Nonequilibrium response spectroscopy of voltage-sensitive ion channel gating.

We describe a new electrophysiological technique called nonequilibrium response spectroscopy, which involves application of rapidly fluctuating (as high as 14 kHz) large-amplitude voltage clamp waveforms to ion channels. As a consequence of the irreversible (in the sense of Carnot) exchange of energy between the fluctuating field and the channel protein, the gating response is exquisitely sensitive to features of the kinetics that are difficult or impossible to adequately resolve by means of traditional stepped potential protocols. Here we focus on the application of dichotomous (telegraph) noise voltage fluctuations, a broadband Markovian colored noise that fluctuates between two values. Because Markov kinetic models of channel gating can be embedded within higher-dimensional Markov models that take into account the effects of the voltage fluctuations, many features of the response of the channels can be calculated algebraically. This makes dichotomous noise and its generalizations uniquely suitable for model selection and kinetic analysis. Although we describe its application to macroscopic ionic current measurements, the nonequilibrium response method can also be applied to gating and single channel current recording techniques. We show how data from the human cardiac isoform (hH1a) of the Na+ channel expressed in mammalian cells can be acquired and analyzed, and how these data reveal hidden aspects of the molecular kinetics that are not revealed by conventional methods.     

Application of the ensemble nonequilibrium response spectroscopy to shaker potassium channel gating

Standard electrophysiology techniques study relaxation transients in voltage-gated ion channels generated by discrete voltage steps. The nonequilibrium response spectroscopy involves analyzing responses to fluctuating potentials. We apply the ensemble NRS method to gating kinetics of Shaker potassium ion channels. We evaluate various proposed Markov models of channel gating from the nonequilibrium response viewpoint. These new NRS protocols can be used to test otherwise indistinguishable models or improve estimates for parameters of channel kinetics models.     

Pharmacological and kinetic analysis of K channel gating currents

We have measured gating currents from the squid giant axon using solutions that preserve functional K channels and with experimental conditions that minimize Na channel contributions to these currents. Two pharmacological agents were used to identify a component of gating current that is associated with K channels. Low concentrations of internal Zn2+ that considerably slow K channel ionic currents with no effect on Na channel currents altered the component of gating current associated with K channels. At low concentrations (10-50 microM) the small, organic, dipolar molecule phloretin has several reported specific effects on K channels: it reduces K channel conductance, shifts the relationship between channel conductance and membrane voltage (Vm) to more positive potentials, and reduces the voltage dependence of the conductance-Vm relation. The K channel gating charge movements were altered in an analogous manner by 10 microM phloretin. We also measured the dominant time constants of the K channel ionic and gating currents. These time constants were similar over part of the accessible voltage range, but at potentials between -40 and 0 mV the gating current time constants were two to three times faster than the corresponding ionic current values. These features of K channel function can be reproduced by a simple kinetic model in which the channel is considered to consist of two, two-state, nonidentical subunits.     

Gating of Shaker K+ channels: I. Ionic and gating currents.

Ionic and gating currents from noninactivating Shaker B K+ channels were studied with the cut-open oocyte voltage clamp technique and compared with the macropatch clamp technique. The performance of the cut-open oocyte voltage clamp technique was evaluated from the electrical properties of the clamped upper domus membrane, K+ tail current measurements, and the time course of K+ currents after partial blockade. It was concluded that membrane currents less than 20 microA were spatially clamped with a time resolution of at least 50 microseconds. Subtracted, unsubtracted gating currents with the cut-open oocyte voltage clamp technique and gating currents recorded in cell attached macropatches had similar properties and time course, and the charge movement properties directly obtained from capacity measurements agreed with measurements of charge movement from subtracted records. An accurate estimate of the normalized open probability Po(V) was obtained from tail current measurements as a function of the prepulse V in high external K+. The Po(V) was zero at potentials more negative than -40 mV and increased sharply at this potential, then increased continuously until -20 mV, and finally slowly increased with voltages more positive than 0 mV. Deactivation tail currents decayed with two time constants and external potassium slowed down the faster component without affecting the slower component that is probably associated with the return between two of the closed states near the open state. In correlating gating currents and channel opening, Cole-Moore type experiments showed that charge moving in the negative region of voltage (-100 to -40 mV) is involved in the delay of the conductance activation but not in channel opening. The charge moving in the more positive voltage range (-40 to -10 mV) has a similar voltage dependence to the open probability of the channel, but it does not show the gradual increase with voltage seen in the Po(V).     

