Restoration of single-channel currents using the segmental k-means method based on hidden Markov modeling

Patch-clamp recording provides an unprecedented means for study of detailed kinetics of ion channels at the single molecule level. Analysis of the recordings often begins with idealization of noisy recordings into continuous dwell-time sequences. Success of an analysis is contingent on accuracy of the idealization. I present here a statistical procedure based on hidden Markov modeling and k-means segmentation. The approach assumes a Markov scheme involving discrete conformational transitions for the kinetics of the channel and a white background noise for contamination of the observations. The idealization is sought to maximize a posteriori probability of the state sequence corresponding to the samples. The approach constitutes two fundamental steps. First, given a model, the Viterbi algorithm is applied to determine the most likely state sequence. With the resultant idealization, the model parameters are then empirically refined. The transition probabilities are calculated from the state sequences, and the current amplitudes and noise variances are determined from the ensemble means and variances of those samples belonging to the same conductance classes. The two steps are iterated until the likelihood is maximized. In practice, the algorithm converges rapidly, taking only a few iterations. Because the noise is taken into explicit account, it allows for a low signal/noise ratio, and consequently a relatively high bandwidth. The approach is applicable to data containing subconductance levels or multiple channels and permits state-dependent noises. Examples are given to elucidate its performance and practical applicability.     

Tetanus toxin channel in phosphatidylserine planar bilayers: conductance states and pH dependence

Tetanus toxin (TeTx) forms ionic channel in phosphatidylserine bilayers. TeTx channels exhibit different modes of channel bursting activity, from a closed state to well defined open states of different amplitudes. At positive applied voltages, TeTx channels flicker continuously between a closed state and the various distinct open states. Furthermore, fast transitions into subconductance states are discernible within the bursts of channel activity. Elementary conductance steps submultiple of the open states were not identified in single channel records owing to rapid transitions between different states. However, statistical analysis shows that conductances cluster with amplitudes multiple of an elementary value: e.g. 25–30 pS at neutral pH. Single channel current amplitudes decrease with the pH of the bulk electrolyte solution. Conductance decrements can be accounted for by the relative decrease of permeant cation concentration at the membrane-water interface, by a relative enrichment of protons that block the channel or by the stabilization of a conformational state of the channel protein. Offprint requests to: F. Gambale     

Thermodynamic and kinetic studies of the gating behavior of a K+- selective channel from the sarcoplasmic reticulum membrane

A voltage-dependent, K+-selective ionic channel from sarcoplasmic reticulum of rabbit skeletal muscle has been studied in a planar phospholipid bilayer membrane. The purpose [corrected] of this work is to study the mechanism by which the channel undergoes transitions between its conducting and nonconducting states. Thermodynamic studies show that the "open" and "closed" states of the channel exist in a voltage-dependent equilibrium, and that the channel displays only a single open state; the channel conductance is 120 pmho in 0.1 M K+. The channel's gating process follows single exponential kinetics at all voltages tested, and the individual opening and closing rate constants are exponentially dependent on voltage. The individual rate constants may also be determined from a stochastic analysis of channel fluctuations among multiple conductance levels. Neither the thermodynamic nor the kinetic parameters of gating depend on the absolute concentration of channels in the bilayer. The results are taken as evidence that the channel gates by an unusually simple two-state conformational mechanism in which the equivalent of 1.1 net charges are moved across the membrane during the formation of the open channel.     

Subconductance states in calcium-activated potassium channels from canine airway smooth muscle

The single-channel patch clamp technique was used to analyze subconductance states in the 260 pS calcium-activated potassium channel from canine airway smooth muscle. More than sixty minutes of single channel data (greater than 87,000 events) from five excised patches were analyzed. Six subconductance amplitudes were clearly established to be 17, 33, 41, 52, 63 and 72% of the full conductance. Subconductance openings were usually brief (milliseconds) and represented less than 5% of the total channel open time, but they also persisted for several seconds on rare occasions. They appeared to be unaffected by voltage or time after seal formation, but may have increased in occurrence with decreasing calcium concentration. Irregular amplitude intervals, and the presence of ramp-like, analog transitions between conductance states, suggest a model for maxi-K subconductance states in which the channel protein undergoes random conformational changes causing a variable pore size.     

