INTRODUCTION

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Large conductance (~250 pS) Ca²⁺-activated K⁺ channels (BK or maxi-K_Ca channels)¹ are an intriguing class of ion channels that are activated in a synergistic fashion by intracellular Ca²⁺ and depolarizing voltage (Latorre, 1994). In Drosophila, maxi-K_Ca channels are encoded by the Slowpoke gene, part of which is homologous to the family of voltage-gated K⁺ channels (K_V channels), including Shaker (Atkinson et al., 1991; Adelman et al., 1992). Both K_V and Slowpoke channels contain a characteristic motif of six membrane-spanning segments called S1-S6. This motif includes the S4 segment involved in voltage sensing and the extracellular P-region between S5 and S6 that determines ionic selectivity. Besides these common structural elements, Slowpoke maxi-K_Ca channels have an additional transmembrane segment at the NH₂ terminus, called S0, plus a unique sequence of ~800 residues at the COOH terminus (Meera et al., 1997). Substantial evidence supports the notion that the COOH-terminal portion of the maxi-K_Ca channel protein corresponds to a large cytoplasmic domain that contains Ca²⁺-binding site(s) involved in channel activation (Wei et al., 1994; Schreiber and Salkoff, 1997). To understand the mechanism of Ca²⁺ activation and biochemical regulation of maxi-K_Ca channels, it is necessary to define the structure and function of this cytoplasmic domain. An underlying objective of the work described in this paper is to characterize intracellular binding sites for peptide ligands that can serve as reference points in studies of the cytoplasmic architecture of the maxi-K_Ca channel.

The charybdotoxin family of small protein toxins is a set of natural ligands that has been effectively used to identify structural determinants in the extracellular pore region of K⁺ channels (Miller, 1995; MacKinnon et al., 1998). By analogy, protein ligands that bind to intracellular sites on maxi-K_Ca channels may similarly be useful for mapping this part of the channel protein. One class of such ligands is the Kunitz family of proteins that includes bovine pancreatic trypsin inhibitor (BPTI) and dendrotoxin-I (DTX-I). This family of ~60-residue proteins shares six conserved Cys residues (see Fig. 1 A) and a common protein fold, but its members exhibit diverse inhibitory activities. BPTI and related Kunitz molecules are potent inhibitors of various members of the chymotrypsin/trypsin family of serine proteinases (Dufton, 1985; Capasso et al., 1997). DTX-I and several homologues from mamba snake venom block various K_V channels from the extracellular side, but are poor inhibitors of serine proteinases (Hollecker et al., 1993; Smith et al., 1997). Calcicludine, another Kunitz homologue from mamba venom, blocks high-threshold voltage-activated Ca²⁺ channels from the extracellular side (Schweitz et al., 1994). Yet another activity exhibited by some Kunitz proteins such as DTX-I and BPTI is a rather distinctive inhibitory effect on maxi-K_Ca channels from the intracellular side (Lucchesi and Moczydlowski, 1990, 1991). This latter effect resembles a slow blocking reaction, but differs in that the individual blocking events mimic subconductance states at the single-channel level. Apparent subconductance events induced by BPTI and DTX-I are actually due to a fast closing and opening reaction of the maxi-K_Ca channel in the ligand-bound state (Moss and Moczydlowski, 1996). For descriptive purposes, this behavior is referred to here simply as "substate behavior" or "substate events." In contrast to the substate-inducing behavior of Kunitz inhibitors, an NH₂-terminal inactivation domain of Shaker K_V channels called the "ball peptide" is known to directly block maxi-K_Ca channels by binding within the internal vestibule or pore (Foster et al., 1992; Toro et al., 1992).

View larger version (55K): [in this window] [in a new window]   Fig. 1.   Titration of a single KCa channel with BPTI. (A) Comparison of the primary sequence of BPTI and DTX-I using the one letter amino acid code (Z, pyroglutamate). A short solid line marks two identical residues and a dotted line indicates chemical similarity. Connecting lines denote three disulfide bonds in both molecules. (B) Representative current records from a single rat muscle KCa channel recorded under control conditions (symmetrical 50 mM KCl, 10 mM MOPS-KOH, pH 7.4, 200 µM internal CaCl2) and after addition of 1, 2, 4, and 8 µM internal BPTI. The holding voltage in this and all other experiments is +30 mV. The dashed line identifies the zero-current level.

To further develop Kunitz inhibitors as structural probes of the intracellular domain of maxi-K_Ca channels, it is necessary to localize the binding site of these inhibitors with respect to the primary sequence of the channel. One line of evidence that such ligands do not occlude or bind directly in the pore is that the blocking affinity of internal Ba²⁺ and internal tetraethylammonium (TEA) is not significantly affected by BPTI and DTX-I, respectively (Lucchesi and Moczydlowski, 1991). Such results lead to the hypothesis that BPTI and DTX-I bind to an intracellular site outside the pore and induce substate behavior by an allosteric mechanism. A potential candidate for the BPTI/DTX-I binding site on the K_Ca channel protein is a region of ~250 residues near the COOH terminus that exhibits similarity to the chymotrypsin family of serine proteinases (Moss et al., 1996a,b). However, serious consideration of this hypothesis leads to an interesting paradox. Since maxi-K_Ca channels are probably formed as homotetramers of four identical -subunits (Shen et al., 1994), how can BPTI and DTX-I bind outside the central pore or common fourfold subunit interface and yet exhibit binding kinetics characteristic of a single site? The allosteric model of substate production invoked above predicts that four binding sites for BPTI/DTX-I must exist on each tetrameric channel complex. Such a model further predicts that the kinetics of BPTI/DTX-I association and dissociation ought to reflect multiple sites of ligand interaction.

To resolve this question, we investigated the interaction of BPTI and DTX-I with rat muscle K_Ca channels inserted into planar lipid bilayers. The titration behavior of single K_Ca channels with BPTI in the presence of DTX-I deviated significantly from simple binding competition of two ligands at a single site. The data are consistent with a model that includes states of simultaneous occupancy by one BPTI and one DTX-I molecule on different subunits of a tetrameric complex. Binding of DTX-I to one subunit lowers the binding affinity for BPTI on another subunit by ~11-fold, and vice versa. To further probe the location of the Kunitz inhibitor site with respect to the pore, we analyzed the single-channel blocking kinetics of a homologue of Shaker ball peptide (BP) in the absence and presence of DTX-I. The results indicate that BP binds to the K_Ca channel with an approximately eightfold lower affinity when DTX-I is simultaneously bound. Detailed analysis revealed that the lower affinity for BP is solely due to a 44-fold reduction in its association rate. Unexpectedly, we found that DTX-I actually stabilizes BP on its binding site by slowing its rate of dissociation by a factor of ~5.6. Overall, these results provide direct evidence of negatively coupled ligand-ligand interactions among sites for Kunitz proteins and ball peptide that take place on the intracellular surface of maxi-K_Ca channels. The unusual asymmetry of energetic effects on rate constants for the interaction between DTX-I and BP can be explained by structural features inherent to a channel-like architecture.

