Correspondence to: Franco Conti, Istituto di Cibernetica e Biofisica, CNR, 16149 Genova, Italy., conti{at}barolo.icb.ge.cnr.it (E-mail), Fax: 39-010-6475-500; (fax)
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Abstract |
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-conotoxin PVIIA is the first conotoxin known to interact with voltage-gated potassium channels by inhibiting Shaker-mediated currents. We studied the mechanism of inhibition and concluded that PVIIA blocks the ion pore with a 1:1 stoichiometry and that binding to open or closed channels is very different. Open-channel properties are revealed by relaxations of partial block during step depolarizations, whereas double-pulse protocols characterize the slower reequilibration of closed-channel binding. In 2.5 mM-[K+]o, the IC50 rises from a tonic value of ~50 to ~200 nM during openings at 0 mV, and it increases e-fold for about every 40-mV increase in voltage. The change involves mainly the voltage dependence and a 20-fold increase at 0 mV of the rate of PVIIA dissociation, but also a fivefold increase of the association rate. PVIIA binding to Shaker
6-46 channels lacking N-type inactivation or to wild phenotypes appears similar, but inactivation partially protects the latter from open-channel unblock. Raising [K+]o to 115 mM has little effect on open-channel binding, but increases almost 10-fold the tonic IC50 of PVIIA due to a decrease by the same factor of the toxin rate of association to closed channels. In analogy with charybdotoxin block, we attribute the acceleration of PVIIA dissociation from open channels to the voltage-dependent occupancy by K+ ions of a site at the outer end of the conducting pore. We also argue that the occupancy of this site by external cations antagonizes on binding to closed channels, whereas the apparent competition disappears in open channels if the competing cation can move along the pore. It is concluded that PVIIA can also be a valuable tool for probing the state of ion permeation inside the pore.
Key Words: voltage-gated potassium channels, ion channel pore, potassium binding site, Xenopus expression system
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Introduction |
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Toxins from the carnivorous marine cone snails have been useful tools for the study of voltage-activated calcium and sodium channels (-conotoxin PVIIA, the first member of a new family of conotoxins that interact with voltage-gated potassium channels (
In this paper, we study the mechanism of inhibition by PVIIA of Shaker channels and Shaker 6-46 channels lacking fast N-type inactivation. Our analysis shows that the voltage-dependent modification of the partially inhibited currents (
6-46 and Shaker wild-type channels are similar, except that inactivation protects partially the latter from the depolarization-induced unblock, in agreement with the assumption that the toxin senses only the conductive state of the channel. In analogy to CTX block of Ca-activated K+ channels (
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Methods |
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The solid-phase peptide synthesis of PVIIA was performed as described in 6-46 (
Oocyte Expression System
Oocytes from Xenopus laevis were prepared as described previously (. Current records were low-pass filtered at 1 kHz (-3 dB) and sampled at 4 kHz. For outside-out patch-clamp recordings (
. The pipette solution contained (mM): 115 KCl, 1.8 EGTA, 10 HEPES, pH 7.2 with KOH. Currents were measured with an EPC-9 patch clamp amplifier driven by the Pulse+PulseFit software package (HEKA Elektronik). Current records were low-pass filtered at 3 kHz (-3 dB) and sampled at a rate of 10 kHz.
The bath solution in the electrophysiological experiments was either normal frog Ringer's (NFR) containing (mM): 115 NaCl, 2.5 KCl, 1.8 CaCl2, 10 HEPES, pH 7.2, with NaOH, or K+-Ringer containing (mM): 115 KCl, 1.8 CaCl2, 10 HEPES, pH 7.2 with KOH. Leak and capacitive currents were corrected on-line by using a P/n method. In all experiments, the vitelline membranes of the oocytes were removed mechanically with fine forceps. Toxin solution was added to the bath chamber with a Gilson tip pipette. The indicated toxin concentrations correspond to the final concentration in the bath chamber.