Ionic channels with conformational substates.

Recent studies of protein dynamics suggest that ionic channels can assume many conformational substates. Long-lived substates have been directly observed in single-channel current records. In many cases, however, the lifetimes of conformational states will be far below the theoretical limit of time resolution of single-channel experiments. The existence of such hidden substates may strongly influence the observable (time-averaged) properties of a channel, such as the concentration dependence of conductance. A channel exhibiting fast, voltage-dependent transitions between different conductance states may behave as an intrinsic rectifier. In the presence of more than one permeable ion species, coupling between ionic fluxes may occur, even when the channel has only a single ion-binding site. In special situations the rate of ion translocation becomes limited by the rate of conformational transitions, meaning that the channel approaches the kinetic behavior of a carrier. As a result of the strong coulombic interaction between an ion in a binding site and polar groups of the protein, rate constants of conformational transitions may depend on the occupancy of the binding site. Under this condition a nonequilibrium distribution of conformational states is created when ions are driven through the channel by an external force. This may lead to an apparent violation of microscopic reversibility, i.e., to a situation in which the frequency of transitions from state A to state B is no longer equal to the transition frequency from state B to state A.     

Hidden Markov model analysis of intermediate gating steps associated with the pore gate of shaker potassium channels.

Cooperativity among the four subunits helps give rise to the remarkable voltage sensitivity of Shaker potassium channels, whose open probability changes tenfold for a 5-mV change in membrane potential. The cooperativity in these channels is thought to arise from a concerted structural transition as the final step in opening the channel. Recordings of single-channel ionic currents from certain other channel types, as well as our previous recordings from T442S mutant Shaker channels, however, display intermediate conductance levels in addition to the fully open and closed states. These sublevels might represent stepwise, rather than concerted, transitions in the final steps of channel activation. Here, we report a similar fine structure in the closing transitions of Shaker channels lacking the mutation. Describing the deactivation time course with hidden Markov models, we find that two subconductance levels are rapidly traversed during most closing transitions of chimeric, high conductance Shaker channels. The lifetimes of these levels are voltage-dependent, with maximal values of 52 and 22 micros at -100 mV, and the voltage dependences of transitions among these states suggest that they arise from equivalent conformational changes occurring in individual subunits. At least one subconductance level is found to be traversed in normal conductance Shaker channels. We speculate that voltage-dependent conformational changes in the subunits give rise to changes in a "pore gate" associated with the selectivity filter region of the channel, producing the subconductance states. As a control for the hidden Markov analysis, we applied the same procedures to recordings of the recovery from N-type inactivation in Shaker channels. These transitions are found to be instantaneous in comparison.     

Comparing the Temperature-Dependent Conductance of the Two Structurally Similar E. coli Porins OmpC and OmpF

The temperature-dependent ion conductance of OmpC, a major outer membrane channel of Escherichia coli, is predicted using all-atom molecular dynamics simulations and experimentally verified. To generalize previous results, OmpC is compared to its structural homolog OmpF at different KCl concentrations, pH values, and a broad temperature range. At low salt concentrations and up to room temperature, the molecular modeling predicts the experimental conductance accurately. At high salt concentrations above 1 M KCl and above room temperature, the simulations underestimate the conductance. Moreover, the temperature dependence of the channel conductance is different from that of the bulk, both in experiment and simulation, indicating a strong contribution of surface effects to the ion conductance. With respect to OmpC, subconductance levels can be observed in experiments only. Subconductance and gating levels can be clearly distinguished by their differences in conductance values and temperature-dependent behavior. With increasing temperature, the probability of a subconductance state to occur, increases, while the dwell time is decreased. The open probability, frequency, and dwell time of such states is largely pH- and KCl concentration-independent, while their amplitudes show a lower increase with increasing salt concentration than gating amplitudes. Voltage dependence of subconductance has been found to be negligible within the uncertainty of the measurements.     