Integrated allosteric model of voltage gating of HCN channels

Hyperpolarization-activated (pacemaker) channels are dually gated by negative voltage and intracellular cAMP. Kinetics of native cardiac f-channels are not compatible with HH gating, and require closed/open multistate models. We verified that members of the HCN channel family (mHCN1, hHCN2, hHCN4) also have properties not complying with HH gating, such as sigmoidal activation and deactivation, activation deviating from fixed power of an exponential, removal of activation "delay" by preconditioning hyperpolarization. Previous work on native channels has indicated that the shifting action of cAMP on the open probability (Po) curve can be accounted for by an allosteric model, whereby cAMP binds more favorably to open than closed channels. We therefore asked whether not only cAMP-dependent, but also voltage-dependent gating of hyperpolarization-activated channels could be explained by an allosteric model. We hypothesized that HCN channels are tetramers and that each subunit comprises a voltage sensor moving between "reluctant" and "willing" states, whereas voltage sensors are independently gated by voltage, channel closed/open transitions occur allosterically. These hypotheses led to a multistate scheme comprising five open and five closed channel states. We estimated model rate constants by fitting first activation delay curves and single exponential time constant curves, and then individual activation/deactivation traces. By simply using different sets of rate constants, the model accounts for qualitative and quantitative aspects of voltage gating of all three HCN isoforms investigated, and allows an interpretation of the different kinetic properties of different isoforms. For example, faster kinetics of HCN1 relative to HCN2/HCN4 are attributable to higher HCN1 voltage sensors' rates and looser voltage-independent interactions between subunits in closed/open transitions. It also accounts for experimental evidence that reduction of sensors' positive charge leads to negative voltage shifts of Po curve, with little change of curve slope. HCN voltage gating thus involves two processes: voltage sensor gating and allosteric opening/closing.     

Gating of single non-Shaker A-type potassium channels in larval Drosophila neurons

The voltage-dependent gating of transient A2-type potassium channels from primary cultures of larval Drosophila central nervous system neurons was studied using whole-cell and single-channel voltage clamp. A2 channels are genetically distinct from the Shaker A1 channels observed in Drosophila muscle, and differ in single-channel conductance, voltage dependence, and gating kinetics. Single A2 channels were recorded and analyzed at -30, -10, +10, and +30 mV. The channels opened in bursts in response to depolarizing steps, with three to four openings per burst and two to three bursts per 480-ms pulse (2.8-ms burst criterion). Mean open durations were in a range of 2-4 ms and mean burst durations in a range of 9-17 ms. With the exception of the first latency distributions, none of the means of the distributions measured showed a consistent trend with voltage. Macroscopic inactivation of both whole-cell A currents and ensemble average currents of single A2 channels was well fitted by a sum of two exponentials. The fast time constants in different cells were in a range of 9-25 ms, and the slow time constants in a range of 60-140 ms. A six-state kinetic model (three closed, one open, two inactivated states) was tested at four command voltages by fitting frequency histograms of open durations, burst durations, burst closed durations, number of openings per burst, and number of bursts per trace. The model provided good fits to these data, as well as to the ensemble averages. With the exception of the rates leading to initial opening, the transitions in the model were largely independent of voltage.     

