-Wyman-Changeux-type model explaining the combined effects of voltage, temperature and menthol on TRPM8 gating.     

Total Charge Movement per Channel : The Relation between Gating Charge Displacement and the Voltage Sensitivity of Activation

One measure of the voltage dependence of ion channel conductance is the amount of gating charge that moves during activation and vice versa. The limiting slope method, introduced by Almers (Almers, W. 1978. Rev. Physiol. Biochem. Pharmacol. 82:96–190), exploits the relationship of charge movement and voltage sensitivity, yielding a lower limit to the range of single channel gating charge displacement. In practice, the technique is plagued by low experimental resolution due to the requirement that the logarithmic voltage sensitivity of activation be measured at very low probabilities of opening. In addition, the linear sequential models to which the original theory was restricted needed to be expanded to accommodate the complexity of mechanisms available for the activation of channels. In this communication, we refine the theory by developing a relationship between the mean activation charge displacement (a measure of the voltage sensitivity of activation) and the gating charge displacement (the integral of gating current). We demonstrate that recording the equilibrium gating charge displacement as an adjunct to the limiting slope technique greatly improves accuracy under conditions where the plots of mean activation charge displacement and gross gating charge displacement versus voltage can be superimposed. We explore this relationship for a wide variety of channel models, which include those having a continuous density of states, nonsequential activation pathways, and subconductance states. We introduce new criteria for the appropriate use of the limiting slope procedure and provide a practical example of the theory applied to low resolution simulation data.     

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.     

Short-range molecular rearrangements in ion channels detected by tryptophan quenching of bimane fluorescence

Ion channels are allosteric membrane proteins that open and close an ion-permeable pore in response to various stimuli. This gating process provides the regulation that underlies electrical signaling events such as action potentials, postsynaptic potentials, and sensory receptor potentials. Recently, the molecular structures of a number of ion channels and channel domains have been solved by x-ray crystallography. These structures have highlighted a gap in our understanding of the relationship between a channel's function and its structure. Here we introduce a new technique to fill this gap by simultaneously measuring the channel function with the inside-out patch-clamp technique and the channel structure with fluorescence spectroscopy. The structure and dynamics of short-range interactions in the channel can be measured by the presence of quenching of a covalently attached bimane fluorophore by a nearby tryptophan residue in the channel. This approach was applied to study the gating rearrangements in the bovine rod cyclic nucleotide-gated ion channel CNGA1 where it was found that C481 moves towards A461 during the opening allosteric transition induced by cyclic nucleotide. The approach offers new hope for elucidating the gating rearrangements in channels of known structure.     

Correlation character of ionic current fluctuations: analysis of ion current through a voltage-dependent potassium single channel

The gating of ion channels has widely been modeled by assuming the transition between open and closed states is a memoryless process. Nevertheless, the statistical analysis of an ionic current signal recorded from voltage dependence K(+) single channel is presented. Calculating the sample auto-correlation function of the ionic current based on the digitized signals, rather than the sequence of open and closed states duration time. The results provide evidence for the existence of memory. For different voltages, the ion channel current fluctuation has different correlation attributions. The correlations in data generated by simulation of two Markov models, on one hand, auto-correlation function of the ionic current shows a weaker memory, after a delayed period of time, the attribute of memory does not exist; on the other hand, the correlation depends on the number of states in the Markov model. For V(p)=-60 mV pipette potential, spectral analysis of ion channel current was conducted, the result indicates that the spectrum is not a flat spectrum, the data set from ionic current fluctuations shows considerable variability with a broad 1/f -like spectrum, alpha=1.261+/-0.24. Thus the ion current fluctuations give information about the kinetics of the channel protein, the results suggest the correlation character of ion channel protein nonlinear kinetics regardless of whether the channel is in open or closed state.