Opening mechanism of a cyclic nucleotide-gated channel based on analysis of single channels locked in each liganded state.

Cyclic nucleotide-gated channels contain four subunits, each with a binding site for cGMP or cAMP in the cytoplasmic COOH-terminal domain. Previous studies of the kinetic mechanism of activation have been hampered by the complication that ligands are continuously binding and unbinding at each of these sites. Thus, even at the single channel level, it has been difficult to distinguish changes in behavior that arise from a channel with a fixed number of ligands bound from those that occur upon the binding and unbinding of ligands. For example, it is often assumed that complex behaviors like multiple conductance levels and bursting occur only as a consequence of changes in the number of bound ligands. We have overcome these ambiguities by covalently tethering one ligand at a time to single rod cyclic nucleotide-gated channels (Ruiz, ML., and J.W. Karpen. 1997. Nature. 389:389-392). We find that with a fixed number of ligands locked in place the channel freely moves between three conductance states and undergoes bursting behavior. Furthermore, a thorough kinetic analysis of channels locked in doubly, triply, and fully liganded states reveals more than one kinetically distinguishable state at each conductance level. Thus, even when the channel contains a fixed number of bound ligands, it can assume at least nine distinct states. Such complex behavior is inconsistent with simple concerted or sequential allosteric models. The data at each level of liganding can be successfully described by the same connected state model (with different rate constants), suggesting that the channel undergoes the same set of conformational changes regardless of the number of bound ligands. A general allosteric model, which postulates one conformational change per subunit in both the absence and presence of ligand, comes close to providing enough kinetically distinct states. We propose an extension of this model, in which more than one conformational change per subunit can occur during the process of channel activation.     

Interactions of protons with single open L-type calcium channels. pH dependence of proton-induced current fluctuations with Cs+, K+, and Na+ as permeant ions

We studied the pH dependence of the proton-induced current fluctuations that appear in single open L-type Ca channels when monovalent ions are the charge carriers. We used different methods of analysis to obtain kinetic measurements even under conditions where the individual transitions were too fast to be resolved directly as discrete current steps between two conductance levels. The reciprocal of the dwell times at the high conductance level increased linearly with the pipette proton activity, with a slope that was similar for Cs, K, and Na as permeant ions. Contrary to the expectation for a simple model in which the high and low conductances represent the unprotonated and protonated states of the channel, respectively, the dwell times at the low conductance level were also pH dependent and lengthened with increasing proton activity. At all pH values the dwell times at the low conductance level were longest with Cs as permeant ion and shortened in the order Cs greater than K greater than Na. We introduce a more general model of the protonation cycle in which the channel is represented by four states and can be protonated and deprotonated both at the high and low conductance levels. The conductance change is represented by a conformational change of the channel protein. We discuss the validity of this model and its implications for the mechanism by which protons interact with ion permeation through L-type Ca channels.     

Monazomycin-induced single channels. I. Characterization of the elementary conductance events

Monazomycin (a positively charged, polyene-like antibiotic) induces voltage-dependent conductance changes in lipid bilayer membranes when added to one of the bathing solutions. These conductance changes have generally been attributed to the existence of channels spanning the membrane. In this article we characterize the behavior of the individual conductance events observed when adding small amounts of monazomycin to one side of a lipid bilayer. We find that there are several apparent channel types with one or sometimes two amplitudes predominating. We find further that these fairly similar amplitudes represent two different states of the same fundamental channel entity, presumed to be the monazomycin channel. The current-voltage characteristics of these channels are weakly hyperbolic functions of applied potential. The average lifetimes are essentially voltage independent (between 50 and 400 mV). The average channel intervals, on the other hand, can be strongly voltage dependent, and we can show that the time-averaged conductance of a membrane is proportional to the average channel frequency.     

