State-dependent action of grayanotoxin I on Na⁺ channels in frog ventricular myocytes

Abstract

1. Distinct properties of grayanotoxin (GTX) among other lipid-soluble toxins were elucidated by quantitative analysis made on the Na⁺ channel in frog ventricular myocytes.

2. GTX-modified current (I_GTX) was induced strictly in proportion to the open probability of Na⁺ channels during preconditioning pulses irrespective of its duration, amplitude or partial removal of inactivation by chloramine-T. This confirms that GTX binds to the Na⁺ channel exclusively in its open state, while batrachotoxin (BTX) was reported to be capable of modifying slow-inactivated Na⁺ channels, and veratridine exhibited voltage-dependent modification.

3. The GTX-modified channel did not show any inactivation property, which is different from reported results with veratridine and BTX.

4. Estimated unbinding rates of GTX were in reverse proportion to the activation curve of GTX-modified Na⁺ channels. This was not the previously reported case with veratridine.

5. A model including unbinding kinetics of GTX and slow inactivation of unmodified Na⁺ channels in which GTX was permitted to bind only to the open state of Na⁺ channels indicated that unbinding reactions of GTX occur only in the closed state.

Some biological toxins that act on ion channels exert their unique actions by modifying specific channel functions. Such toxins have been employed to exhibit the structure- function relationship of Na⁺ channels, as exemplified by the use of tetrodotoxin (TTX) for defining the external vestibule of Na⁺ channels. Grayanotoxin (GTX), batrachotoxin (BTX), veratridine and aconitine, which are classified as toxins binding to Site 2 of the Na⁺ channel (Catterall, 1980), also have unique actions on Na⁺ channels, such as: (1) causing a shift of Na⁺ channel activation to hyperpolarizing transmembrane potentials, (2) the elimination of Na⁺ channel inactivation and (3) binding to the Na⁺ channel in its open state, as is known from the observation that these toxins require repetitive rather than single long-lasting, depolarizing stimuli to modify Na⁺ channels in excitable cells of vertebrates. Besides these common properties among lipid-soluble toxins, there are differences. Unbinding rates of veratridine (Leibowitz et al. 1986) and GTX (Yakehiro et al. 1997) are much faster than that of BTX (Khodorov & Revenko, 1979; Tanguy & Yeh, 1991). Deactivation of veratridine- modified currents (Leibowitz et al. 1986) is much slower than that of GTX (Yakehiro et al. 1997) and BTX (Khodorov & Revenko, 1979), so that tail currents of veratridine-modified currents are prominently large and slower than those of GTX and BTX. Detailed analysis of differences between GTX and other lipid-soluble toxins provides important clues in solving the molecular mechanism responsible for gating functions of Na⁺ channels, when combined with accumulated knowledge on the molecular mechanisms of GTX (Seyama et al. 1988; Tsuji et al. 1991; Yakehiro et al. 1993, 1997, 2000) and its binding sites on the Na⁺ channel protein (Ishii et al. 1999; Kimura et al. 2000). For example, in parallel with common properties among lipid-soluble toxins, common binding sites (I433, N434 and L437 of the μ1 Na⁺ channel isoform) among GTX (Ishii et al. 1999), BTX (Wang & Wang, 1998) and veratridine (Wang et al. 2000) have been reported in D1S6. On the other hand, Y1586 in D4S6 is relevant only to GTX action (Kimura et al. 2000). However, quantitative information of GTX modification is still insufficient to explain these differences. We need to address questions such as: (1) does GTX modification occur exclusively in the open state? (2) how does inactivation interfere with GTX modification, or vice versa? and (3) how does GTX dissociate from the Na⁺ channel? Thus, in the present study, a quantitative analysis was made to reveal distinct properties of GTX among other lipid-soluble toxins. From these observations we could propose a model that would explain the common behaviour of lipid-soluble toxins as well as those specific to GTX.