Voltage- and [ATP]-dependent Gating of the P2X2 ATP Receptor Channel

P2X receptors are ligand-gated cation channels activated by extracellular adenosine triphosphate (ATP). Nonetheless, P2X₂ channel currents observed during the steady-state after ATP application are known to exhibit voltage dependence; there is a gradual increase in the inward current upon hyperpolarization. We used a Xenopus oocyte expression system and two-electrode voltage clamp to analyze this “activation” phase quantitatively. We characterized the conductance–voltage relationship in the presence of various [ATP], and observed that it shifted toward more depolarized potentials with increases in [ATP]. By analyzing the rate constants for the channel''s transition between a closed and an open state, we showed that the gating of P2X₂ is determined in a complex way that involves both membrane voltage and ATP binding. The activation phase was similarly recorded in HEK293 cells expressing P2X₂ even by inside-out patch clamp after intensive perfusion, excluding a possibility that the gating is due to block/unblock by endogenous blocker(s) of oocytes. We investigated its structural basis by substituting a glycine residue (G344) in the second transmembrane (TM) helix, which may provide a kink that could mediate “gating.” We found that, instead of a gradual increase, the inward current through the G344A mutant increased instantaneously upon hyperpolarization, whereas a G344P mutant retained an activation phase that was slower than the wild type (WT). Using glycine-scanning mutagenesis in the background of G344A, we could recover the activation phase by introducing a glycine residue into the middle of second TM. These results demonstrate that the flexibility of G344 contributes to the voltage-dependent gating. Finally, we assumed a three-state model consisting of a fast ATP-binding step and a following gating step and estimated the rate constants for the latter in P2X₂-WT. We then executed simulation analyses using the calculated rate constants and successfully reproduced the results observed experimentally, voltage-dependent activation that is accelerated by increases in [ATP].     

Kinetic properties of a voltage-dependent junctional conductance

We have proposed that the gap junctions between amphibian blastomeres are comprised of voltage-sensitive channels. The kinetic properties of the junctional conductance are here studied under voltage clamp. When the transjunctional voltage is stepped to a new voltage of the same polarity, the junctional conductance changes as a single exponential to a steady-state level. The time constant of the conductance change is determined by the existing transjunctional voltage and is independent of the previous voltage. For each voltage polarity, the relations between voltage, time constant, and steady-state conductance are well modeled by a reversible two-state reaction scheme in which the calculated rate constants for the transitions between the states are exponential functions of voltage. The calculated rate constant for the transition to the low-conductance state is approximately twice as voltage dependent as that for the transition to the high-conductance state. When the transjunctional voltage polarity is reversed, the junctional conductance undergoes a transient recovery. The polarity reversal data are well modeled by a reaction scheme in which the junctional channel has two gates, each with opposite voltage sensitivity, and in which an open gate may close only if the gate in series with it is open. A simple explanation for this contingent gating is a mechanism in which each gate senses only the local voltage drop within the channel.     

Testing for microscopic reversibility in the gating of maxi K+ channels using two-dimensional dwell-time distributions.

An assumption usually made when developing kinetic models for the gating of ion channels is that the transitions among the various states involved in the gating obey microscopic reversibility. If this assumption is incorrect, then the models and estimated rate constants made with the assumption would be in error. This paper examines whether the gating of a large conductance Ca-activated K+ channel in skeletal muscle is consistent with microscopic reversibility. If microscopic reversibility is obeyed, then the number of forward and backward transitions per unit time for each individual reaction step will, on average, be identical and, consequently, the gating must show time reversibility. To look for time reversibility, two-dimensional dwell-time distributions of the durations of open and closed intervals were obtained from single-channel current records analyzed in the forward and in the backward directions. Two-dimensional dwell-time distributions of pairs of open intervals and of pairs of closed intervals were also analyzed to extend the resolution of the method to special circumstances in which intervals from different closed (or open) states might have similar durations. No significant differences were observed between the forward and backward analysis of the two-dimensional dwell-time distributions, suggesting time reversibility. Thus, we find no evidence to indicate that the gating of the maxi K+ channel violates microscopic reversibility.     

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.     

Transfection of mammalian cells with connexins and measurement of voltage sensitivity of their gap junctions

Vertebrate gap junction channels are formed by a family of more than 20 connexin proteins. These gap junction proteins are expressed with overlapping cellular and tissue specificity, and coding region mutations can cause human hereditary diseases. Here we present a summary of what has been learned from voltage clamp studies performed on cell pairs either endogenously expressing gap junctions or in which connexins are exogenously expressed. General protocols presented here are currently used to transfect mammalian cells with connexins and to study the biophysical properties of the heterologously expressed connexin channels. Transient transfection is accomplished overnight with maximal expression occurring at about 36 h; stable transfectants normally can be generated within three or four weeks through colony selection. Electrophysiological protocols are presented for analysis of voltage dependence and single-channel conductance of gap junction channels as well as for studies of chemical gating of these channels.     