	MATERIALS AND METHODS

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Planar Bilayer Recording

Planar bilayers were formed on a 0.2-mm diameter hole drilled in a cylindrical cup made of polystyrene or delrin as supplied by Warner Instrument Corp. The membrane was cast from a solution of 25 mg/ml phospholipids in decane. Bilayer formation was monitored by capacitance measurement. The lipid composition was a mixture of 80% 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphoethanolamine and 20% 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (Avanti Polar Lipids). Plasma membrane vesicles were prepared from adult rat skeletal muscle using the procedure described in Favre et al. (1999). The final recording solution on both sides of the bilayer contained 50 mM KCl, 10 mM MOPS-KOH, pH 7.4. Incorporation of maxi-K_Ca channels from membrane vesicles into planar bilayers followed methods described previously (Lucchesi and Moczydlowski, 1991). Only bilayers containing single maxi-K_Ca channels were used for these experiments. The intracellular or internal side of the bilayer is defined as the side that responds to activation of K_Ca channels by Ca²⁺ and positive voltage. For all experiments in this work, the holding voltage was +30 mV using the physiological convention of extracellular ground. The internal Ca²⁺ concentration was usually 200 µM, but was increased to 500 µM in some experiments to maintain the open state probability of intrinsic K_Ca channel gating at >0.9.

Single channel currents were recorded at room temperature (20-23°C) using a patch clamp amplifier (3900A; Dagan Corp.) with an expander (3910; Dagan Corp.) for bilayer capacitance measurements. The patch clamp headstage was connected to the bilayer chamber via Ag/AgCl electrodes and agar-KCl bridges. Single channel recordings were stored on VCR tape using a digital data recorder (VR-10; Instrutech Corp.). Data were filtered at a corner frequency of 100-500 Hz with an eight-pole low pass Bessel filter (902LPF; Frequency Devices Inc.) and sampled at five times the filter frequency or greater for subsequent analysis.

Bovine pancreatic trypsin inhibitor was purchased from Sigma Chemical Co. Dendrotoxin I (or toxin I from Dendroaspis polylepis) was obtained from Alomone Labs. A peptide homologue (BP) of the Shaker ball peptide with the primary sequence MAAVAVLYVLGKKRQHRKKQ was synthesized by the W.M. Keck Biotechnology Resource Center at Yale University Medical School (New Haven, CT). The purity of the peptide was confirmed by reverse phase HPLC and mass spectroscopy (mol wt, 2,325). Concentrated stock solutions of 500 µM BP were prepared in H₂O. Problems associated with adsorption of BP to the plastic chambers were minimized by adding vesicles and BP to the front chamber, composed of black delrin, rather than the rear cup chamber, composed of polystyrene. Peptide concentrations are based on dry weight and supplier information. Therefore, derived k_on and K_d values should be regarded as relative rather than absolute measurements.

Single Channel Analysis

These experiments involved long recordings (~1-5 h) of single maxi-K_Ca channels exposed to the following inhibitors: DTX-I, BPTI, BP, TEA, and charybdotoxin (ChTX). After addition of a particular concentration of an inhibitor that induced discrete events, channel activity was continuously recorded for a time sufficient to collect ~100 events when possible. Then, the next concentration of inhibitor was added, channel activity was recorded, etc., until the bilayer broke. Substate events induced by DTX-I (mean dwell time ~38 s) were the longest events that were measured and analyzed. Durations of these latter events were measured directly from chart records with the aid of a digitizing tablet (TG1017; Houston Instrument). Substate events induced by BPTI (mean dwell time  0.41 s) and BP blocking events (mean dwell time  1.7 s) were automatically measured from digitized records using an LSI 1173 computer system (Indec). For this purpose, single-channel data was filtered at 100 Hz and sampled at 1 kHz. Transitions were detected using a 50% threshold criterion set between the substate current level and the open state for BPTI or between the zero current (blocked state) and open state for BP. To exclude brief closures due to intrinsic channel gating, a cutoff limit of  = 0.1 s was used for the shortest acceptable substate closure or blocked state event. This cutoff limit excludes >95% of Ca²⁺- and voltage-dependent closures due to channel gating under these conditions (200 µM internal Ca²⁺ and +30 mV).

Lifetimes of BPTI-substate, BP-blocked, ChTX-blocked, or unblocked state events were generally measured from populations of dwell times (n > 100 events) that were binned, plotted as cumulative probability distributions, and fit to an exponential function of time. These distributions were invariably well described by a single exponential (Lucchesi and Moczydlowski, 1991). Measured lifetimes of the unoccupied open state or unblocked state were corrected for a small amount of artificial lengthening due to the minimum cutoff limit for closures of  = 0.1 s using the following formula (Colquhoun and Sigworth, 1983): _corrected = _observed exp(/_closed). Certain types of event samples such as DTX-I substates, burst lengths, or BP-blocked events in the presence of DTX-I were measured as simple arithmetical means. Arithmetical means were used in these latter cases, either because the sample size was often <100 events and not well suited to histogram fitting, or because the analysis focused on the behavior of the actual mean dwell time of more complex distributions (e.g., see Eq. 19). Dwell-time histograms obtained in the presence of DTX-I and BP exhibited two exponential components. These data were also plotted as probability density functions and fit to a sum of two exponentials using PCLAMP analysis software from Axon Instruments.

Single-channel block by external TEA was manifested as a "fast block" corresponding to an apparent decrease in unitary current (e.g., Moczydlowski, 1992). Unitary current as a function of [TEA] was measured with the use of all-points amplitude histograms to determine the mean value of the closed and apparent open state current levels. Kinetic parameters directly measured from single-channel data are reported as the mean ± SD or SEM as noted in the text. Estimates of propagated errors for parameters calculated from kinetic equations are based on standard rules for the additivity of variance (i.e., absolute variance is additive for addition and subtraction; relative variance is additive for multiplication and division). Nonlinear curve fitting to various equations was carried out using SigmaPlot software (SPSS Inc.) based on the Marquardt-Levenberg algorithm.