METHODS

Cell preparations

Frogs (Rana catesbeiana) were killed by decapitation and the spinal cords were destroyed. Animals were used in accordance with the guiding principles for the care and use of animals approved by the council of the Physiological Society of Japan. Single ventricular myocytes were taken from the hearts using essentially the same technique as described previously (Seyama & Yamaoka, 1988). Briefly, the heart was mounted on a Langendorff apparatus and perfused retrogradely via the aorta with a Ca²⁺-free solution containing (mm): 93.5 NaCl, 5.4 KCl, 5.0 MgSO₄, 20 glucose, 20 taurine, and 10 Hepes, pH 7.2 (adjusted with NaOH), plus a mixture of Yakult collagenase (0.040 mg ml⁻¹; Yakult, Tokyo, Japan), Wako collagenase (0.40 mg ml⁻¹; Wako Pure Chemical Industries Ltd, Osaka, Japan), type I or type III trypsin (0.06 mg ml⁻¹; Sigma Ltd, St Louis, MO, USA), and crystallized bovine serum albumin (0.5 mg ml⁻¹; Seikagaku corporation, Tokyo, Japan) for 20 min at 32 °C. The dispersed cells were rinsed in KB medium (Isenberg & Klockner, 1982) containing (mm): 70 KCl, 20 K₂HPO₄, 5.0 MgSO₄, 5.0 pyruvate, 20 taurine, 5.0 creatine, 5.0 succinate, 10 glucose, and 0.04 EGTA, pH 7.0 (adjusted with KOH). Then, the cells were centrifuged for 1 min at 65 g. After eliminating the cell debris, the collected cells were maintained at room temperature for 1 h and then stored at 4 °C until needed for experimental use.

Experimental solutions and chemicals

For measuring the whole-cell Na⁺ current, the composition of the external solution was (mm): 90 NaCl, 15 tetraethylammonium chloride, 9 MgCl₂, 1 CaCl₂, 0.005 LaCl₃, and 10 Hepes. The pH of the external solution was adjusted to 7.2 with NaOH. The internal solution consisted of (mm): 60 CsF, 40 CsCl, 20 NaF, 5 EGTA, and 5 Hepes. The pH of the internal solution was adjusted to 7.0 with CsOH.

To assess the effects of grayanotoxin I (GTX I) on whole-cell Na⁺ currents, GTX I (300 μm) was added to the pipette solution, because GTX is known to act intracellularly (Seyama et al. 1988).

The structural formula of GTX I is shown in Fig. 1A. GTX I was kindly provided by Professor Emeritus J. Iwasa of Okayama University, Faculty of Agriculture, Okayama, Japan. Stock solutions of GTX I were dissolved in dimethyl sulfoxide at a concentration of 10⁻¹m.

Figure 1. GTX modification of Na⁺ channels.

A, structure of GTX I. B, family of unmodified Na⁺ currents elicited by a variable step depolarization (-100 to +50 mV) from the holding potential (-120 mV), in 10 mV increments. C, family of modified Na⁺ currents elicited by clamp steps, as in A, but preceded by 300 conditioning prepulses from -80 to -30 mV (pulse duration and interpulse interval, 20 and 100 ms, respectively). Experiments in B and C were conducted with pipette solutions containing 300 μm GTX I. D, I-V relation for I_Na (▪) and I_GTX (○) obtained from current families shown in B and C, respectively. E, activation curve for peak I_Na (▪) (n = 10) and I_GTX (○) (n = 19). Data were fitted by Boltzmann's equation (1 - 1/(1 + exp((V - V_½)/k))). V_½ values and slope factors (k) were -72.5 and 8.94 mV for I_GTX and -22.3 and 7.42 mV for I_Na.

Ionic current recordings

Whole-cell patch pipettes with a resistance of less than 2 MΩ were used for obtaining optimum voltage control. Whole-cell currents (filtered at 5 kHz) were recorded using a TM-1000 amplifier (ACT ME Laboratories, Tokyo, Japan). More than 80 % of the series resistance was compensated to minimize voltage-clamp errors. Recordings were started 10 min after establishing a whole-cell recording configuration. The whole-cell membrane currents were digitized at a sampling rate of 20-100 kHz with a 12-bit analog-to-digital converter (DigiData 1200 interface; Axon Instruments, Foster City, CA, USA), controlled by pCLAMP software (Axon Instruments). Digitized currents were saved to a computer hard drive. We always isolated TTX-sensitive currents in measuring GTX-modified Na⁺ currents, such that the background current recorded in the presence of TTX (0.3 μm) was subtracted from the total current. All experiments were conducted at room temperature (23-26 °C). Data are presented as means ±s.d. along with the number of observations (n), unless otherwise stated. Statistical significance between groups was determined by Student's t test with P < 0.05 considered statistically significant. Numerical solutions for differential equations were computed using either Berkeley Madonna (University of California Department of Molecular and Cellular Biology, Berkeley, CA, USA) or homemade software with the aid of Microsoft Visual Basic (Microsoft, Redmond, WA, USA).