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Results |
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Open-Channel Block by PVIIA in Low [K]o (NFR)
As shown by
Figure 1 A shows superimposed current responses to three different step depolarizations, recorded from the same oocyte before and after the addition to the bath of 500 nM PVIIA. All peak amplitudes are reduced roughly 10-fold under toxin, corresponding to an IC50 of PVIIA block of ~50 nM. A closer inspection reveals, however, that the time course of the currents is sensibly modified. Figure 1 B shows that the ratio, U (for unblock probability), of toxin to control responses for the same voltage increases after the time to peak approaching a late steady state value that, for V = 60 mV, is about five times larger. Although developing during the onset of inactivation, this effect cannot be attributed to an unblock of inactivated channels because it increases strongly with V in a range where the steady state probability and the time constant of inactivation are fairly constant, ~0.9 and ~3.5 ms, respectively. The solid lines in Figure 1 B are single-exponential fits of U(t), yielding asymptotic values that increase from 0.21 at V = 0 mV to 0.46 at V = 60 mV, while the time constants decrease from 27 to 6.3 ms. These data could be related to some average relaxation of toxin binding to open and inactivated channels, but the unfolding of binding and inactivation processes would not be straightforward since their kinetics appear to occur in a similar time range. Nevertheless, the fitted asymptotic values of U(t) can be used to estimate an apparent dissociation constant, K(O)app, of PVIIA binding to open (noninactivated) channels. K(O)app estimates in the voltage range -20 to +60 mV were fairly well fitted by: K(O)app(V) = K(O)app(0)*exp(V/vs). Data from the experiment in Figure 1 are shown in Figure 4 C as and fitted with K(O)app(0) = 115 nM and vs = 45 mV. Mean values of K(O)app(0) and vs from four different oocytes tested with toxin concentrations between 100 and 500 nM were 125 nM and 46 mV (Table 1, columns 2 and 5).
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Evidence that the inactivation of Shaker-H4 channels is a damping factor rather than the cause of the above effects is provided by the study of the deletion mutant Shaker6-46 (Sh-
) that lacks fast inactivation (
channels appear even more strongly modified by the presence of partially blocking concentrations of extracellular PVIIA. Figure 2 A shows voltage-clamp currents for steps to -10, +10, and +30 mV, recorded from an oocyte expressing Sh-
channels before and after the bath addition of 200 nM PVIIA. It is seen that the toxin reduces strongly the early phase, but has much less effect on the steady state of the currents. The currents measured at the half-activation time of the normal responses are reduced at all voltages slightly more than fivefold, indicating a PVIIA dissociation constant from the blocking site of ~50 nM, close to that estimated for Shaker-H4 channels from the reduction of peak currents. However, this early reduction diminishes during the pulse, and the currents approach asymptotic values that are progressively closer to the toxin-free levels at increasing depolarization. As opposed to the case of the gating modifier Hanatoxin from spider venom (
(O), that depend on the step voltage. For V
-20 mV, the open-channel probability is close to its maximum and we find that
(O) is always much larger than the half-activation time of normal currents. Therefore, these relaxations develop almost exclusively while the channels are fully activated, and this justifies the use of the superscript (O) for the parameters that characterize them.
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A second expectation is that the dependence of both U(C) and U(O) on the toxin concentration, [T], should follow simple Langmuir isotherms:
where K(C) and K(O) are the dissociation constants characterizing, respectively, the equilibrium binding of PVIIA to resting (closed) or activated (open) channels. Figure 3 illustrates a single experiment in which [T] was changed progressively from 0 to 10, 20, 50, 100, 200, 500 nM, 1 µM, and back to 0. At each [T], a standard series of currentvoltage responses to various pulse potentials, Vp, was recorded with 5-s stimulation intervals at a holding potential of -100 mV. Figure 3 A shows the [T] dependence of the responses to Vp = 20 mV. Notice that the record obtained after washing-out the 1-µM PVIIA solution shows a small "run up" of the preparation and a very small residual unblock that we attribute to the remaining presence of a few nanomolar PVIIA around the oocyte. Ratios of the toxin to the initial control responses of Figure 3 A are shown in B, together with single-exponential fits that are almost indistinguishable from the data at all times after 1 ms from the half-activation time of the control response. Estimates of U(C) and U(O) from these fits are plotted in Figure 3 C as a function of [T]. The solid lines show that the data are indeed well fitted by Langmuir isotherms, yielding in this case K(C) = 36 nM and K(O) = 330 nM.