	RESULTS

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Kinetics of BPTI-induced Substate Events Are Well Described by a One-Site Process

Previous studies of DTX-I- and BPTI-induced substate events suggested that these ligands bind reversibly to a single intracellular site or homogeneous class of sites on maxi-K_Ca channels that is located outside the pore (Lucchesi and Moczydlowski, 1990, 1991). However, this conclusion appears to be in conflict with the known tetrameric structure of K⁺ channels and the prevailing idea that the functional unit of maxi-K_Ca channels is a tetramer of ~130 kD -subunits (Shen et al., 1994; Doyle et al., 1998). A nonpore binding site on a homotetrameric channel structure implies that there should be four symmetrically located sites on the cytoplasmic side of the protein. To pursue this question, we re-examined the kinetics of BPTI-induced substate events as a function of BPTI concentration to ascertain whether one-site behavior is strictly obeyed.

Fig. 1 B shows typical results from an experiment in which a single K_Ca channel recorded at a high open-state probability is consecutively exposed to 1, 2, 4, and 8 µM internal BPTI. These records show that BPTI induces a noisy but well-defined substate at ~27% of the unitary current and that the channel's probability of residing in this substate increases with BPTI concentration. The records also show a few examples of well resolved closures to the zero current level, plus other subconductance levels that are occasionally observed under these conditions. However, these latter events are quite rare compared with the time the channel spends in the open state and the major substate. They are ignored for this analysis since they occur too infrequently for quantitative evaluation.

A possible model for binding of BPTI to four equivalent sites on a homotetramer is shown in Fig. 2, Scheme 1. For the sake of discussion, this model assumes that the microscopic association rate constants, k₁, for binding to a site on each of the four subunits of the unliganded U state are equivalent. With this assumption, the observed macroscopic association rate constant for binding of one BPTI molecule to the U state would be 4k₁. Similar statistical factors apply to the other association and dissociation steps involving binding to or unbinding from multiply occupied states. Fig. 2, Scheme 1, is only one possible example of a sequential reaction that could describe ligand binding to a homotetrameric protein. Many other ligand binding schemes are possible, including mechanisms that involve conformational changes of individual subunits or the whole complex. The essential point is that ligand binding to multisubunit complexes can potentially display complex behavior including positive and negative cooperativity.

View larger version (18K): [in this window] [in a new window]   Fig. 2.   Kinetic analysis of BPTI substate events. Scheme 1 is a hypothetical five-state model for binding of a ligand such as BPTI to four equivalent sites on a homotetrameric KCa channel. , unoccupied subunits; , BPTI-occupied subunits. Upper rate constants, k1, k2, k3, and k4, are bimolecular association rate constants; lower rate constants, k1, k2, k3, and k4, are first order dissociation rate constants. Integers preceding the rate constants are statistical factors. (A) Lifetime of BPTI-substate events as a function of [BPTI]. (B) Lifetime of dwell times between adjacent BPTI-substate events as a function of [BPTI]. Data points and error bars in A and B are the mean ± SEM for seven to eight single channels. The solid line and two dotted lines in A are the mean ± SD of four data points used to measure k1 from the lifetime S of substate S1 (Eq. 1). The solid line in B is a fit to Eq. 2 used to measure 4k1 from the lifetime U of state U (Eq. 2). The inset shows the same data plotted as the reciprocal lifetime. (C) Time-averaged probability of a channel being in the unoccupied (BPTI-free) state as a function of [BPTI]. Each point was calculated from 6.3-6.9 h of data pooled from seven or eight single channels. The solid line in C is a fit to PU = K1/(K1 + [BPTI]) used to measure the equilibrium constant K1 as described in the text.

If more than one BPTI molecule can bind to a single tetrameric K_Ca channel complex, one would expect to observe some indication of the existence of more than one class of ligand-bound states in single channel records. In the experiment of Fig. 1 B, increasing BPTI concentration from 0 to 8 µM decreases the probability of the channel residing in the fully open conductance state from 1.0 to ~0.15. However, evidence for different states of BPTI occupancy (e.g., states S₁-S₄ of Fig. 2, Scheme 1) is not obvious from the single-channel record. One explanation may be that the binding of one, two, three, or four BPTI molecules produces a channel with exactly the same conductance behavior, corresponding to the ~27% substate level. However, if this were the case, the probability distribution for the dwell time in the substate would correspond to the distribution of a group of four states, S1, S2, S3, and S4, within the framework of Fig. 2, Scheme 1. The predicted theoretical form for this distribution would be a sum of four exponential components. Furthermore, Fig. 2, Scheme 1 predicts that the distribution of substate dwell times would be dependent on BPTI concentration. Thus, the mean substate dwell time should lengthen with BPTI concentration if Fig. 2, Scheme 1 is applicable.

To search for such behavior, dwell time histograms of BPTI-substate events were compiled for eight different single channels at 1, 2, 4, and 8 µM BPTI, as described in MATERIALS AND METHODS. Consistent with previous work (Lucchesi and Moczydlowski, 1991), these histograms conformed to a single exponential distribution at all BPTI concentrations (not shown). The mean lifetime of the exponentially distributed BPTI substate (_s) was equal to 0.411 ± 0.022 s (Fig. 2 A). Although there is a slight tendency for _s to increase with [BPTI] in Fig. 2 A, the data points at 1, 2, 4, and 8 µM BPTI are not statistically different by the usual criterion of P  0.05. Thus, there is no hard evidence that the mean duration of the BPTI-induced substate lengthens significantly with increasing [BPTI] or that there is a kinetically distinct population containing >5% of the total substate events. These results confirm that the kinetics of BPTI-induced substate events are well described by a one-site process such as that represented by Fig. 2, Scheme 1A.

Fig. 2, Scheme 1A, predicts the following relationships for the lifetime, _S, of the S1 BPTI substate, and for the lifetime, _U, of the unliganded U state:

(1)

(2)

The dissociation rate constant, k₁, calculated according to Eq. 1 from the reciprocal of the mean of four _S measurements in Fig. 2 A is k₁ = 2.43 ± 0.13 s¹ (±SEM). The observed association rate constant, 4k₁, can be obtained from the reciprocal relationship between _U and [BPTI] according to Eq. 2. Probability histograms of unliganded U-state events between adjacent BPTI substates were also uniformly well described by a single exponential function (not shown). The mean lifetime of _U measured for eight different single channels at each BPTI concentration is plotted in Fig. 2 B and fit to Eq. 2. This fit gives an estimate of 4k₁ = 1.63 ± 0.07 × 10⁶ s¹M¹ for the apparent BPTI-association rate constant. The kinetic ratio, k₁/4k₁, or K₁ = 1.49 ± 0.10 µM, is the equilibrium dissociation constant for BPTI in Fig. 2, Scheme 1A.