RESULTS

GTX-evoked modification of Na⁺ channels in frog ventricular myocytes

Internal application of 300 μm GTX I produced little modification of the Na⁺ current in the absence of repetitive conditioning prepulses (Fig. 1B); by contrast, with 300 conditioning prepulses, GTX I produced extensive Na⁺ channel modification. The transient currents, which appeared at membrane potentials more positive than -40 mV, were suppressed in amplitude, and sustained currents started to flow at large negative membrane potentials (Fig. 1C and D). We refer to these sustained currents, elicited by depolarizing prepulses, as currents through GTX-modified Na⁺ channels (I_GTX). The transient currents evoked without prepulses are referred to as currents through unmodified Na⁺ channels (I_Na). The activation curves for unmodified and GTX-modified Na⁺ channels (Fig. 1E) were obtained by normalizing the chord conductance at each potential to the corresponding maximum chord conductance, as previously described (Yakehiro et al. 2000). One noteworthy point is that GTX I shifts the activation curve in the hyperpolarizing direction by 50 mV.

Having shown that GTX I modifies activation of the Na⁺ channel, we next examined how GTX I affects channel deactivation. Figure 2A and B shows typical tail currents through unmodified and GTX-modified Na⁺ channels, respectively. Dashed lines superimposed on decaying currents in Fig. 2B indicate single exponential fits. The time constants (τ) fitted to these tails are plotted in Fig. 2C against selected membrane potentials at which we recorded the I_Na tails (-160 to -40 mV) or I_GTX tails (-160 to -80 mV). The values below -120 mV for GTX-modified channels and -60 mV for unmodified channels given in Fig. 2C reflect only channel deactivation, because activation of Na⁺ currents cannot occur at potentials more negative than these threshold potentials (-120 mV and -60 mV). Time constants (τ) for unmodified Na⁺ channels showed little voltage dependency between -160 mV (0.07 ± 0.02 ms (n = 4)) and -60 mV (0.12 ± 0.03 ms (n = 4)), whereas τ for GTX-modified Na⁺ channels had a steep voltage dependency between -160 mV (0.09 ± 0.04 ms (n = 4)) and -120 mV (0.57 ± 0.26 ms (n = 4)). These data indicate that GTX I affected deactivation of the Na⁺ channel.

Figure 2. Effect of GTX I modification on deactivation.

A, family of tail currents through unmodified Na⁺ channels. Membranes at a holding potential of -120 mV were subjected to a brief (1 ms) step depolarization to 0 mV to open unmodified Na⁺ channels and then repolarized to a potential between -40 and -160 mV (20 mV steps) to evoke current tails. B, family of tail currents through GTX-modified Na⁺ channels. Tail currents were obtained from the same cell as in A. Following 300 conditioning prepulses to modify Na⁺ channels, I_GTX was elicited by a 150 ms step depolarization from the holding potential (-120 mV) to 0 mV and then repolarized to a potential between -40 and -160 mV (20 mV steps) to evoke modified current tails. GTX-modified tail currents decayed monotonically as the single exponential fits are superimposed on the currents with dashed lines. C, time constants of tail currents for unmodified and GTX-modified Na⁺ channels. Each tail current in A or B was fitted by a single exponential function and time constants were plotted against membrane potential on a semilogarithmic scale. A pair of data for modified and unmodified Na⁺ channels were taken from identical cells (n = 4). * Significant difference (P < 0.05) between unmodified and modified tail currents at the same membrane potential.

Development of GTX modification

To assess the time course for development of GTX modification, we measured I_GTX (at -80 mV) as a function of the number of conditioning prepulses (-30 mV, 20 ms). I_GTX amplitude has been plotted in Fig. 3 (filled squares) against the cumulative duration of conditioning prepulses. As the number of prepulses was increased from 0 to around 300 (corresponding to 36 s in conditioning period in Fig. 3), I_GTX grew exponentially to a plateau, which began to decay with the application of > 400 prepulses due to slow inactivation (see detail in Discussion). Therefore, a single exponential curve was fitted to data obtained with < 300 prepulses, giving a time constant of 8.18 ± 1.80 s (68.1 ± 15.0 prepulses; n = 5).

