Automated electrophysiology in drug discovery.

Ion channels play essential roles in nervous system signaling, electrolyte transport, and muscle contraction. As such, ion channels are important therapeutic targets, and the search for compounds that modulate ion channels is accelerating. In order to identify and optimize ion channel modulators, assays are needed that are reliable and provide sufficient throughput for all stages of the drug discovery process. Electrophysiological assays offer the most direct and accurate characterization of channel activity and, by controlling membrane potential, can provide information about drug interactions with different conformational states. However, these assays are technically challenging and notoriously low-throughput. The recent development of several automated electrophysiology platforms has greatly increased the throughput of whole cell electrophysiological recordings, allowing them to play a more central role in ion channel drug discovery. While challenges remain, this new technology will facilitate the pharmaceutical development of ion channel modulators.

Molecular analysis of two cytochrome P450 monooxygenase genes required for paxilline biosynthesis in Penicillium paxilli, and effects of paxilline intermediates on mammalian maxi-K ion channels.

The gene cluster required for paxilline biosynthesis in Penicillium paxilli contains two cytochrome P450 monooxygenase genes, paxP and paxQ. The primary sequences of both proteins are very similar to those of proposed cytochrome P450 monooxygenases from other filamentous fungi, and contain several conserved motifs, including that for a haem-binding site. Alignment of these sequences with mammalian and bacterial P450 enzymes of known 3-D structure predicts that there is also considerable conservation at the level of secondary structure. Deletion of paxP and paxQ results in mutant strains that accumulate paspaline and 13-desoxypaxilline, respectively. These results confirm that paxP and paxQ are essential for paxilline biosynthesis and that paspaline and 13-desoxypaxilline are the most likely substrates for the corresponding enzymes. Chemical complementation of paxilline biosynthesis in paxG (geranygeranyl diphosphate synthase) and paxP, but not paxQ, mutants by the external addition of 13-desoxypaxilline confirms that PaxG and PaxP precede PaxQ, and are functionally part of the same biosynthetic pathway. A pathway for the biosynthesis of paxilline is proposed on the basis of these and earlier results. Electrophysiological experiments demonstrated that 13-desoxypaxilline is a weak inhibitor of mammalian maxi-K channels (Ki=730 nM) compared to paxilline (Ki=30 nM), indicating that the C-13 OH group of paxilline is crucial for the biological activity of this tremorgenic mycotoxin. Paspaline is essentially inactive as a channel blocker, causing only slight inhibition at concentrations up to 1 microM.

Oxidative regulation of large conductance calcium-activated potassium channels.

Reactive oxygen/nitrogen species are readily generated in vivo, playing roles in many physiological and pathological conditions, such as Alzheimer's disease and Parkinson's disease, by oxidatively modifying various proteins. Previous studies indicate that large conductance Ca(2+)-activated K(+) channels (BK(Ca) or Slo) are subject to redox regulation. However, conflicting results exist whether oxidation increases or decreases the channel activity. We used chloramine-T, which preferentially oxidizes methionine, to examine the functional consequences of methionine oxidation in the cloned human Slo (hSlo) channel expressed in mammalian cells. In the virtual absence of Ca(2+), the oxidant shifted the steady-state macroscopic conductance to a more negative direction and slowed deactivation. The results obtained suggest that oxidation enhances specific voltage-dependent opening transitions and slows the rate-limiting closing transition. Enhancement of the hSlo activity was partially reversed by the enzyme peptide methionine sulfoxide reductase, suggesting that the upregulation is mediated by methionine oxidation. In contrast, hydrogen peroxide and cysteine-specific reagents, DTNB, MTSEA, and PCMB, decreased the channel activity. Chloramine-T was much less effective when concurrently applied with the K(+) channel blocker TEA, which is consistent with the possibility that the target methionine lies within the channel pore. Regulation of the Slo channel by methionine oxidation may represent an important link between cellular electrical excitability and metabolism.

Correolide and derivatives are novel immunosuppressants blocking the lymphocyte Kv1.3 potassium channels.