A third expectation is that (O) should depend on [T] according to:
Estimates of (O) from the single exponential fits of Figure 3 B are plotted as a function of [T] in D. The solid line is the least-squares fit of the data according to the above relationship, which is clearly well obeyed.
Finally, we expect a simple relationship between the estimates of k(O)off and k(O)on from the above fit of the [T] dependence of (O) and the equilibrium dissociation constant K(O) estimated from the fit of U(O) data: K(O) = k(O)off/k(O)on.
The values of k(O)off and k(O)on fitting the (O) data of Figure 3 D, respectively, 29 s-1 and 88 µM-1 s-1, yield indeed the same estimate of K(O) ~ 330 nM as the fit of the U(O) data of Figure 3 C.
In most experiments, only two toxin concentrations were tested on the same oocyte, or experiments were done for a single [T] value in the range of 100500 nM. The consistency of the results of these experiments with the bimolecular character of the toxin-block reaction was shown indirectly by the agreement of the estimates of K(O), k(O)off, and k(O)on obtained from single measurements of U(O) and (O) in any given condition according to the inverse relationships:
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(1) |
The most interesting feature of PVIIA-block relaxations is their strong voltage dependence. In the experiment of Figure 2, U(O) increased from 0.51 to 0.8 and (O) decreased from 23 to 8.5 ms as V was increased from 0 to 60 mV. Converting these data according to Equation 1 yields the voltage dependencies of the binding parameters shown in Figure 4 as
. The figure shows also plots of similar data from a representative experiment in K+-Ringer to be described later (Figure 4, , see Figure 7). Figure 4A and Figure C, shows that both k(O)off and K(O) increase with voltage according to a simple exponential law. The straight lines fitting the semilogarithmic plots of k(O)off and K(O) were drawn according to the expressions: k(O)off(V) = k(O)off(0)*exp(V/vs), [k(O)off(0) = 22 s-1; vs = 42 mV], and K(O)(V) = K(O)(0)*exp(V/vs), [K(O)(0) = 200 nM; vs = 44 mV]. Consistently, Figure 4 B shows that k(O)on has no systematic trend with a mean value of 110 s-1 µM-1. Mean values of k(O)on, k(O)off(0), K(O)(0), and vs (n = 10) are given in columns 25 of Table 1.
Figure 4 C shows also that the apparent dissociation constant, K(O)app, estimated from the unblock of Shaker-H4 channels, is systematically lower than K(O). This is consistent with the idea that the reduction of toxin block occurs in the open state, so that the effect is strongly reduced if the channels visit frequently, and for relatively long periods, the inactivated (closed) state.
Binding of PVIIA to Closed Channels in Low [K]o (NFR)
PVIIA has obviously free access to the site of block also when the channels are closed during resting hyperpolarizations. The dissociation constant of PVIIA binding to closed channels, K(C), can be easily measured by the reduction with [T] of the early responses to pulse stimulations under resting conditions. Our estimates of K(C) in NFR, in the range of 3580 nM, were not significantly different for Shaker-H4 or Shaker- channels (Table 1, column 6). These estimates are approximately fourfold lower than those of K(O)(0) and it is important to know what changes in the kinetic parameters of toxin-binding contribute to this difference.