Figure 3. Development of GTX modification.

GTX modification as a function of prepulse number. Channels were modified by progressively increasing the number of conditioning prepulses; in each case, I_GTX was elicited 10 ms after the final prepulse by a test depolarization from the holding potential (-120 mV) to -80 mV (see inset). Test I_GTX has been normalized to the value at 36 s (equivalent to 300 prepulses), and plotted against elapsed time following conditioning period (▪). A single exponential function has been fitted to the data points below 300 prepulses, giving a time constant of 8.18 ± 1.80 s (68.1 ± 15.0 pulses) (n = 5). Recordings of GTX-modified current induced by the indicated number of conditioning prepulses are shown in the panel above the graph.

Recovery from modification of GTX I

We determined the time course of Na⁺ channel recovery from GTX modification (Fig. 4A) using the four-step protocol depicted in the inset to Fig. 4A: (1) Na⁺ channels were modified (300 conditioning prepulses), (2) I_GTX was evoked at -80 mV, 10 ms after the final prepulse, (3) modified channels were permitted to recover at the holding potential (-120 to 0 mV) for a variable interval, and (4) the extent of recovery was assessed by a test pulse. Test I_GTX was normalized to the current evoked 10 ms after the conditioning period. The resultant plots in Fig. 4A display the time course for recovery from modification at different holding potentials. The time course was well fitted by an exponential function. The monoexponential time course for I_GTX recovery, which reflects a single kinetic process, is likely to result from a balance between channel dissociation and association rates of GTX. During the recovery period further channel modification probably did not occur, because the exponential curves in Fig. 4A fell asymptotically to zero. Recovery time constants were plotted against the holding potential in Fig. 4B (filled squares), and these data were adequately fitted by Boltzmann's equation. The voltage dependency of the time constants for recovery from modification and activation of GTX-modified Na⁺ channels coincided to a striking degree (see Fig. 1E), indicating that the kinetics of GTX unbinding are closely related to the activation voltage dependence for GTX-modified Na⁺ channels. The result contrasts with reported unbinding time constants of veratridine, which exhibited a voltage dependency that is far from that of the activation of veratridine-modified Na⁺ channels (Fig. 10 in Leibowitz et al. 1986). A quantitative analysis of this phenomenon is given in Discussion.

Figure 4. Recovery from GTX modification.

A, time course for recovery from GTX modification, using the protocol depicted in the inset. GTX modification was induced as in Fig. 1C. Following conditioning, the membrane was repolarized to -120 mV for 10 ms and a reference I_GTX was elicited by a 40 mV step depolarization (t = 0 s and I_GTX(t)/I_GTX(t = 0) = 1). Then, channels were permitted to recover from modification for a variable period (0-150 s) at a holding potential between -120 and 0 mV. Recovery from modification was assessed by a clamp back to -120 mV for 10 ms and again recording I_GTX elicited by a 40 mV clamp step. The time course of recovery from GTX modification followed single exponential kinetics at all potentials examined. B, the time constants (τ) for recovery from modification, obtained in A, have been plotted against holding potential (▪). Data have been fitted by an empirical form of Boltzmann's equation, i.e. 62.3 s + (17.4 s - 62.3 s)/(1 + exp((E+ 67.2 mV)/10.8 mV)) (dashed line), where E is membrane potential. ○, numerical prediction of a kinetic scheme in which GTX is permitted to dissociate only from the closed state of the Na⁺ channel (see Discussion). C, replot of decaying test I_GTX in various membrane potentials in A against the membrane potential. This presentation can be interpreted as steady-state inactivation property of GTX-modified Na⁺ channels at various membrane potentials with various further reductions of I_GTX due to unbinding of GTX. However, data within 5 s are almost free from the unbinding effect of GTX.

Steady-state inactivation of GTX-modified Na⁺ channels

A property of steady-state inactivation of GTX-modified Na⁺ channels can be examined by applying the pulse protocol shown in Fig. 4A. A replot of the test I_GTX in Fig. 4A against the membrane potential is shown in Fig. 4C. At 1 s, where the effect of unbinding is minimal, no appreciable steady-state inactivation is detected. Further continuation of the conditioning pulse to 5 s did not show an apparent reduction in test I_GTX between -60 and 0 mV, although a reduction in test I_GTX was observed due to unbinding of GTX at more hyperpolarized potentials. These data contrast with a BTX study (Fig. 2 in Wang & Wang, 1992), where about 40 % reduction in BTX-modified current was observed at -60 mV with 5 s conditioning pulses.