The voltage-gated potassium channel, Kv1.3, is specifically expressed on human lymphocytes, where it controls membrane potential and calcium influx. Blockade of Kv1.3 channels by margatoxin was previously shown to prevent T cell activation and attenuate immune responses in vivo. In the present study, a triterpene natural product, correolide, was found to block Kv1.3 channels in human and miniswine T cells by electrophysiological characterization. T cell activation events, such as anti-CD3-induced calcium elevation, IL-2 production, and proliferation were inhibited by correolide in a dose-dependent manner. More potent analogs were evaluated for pharmacokinetic profiles and subsequently tested in a delayed-type hypersensitivity (DTH) response to tuberculin in the miniswine. Two compounds were dosed orally, iv, or im, and both compounds suppressed DTH responses, demonstrating that small molecule blockers of Kv1.3 channels can act as immunosuppressive agents in vivo. These studies establish correolide and its derivatives as novel immunosuppressants.

Mechanism of maxi-K channel activation by dehydrosoyasaponin-I.

Dehydrosoyasaponin-I (DHS-I) is a potent activator of high-conductance, calcium-activated potassium (maxi-K) channels. Interaction of DHS-I with maxi-K channels from bovine aortic smooth muscle was studied after incorporating single channels into planar lipid bilayers. Nanomolar amounts of intracellular DHS-I caused the appearance of discrete episodes of high channel open probability interrupted by periods of apparently normal activity. Statistical analysis of these periods revealed two clearly separable gating modes that likely reflect binding and unbinding of DHS-I. Kinetic analysis of durations of DHS-I-modified modes suggested DHS-I activates maxi-K channels through a high-order reaction. Average durations of DHS-I-modified modes increased with DHS-I concentration, and distributions of these mode durations contained two or more exponential components. In addition, dose-dependent increases in channel open probability from low initial values were high order with average Hill slopes of 2.4-2.9 under different conditions, suggesting at least three to four DHS-I molecules bind to maximally activate the channel. Changes in membrane potential over a 60-mV range appeared to have little effect on DHS-I binding. DHS-I modified calcium- and voltage-dependent channel gating. 100 nM DHS-I caused a threefold decrease in concentration of calcium required to half maximally open channels. DHS-I shifted the midpoint voltage for channel opening to more hyperpolarized potentials with a maximum shift of -105 mV. 100 nM DHS-I had a larger effect on voltage-dependent compared with calcium-dependent channel gating, suggesting DHS-I may differentiate these gating mechanisms. A model specifying four identical, noninteracting binding sites, where DHS-I binds to open conformations with 10-20-fold higher affinity than to closed conformations, explained changes in voltage-dependent gating and DHS-I-induced modes. This model of channel activation by DHS-I may provide a framework for understanding protein structures underlying maxi-K channel gating, and may provide a basis for understanding ligand activation of other ion channels.

Blockade of the voltage-gated potassium channel Kv1.3 inhibits immune responses in vivo.

The voltage activated K+ channel (Kv1.3) has recently been identified as the molecule that sets the resting membrane potential of peripheral human T lymphoid cells. In vitro studies indicate that blockage of Kv1.3 inhibits T cell activation, suggesting that Kv1.3 may be a target for immunosuppression. However, despite the in vitro evidence, there has been no in vivo demonstration that blockade of Kv1.3 will attenuate an immune response. The difficulty is due to species differences, as the channel does not set the membrane potential in rodent peripheral T cells. In this study, we show that the channel is present on peripheral T cells of miniswine. Using the peptidyl Kv1.3 inhibitor, margatoxin, we demonstrate that Kv1.3 also regulates the resting membrane potential, and that blockade of Kv1.3 inhibits, in vivo, both a delayed-type hypersensitivity reaction and an Ab response to an allogeneic challenge. In addition, prolonged Kv1.3 blockade causes reduced thymic cellularity and inhibits the thymic development of T cell subsets. These results provide in vivo evidence that Kv1.3 is a novel target for immunomodulation.

High-conductance calcium-activated potassium channels; structure, pharmacology, and function.