The kinetics of PVIIA binding to closed channels cannot easily be measured from wash-in/wash-out experiments because testing toxin block at any time grossly upsets the block itself and changes the meaning of later tests. A correct wash-in/wash-out experiment should be performed repetitively with a fast-perfusion system testing in each trial PVIIA block at a different time from wash-in. However, the marked change of PVIIA block caused by a pulse depolarization allows us to perform a conceptually identical experiment, by testing at different times the after-pulse re-equilibration of PVIIA binding to closed channels. Figure 5 shows the results of a double-pulse experiment on an oocyte expressing Sh- channels. Each stimulation consisted of two successive pulses of 40 ms to 40 mV separated by a variable resting period, Ti, at -100 mV. Figure 5, top, shows the responses for Ti increasing from 5 to 200 ms, recorded before and after the addition of 200 nM PVIIA to the bathing NFR solution. It is seen that the two successive responses in the control experiment are always virtually identical, indicating that the channels recover completely their resting state after 5 ms at -100 mV. With PVIIA, however, the second response reveals a long memory of the effects induced by the first pulse: for short interpulses it is dominated by a fast rising phase much as the toxin-free response, and its "tonic" characteristics are not fully recovered even after 200 ms. Figure 5, bottom left, plots as a function of Ti the ratio of the early currents elicited by the second and first pulses at the half-time of the toxin-free response. This ratio, which is virtually unity in control measurements at all Ti, with PVIIA is ~4 for Ti = 5 ms, and is still ~2 for Ti = 200 ms. We interpret this phenomenon as due to a relatively slow reequilibration of PVIIA binding to closed channels, and we take the early amplitude of the second response, normalized to control, as the fraction of toxin-free channels at the time of onset of the second pulse. As shown in Figure 5, bottom right, this quantity decays with Ti as a single exponential, from U(O) = 0.86 to U(C) = 0.22, with a time constant,
(O), of 190 ms. We interpret U(O) as the toxin-free probability of open channels at the end of the conditioning pulse, U(C) as the equilibrium toxin-free probability of closed channels, and
(C) as the relaxation time of PVIIA binding to closed channels. Accordingly, the last two quantities yield estimates of the association and dissociation rate constants, k(C)on and k(C)off, of PVIIA binding to closed channels. From the experiment of Figure 5, we obtain: k(C)on = 21 µM-1 s-1, k(C)off = 1.2 s-1, K(C) = 56 nM. Mean estimates (n = 8) are given in Table 1. Compared with open-channel properties, both the on and off rates of PVIIA binding to closed channels are much slower. The approximately fourfold higher value of K(O)(O) relative to K(C) results from the combination of an increase of the rate of PVIIA dissociation by a factor of ~24 and an increase of the association rate by a factor of ~6. The most important conclusion from these measurements is that, while the low value of k(C)off could be thought as an extrapolation to hyperpolarized potentials of the voltage dependence of k(O)off (see Figure 4 A), the sixfold lower value of k(C)on is incompatible with the voltage independence of k(O)on (see Figure 4 B) and indicates that closed channels indeed have different toxin-binding properties. In two oocytes, the above double-pulse protocol was applied using variable holding potentials between -60 and -120 mV and we observed no significant change in the estimates of the binding parameters (data not shown). Thus, unlike for open channels, the interaction of PVIIA with closed channels appears to be voltage insensitive and this conclusion is also qualitatively consistent with the above reported observation that even at large positive potentials Shaker-H4 channels that are closed by the inactivation gate appear protected from toxin unblock.
Due to inactivation, the recovery of the tonic binding of PVIIA to Shaker-H4 channels after a conditioning stimulus appears rather peculiar, as illustrated by Figure 6. The control recordings from a double-pulse protocol follow a classical pattern showing that the second response increases with Ti as more channels recover from the inactivation produced by the conditioning pulse: the ratio of second to first peak current approaches 1 as a single exponential with a time constant of 28 ms (Figure 6, and solid line in bottom left). The recordings with 100 nM PVIIA added to the bath show instead a marked overshoot of the second response that subsides very slowly. This effect has a simple explanation if we assume that the recovery from the unblock induced by the conditioning pulse is much slower than recovery from inactivation. Consistently, as shown in Figure 6, bottom right, the fraction of toxin-free channels, estimated from the toxin to control ratio of the second peak response, decreases monotonically with Ti. Fitting this decay towards the steady state ratio of the first peak responses with a single exponential yields
(C) = 270 ms. Combining this estimate with that of the asymptotic toxin-free probability, U(C) = 0.44, we estimate in this experiment: k(C)off = 1.6 s-1, k(C)on = 21 µM-1 s-1, K(C) = 78 nM. Mean estimates of the parameters of PVIIA binding to closed Shaker-H4 channels are given in Table 1. It is seen that they are not significantly different from those of Shaker-
channels, supporting the idea that PVIIA does not distinguish the resting state of the two phenotypes.