GTX modification by a single prepulse

As GTX is thought to bind to the open state of Na⁺ channels, we also examined the relationship between the running time integral of Na⁺ channel conductance (T_oNa in eqn (1a) below) and I_GTX (Fig. 5A). Total charge flowing through Na⁺ channels during a prepulse was computed by integrating I_Na evoked by the prepulse. We divided the total charge by the driving force for Na⁺ to obtain the integrated channel conductance (T_oNa):

(1a)

or

(1b)

where E is the potential at which I_Na was elicited, and E_Na is the reversal potential for Na⁺. On a single channel basis (eqn (1b)), N is the functional number of channels in a cell, g_Na is the single channel conductance and P_o is the open probability.

Figure 5. Relationship between the extent of channel opening and degree of modification by GTX.

A, GTX modification induced by a single conditioning prepulse of variable duration. Pulse protocol used is depicted in inset. From a holding potential of -120 mV, a prepulse of variable duration was used to modify Na⁺ channels at -30 mV. The extent of the modification was assessed with a test pulse to -80 mV at an interpulse interval of 10 ms. Test I_GTX was averaged over 6 trials in one cell and plotted against the prepulse duration (▪). The integrated channel conductance during the prepulse, T_oNa, has also been plotted as a function of prepulse duration (continuous line) and scaled to match the time course of I_GTX. T_oNa, which was calculated according to eqn (1a) (see Results), provides an index of total amount of channel opening during a prepulse. B, I_GTX obtained at various prepulse durations and voltage levels (as indicated) were plotted against T_oNa. The inset graph is a replot of the data on compressed scales. Filled and open symbols represent data obtained without and with application of chloramine-T (CT, 1 mm), respectively. The association rate constant for GTX, k_on = 1.54× 10⁴ s⁻¹m⁻¹ (‘composite’ value in Table 1) was calculated from the slope of the best-fitting linear function (continuous line).

Membranes, clamped to a holding potential of -120 mV, were subjected to a 90 mV conditioning depolarization of variable duration, then to a brief interval (10 ms) of repolarization at the holding potential, and finally to a test pulse to -80 mV to assess I_GTX as a function of prepulse duration (Fig. 5A, inset). Test currents were averaged over 6-15 trials. Because I_GTX (Fig. 5A, squares) and T_oNa (Fig. 5A, continuous line) were virtually identical functions of the prepulse duration, we concluded that GTX modifies the Na⁺ channel exclusively in its open state. The relationship between I_GTX evoked by a single prepulse of variable duration or amplitude and T_oNa is shown in Fig. 5B for all examined cells. The relationship between T_oNa and I_GTX is seen to be linear regardless of the amplitude or duration of the conditioning prepulse, thereby indicating that GTX modification occurred in proportion to the integral of Na⁺ channel conductance. Thus, once the channels were open, modification rates by GTX were not influenced by voltage. This result is not totally compatible with that of veratridine. Sutro compared the voltage dependency of veratridine-evoked tail currents with the integral of Na⁺ permeability during a single pulse (Fig. 8 in Sutro, 1986). In his case, veratridine-evoked tail currents did not follow the integral of Na⁺ permeability above -35 mV.

In order to confirm that GTX binds to the open state of the Na⁺ channel, we used chloramine-T (CT) to remove Na⁺ channel inactivation. After applying 1 mm CT for 1-2 min in the bath solution, the inactivation rate was slowed and a substantial non-inactivating current component was observed (Fig. 6A). CT did not modify the I-V relation for the peak Na⁺ current as steady-state current developed (bottom left in Fig. 6A) as was shown in a previous study (Wang, 1984). When I_GTX, induced by a single conditioning pulse, was compared before and after application of CT (Fig. 6B filled squares and open circles, respectively), the degree of GTX modification was far greater after CT treatment. In CT-treated cells, I_GTX was increased as a function of time and did not approach a steady state, indicating that GTX modification continued to occur throughout the conditioning period used, presumably due to an abundance of non-inactivated Na⁺ channels. In contrast, in untreated cells, GTX modification quickly reached saturation at a relatively low level, indicating that fewer channels were available for modification. Although there was a considerable difference between CT-treated and untreated cells in the degree of GTX modification, the relation between I_GTX and T_oNa was the same (Fig. 5B). These results indicate that the degree of channel modification depended only on how much channel opening occurred in the conditioning period regardless of any difference in the time course of inactivation. Thus, the inactivation process diminished channel modification only by means of a reduction in the availability of the open state.