Mechanosensitive channel gating transitions resolved by functional changes upon pore modification

The mechanosensitive channel of large conductance acts as a biological "emergency release valve" that protects bacterial cells from hypoosmotic stress. Although structural and functional studies and molecular dynamic simulations of this channel have led to several models for the structural transitions that occur in the gating process, inconsistencies linger and details are lacking. A previous study, using a method coined as the "in vivo SCAM", identified several residues in the channel pore that were exposed to the aqueous environment in the closed and opening conformations. Briefly, the sulfhydryl reagent MTSET was allowed to react, in the presence or absence of hypoosmotic shock, with cells expressing mechanosensitive channel of large conductance channels that contained cysteine substitutions; channel dysfunction was assessed solely by cell viability. Here we evaluate the MTSET-induced functional modifications to these mechanosensitive channel activities by measuring single channel recordings. The observed changes in residue availability in different states, as well as channel kinetics and sensitivity, have allowed us to elucidate the microenvironment encountered for a number of pore residues, thus testing many aspects of previous models and giving a higher resolution of the pore domain and the structural transitions it undergoes from the closed to open state.     

Discrete-state theory in nerve impulse modelling.

Hodgkin-Huxley models have been the standard for describing ionic current kinetics. However, many single channel behaviors cannot be described using traditional Hodgkin-Huxley models; they can be described by expanding the Hodgkin-Huxley models to have multiple resting and inactivated states. The model, based on charge translocation between a finite number of discrete Markovian states, is a biophysical kinetic model, according to current generalizations of channel structure, capable of reproducing channel behavior. The elaboration of the model is based on the Markov process. This type of model assumes that each channel has a discrete number of states that are connected by a kinetic diagram that defines the allowable transitions between these states and the rates at which these transitions occur. The application of the model presented here leads to results in accordance with the experimental data regarding the shape and characteristics of the nerve impulse registered along the nerve fibre. Unlike the traditional Hodgkin-Huxley models, the model based on the Markov processes has the advantage of removing the empirical equations, simplifying the computation of the membrane potential and revealing the single-channel variables. The average behavior is obtained by the repetition in one channel of the same stimulus, a number of times equal to the number of channels, which means that the macroscopic variables are predictable by the repetition, a certain number of times, of the same observations in a single channel.     

Electrical properties of ionic channels formed by Helix pomatia hemocyanin in planar lipid bilayers

Helix pomatia hemocyanin forms ion-conducting channels in planar lipid bilayer membranes when added at mg/ml concentration. These channels have several original features. They fluctuate between one conducting and some poorly conducting states and fluctuations can be grouped in bursts. Different channels can have widely different conductance amplitudes. Both channel conductance and burst lifetime are dependent on the applied voltage. Fluctuations within a burst show a complex kinetic behaviour which has been explained developing a multistate model. The model calls for one single open state and six different closed states. Transitions are allowed only between one of the closed states and the open one and obey first order kinetics. This model is able to fit all our experimental curves obtained in single channel experiments.     

Determination of the functional unit of the cystic fibrosis transmembrane conductance regulator chloride channel. One polypeptide forms one pore

The magnitudes and distributions of subconductance states were studied in chloride channels formed by the wild-type cystic fibrosis transmembrane conductance regulator (CFTR) and in CFTRs bearing amino acid substitutions in transmembrane segment 6. Within an open burst, it was possible to distinguish three distinct conductance states referred to as the full conductance, subconductance 1, and subconductance 2 states. Amino acid substitutions in transmembrane segment 6 altered the duration and probability of occurrence of these subconductance states but did not greatly alter their relative amplitudes. Results from real time measurements indicated that covalent modification of single R334C-CFTR channels by [2-(trimethylammonium)ethyl]methanethiosulfonate resulted in the simultaneous modification of all three conductance levels in what appeared to be a single step, without changing the proportion of time spent in each state. This behavior suggests that at least a portion of the conduction path is common to all three conducting states. The time course for the modification of R334C-CFTR, measured in outside-out macropatches using a rapid perfusion system, was also consistent with a single modification step as if each pore contained only a single copy of the cysteine at position 334. These results are consistent with a model for the CFTR conduction pathway in which a single anion-conducting pore is formed by a single CFTR polypeptide.     