High-conductance calcium-activated potassium (maxi-K) channels comprise a specialized family of K+ channels. They are unique in their dual requirement for depolarization and Ca2+ binding for transition to the open, or conducting, state. Ion conduction through maxi-K channels is blocked by a family of venom-derived peptides, such as charybdotoxin and iberiotoxin. These peptides have been used to study function and structure of maxi-K channels, to identify novel channel modulators, and to follow the purification of functional maxi-K channels from smooth muscle. The channel consists of two dissimilar subunits, alpha and beta. The alpha subunit is a member of the slo Ca(2+)-activated K+ channel gene family and forms the ion conduction pore. The beta subunit is a structurally unique, membrane-spanning protein that contributes to channel gating and pharmacology. Potent, selective maxi-K channel effectors (both agonists and blockers) of low molecular weight have been identified from natural product sources. These agents, together with peptidyl inhibitors and site-directed antibodies raised against alpha and beta subunit sequences, can be used to anatomically map maxi-K channel expression, and to study the physiologic role of maxi-K channels in various tissues. One goal of such investigations is to determine whether maxi-K channels represent novel therapeutic targets.

Paxilline inhibition of the alpha-subunit of the high-conductance calcium-activated potassium channel.

High conductance calcium-activated (maxi-K) channels are potently blocked by a family of indole diterpenes that includes paxilline. Paxilline stimulates binding of charybdotoxin (ChTX) to maxi-K channels in vascular smooth muscle and blocks these channels in electrophysiological experiments (Knaus et al., 1994b). These results suggested that paxilline blocked maxi-K channels at a site distance from the ChTX binding site located near the external entrance to the pore. Here we have examined block of the cloned alpha subunit (slo) of the maxi-K channel in excised membrane patches after internal application of paxilline. Paxilline caused a reversible inhibition of channel currents with slow washout kinetics. In the presence of 10 muM intracellular calcium, paxilline blocked currents elicited by brief voltage pulses with a Ki of 1.9 nM and a Hill coefficient near one. Changing the internal calcium by the fold caused a two to three fold change in the Ki for paxilline block, with less block occurring at high calcium concentrations. Paxilline reduced the maximum of the conductance-voltage relation in a calcium-sensitive manner with less block occurring at high calcium concentrations, and caused a 20 mV depolarizing shift in the midpoint for channel opening. The time-course of relief of paxilline block by elevated calcium was more rapid than washout of paxilline suggesting an allosteric interaction between calcium and paxilline.

Functional role of the beta subunit of high conductance calcium-activated potassium channels.

Mammalian high conductance, calcium-activated potassium (maxi-K) channels are composed of two dissimilar subunits, alpha and beta. We have examined the functional contribution of the beta subunit to the properties of maxi-K channels expressed heterologously in Xenopus oocytes. Channels from oocytes injected with cRNAs encoding both alpha and beta subunits were much more sensitive to activation by voltage and calcium than channels composed of the alpha subunit alone, while expression levels, single-channel conductance, and ionic selectivity appeared unaffected. Channels from oocytes expressing both subunits were sensitive to DHS-I, a potent agonist of native maxi-K channels, whereas channels composed of the alpha subunit alone were insensitive. Thus, alpha and beta subunits together contribute to the functional properties of expressed maxi-K channels. Regulation of co-assembly might contribute to the functional diversity noted among members of this family of potassium channels.

Tremorgenic indole alkaloids potently inhibit smooth muscle high-conductance calcium-activated potassium channels.

Tremorgenic indole alkaloids produce neurological disorders (e.g., staggers syndromes) in ruminants. The mode of action of these fungal mycotoxins is not understood but may be related to their known effects on neurotransmitter release. To determine whether these effects could be due to inhibition of K+ channels, the interaction of various indole diterpenes with high-conductance Ca(2+)-activated K+ (maxi-K) channels was examined. Paspalitrem A, paspalitrem C, aflatrem, penitrem A, and paspalinine inhibit binding of [125I]charybdotoxin (ChTX) to maxi-K channels in bovine aortic smooth muscle sarcolemmal membranes. In contrast, three structurally related compounds, paxilline, verruculogen, and paspalicine, enhanced toxin binding. As predicted from the binding studies, covalent incorporation of [125I]ChTX into the 31-kDa subunit of the maxi-K channel was blocked by compounds that inhibit [125I]ChTX binding and enhanced by compounds that stimulate [125I]ChTX binding. Modulation of [125I]ChTX binding was due to allosteric mechanisms. Despite their different effects on binding of [125I]ChTX to maxi-K channels, all compounds potently inhibited maxi-K channels in electrophysiological experiments. Other types of voltage-dependent or Ca(2+)-activated K+ channels examined were not affected. Chemical modifications of paxilline indicate a defined structure-activity relationship for channel inhibition. Paspalicine, a deshydroxy analog of paspalinine lacking tremorgenic activity, also potently blocked maxi-K channels. Taken together, these data suggest that indole diterpenes are the most potent nonpeptidyl inhibitors of maxi-K channels identified to date. Some of their pharmacological properties could be explained by inhibition of maxi-K channels, although tremorgenicity may be unrelated to channel block.