Effect of [K]o on the Binding of PVIIA
The voltage dependence of PVIIA dissociation from open channels is strongly reminiscent of the properties of CTX block of Ca-activated potassium channels ( channels using high extracellular concentrations of potassium ions, [K]o = 115 mM. For more reliable measurements in the voltage range of negative-resistance characteristics of this preparation, few experiments were performed on excised outside-out patches, but very similar results were also obtained outside of this range from experiments on whole oocytes.
Figure 7 illustrates a representative experiment on an outside-out patch exposed to symmetric 115-mM K+ solutions. Figure 7 A shows superimposed current records from standard currentvoltage stimulation protocols applied before (left) and after (middle) the addition to the external bath of 1 µM PVIIA. The right diagram gives plots of the late currents at the end of 100-ms pulses as a function of pulse voltage. It is seen that 1 µM PVIIA blocks most of the inward currents, but has a much smaller effect on the outward currents at large depolarizations. This is consistent with the results obtained with NFR ([K]o = 2.5 mM) in the external bath. By interpreting the steady state ratios of toxin to control currents as toxin-free probabilities, we obtain for the open-channel dissociation constant, K(O), similar estimates and the same voltage dependence as in NFR (Figure 4 C, , and mean estimates in Table 1).
The comparison of the whole time course of test and control responses also reveals that toxin-block relaxations have properties similar to those observed in low K+ solutions, although starting from a different resting-block equilibrium. Figure 7 B shows three of the control records in A (for V = -40, +20, and +60 mV) superimposed with the respective records under toxin scaled by a constant factor of 3.3. It is seen that this scaling makes the currents recorded at +20 mV match almost exactly for the whole duration of the pulse, whereas the match for the other records is good only for the initial rising phase. At later times, the inward currents at -40 mV are further depressed approximately fourfold and the outward currents at +60 mV undergo an approximately twofold increase. The most obvious interpretation of these results is that two thirds of the channels are tonically blocked at 1 µM PVIIA according to a toxin dissociation constant from closed channels, K(C) ~ 430 nM, which is about equal to K(O) at +20 mV, whereas depolarizations below or above +20 mV, leading to lower or higher K(O) values, cause an increase or decrease of PVIIA block. In agreement with this interpretation, the current ratios after almost complete activation follow single-exponential relaxations (Figure 7 C, smooth lines), as expected from the reequilibration of a toxin-block reaction. The fitting parameters of these relaxations can be used to estimate the rate constants characterizing the binding of PVIIA to open channels. These estimates for the experiment of Figure 7 are plotted in Figure 4A and Figure B, . The comparison with the data obtained in NFR (Figure 4, ) shows that both the association and dissociation rate constants of PVIIA binding to open channels are insensitive to changes of [K]o. Mean estimates of k(O)on, k(O)off(0), K(O)(0), and vs from four different experiments are given in columns 25 of Table 1.
From the data of Figure 7 B, we estimate a tonic block of 66% in 1 µM PVIIA, which corresponds to a PVIIA dissociation constant of 430 nM and shows that, at variance with the open channel properties, the binding of PVIIA to closed channels is very sensitive to [K]o. Our mean estimate of K(C) from five oocytes at [K]o = 115 mM was ~400 nM, about a factor of 8 higher than at [K]o = 2.5 mM. We can ask whether the lower affinity of PVIIA at [K]o = 115 mM is due to a smaller rate of association or to a larger rate of dissociation by analyzing a double-pulse experiment such as that illustrated in Figure 8. The experiment was done on a whole oocyte in the presence of 1 µM PVIIA and the protocol consisted of several double stimulations, with pulses to -20 mV separated by a variable interpulse interval (Ti) allowing resting periods of at least 3 s between successive stimulations. Figure 8 A shows a sample of the responses obtained for Ti values between 30 and 420 ms. In agreement with what we described above, we observe that the conditioning pulse induces an increase of toxin block that appears as a reproducible peak in the first response of each successive double stimulation. However, for small Ti values, the second response has a more normal appearance and no peak, indicating that the fraction of blocked channels is near the equilibrium for open-channel block at -20 mV that was already achieved by the end of the conditioning pulse. We can judge qualitatively the slow recovery of the lower equilibrium probability of PVIIA binding to closed channels by the reappearance of a peak in the second response, which is clearly seen only in the records with Ti = 180 or 420 ms. A more quantitative