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.     

Asymmetric electrostatic effects on the gating of rat brain sodium channels in planar lipid membranes.

The effects of ionic strength (10-1,000 mM) on the gating of batrachotoxin-activated rat brain sodium channels were studied in neutral and in negatively charged lipid bilayers. In neutral bilayers, increasing the ionic strength of the extracellular solution, shifted the voltage dependence of the open probability (gating curve) of the sodium channel to more positive membrane potentials. On the other hand, increasing the intracellular ionic strength shifted the gating curve to more negative membrane potentials. Ionic strength shifted the voltage dependence of both opening and closing rate constants of the channel in analogous ways to its effects on gating curves. The voltage sensitivities of the rate constants were not affected by ionic strength. The effects of ionic strength on the gating of sodium channels reconstituted in negatively charged bilayers were qualitatively the same as in neutral bilayers. However, important quantitative differences were noticed: in low ionic strength conditions (10-150 mM), the presence of negative charges on the membrane surface induced an extra voltage shift on the gating curve of sodium channels in relation to neutral bilayers. It is concluded that: (a) asymmetric negative surface charge densities in the extracellular (1e-/533A2) and intracellular (1e-/1,231A2) sides of the sodium channel could explain the voltage shifts caused by ionic strength on the gating curve of the channel in neutral bilayers. These surface charges create negative electric fields in both the extracellular and intracellular sides of the channel. Said electric fields interfere with gating charge movements that occur during the opening and closing of sodium channels; (b) the voltage shifts caused by ionic strength on the gating curve of sodium channels can be accounted by voltage shifts in both the opening and closing rate constants; (c) net negative surface charges on the channel's molecule do not affect the intrinsic gating properties of sodium channels but are essential in determining the relative position of the channel's gating curve; (d) provided the ionic strength is below 150 mM, the gating machinery of the sodium channel molecule is able to sense the electric field created by surface changes on the lipid membrane. I propose that during the opening and closing of sodium channels, the gating charges involved in this process are asymmetrically displaced in relation to the plane of the bilayer. Simple electrostatic calculations suggest that gating charge movements are influenced by membrane electrostatic potentials at distances of 48 and 28 A away from the plane of the membrane in the extracellular sides of the channel, respectively.     

Linear impedance studies of voltage-dependent conductances in tissue cultured chick heart cells.

Plateau and pacemaker currents from tissue cultured clusters of embryonic chick heart cells were studied in the time domain, using voltage-clamp steps, and in the frequency domain, using a wide-band noise input superimposed on a steady holding voltage. In the presence of tetrodotoxin to block the sodium channel, a depolarizing voltage step into the plateau range elicited: (a) a rapid (approximately equal to 2 ms) activation of the slow inward current; (b) a subsequent slower (approximately equal to 25 ms) decline in the slow inward current; and (c) activation of a very slow (5 to 10 s) outward current. Impedance studies in this voltage range could clearly resolve two voltage-dependent processes, which appeared to correspond to points b and c above because of their voltage dependence, pharmacology, and time constants. A correlate of point a was also probably present but difficult to resolve owing to the fast time constant of activation for the slow inward channel. At voltages negative to -50 mV a new voltage-dependent process could be resolved, which, because of its voltage dependence and time constant, appeared to represent the pacemaker channel (also termed If or IK2). In the Appendix, linear models of voltage-dependent channels and ion accumulation/depletion are derived and these are compared with our data. Most of the above-mentioned processes could be attributed to voltage-dependent channels with kinetics similar to those observed in time domain, voltage-clamp studies. However, the frequency domain correlate of the decline of the slow inward current was incompatible with channel gating, rather, it appears accumulation/depletion of calcium may dominate the decline in this preparation.     