Purification and reconstitution of the high-conductance, calcium-activated potassium channel from tracheal smooth muscle.

The high-conductance Ca(2+)-activated K+ (maxi-K) channel from bovine tracheal smooth muscle was purified to apparent homogeneity by a combination of conventional chromatographic techniques and sucrose density gradient centrifugation. Fractions with the highest specific activity for binding of monoiodotyrosine charybdotoxin, [125I]ChTX, were enriched approximately 2000-fold over the initial digitonin-solubilized material up to a specific activity of 1 nmol/mg protein. Silver staining after SDS-polyacrylamide gel electrophoresis of the fractions from the last step of the purification indicates that binding activity is correlated with a major component of the preparation that displays an apparent molecular weight of 62,000. Labeling the same preparation with 125I-Bolton-Hunter reagent reveals the existence of both 62 (alpha)- and 31 (beta)-kDa subunits, in an apparent stoichiometry of 1:1, comigrating with binding activity. The beta subunit is heavily glycosylated. Deglycosylation studies indicate that the beta subunit represents the protein to which [125I]ChTX is covalently incorporated in the presence of the bifunctional cross-linking reagent disuccinimidyl suberate. Binding of [125I]ChTX to the purified ChTX receptor displayed the same pharmacological profile that has been found previously for toxin binding to native membranes, including inhibition by iberiotoxin, limbatustoxin, tetraethylamonium, potassium, cesium, and barium. The purified preparation was reconstituted into liposomes which were then fused with artificial lipid bilayers. Single channels were readily observed with a conductance of 235 picosiemens in 150 mM KCl that displayed selectivity for potassium over chloride and that were blocked by ChTX. The open probability of these channels was increased by depolarizing membrane potentials and by raising the internal calcium concentration. These data suggest that the maxi-K channel purified from tracheal smooth muscle is composed of two subunits.

Opening and closing transitions for BK channels often occur in two steps via sojourns through a brief lifetime subconductance state.

Single channel currents were recorded with microsecond time resolution from large-conductance calcium-activated K+ channels to examine the details of the opening and closings transitions. Analysis of averaged closing transitions indicated that the initial average conductance step for closing was to the 90-95% closed channel current level. Averaged brief closings (approximately 50 microseconds) reopened from the initial 90-95% level, whereas averaged longer closings (> 300 microseconds) closed completely from this level over the next 50-100 microseconds. The 90-95% initial closed level in the averaged current records resulted typically from the average of both complete and partial closings. From 45-80% of the initial closings were complete and 20-55% were to brief lifetime (approximately 50 microseconds) subconductance levels at 65-90% of the completely closed level. Averaged opening transitions were typically mirror images of averaged closing transitions. To extend the analysis to the very brief conductance changes that underlie the flickers of the single channel current toward the closed current level, flickers, brief closings, and longer closings were averaged separately and their slopes compared. The slopes were similar (within the 3% resolution of the method), suggesting similar initial conductance steps. Similar initial closing properties for both the briefer and longer closings would be expected if the channel first passed through the kinetic and subconductance states associated with the briefer closings (including flickers) before entering the longer closed states. Such transitions would provide an explanation for the observation that openings and closings often occur in two steps.

An activator of calcium-dependent potassium channels isolated from a medicinal herb.