analysis is shown in Figure 8 B by plotting, as a function of Ti, the ratio of the early amplitudes of test and conditioning responses taken as means in the time interval of 2575% rise of the toxin-free response. These data are well fitted by a single exponential increase with Ti with a time constant of 430 ms. Assuming this value as an estimate of (C) and using the value of U(C) = 0.28 measured from the early fraction of unblocked currents (data not shown), we estimate in this experiment: K(C) = 380 nM, k(C)off = 0.65 s-1, k(C)on = 1.7 µM-1 s-1. Mean estimates obtained from three experiments of this type are k(C)off = 0.79 s-1 and k(C)on = 1.76 µM-1 s-1 (see Table 1). The value of K(C)off at [K]o = 115 mM appears equal to that in [K]o = 2.5 mM within the experimental error. On the contrary, increasing [K]o from 2.5 to 115 mM decreases by more than one order of magnitude the apparent value of k(C)on, which seems to be the only parameter of PVIIA binding to Shaker channels that is very sensitive to [K]o. Notice that we studied the effect of increasing [K]o by substituting Na+ with K+, so that this effect is not comparable to the large decrease of toxin association rates observed at increasing ionic strength for CTX block of Ca2+-activated channels (
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Discussion |
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PVIIA Is a Pore Blocker
We have described in this paper the dose, voltage, and time dependence of PVIIA effects on the currents mediated by Shaker channels. Our results are consistent with the hypothesis that the most prominent effect of toxin-channel association is the block of the channel conductance and rule out a substantial modification of channel gating as observed, e.g., when the channels bind the spider venom toxin Hanatoxin (
PVIIA Block Is State Dependent
An important result of our study for mechanistic interpretations is that the different binding of PVIIA to closed or open channels cannot be attributed solely to the voltage dependence of the reaction rates. First of all, while the low value of k(C)off could be thought as the extrapolation of k(O)off(V) to hyperpolarizing potentials, the independence of K(O)on on voltage and [K]o is incompatible with the 6- or 90-fold lower estimates of K(C)on at [K]o = 2.5 or 115 mM. Secondly, our observation that the relaxations of closed-channel block are independent of the holding potential in the range of -60 to -120 mV shows that, in sharp contrast to the case of open channels, the binding of PVIIA to closed channels is fairly insensitive to the transmembrane voltage. Indeed, the fact that inactivation protects significantly depolarized Shaker-H4 channels from toxin-unbinding is consistent with a similar binding of PVIIA to any nonconducting state of the channels at any voltage.
An important consideration that justifies a posteriori most of our experimental analysis is that the relaxations of toxin binding to open or closed channels occur on very different time scales. The mean properties that we expect from flickering between open and closed states are weighted for each state in direct proportion to the probability of that state and in inverse proportion to the time constant of the binding relaxation in that state. Since the binding kinetics for closed channels is at least 10x slower than for open channels, the relative weight of the open state in Sh- channels that do not inactivate would be >0.9 for any open probability, P(O) > 0.5. Therefore, it is fair to assume that, during depolarizations of noninactivating channels, we are essentially measuring the binding to open channels. The situation is less favorable for Shaker-H4 channels, where P(O) ~ 0.1. In this case, we expect that the relative weight of the open state is ~0.53, and this is indeed fairly consistent with our finding that the K(O)app measured for Shaker-H4 channels is ~0.6 K(O).
Analogy between PVIIA and CTX
The structural similarity of PVIIA with the scorpion toxins of the charybdotoxin family (
As for the case of CTX block of Ca2+-activated K+ channels (
The only clear difference between CTX and PVIIA appears to be that the latter binds with much faster kinetics, due to a much higher dissociation rate constant. However, several CTX variants also block open Shaker channels with relatively fast kinetics that have been observed by fast perfusion of macropatches during long depolarizing sweeps (
A Model for the State Dependency of PVIIA Block
While we cannot exclude that a PVIIA molecule bound to an open channel senses a significant fraction of the transmembrane electric field, the above discussed analogies with CTX and the antagonizing action of high-K+ solutions on tonic PVIIA block suggest that the unblock observed upon opening the channels in low external K+ may largely arise from the destabilization of toxin binding by internal K+, as in the case of CTX (
From now on, we shall refer to this site as if it was the only K+-binding site. The general scheme that we can use to interpret our data is shown in Figure 11.