Gating of Na channels in the rat cortical collecting tubule: effects of voltage and membrane stretch

The gating kinetics of apical membrane Na channels in the rat cortical collecting tubule were assessed in cell-attached and inside-out excised patches from split-open tubules using the patch-clamp technique. In patches containing a single channel the open probability (Po) was variable, ranging from 0.05 to 0.9. The average Po was 0.5. However, the individual values were not distributed normally, but were mainly < or = 0.25 or > or = 0.75. Mean open times and mean closed times were correlated directly and inversely, respectively, with Po. In patches where a sufficient number of events could be recorded, two time constants were required to describe the open-time and closed-time distributions. In most patches in which basal Po was < 0.3 the channels could be activated by hyperpolarization of the apical membrane. In five such patches containing a single channel hyperpolarization by 40 mV increased Po by 10-fold, from 0.055 +/- 0.023 to 0.58 +/- 0.07. This change reflected an increase in the mean open time of the channels from 52 +/- 17 to 494 +/- 175 ms and a decrease in the mean closed time from 1,940 +/- 350 to 336 +/- 100 ms. These responses, however, could not be described by a simple voltage dependence of the opening and closing rates. In many cases significant delays in both the activation by hyperpolarization and deactivation by depolarization were observed. These delays ranged from several seconds to several tens of seconds. Similar effects of voltage were seen in cell-attached and excised patches, arguing against a voltage-dependent chemical modification of the channel, such as a phosphorylation. Rather, the channels appeared to switch between gating modes. These switches could be spontaneous but were strongly influenced by changes in membrane voltage. Voltage dependence of channel gating was also observed under whole-cell clamp conditions. To see if mechanical perturbations could also influence channel kinetics or gating mode, negative pressures of 10-60 mm Hg were applied to the patch pipette. In most cases (15 out of 22), this maneuver had no significant effect on channel behavior. In 6 out of 22 patches, however, there was a rapid and reversible increase in Po when the pressure was applied. In one patch, there was a reversible decrease. While no consistent effects of pressure could be documented, membrane deformation could contribute to the variation in Po under some conditions.     

Electrostatics explains the shift in VDAC gating with salt activity gradient

We have analyzed voltage-dependent anion-selective channel (VDAC) gating on the assumption that the states occupied by the channel are determined mainly by their electrostatic energy. The voltage dependence of VDAC gating both in the presence and in the absence of a salt activity gradient was explained just by invoking electrostatic interactions. A model describing this energy in the main VDAC states has been developed. On the basis of the model, we have considered how external factors cause the redistribution of the channels among their conformational states. We propose that there is a difference in the electrostatic interaction between the voltage sensor and fixed charge within the channel when the former is located in the cis side of membrane as opposed to the trans. This could be the main cause of the shift in the probability curve. The theory describes satisfactorily the experimental data (Zizi et al., Biophys. J. 1998. 75:704-713) and explains some peculiarities of VDAC gating. The asymmetry of the probability curve was related to the apparent location of the VDAC voltage sensor in the open state. By analyzing published experimental data, we concluded that this apparent location is influenced by the diffusion potential. Also discussed is the possibility that VDAC gating at high voltage may be better described by assuming that the mobile charge consists of two parts that have to overcome different energetic barriers in the channel-closing process.     

Chloride channels in toad skin

A study of the voltage and time dependence of a transepithelial Cl- current in toad skin (Bufo bufo) by the voltage-clamp method leads to the conclusion that potential has a dual role for Cl- transport. One is to control the permeability of an apical membrane Cl-pathway, the other is to drive Cl- ions through this pathway. Experimental analysis of the gating kinetics is rendered difficult owing to a contamination of the gated currents by cellular ion redistribution currents. To obtain insight into the effects of accumulation-depletion currents on voltage clamp currents of epithelial membranes, a mathematical model of the epithelium has been developed for computer analysis. By assuming that the apical membrane Cl- permeability is governed by a single gating variable (Hodgkin-Huxley kinetics), the model predicts fairly well steady-state current-voltage curves, the time course of current activations from a closed state, and the dependence of unidirectional fluxes on potential. Other predictions of the model do not agree with experimental findings, and it is suggested that the gating kinetics are governed by rate coefficients that also depend on the holding potential. Evidence is presented that Cl- transport through open channels does not obey the constant-field equation.     