The K₁ equilibrium constant can also be estimated from the time-averaged probability of the unliganded state, P_U. Fig. 2, Scheme 1A, predicts that P_U = K₁/(K₁ + [BPTI]). A fit of the data in Fig. 2 C to this latter function yields K₁ = 1.28 ± 0.07 µM, in agreement with the kinetic ratio of k₁/4k₁. For models such as Fig. 2, Scheme 1, where there is a substantial population of multi-liganded states, Hill coefficients (n) higher than n = 1 are also predicted. The fact that the data of Fig. 2 C is closely fit using an n of 1.0 is additional evidence that Fig. 2, Scheme 1A, or an equivalent one-site model describes the interaction of BPTI with the maxi-K_Ca channel. Thus, if the K_Ca channel does contain four structurally homologous BPTI binding sites in the tetrameric complex, the kinetic data imply that the binding of BPTI to one of the sites essentially precludes the binding of a second BPTI molecule to any of the remaining three sites.

Complex Behavior of BPTI Burst Durations in the Presence of DTX-I Is Evidence for Simultaneous Occupancy by BPTI and DTX-I

The sequence alignment of Fig. 1 A illustrates that BPTI (58 residues) and DTX-I (60 residues) are 32% identical, including the presence of six conserved Cys residues. It is also known that these two small proteins share a common fold at the tertiary structural level (Berndt et al., 1993; Lancelin et al., 1994; Skarzynski, 1992). Like BPTI, DTX-I also induces discrete substate events when added to the intracellular side of maxi-K_Ca channels, but the average duration of the DTX-I- induced substate is ~38 s compared with ~0.41 s for BPTI. Fig. 3 (top) shows a segment of a typical single-channel recording taken after addition of 460 nM DTX-I. Long-lived substate events induced by DTX-I typically exhibit less excess noise and a higher mean current level (~60% of unitary current at +30 mV) than the shorter duration BPTI substate (Fig. 1 B). Previous studies have also established that the kinetics of interaction of DTX-I with single K_Ca channels is well described by a one-site process equivalent to Fig. 2, Scheme 1A, discussed above for BPTI (Lucchesi and Moczydlowski, 1990, 1991). To investigate the physical relationship of binding sites for BPTI and DTX-I, we examined the effect of titrating single maxi-K_Ca channels with increasing concentrations of BPTI in the presence of a nearly saturating concentration of DTX-I.

View larger version (42K): [in this window] [in a new window]   Fig. 3.   Representative segments of current records from a single KCa channel recorded in the presence of DTX-I and increasing concentrations of BPTI. (A) A single rat muscle KCa channel was recorded under control conditions described in Fig. 1. DTX-I (460 nM) was added to the internal side followed by 1, 2, 4, and 8 µM internal BPTI, as indicated. The dotted line marks the zero current level.

In the presence of 460 nM DTX-I alone (Fig. 3, top), single K_Ca channels exhibit two distinct states or modes of activity: (a) long-lived substates at ~60% of the unitary current that correspond to residence times of DTX-I on the channel, and (b) shorter intervals between adjacent DTX-substates defined as "inter-DTX periods." The latter periods correspond to waiting times of the unoccupied channel between the dissociation of one DTX-I molecule and association of another. If BPTI can bind to a channel that is already occupied by DTX-I, one might expect to observe discrete interruption of the long-lived DTX substate with short BPTI-like substate events. Alternatively, if binding of BPTI to the unoccupied channel is greatly favored over binding to the DTX-occupied channel, then brief BPTI-substates should occur only within inter-DTX periods.

The data of Fig. 3 illustrate that the system is best described by the latter alternative. Long recordings from such experiments reveal that titration of BPTI in the presence of DTX-I exhibits a pattern of activity that may be roughly described as bursts of BPTI-substate activity punctuated by DTX substates. In particular, records of Fig. 3 obtained in the presence of both ligands show that two adjacent DTX-substate events are nearly always flanked on both the exit and entry side by transitions to the fully open current level. This implies that DTX-I usually dissociates before a burst of shorter BTPI-binding events begins and that BPTI usually dissociates before DTX-I can bind to produce a long-lived substate. To quantitate this latter observation, 458 inter-DTX periods were examined for the type of first transition flanking the exit from the DTX-substate current level and the entry back to the next DTX substate. This analysis revealed that 96.1% of all DTX substates were terminated by an opening to the fully open current level and 95.6% of all inter-DTX periods were terminated by a transition from the fully open current level to the DTX-substate level. These measurements confirm the visual impression from the single-channel records that DTX-I preferentially dissociates before BPTI can bind to the channel, and vice versa.

Such behavior is expected for a mechanism like that shown in Fig. 4, Scheme 2A. This model is an extension of Fig. 2, Scheme 1A, for formation of the BPTI substate (S_BPTI) that includes binding of DTX-I to the unoccupied channel (U) to produce the DTX substate (S_DTX). The implicit assumption of Fig. 4, Scheme 2A, is that, by virtue of structural homology, BPTI and DTX-I bind to the same site(s) on a K_Ca channel tetramer, but that some mechanism strongly inhibits binding of more than one of these molecules at a time. Although there are four potentially available sites on the tetrameric complex, Fig. 4, Scheme 2A, is formally equivalent to simple, mutually exclusive competition of two ligands at a single site and may be referred to as "pseudo one-site competition."

View larger version (18K): [in this window] [in a new window]   Fig. 4.   Kinetic analysis of ligand interactions between DTX-I and BPTI. Scheme 2A shows a three-state model for simple binding competition between two different Kunitz inhibitor ligands. The model assumes that only one BPTI or DTX-I molecule can bind on a KCa channel homotetramer at any given time and that equivalent rates are observed for each of the four subunits. , unoccupied subunits; , a BPTI-bound subunit; and , a DTX-I-bound subunit. Scheme 2B shows a more complex four-state model that allows for the possibility that one BPTI molecule and one DTX-I molecule can bind simultaneously on two different subunits. (A) Lifetime of the apparent DTX-I substate as a function of BPTI concentration. Events identified as apparent DTX-I substates were pooled from 5-18 single channels for each condition. Each data point represents the mean ± SEM for samples of 71-358 events. The dashed line is the behavior expected for Scheme 2A according to Eq. 5. The solid line is a fit to Eq. 8 derived for Scheme 2B. (B) Lifetime, as a function of [BPTI], of the complex burst state defined as the interval between two consecutive DTX-I substates. The data pool and sample sizes used for calculating the mean ± SEM were the same as that for A. The dashed line is the behavior expected for Scheme 2A according to Eq. 6. The solid line is a fit to Eq. 7 derived for Scheme 2B. (C) Time-averaged probability of residing in the apparent DTX-I substate as a function of BPTI concentration. The measured probability of the DTX-I substate is normalized to that in the absence of BPTI (P0S-DTX = 0.968). The dashed line is the prediction for Scheme 2A according to Eqs. 10 and 11. The solid line is a fit to Eq. 10 using KApp = 17.8 µM.