Large-conductance calcium-dependent potassium (maxi-K) channels play an important role in regulating the tone of airway smooth muscle and the release of bronchoconstrictive substances from nerves in the lung. Crude extracts of Desmodium adscendens, a medicinal herb used in Ghana as a treatment for asthma, inhibit binding of monoiodotyrosine charybdotoxin (125I-ChTX) to receptor sites in bovine tracheal smooth muscle membranes that have been shown to be associated with maxi-K channels. Using this assay, three active components have been purified and identified by NMR and MS. Comparison with authentic samples revealed the three active components as the known triterpenoid glycosides dehydrosoyasaponin I (DHS-I), soyasaponin I, and soyasaponin III. The most potent of these compounds, DHS-I, is a partial inhibitor of 125I-ChTX binding (Ki = 120 nM, 62% maximum inhibition). Inhibition of 125I-ChTX binding is primarily due to a decrease in the observed maximum number of binding sites, with a smaller decrease in affinity. DHS-I increases the rate of toxin dissociation from its receptor, suggesting that modulation of ChTX binding occurs through an allosteric mechanism. DHS-I reversibly increases the open probability of maxi-K channels from bovine tracheal smooth muscle incorporated into planar lipid bilayers when applied to the intracellular, but not the extracellular, side of the membrane at concentrations as low as 10 nM. In contrast, DHS-I had no effect on several other types of potassium channels or membrane transporters. This natural product is the first example of a high-affinity activator of calcium-dependent potassium channels and is the most potent known potassium channel opener.

Synthetic charybdotoxin-iberiotoxin chimeric peptides define toxin binding sites on calcium-activated and voltage-dependent potassium channels.

Charybdotoxin (ChTX) and iberiotoxin (IbTX) are highly charged peptidyl toxins which exhibit 68% sequence identity and share a similar three-dimensional structure. Despite these structural similarities, IbTX and ChTX differ in their selectivity for two types of potassium channels; large conductance calcium-activated potassium (maxi-K) channels and slowly inactivating voltage-gated (Kv1.3) potassium channels. ChTX blocks with high affinity both maxi-K and Kv1.3 channels, while IbTX blocks the maxi-K but not the voltage-gated channel. To identify regions of the toxins which impart this this selectivity, we have constructed by solid-phase synthesis two chimeric toxins, ChTX1-19IbTX20-37 (Ch-IbTX) and IbTX1-19ChTX20-37 (Ib-ChTX), as well as a truncated peptide, ChTX7-37. These peptides were assayed for their ability to inhibit [125I]ChTX binding in sarcolemmal vesicles from smooth muscle (maxi-K binding) and [125I]ChTX binding to plasma membranes from brain (Kv1.3 binding). The ability of the peptides to block the maxi-K channel was determined from recordings of single maxi-K channels incorporated into planar lipid bilayers. Block of Kv1.3 was determined from recordings of whole cell currents in Xenopus oocytes injected with mRNA encoding the cloned Kv1.3 channel. Both chimeric toxins inhibited [125I]ChTX binding to sarcolemmal membranes from smooth muscle, and they both blocked the maxi-K channel in planar lipid bilayers. In contrast, [125I]ChTX binding in brain and Kv1.3 currents expressed in oocytes were inhibited only by the chimera Ib-ChTX.(ABSTRACT TRUNCATED AT 250 WORDS)

Mechanism of iberiotoxin block of the large-conductance calcium-activated potassium channel from bovine aortic smooth muscle.

The interaction of iberiotoxin (IbTX) with the large-conductance calcium-activated potassium (maxi-K) channel was examined by measuring single-channel currents from maxi-K channels incorporated into planar lipid bilayers. Addition of nanomolar concentrations of IbTX to the external side of the channel produced long nonconducting silent periods, which were interrupted by periods of normal channel activity. The distributions of durations of blocked and unblocked periods were both described by single exponentials. The mean duration of the unblocked periods decreased in proportion with the external concentration of IbTX, while the mean duration of the blocked periods was not affected. These results suggest that IbTX blocks the maxi-K channel through a simple bimolecular binding reaction where the silent periods represent times when a single toxin molecule is bound to the channel. In symmetric solutions of 150 mM KCl, with a membrane potential of 40 mV, the mean duration of the blocked periods produced by IbTX was 840 s, and the association rate was 1.3 x 10(6) M-1 s-1, yielding an equilibrium dissociation constant of about 1 nM. Raising the internal potassium concentration increased the dissociation rate constant of IbTX in a manner which was well described by a saturable binding function for potassium. External tetraethylammonium ion increased the average duration of the unblocked periods without affecting the blocked periods, suggesting that tetraethylammonium and IbTX compete for the same site near the conductance pathway of the channel. Increasing the external concentration of monovalent cations from 25 to 300 mM with either potassium or sodium decreased the rate of binding of IbTX to the channel by approximately 24-fold, with little effect on the rate of toxin dissociation.(ABSTRACT TRUNCATED AT 250 WORDS)