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

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

Properties of amphotericin B channels in a lipid bilayer

Properties of individual ionic channels formed by polyene antibiotic Amphotericin B were studied on brain phospholipid membranes containing cholesterol. The ionic channels have a closed state and an open one (with conductance of about 6.5 pS in 2 M KCl). The conductance value of an open channel is independent of cholesterol concentration in the membrane and of pH in the range from 3.5 to 8.0. The voltage-current characteristics of a single channel are superlinear. Zero current potential value in the case of different KCl concentrations in the two solutions indicates preferential but not ideal anionic selectivity of a single channel. Channel conductivity grows as the electrolyte concentration is increased and tends to a limiting value at high concentrations. A simple model having only one site for an ion was shown to represent satisfactorily an open channel behaviour under different conditions. An individual ionic channel performs a large number of transitions between the open and closed states during its life-time of several minutes. Rate constants of these transitions depend on the kind and concentration of salt in aqueous solutions. The switching system functioning is not influenced by an ion situated inside the pore.     

K channel subconductance levels result from heteromeric pore conformations

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

大脑皮层神经元上ATP激活的多电导单通道

用膜片箝技术的细胞贴附式（ｃｅｌｌ—ａｔｔａｃｈｅｄ）和内面向外式（ｉｎｓｉｄｅ—ｏｕｔ）,在机械分离的新生大鼠的大脑皮层神经元上,记录到ＡＴＰ激活的单通道电流。按电流幅度可以分为三类,其电导分别为２０ｐＳ、３２ｐＳ和５８ｐＳ,各占全部开放事件数的１２％、６７％和２１％,其中３２ｐＳ为优势电导。三种电导状态之间可直接转换。３２ｐＳ和５８ｐＳ以及３２ｐＳ和２０ｐＳ之间的转换最为常见。结果表明：新生ＳＤ大鼠的大脑皮层神经元上存在ＡＴＰ激活的多电导单通道。     

Redistribution of the electric field within the pore contributes to the voltage-dependence of mitochondrial porin channel.

The effects of pH on the integral conductance and on the properties of single channels induced by porin from rat liver mitochondria in a lipid bilayer have been studied. When the membrane potential increases, the conductance of the multi-channel membrane decreases more sharply at acidic pH than at neutral or basic pH. The channel is shown to have several states with different conductance and selectivity. The number of levels and their conductance do not depend on pH, while the selectivity as well as the dependence of steady-state probabilities of different levels on the membrane potential are substantially affected by a pH change. This dependence curve steepens in the pH region where charges of carboxyl groups of aspartic and glutamic amino acids are neutralized. It is concluded that at neutral pH the channel gate is controlled by a great number of the positively and negatively charged groups. The high steepness of the conductance-voltage curve in the acidic region suggests that at least 60 positive charges participate in controlling the channel gate. This number, compared with that of the positively charged side chain amino acids per channel, according to the amino acid analysis of the porin, led us to conclude that almost all amino groups of the channel former must pass through the entire membrane potential difference upon random motion of the channel among the states. The assumption that channel closing leads to redistribution of the electric field within the pore, changing the energy of the charges on the voltage sensor, may be the only explanation of this phenomenon.     

The Nature of the Negative Resistance in Bimolecular Lipid Membranes Containing Excitability-Inducing Material

When sufficiently small amounts of excitability-inducing material (EIM) are added to a bimolecular lipid membrane, the conductance is limited to a few discrete levels and changes abruptly from one level to another. From our study of these fluctuations, we have concluded that the EIM-doped bilayer contains ion-conducting channels capable of undergoing transitions between two states of different conductance. The difference in current between the "open" and "closed" states is directly proportional to the applied membrane potential, and corresponds to a conductance of about 3 x 10^-10 ohm^-1. The fraction of the total number of channels that is open varies from unity to zero as a function of potential. The voltage-dependent opening and closing of channels explains the negative resistance observed for bimolecular lipid membranes treated with greater amounts of EIM.