Quantitative analysis of the voltage-dependent gating of mouse parotid ClC-2 chloride channel

Various ClC-type voltage-gated chloride channel isoforms display a double barrel topology, and their gating mechanisms are thought to be similar. However, we demonstrate in this work that the nearly ubiquitous ClC-2 shows significant differences in gating when compared with ClC-0 and ClC-1. To delineate the gating of ClC-2 in quantitative terms, we have determined the voltage (V(m)) and time dependence of the protopore (P(f)) and common (P(s)) gates that control the opening and closing of the double barrel. mClC-2 was cloned from mouse salivary glands, expressed in HEK 293 cells, and the resulting chloride currents (I(Cl)) were measured using whole cell patch clamp. WT channels had I(Cl) that showed inward rectification and biexponential time course. Time constants of fast and slow components were approximately 10-fold different at negative V(m) and corresponded to P(f) and P(s), respectively. P(f) and P(s) were approximately 1 at -200 mV, while at V(m) > or = 0 mV, P(f) approximately 0 and P(s) approximately 0.6. Hence, P(f) dominated open kinetics at moderately negative V(m), while at very negative V(m) both gates contributed to gating. At V(m) > or = 0 mV, mClC-2 closes by shutting off P(f). Three- and two-state models described the open-to-closed transitions of P(f) and P(s), respectively. To test these models, we mutated conserved residues that had been previously shown to eliminate or alter P(f) or P(s) in other ClC channels. Based on the time and V(m) dependence of the two gates in WT and mutant channels, we constructed a model to explain the gating of mClC-2. In this model the E213 residue contributes to P(f), the dominant regulator of gating, while the C258 residue alters the V(m) dependence of P(f), probably by interacting with residue E213. These data provide a new perspective on ClC-2 gating, suggesting that the protopore gate contributes to both fast and slow gating and that gating relies strongly on the E213 residue.     

A nitric oxide concentration clamp.

We report a new method of generating nitric oxide (NO) that possesses several advantages for experimental use. This method consists of a photolysis chamber where NO is released by illuminating photolabile NO donors with light from a xenon lamp, in conjunction with feedback control. Control of the photolysis light was achieved by selectively gating light projected through a shutter before the light was launched into a light guide that conveyed the light to the photolysis chamber. By gating the light in proportion to a sensor that reported nearly instantaneous concentration from the photolysis chamber, a criterion NO concentration could be achieved, which could be easily adjusted to higher or lower criterion levels. To denote the similarity of this process with the electrophysiological process of voltage clamp, we term this process a concentration "clamp." This development enhances the use of the fiber-optic-based system for NO delivery and should enable the execution of experiments where the in situ concentration of NO is particularly critical, such as in biological preparations.     

Estimating kinetic parameters for single channels with simulation. A general method that resolves the missed event problem and accounts for noise.

Analysis of currents recorded from single channels is complicated by the limited time resolution (filtering) of the data which can prevent the detection of brief intervals. Although a number of approaches have been used to correct for the undetected intervals (missed events) when identifying kinetic models and estimating parameters, none of them provide a general method which takes into account the true effects of noise and limited time resolution. This paper presents such a method. The approach is to use simulated single-channel currents to incorporate the true effects of filtering and noise on missed events and interval durations. The simulated currents are then analyzed in a manner identical to that used to analyze the experimental currents. An iterative search process using likelihood comparison of two-dimensional dwell-time distributions obtained from the simulated and experimental single-channel currents then allows the most likely rate constants to be determined. The large errors and false solutions that can result from the more typically applied assumptions of no noise and an absolute dead time (idealized filtering) are excluded by the iterative simulation method, and the correlation information contained in the two-dimensional distributions should increase the ability to distinguish among different gating mechanisms. The iterative simulation method is generally applicable to channels which typically open to a single conductance level. For these channels the method places no restrictions on the proposed gating mechanism or the form of the predicted dwell-time distributions.