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Figure 11 assumes that the toxin (Tx) can bind to whatever state of the channels with the same second-orderassociation rate constant, k1, whereas its first-orderdissociation rate constant is k(K)-1 or k(0)-1, depending on whether or not the K+-binding site is occupied, and k(K)-1 >> k(0)-1. All the rate constants are otherwise assumed to be voltage independent. The scheme assumes also that K+ binding is in fast equilibrium and is governed by different dissociation constants, K(Tx)d or K(0)d, depending on whether or not there is a bound toxin in the outer pore vestibule. While a bound toxin is blocking the extracellular access, K+ binding to the pore is assumed to be in equilibrium only with the cytoplasmic K+ concentration, [K]i, and the parenthesis in the transition C:Tx C:K+:Tx indicates that this transition can occur only when the channel is open. A possible molecular picture of the states C:Tx and C:K+:Tx is shown in the cartoon of Figure 9. When the channel is closed and not blocked by PVIIA [K] stands for the extracellular K+ concentration, whereas when the channel is open [K] is determined by the flux of ions in the pore.
In the case of open channels, it is easily seen that the above scheme reduces to the simple two-state Figure 10, provided we identify k(O)on with k1, and k(O)off with an average of k(K)-1 and k(0)-1 weighted according to the relative probabilities of states C:K+:Tx and C:Tx. Assuming for K(Tx)d a voltage dependence associated with the charge translocation occurring along the pore in the transition C:Tx C:K+:Tx, we can express k(O)off as:
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(2) |
where K(Tx)d(0) is the dissociation constant at 0 mV and the voltage dependence is equivalently expressed as if the charge translocation involved the movement of a single K+ across a fraction = 25 mV/vs of the transmembrane voltage.
It is important to notice that Equation 2 and the condition k(O)on = k1 bear no reference whatsoever to the extracellular solution conditions, a strong prediction of Figure 11 that was verified in our comparative experiments with low- or high-K+ solutions. Notice also that Figure 11 leads us to conclude that our voltage-independent estimates of k(O)on provide a direct measurement of the true rate constant of PVIIA association to open channels.
The expression of k(O)off according to Equation 2 is the same as that used by
In the study of single channels reconstituted in lipid bilayers, close to 1. As discussed below, it is practically impossible in the oocyte preparation to study open-channel block by PVIIA outside the range of the exponential rise of k(O)off, so that imposing the consistency of our data with Equation 2 yields only lower estimates for K(Tx)d(0) and k(K)-1 and a good estimate of vs. Our overall mean estimate of vs ~ 40 mV, corresponding to
= 0.63, is in good agreement with the estimates of
= 0.55 obtained by
(O) at low [T] values for which
(O) ~ 1/k(O)off. Low estimates of
, ranging from 0.31 to 0.62, were also found in the study by
Our measurements of k(O)off do not show any obvious deviation from an exponential rise up to V = +80 mV, where k(O)off ~ 200 s-1 (Figure 4 A). Thus, for consistency with Equation 2, these data imply k(K)-1 >> 200 s-1 and K(Tx)d(0) >> [K]i*e2; i.e., K(Tx)d(0) >> 0.8 M, in qualitative agreement with the studies of CTX block. The large lower estimate of k(K)-1 explains why also the low pedestal predicted by Equation 2 at negative voltages is not seen in our data. According to Figure 11, k(0)-1 is a lower bound for the dissociation rate constant in any channel configuration, so that k(0)-1 k(C)off ~ 1 s-1. Since k(O)off is ~26 s-1 at V = 0, we expect that k(O)off approaches its low pedestal only for voltages more negative than -80 mV, where open channels are impossible to explore.