Accounting for the Ca(2+)-dependent kinetics of single large-conductance Ca(2+)-activated K+ channels in rat skeletal muscle.

1. The Ca(2+)-dependent kinetics of large-conductance Ca(2+)-activated K+ channels from cultured rat skeletal muscle were studied with the patch clamp technique. Data were collected in the absence of Na+ and Mg2+, which can alter the kinetics. About 2 x 10(5) open and shut intervals were analysed from each of five different excised membrane patches containing a single active channel. Analysis was restricted to activity in the normal mode, which includes 96% of the intervals. 2. The open probability (Popen) and dwell-time distributions of open and shut intervals were obtained at three to four different [Ca2+]i for each of the channels. Popen data were also obtained from some multichannel patches. 3. Increasing [Ca2+]i increased Popen. At a pH of 7.0 the Hill coefficient was 3.7 +/- 0.8 (range of 3.0-5.0) and a Popen of 0.5 occurred at 14 +/- 7 microM [Ca2+]i (K0.5) for data obtained at +30 mV (n = 6). At a pH of 7.2 the Hill coefficient was 3.0 +/- 0.5 (range of 2.2-3.7) and K0.5 was 9 +/- 6 microM-Ca2+ (n = 7). The large standard deviations for K0.5 reflect the observation that fourfold differences in K0.5 could be observed for different channels studied under the same experimental conditions. 4. Hill coefficients that can be greater than 3 suggest that the channel may bind four or more Ca2+ to become fully activated. The binding of four Ca2+ before opening would require a minimum of five shut states. This estimate of the minimum number of shut states is in general agreement with that obtained from the number of exponential components in the dwell-time distributions of shut intervals. Thus, two different methods give similar estimates of the minimum number of shut states. If the channel can open with different numbers of bound Ca2+, then this could give rise to the three to four open states suggested by the three to four exponential components in the open dwell-time distributions. 5. Kinetic schemes consistent with the Ca(2+)-dependent kinetics were developed by simultaneously fitting open and shut dwell-time distributions obtained at three to four different [Ca2+]i, using maximum likelihood techniques and corrections for missed events. Such simultaneous fitting can provide an increased ability to define models and rate constants.(ABSTRACT TRUNCATED AT 400 WORDS)

Calcium-activated potassium channels: regulation by calcium.

A wide variety of calcium-activated K channels has been described and can be conveniently separated into three classes based on differences in single-channel conductance, voltage dependence of channel opening, and sensitivity to blockers. Large-conductance calcium-activated K channels typically require micromolar concentrations of calcium to open, and their sensitivity to calcium increases with membrane depolarization, suggesting that they may be involved in repolarization events. Small-conductance calcium-activated K channels are generally more sensitive to calcium at negative membrane potentials, but their sensitivity to calcium is independent of membrane potential, suggesting that they may be involved in regulating membrane properties near the resting potential. Intermediate-conductance calcium-activated K channels are a loosely defined group, where membership is determined because a channel does not fit in either of the other two groups. Within each broad group, variations in calcium sensitivity and single-channel conductance have been observed, suggesting that there may be families of closely related calcium-activated K channels. Kinetic studies of the gating of calcium-activated potassium channels have revealed some basic features of the mechanisms involved in activation of these channels by calcium, including the number of calcium ions participating in channel opening, the number of major conformations of the channels involved in the gating process, and the number of transition pathways between open and closed states. Methods of analysis have been developed that may allow identification of models that give accurate descriptions of the gating of these channels. Although such kinetic models are likely to be oversimplifications of the behavior of a large macromolecule, these models may provide some insight into the mechanisms that control the gating of the channel, and are subject to falsification by new data.

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.