The cursory description of data from experiments of Fig. 3 outlined so far generally supports Fig. 4, Scheme 2A. However, there are indications that the system is actually more complex. Particularly at higher concentrations of BPTI, current records of Fig. 3 (8 µM BPTI) display a new type of event. Many of the inter-DTX periods exhibit one or more states of very low conductance or "nearly blocked" events that last several seconds in duration. These latter events begin with a decrease in current from the BPTI-substate level to a level near zero current and terminate with an increase in current directly back to the BPTI-substate level. Such events are quite rare in the presence of BPTI alone (Fig. 1 B), but they are noticeably more frequent in the presence of DTX-I. These latter observations lead to the hypothesis that the BPTI substate is susceptible to conversion to a different type of low-conductance state in the presence of DTX-I. With BPTI alone, doubly bound states (Fig. 2, Scheme 1, S2) may occur with very low probability such that their contribution to the time-averaged behavior is hard to rigorously detect (e.g., on the order of 1% or less). However, in the presence of DTX-I plus BPTI, a state in which both ligands are bound simultaneously may occur with a probability that is high enough to measure a significant deviation from purely one-site behavior.

To pursue this latter conjecture, we analyzed whether the detailed kinetic behavior obeys the strict predictions of Fig. 4, Scheme 2A. The first step in this analysis requires determination of the dissociation and apparent association rate constants (j₁, 4j₁, respectively) for DTX-I in the absence of BPTI from relationships analogous to those of Eqs. 1 and 2:

(3)

(4)

The mean dwell time of the DTX substate, _S-DTX, was measured as 37.6 ± 2.1 s (±SEM) from a population of 358 events pooled from 18 different single K_Ca channels. Likewise, the mean dwell time of the unoccupied channel measured in the presence of 460 nM DTX-I, _U, was 1.35 ± 0.09 s (±SEM). These values were used to calculate the rate constants, j₁ = 0.0266 ± 0.0015 s¹ and 4j₁ = 1.61 ± 0.11 × 10⁶ s¹M¹ from Eqs. 3 and 4, respectively. The apparent equilibrium dissociation constant for DTX-I is obtained as follows: J₁ = j₁/4j₁ = 16.5 ± 1.4 nM.

For a system that strictly adheres to the pseudo one-site competition mechanism of Fig. 4, Scheme 2A, the dwell time of the apparent DTX substate is expected to be independent of BPTI concentration. In contrast, the dwell time between adjacent DTX substates is expected to increase with BPTI concentration, as the channel spends more time in the combined burst state of U and S_BPTI. These relationships can be derived from Fig. 4, Scheme 2A, as follows:

(5)

(6)

Durations of the apparent DTX substate corresponding to the lifetime predicted by Eq. 5 and inter-DTX periods or BPTI "bursts" corresponding to the lifetime predicted by Eq. 6 can be readily identified and measured from current records of such experiments. Fig. 4 A shows a plot of the lifetime of the apparent DTX substate at 460 nM DTX-I as [BPTI] is varied over the range of 0-8 µM. The dashed line in Fig. 4 A is the prediction of Scheme 2A as stated by Eq. 5. In contrast to predicted independence with respect to [BPTI], the data reveal a significant lengthening of _S-DTX with increasing BPTI concentration. In quantitative terms, there is a 47% increase in the mean value of _S-DTX over the range of 0-8 µM BPTI. The underlying basis for the increase in _S-DTX with increasing [BPTI] appears to be an increased frequency of discrete low conductance events of several seconds in duration that occasionally interrupt DTX substates (not shown). Fig. 4 B shows a plot of the measured lifetime of inter-DTX periods or BPTI bursts as a function of [BPTI]. The dashed line in Fig. 4 B is the prediction for the simple competition mechanism of Scheme 2A according to Eq. 6, using previous derived values for 4j₁ and K₁. The results of Fig. 4 B reveal a large deviation from the mechanism of Scheme 2A since the slope of the line described by the data (3.25 s/µM) is 3.6-fold greater than the slope of the dashed line predicted from Eq. 6 (0.91 s/µM). Thus, although the current records from experiments of Fig. 3 exhibit the type of behavior that is qualitatively expected for the pseudo one-site model of Fig. 4, Scheme 2A, the results of Fig. 4, A and B, show that there is a significant quantitative discrepancy.

A possible model to explain this discrepancy is shown in Fig. 4, Scheme 2B. This scheme assumes that one DTX-I molecule can bind with a certain affinity (equilibrium dissociation constant, J₂) to an unoccupied site on a channel that is already occupied by one BPTI molecule on a different subunit. We hypothesize that these latter DTX-binding events result in a doubly occupied mixed state (S_BPTI/DTX) that functionally corresponds to the very low conductance or "nearly blocked" states within BPTI bursts that were noted above in the description of Fig. 3. Fig. 4, Scheme 2B, predicts additional lengthening of apparent BPTI bursts as compared with Scheme 2A due to the low conductance interruptions caused by S_BPTI/DTX states. In accord with Fig. 4, Scheme 2B, we assume that BPTI burst events represent dwell times in the compound state consisting of U, S_BPTI, and S_BPTI/DTX. Such burst events are defined as beginning with the appearance of the U state after dissociation of DTX from the S_DTX state, followed by prolonged sojourn in the U  S_BPTI  S_BPTI/DTX equilibria, and ending with a transition from the U state back to the S_DTX state. With this definition, the following relationship applies:

(7)

Eq. 7 still requires that _BURST is a linear function of [BPTI] as observed in Fig. 4 B; however, it predicts a larger slope due to the additional factor of (1 + [DTX]/J₂). Within this interpretive framework, Eq. 7 can be used to calculate the J₂ equilibrium constant for DTX binding to the S_BPTI state from the slope of _BURST vs. [BPTI] in Fig. 4 B (slope = 3.25 s/µM) and the values of 4j₁ and K₁ derived previously. This calculation yields a value of 178 ± 17 nM for J₂. This estimate for J₂ implies that DTX binds to a channel that is occupied by BPTI with an affinity (J₂ = 178 nM) that is 10.8-fold weaker than that for DTX binding to the unoccupied channel (J₁ = 16.5 nM).