In conclusion, the predictions of Figure 11 are consistent with our data on PVIIA binding to open channels according to the following quantitative estimates:
We discuss now the predictions of Figure 11 for the case of closed channels. As already anticipated, the most important difference with respect to the previous case is the absence of C:Tx C:K+:Tx transitions. An additional important difference is the fact that C:
C:K+ transitions involve only a very fast equilibration with external K+. With these two conditions, Figure 11 reduces to Figure 12, where {U} lumps together the unblocked states C: and C:K+, and p is the probability that a U state is a C:K+ state. A further simplification arises from the above consideration that k(K)-1 is several hundred times larger than k(0)-1, which implies that the probability of state C:K+:Tx is insignificant relative to that of state C:Tx for p < 0.99. This reduces Figure 12 to a simple two-state scheme (Figure 13), where k(C)off = k(0)-1 and k(C)on = (1 - p)*k1. Both our findings that k(C)off is independent of [K]o and k(C)on decreases upon increasing [K]o are fully consistent with this interpretation. In principle, the [K]o dependence of k(C)on could be used to estimate the dissociation constant of K+ binding to the outer site, K(0)d. With the questionable assumption that sodium ions do not compete significantly for the same site, we can tentatively use for p the expression:
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Since we have data only for two values of [K]o, 2.5 and 115 mM, our estimates of K(0)d can be only very crude. For [K]o = 2.5 mM, we estimate k(C)on ~ 1/6 k(O)on (i.e., (1 - p) ~ 1/6) and for [K]o = 115 mM k(C)on ~ 1/90 k(O)on [i.e., (1 - p) ~ 1/90]. These two data are roughly consistent, yielding K(0)d estimates of 0.5 or 1.3 mM, respectively. Notice that these guesses imply that the ratio K(Tx)d(0)/K(0)d is in the order of 103, close to our lower estimate for the ratio k(K)-1/k(0)-1. This is an important verification of the physical consistency of Figure 11, which requires that the destabilization of PVIIA binding by K+ entrains a reciprocal effect of PVIIA on K+ binding.
The low value accounting for the voltage-dependent destabilization of PVIIA binding to open Shaker channels may appear in contrast with the model underlying Figure 11. Finding a value of
close to 1 was used by
as the true electrical distance traversed by a single K+ that leaves the cytoplasmic medium and goes all the way through the pore to reach the outermost binding site in the conduction pathway. A plausible, more realistic interpretation is illustrated by the cartoon in Figure 9. The conduction pore can be safely assumed to contain three binding sites, in agreement with classical models proposed to explain single-file diffusion properties of potassium channels (Hille and Schwartz, 1978; see
value of 1/3, and this would yield an apparent overall
of 2/3 = 0.66, consistent with our measurements.
Conclusions
As a consequence of our study, we propose that the dependence of the PVIIA block on channel conductance does not involve state-dependent changes of the molecular interactions of the toxin with the residues that shape the pore vestibule, but rather the indirect modulation of toxin binding by the interaction with cations occupying nearby sites. For our comprehensive modeling of the voltage, [K]o, and state dependence of PVIIA block, we have used a somewhat natural expansion of the scheme proposed by MacKinnon and Miller (1998) for CTX block. Therefore, we believe that a similar analysis could be applied to CTX variants with relatively fast binding kinetics like PVIIA. In general, our analysis suggests an additional potential value of pore-blocking molecules for the study of ion channels, besides their use as probes of the pore-mouth structure. Indeed, a detailed study of the interaction of these substances with permeant ions, by an appropriate evaluation of the effects of such interaction upon the pore blockade, may also provide important information about more intimate properties of the ion-conduction pathway.
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Footnotes |
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Portions of this work have been previously published in abstract form (Terlau, H., A. Boccaccio, B.M. Olivera, and F. Conti. 1999. Biophys. J. 76:A150).
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Acknowledgements |
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We thank Dr. Martin Stocker for providing the Shaker-H4 and Shaker-6-46 RNA. The helpful comments of Dr. Chris Miller on the manuscript are greatly appreciated.
H. Terlau was supported by a grant from the CNR and the SFB "Synaptische Interaktionen in neuronalen Zellmembranen," and F. Conti by Telethon grant 926.
Submitted: March 3, 1999; Revised: May 3, 1999; Accepted: May 11, 1999.
1used in this paper: CTX, charybdotoxin; NFR, normal frog Ringer; Sh-, Shaker
6-46; Tx, toxin
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References |
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