Figure 6. Effect of chloramine-T on GTX modification.

A, top left: I_Na in the absence of chloramine-T (CT). Family of I_Na was evoked by step depolarization from the holding potential (-120 mV) to a potential between -100 and +40 mV (in 10 mV steps). Bottom left: I_Na in the presence of CT (1 mm). Family of Na⁺ currents was evoked after 2 min in CT by the identical pulse protocol employed in the absence of CT. Right: I-V relationships with (○) and without CT (▪). B, relationship between prepulse duration and I_GTX or T_oNa. Protocol used is depicted in Fig. 5A, with prepulse potential set to 0 mV instead of -30 mV, in order to maximize the difference in inactivation time course imposed by CT. Test I_GTX was assessed at -80 mV in the absence (▪) or presence of 1 mm CT (○). T_oNa has been scaled to match the time course of I_GTX without (continuous line) or with CT (dashed line).

Effect of slow inactivation on GTX modification

As Furue et al. (1998) have shown, there is a slow inactivation characteristic in the frog cardiac Na⁺ channel that develops in a few seconds to several minutes. Thus, during long repetitive preconditioning pulses, developed slow inactivation might affect the availability of the Na⁺ channel so that it reduces the GTX-modification rate as shown in Fig. 3. We determined the I_GTX-T_oNa relationship (Fig. 7A) during development of slow inactivation as in Fig. 5B. As shown in the inset of Fig. 7A, development of slow inactivation can be assessed by comparing unmodified fast inactivating currents elicited by brief depolarizations to -20 mV before and after a long deporarization (51 s) to -20 mV. Modified currents elicited by pulses to -80 mV (I_GTX) are plotted against the running time integral of unmodified currents elicited by preceding brief (≈2-15 ms) test pulses. This procedure revealed a linear relationship exactly the same as that with a fast inactivation process or with a partially disturbed inactivation by CT (the continuous straight line in Fig. 7A is identical to the one in Fig. 5B). Thus, here we conclude that the Na⁺ channel cannot be modified by GTX in the slow inactivated state.

Figure 7. Interference of slow inactivation with GTX modification.

A, effect of slow inactivation on GTX modification. In the presence of 300 μm GTX I, GTX modification induced by channel openings elicited with a brief (≈2-15 ms) conditioning pulse was assessed by the difference between I_GTX before and after the conditioning pulse to -20 or 0 mV for ≈2-15 ms (I_GTX) using a triple pulse protocol (a combination of three pulses to -80 mV for 50 ms, to -20 mV or 0 mV for ≈2-15 ms and to -80 mV for 50 ms separated by brief gaps to -120 mV for 10 ms). I_GTX with (○) and without (▪) a long depolarization for 51 s set between the I_GTX-obtaining triple pulse protocol were plotted against T_oNa. Conditioning pulses (the second pulse of the I_GTX-obtaining triple pulse protocol) were varied in amplitude (-20 or 0 mV) or duration (2-15 ms) to change T_oNa. I_GTX-T_oNa plots (averages of 10 trials for each plot, shown with s.d.; data were obtained from three cells) are on the same linear line irrespective of whether slow inactivation was induced or not. This continuous straight line is identical to the one that exhibits the linear relation of data in Fig. 5B. B, time course of slow inactivation. The time courses of development of slow inactivation of the Na⁺ channel were measured with or without GTX I in the pipette solution using the double pulse protocol shown in the inset (a gap of 40 ms between the two pulses was sufficient to allow full recovery of fast inactivation). Peak I_Na was normalized to that at t = 0. The conditioning pulses to -20 mV were varied between 0 and 500 s so that slow inactivation proceeded with two time constants, τ_slow and τ_ultraslow (τ_slow = 3.0 ± 0.53 s and τ_ultraslow = 276 ± 60 s with GTX, n = 3; τ_slow = 3.0 ± 0.34 s and τ_ultraslow = 222 ± 2 s, n = 3 without GTX). Representative recordings of I_Na (without GTX) elicited by test pulses are displayed matching the time scale of the graph below.