Fig. 4, Scheme 2B, can also be used to explain the results of Fig. 4 A. If we define the apparent DTX substate as beginning with an entry to the S_DTX state from the U state, followed by a possible sojourn in the S_DTX  S_BPTI/DTX equilibria, and ending with a transition from the S_DTX state back to the U state, then the following relation gives the predicted lifetime of this apparent DTX substate:

(8)

Comparison of Eqs. 8 and 5 shows that the apparent DTX substate, defined for Fig. 4, Scheme 2B, to include closures to the mixed S_BPTI/DTX state, is lengthened relative to the DTX substate of Scheme 2A by the K₂ equilibrium. A fit of the data of Fig. 4 A to Eq. 8 yields a value of K₂ = 17.5 ± 2.9 µM for K₂. This result implies that the affinity for BPTI binding to the DTX-occupied channel (K₂ = 17.5 µM) is 11.7-fold weaker than that for the unoccupied channel (K₁ = 1.49 µM).

Although Fig. 4, Scheme 2B, seems to explain aspects of the bursting behavior of the two-ligand system of DTX-I and BPTI, there are indications of even further complexity. Specifically, the behavior of the nearly blocked events, assumed to represent the doubly occupied S_BPTI/DTX state, appears to depend on which ligand binds first. Careful inspection of many current records reveals that such blocked states virtually always end with a transition back to the BPTI substate if they first begin with a transition from the BPTI substate. Similarly, such nearly blocked states virtually always end with a transition back to the DTX substate if they first begin with a transition from the DTX substate. This implies that the last ligand that binds to the channel is always the first ligand to come off the channel. For a simple cyclic equilibrium such as Fig. 4, Scheme 2B, the allowable routes of leaving a state should not depend on how the state was entered. This suggests that there is more than one type of doubly liganded state, S_BPTI/STX, and that the system is far more complex than that represented by the four-state equilibrium of Fig. 4, Scheme 2B. Nevertheless, we can evaluate whether Fig. 4, Scheme 2B, approximates a cyclic equilibrium by checking whether the following relationship holds:

(9)

Using the estimated values for K₁, K₂, J₁, and J₂ obtained above, the ratio of the left side of Eq. 9 is 17.5/1.49 µM = 11.7 ± 2.1, and the ratio of the right side of Eq. 9 is 178/16.5 nM = 10.8 ± 1.4. The fact that these ratios are equivalent within the propagated error of our measurements supports the hypothesis that a coupled ligand interaction like that of Fig. 4, Scheme 2B, underlies the deviation from the pseudo one-site competition model of Scheme 2A.

Another parameter that is easily measured is the time-averaged probability of residing in the DTX substate, P_S-DTX. This probability was computed by dividing the sum of the durations of all recognized DTX substates at the 60% current level by the total time of the records. This measurement was made for data pooled from 6-18 single K_Ca channels for experiments of Fig. 3 at each tested concentration of BPTI. The resulting probability was normalized to obtain the probability ratio, P_S-DTX/P  ⁰_S-DTX, by dividing P_S-DTX by the probability of the DTX substate measured at 460 nM DTX in the absence of BPTI, P  ⁰_S-DTX. The theoretical dependence on [BPTI] of this latter normalized probability can be derived for Fig. 4, Schemes 2A and 2B, as follows:

(10)

(11)

(12)

Both Schemes 2A and 2B of Fig. 4 predict an apparent "relief" of the normalized probability of the DTX substate with increasing [BPTI] that follows a titration curve given by Eq. 10. The parameter, K_App, of Eq. 10 is an apparent equilibrium constant that is given by Eq. 11 for Fig. 4, Scheme 2A, and Eq. 12 for Scheme 2B. The data points in Fig. 4 C are the values of the normalized probability (P_S-DTX/P  ⁰_S-DTX) of the DTX substate measured in our experiments at 1, 2, 4, and 8 µM BPTI. The data shows that there is ~30% relief of the DTX substate at 8 µM BPTI. The theoretical curve, shown as a dashed line in Fig. 4 C, was calculated from Eqs. 10 and 11, where the K_App = 43.0 µM for Fig. 4, Scheme 2A, using the known values of K₁, J₁, and [DTX]. The fact that the measured data points clearly lie to the left of this curve with a significantly lower value for K_App is an independent piece of evidence that the system does not strictly obey the model of Scheme 2A. A nonlinear fit of the data in Fig. 4 C to Eq. 10 gives a best-fit value of K_App = 17.8 ± 1.7 µM. This latter estimate for K_App is close to the value of K_App = 12 ± 1.8 µM predicted for Fig. 4, Scheme 2B, using Eq. 12. The underlying reason that K_App is lower for Fig. 4, Scheme 2B, than Scheme 2A is that the reaction corresponding to the J₂ equilibrium constant provides additional relief of the 60% DTX substate (S_DTX) due to a significant level of DTX binding within the BPTI burst.

In summary, detailed analysis of single K_Ca channels shows that the ligand interaction between DTX-I and BPTI is not consistent with the pseudo one-site competition mechanism of Fig. 4, Scheme 2A. Most likely, additional state(s) of simultaneous binding of these two different Kunitz inhibitor molecules contribute to the observed behavior. At minimum, the results implicate the simultaneous binding of one DTX-I and one BPTI molecule on the tetrameric channel as represented in Fig. 4, Scheme 2B. It is also clear that there is a strongly antagonistic interaction between DTX-I and BPTI that lowers the affinity for binding of each ligand by a factor of ~11 in the doubly occupied state. This evidence for simultaneous but antagonistic ligand occupancy by BPTI and DTX-I provides an explanation for the mechanistic quandary posed at the beginning of the RESULTS; i.e., how can the interaction kinetics of BPTI with a nonpore site on a homotetrameric complex approximate one-site behavior. Despite this satisfying resolution, our experience with the practical limitations in collecting such data sets and the formidable kinetic complexities that would be faced in attempting to analyze the interaction of BPTI and DTX-I in greater detail dissuaded us from pursuing this system. Instead, we focused next on ligand interactions between DTX-I and a homologue of the Shaker ball peptide.

A Homologue of the Shaker Ball Peptide Exhibits Slow Blocking Activity Described by a One-Site Process

The evidence for simultaneous binding of BPTI and DTX-I presented above is compatible with the idea that the binding sites for these inhibitors are off-center from the pore, as it is difficult to envision that both of these large molecules with approximate dimensions of ~19 × 19 × 29 Å could simultaneously fit inside the central channel. As mentioned in the INTRODUCTION, previous work showed that internal Ba²⁺ readily blocks the BPTI-occupied channel, and internal TEA readily blocks the DTX-occupied channel (Lucchesi and Moczydlowski, 1991). The latter findings were actually the first indication that the binding sites for BPTI/DTX-I are not located within the pore. However, we wondered whether it might be possible to detect interactions between Kunitz inhibitors and pore blockers by using a larger blocking molecule. The Shaker ball peptide and its homologues are currently the largest molecules known to block K_V channels by binding within the pore. Fig. 5 A shows the sequence of the 20-residue NH₂ terminus of the Shaker K⁺ channel of Drosophila that mediates rapid inactivation by a ball-and-chain type of mechanism (Hoshi et al., 1990; Zagotta et al., 1990). Even though most maxi-K_Ca channels do not exhibit rapid inactivation and do not have a ball peptide sequence at the NH₂ terminus, the Shaker ball peptide is known to block maxi-K_Ca channels by a pore-occlusion mechanism (Foster et al., 1992; Toro et al., 1992). This finding has been explained by the idea that K_Ca channels possess a vestigial or surrogate receptor site for the ball peptide that confers sensitivity to block by such peptides. To investigate the relationship between the binding sites for Kunitz inhibitor proteins and the internal pore region, we studied the interaction between DTX-I and a ball peptide homologue.

View larger version (44K): [in this window] [in a new window]   Fig. 5.   Titration of a single KCa channel with a homologue of Shaker ball peptide. (A) Primary sequences of the native Shaker ball peptide and a homologue (BP) also known as G6VG9VE12KD13K (Toro et al., 1994). (B) Representative current records from a KCa channel recorded under control conditions and after addition of 20, 40, 80, and 160 nM BP on the internal side. Voltage, +30 mV. The dashed line denotes zero current.

The sequence of the particular ball peptide homologue that we chose for this study is shown in Fig. 5 A. The BP homologue has four amino acid substitutions of the native peptide, G6V, G9V, E12K, and D13K, that result in increased hydrophobicity and net positive charge (z = +6) compared with that of native BP (z = +2). This particular BP homologue was first described by Toro et al. (1994), who showed it has ~200-fold greater blocking affinity than the native Shaker ball peptide for a maxi-K_Ca channel from pig. Fig. 5 B shows the effect of titrating a single rat muscle K_Ca channel with BP homologue at +30 mV and 50 mM symmetrical KCl. The BP homologue induces the appearance of discrete blocking events of several seconds duration in the single channel record and the probability of this blocked state progressively increases with BP concentration over the range of 0-160 nM.

The kinetics of interaction of BP homologue with single K_Ca channels were analyzed by compiling dwell time histograms of blocked events and unblocked waiting times between adjacent blocked states. The probability histograms for these two types of events are well described by single-exponential functions. For example, Fig. 10 A shows a dwell time histogram of BP-blocked events plotted in the format of square root of events vs. log time. The binned dwell time data exhibits one predominant exponential component as shown by the superimposed fit. Fig. 6, A and B, plot mean lifetimes of the blocked state, _B, and the unblocked state, _U, as a function of the concentration of BP homologue. Fig. 6 A shows that _B is essentially independent of blocker concentration over the range of 10-160 nM peptide with a mean value of 1.71 ± 0.07 s (±SEM, n = 6). Fig. 6 B shows that _U is inversely related to the blocker concentration. The results of Figs. 6, A and B, are consistent with a simple reversible blocking reaction like that of Fig. 6, Scheme 3. Fig. 6, Scheme 3, demands the following relationships:

(13)

(14)

(15)

View larger version (17K): [in this window] [in a new window]   Fig. 10.   Probability density histograms of BP-blocked events recorded in the absence and presence of DTX-I. (A) Dwell time histogram of blocked events recorded from single KCa channels in the presence of 160 nM BP. Blocked events from seven different single KCa channels were pooled to obtain a sample of 857 events. The sample of events was binned and plotted according to the method of Sigworth and Sine (1987) using the square root versus log time format. The solid line is a fit of the data to a single exponential with a time constant of 1.73 s. (B) Dwell-time histogram of blocked events recorded in the presence of 460 nM DTX-I plus 160 nM BP. The sample contains 899 events pooled from five single KCa channels. The solid line is a fit to a sum-of-two-exponentials function with a short time constant of 0.90 s (amplitude, 0.53) and a long time constant of 6.22 s (amplitude, 0.47).

View larger version (16K): [in this window] [in a new window]   Fig. 6.   Analysis of BP blocking kinetics. Scheme 3 represents a binding reaction for the reversible association of BP with a single site in the KCa channel pore. , unoccupied subunits; *, represents BP bound to the pore. The association rate constant of BP is b1, and the dissociation rate constant is b1. U, the unoccupied state of the channel; B, the BP-blocked state. (A) Lifetime of the BP-blocked state as a function of [BP]. (B) Lifetime of dwell times between adjacent BP-blocked states as a function of [BP]. Data points and error bars in A and B are the mean ± SEM for three to seven single channels. The solid line and two dotted lines in A are the mean ± SD of the six data points used to measure b1 from the lifetime B of state B (Eq. 13). The solid line in B is a fit to Eq. 14 used to measure b1 from the lifetime U of state U. The inset shows the same data plotted as the reciprocal lifetime. (C) Time-averaged probability of a channel being in the unoccupied (BP-free) state as a function of BP. Each point was calculated from 4.5-6.5 h of data pooled from three to seven single channels. The solid line in C is a fit to Eq. 15 used to measure the equilibrium constant B1 as described in the text.

The mean lifetime of the BP-blocked events obtained from the data in Fig. 6 A yields a value of b₁ = 0.585 ± 0.025 s¹ for the dissociation rate constant of BP according to Eq. 13. The data of Fig. 6 B were fit to Eq. 14 to obtain a value of b₁ = 8.17 ± 0.73 × 10⁷ s¹M¹ for the bimolecular association rate constant of BP. The kinetic ratio of b₁/b₁ gives a value of B₁ = 7.16 ± 0.71 nM for the equilibrium dissociation constant of BP under these conditions. The assumption of a single class of binding sites for BP was also tested by plotting the time-averaged probability of the unblocked U state, P_U, vs. [BP] as shown in Fig. 6 C. A nonlinear fit of these data to Eq. 15 gives a value of B₁ = 8.85 ± 0.71 nM, which closely agrees with the corresponding ratio of rate constants. Thus, the blocking behavior of the particular high-affinity BP homologue that we have studied is well described by a one-site blocking reaction. This blocking site is assumed to be located directly within the inner pore because the smaller pore-blocking molecule, TEA, inhibits ball peptide block of the maxi-K_Ca channel in a strictly competitive fashion (Toro et al., 1992). External K⁺ has also been found to relieve the block by internal BP (Foster et al., 1992; Toro et al., 1992). We have also confirmed that internal TEA decreases the association rate of BP homologue in a competitive fashion under our conditions (data not shown). This characterization of a BP homologue as a pore blocker thus provides the groundwork for investigating ligand-ligand interactions between the Kunitz inhibitor site and the BP blocking site.