The development of the slow inactivation process is not affected by GTX. We compared development of slow inactivation in the absence (filled squares) with that in the presence (open circles) of 300 μm GTX I (Fig. 7B). There was no appreciable difference. This result enabled us to incorporate the slow inactivation property (Fig. 8B) obtained separately from GTX-modifying experiments.

Figure 8. Reconstruction of the development of GTX modification during repetitive prepulses.

A, kinetic scheme for interactions of GTX I with the Na⁺ channel, indicating states of the unmodified and GTX-modified (*) Na⁺ channel. Transitions between states are essentially based on the Hodgkin-Huxley equation except that activation of modified channels obeys first order m kinetics. Rate constants for some reactions are given adjacent to arrows. B, original recordings of unmodified Na⁺ current (without GTX I). Currents, sampled every 2.5 s during a train of repetitive prepulses (duration, 20 ms), were divided by Na⁺ driving force and displayed as Na⁺ conductance. Changes in prepulse potential or interval between prepulses greatly affected the time course of Na⁺ channel inactivation. Positions of the individual currents have been matched to the time scale in C. C, reconstruction of the development of I_GTX during repetitive conditioning prepulses, based on the state diagram in A. Simulated values of I_GTX have been plotted against the cumulative duration of the conditioning prepulses (Prepulse duration) for comparison with experimental data. Simulation was performed by including inactivation parameters derived from the experimental data in B (thick lines). The thin dashed line represents an estimate of I_GTX, assuming complete absence of slow inactivation of I_Na during repetitive prepulses. ▪, experimental data taken from Fig. 3; other symbols also correspond to experimental data (see text for further details). Inset shows I-V relationships for unmodified Na⁺ current (▪), for which data were obtained from the same cell that was used in B, and the simulated I-V relationship for GTX-modified current (○).

DISCUSSION

Our quantitative approach to examining functional properties of GTX could reveal unique characteristics of GTX among other lipid-soluble toxins: voltage independency of the rate of modification, a unique unbinding property, no inactivating property of GTX-modified channels. These uncovered features combined with accumulated data for GTX and frog Na⁺ channels previously published, e.g. channel conductance and open probability of GTX-modified channels, conductance ratio of modified channels to unmodified channels (Yakehiro et al. 1997, 2000) and properties of slow inactivation of frog Na⁺ channels (Furue et al. 1998), etc., enabled us to build a complete model explaining GTX modification. The model is based on the Hodgkin-Huxley equation with the modification that a GTX-modified channel has a lower single-channel conductance (one-quarter of the unmodified conductance) and follows first order m kinetics. This model ultimately uses only two simple hypotheses; namely, that GTX can bind only to open unmodified channels and unbind only from closed modified channels, and is capable of simulating all behaviour specific to GTX as well as those common to lipid-soluble toxins.

Basis for the open-state dependency of GTX binding

The reaction describing GTX binding to the Na⁺ channel is specified as follows:

(2)

Therefore, taking G* to represent the number of GTX-modified channels, and O as the number of unmodified open channels, we obtain:

(3)

G* and O, in terms of recorded Na⁺ currents, are given in eqns (4) and (5):

(4)

(5)

where E_test represents the voltage applied during test pulses to evoke I_GTX; E_cond, the voltage applied during a conditioning pulse to induce Na⁺ channel opening; g, the single channel conductance; and P_oGTX, the open-state probability of modified channels. Combining eqns (3) to (5) and substituting the experimentally derived values, g_GTX/g_Na = 0.25 (Yakehiro et al. 2000) and P_oGTX = 0.18 at -80 mV (see below), we obtain eqn (6):

(7)

in which

In the experiments shown in Fig. 5A, data for I_GTX and I_Na were simultaneously available. Hence, eqn (6) was fitted to these experimental data by substituting values for k_on or k_off. The calculations yielded a k_on value of 2.08 (± 0.28) × 10⁴ s⁻¹m⁻¹. k_off turned out to be too small to be accurately determined. To simplify subsequent analysis, we eliminated the k_offI_GTX term from eqn (6). This was justified for the following reasons: (a) GTXk_on is much larger than k_off, (b) I_GTX induced by a single conditioning pulse is far too small compared with I_Na, and (c) the dissociation time constant for GTX at -80 mV (k_off, ≈30 s) is too slow to affect I_GTX in the type of experiment shown in Fig. 5A, in which comparatively brief pulses (≈100 ms) were used to modify Na⁺ channels. We integrated the modified form of eqn (6) to yield eqn (7):

(7)

Equation (7) predicts that the slope of the linear relationship between I_GTX and T_oNa (see Fig. 5B) should be proportional to k_on. Using eqn (7), we determined k_on at different membrane potentials, and in the absence or presence of Na⁺ channel inactivation (eliminated by CT). The calculated values of k_on are listed in Table 1.