A Complex Pattern of Blocking Activity by Ball Peptide Homologue in the Presence of DTX-I Reflects Simultaneous Binding of Two Ligands

If the binding site for BP overlaps with that of DTX-I, then BP-blocking events should only interrupt dwell time durations in the open state when the channel is unoccupied by DTX-I. Alternatively, if the binding site for BP is physically distinct from that of DTX-I, then BP-blocking events should also interrupt the long-lived DTX substate. The current records of Fig. 7 demonstrate that the latter alternative prevails. In this experiment, 460 nM DTX-I induced long-lived DTX-substate events that comprised ~97% of the time-averaged activity of a single K_Ca channel. Subsequent addition of 20 nM BP to the internal side resulted in a complex pattern of blocking activity consisting of four easily recognized types of discrete blocking events that can be defined on the basis of how they begin and end. Some of the discrete blocking events are flanked at both the entry and exit transitions by the DTX substate. This type of event would be expected to occur if BP binds to the DTX-occupied channel and dissociates again before DTX-I has a chance to dissociate. A second type of discrete blocking event is initiated from a DTX substate and is terminated by a transition to a fully open current level. This may correspond to an event in which BP first binds to a DTX-occupied channel, followed by electrically silent dissociation of DTX-I, and then by dissociation of BP. A third class of discrete blocking events are initiated from a fully open state and terminated by a transition to a DTX sublevel. This may correspond to a blocking event that starts with BP binding to an unoccupied channel, followed by the electrically silent binding of DTX-I to the fully blocked channel, and terminated by dissociation of BP from the DTX-occupied channel. The fourth type of blocking event begins and ends with the fully open state. This class of events would be expected to occur when BP binds and dissociates from the channel during periods when DTX is never bound. The latter events could also occur when BP binds to an unoccupied channel and DTX-I binds and then dissociates one or more times before BP finally dissociates. If the binding of another ligand to the BP-blocked state is presumed to be electrically silent, the various classes of blocked states described above could also reflect multiple numbers of silent DTX-I- binding events. This preliminary discussion of the single-channel behavior in the presence of DTX-I and BP points to a mechanism that involves simultaneous occupancy and unordered binding of these two ligands.

View larger version (33K): [in this window] [in a new window]   Fig. 7.   Representative records from a single KCa channel recorded in the presence of DTX-I alone and DTX-I plus two different concentrations of BP. The top trace was obtained under control conditions before addition of peptide and the second trace from the top was recorded after the addition of 460 nM DTX-I to the internal side of the bilayer. The next two groups of three traces are continuous segments of recordings taken after the addition of 20 and 40 nM internal BP, respectively, to the same channel. The dotted line marks the zero current level.

The Association Rate of Ball Peptide Homologue Is Slower when the Channel Is Occupied by DTX-I

To analyze this two-ligand system, we first measured the durations of the following two types of events: (a) unconditional BP-blocked events defined as any uninterrupted residence time in the fully blocked state, and (b) unconditional DTX-substate events defined as any uninterrupted residence time in the ~60% DTX-substate current level. Samples of these two types of events containing 50-350 dwell times were manually identified and pooled from five different single channel bilayers each at seven different concentrations of BP ranging from 5 to 320 nM. The simple arithmetical mean of these samples is plotted as a function of BP concentration in Fig. 8, A and B. Fig. 8 A shows that the mean unconditional dwell time of the BP-blocked state, _BP, is independent of [BP] and has a value of 4.62 ± 0.13 s (±SEM, n = 7) averaged over all BP concentrations. This result is inconsistent with one-site competition. Such a mechanism (Fig. 8, Scheme 4A) predicts that the lifetime of the BP-blocked state is equal to the reciprocal of the BP dissociation rate constant, 1/b₁, which was previously measured as 1.71 ± 0.07 s from the mean blocked time in the absence of DTX-I (Fig. 6 A). This comparison shows that average duration of the BP-blocked state is increased by a factor of 4.62/1.71 s = 2.7 in the presence of 460 nM DTX-I vs. the absence of DTX-I. Fig. 8, Scheme 4A, also predicts that the unconditional lifetime of the DTX substate is equal to the reciprocal of the DTX-I dissociation rate constant, 1/j₁, and is independent of [BP]. This is inconsistent with the results of Fig. 8 B, which show that the mean unconditional dwell time of the DTX substate varies inversely with [BP]. Thus, two major predictions of Fig. 8, Scheme 4A, are clearly violated, ruling out an overlapping binding site for BP and DTX-I.

View larger version (20K): [in this window] [in a new window]   Fig. 8.   Kinetic analysis of ligand interactions between DTX-I and BP. Scheme 4A shows a hypothetical three-state model for simple binding competition between DTX-I and BP. This scheme would be expected to describe a situation where binding sites of two different ligands physically overlap. This model assumes that DTX-I can bind to only one of the four subunits at a time. , unoccupied subunits; , DTX-bound subunit; and *, BP bound to the pore. Scheme 4B shows a four-state model that describes binding of DTX-I to a nonpore site on any one subunit at a time and simultaneous binding of BP to a single site in the pore. U is the unoccupied state, SDTX is the DTX-bound substate, BBP is the BP-blocked state, and BBP/DTX is the doubly occupied blocked state. (A) Mean dwell time of the unconditional BP-blocked state as function of BP. Events identified as fully blocked states were pooled from five different single KCa channels at each concentration of BP. The pooled samples contained from 67 to 899 events. The data points and error bars correspond to the arithmetic mean ± SEM. The solid line and two dotted lines correspond to the mean ± SEM of the seven data points used to calculate the J3 equilibrium constant from Eq. 19. (B) Measured lifetime of the DTX substate as a function of BP concentration. Events identified as uninterrupted dwell times in the DTX substate were pooled from five different KCa channels at each concentration of BP. These samples containing 50-328 events were well-described by simple exponential distributions. Data points represent the arithmetic mean ± SEM of these samples. The solid line is a fit to Eq. 16 that was used to measure the rate constant, b2