Table 1.

Estimated k_on (s⁻¹ M⁻¹) for GTX binding

Membrane potential of prepulse	Estimated kon± S.D	Number of cells
−40 mV	1.70 (± 1.34) × 104	3
−30 mV	1.92 (± 0.07) × 104	10
−20 mV	1.54 (± 0.13) × 104	3
0 mV	1.59 (± 0.16) × 104	6
0 mV (CT)	1.50 (± 0.03) × 104	7
Composite data*	1.54 (± 0.03) × 104	29

^*Value calculated from best-fitting linear function through all data points in Fig. 5B (for prepulse potentials between −40 and 0 mV).

Computed values of k_on were similar over a wide range of membrane potentials and were not affected by removal of Na⁺ channel inactivation. Thus, the binding kinetics of GTX reflected the extent of channel opening rather than the level of transmembrane potential or the kinetics of channel inactivation.

GTX I cannot unbind from GTX-modified channels in the open state

The relation between the time constant for recovery from channel modification and membrane potential had a rather characteristic feature: time constants at potentials below -40 mV became larger by depolarization, but above -40 mV, reached a steady state. There are two possible explanations. First, dissociation of GTX I from the channel could be state dependent, and the resultant time constant for recovery could be the outcome of GTX I dissociation from the two different states (i.e. open and closed), each having a unique dissociation rate. Thus, changes in voltage could produce various combinations of the two states, resulting in the observed variation of the overall time constant with membrane potential. Second, time constants could simply be a function of the membrane potential, as predicted by Boltzmann's equation. One line of evidence favouring the former hypothesis is that the relationship between the time constant for recovery from modification and membrane potential is remarkably similar to the activation curve for the modified channels, indicating that unbinding of the ligand could be governed by channel activation kinetics. To gain insight into the mechanism of unbinding, we reconstructed the unbinding process in a framework in which GTX I is permitted to bind to the channel only in the open state. The calculations required an estimate of open state probability (P_o) of modified and unmodified sodium channels as a function of membrane potential. Fortunately, this information was available from a single-channel study conducted in the same preparation used in the present study (Yekahiro et al. 2000). Maximum P_o for unmodified Na⁺ channels (P_oNa) in frog ventricular myocytes was reported to be 0.32 at -10 mV, and steady-state P_o for GTX-modified channels (P_oGTX) was 0.50 at -60 mV (Yakehiro et al. 2000). These data enabled us to deduce the open-state probability at any potential by matching the P_o for unmodified (0.32 at -10 mV) and modified (0.50 at -60 mV) channels to the corresponding point on our activation curves (Fig. 1E). These curves provide respective values of 0.78 and 0.77 for unmodified (-10 mV) and modified channels (-60 mV); hence, P_oNa =m(E)× 0.32/0.78 and P_oGTX =m*(E)× 0.50/0.77, where m(E) and m*(E) represent the fraction of unmodified and modified channels at membrane potential E on the activation curve. Using the above rationale, maximal open probability of the modified channels (P_oGTX) attained at potentials more positive than -40 mV was estimated to be 0.65. The time constant for recovery from the GTX-modified state can be computed from:

(8)

where τ_c and τ_o indicate recovery time constants for each component (from closed and open state, respectively), based on the following two assumptions. Only the two discrete unbinding rates characteristic of the open and closed state govern the unbinding of GTX. There is no flux of binding during the recovery phase of GTX modification, because steady-state values of the fraction of modified channels approach asymptotically zero at all membrane potentials examined in the experiment of Fig. 4A.

Using estimated values of P_oGTX (appropriate to each membrane potential), eqn (8) was fitted to the experimental data in Fig. 4B (filled squares); τ_c and τ_o were thus determined to be 21.7 s and 1.13 × 10⁵ s, respectively. This indicates that dissociation of GTX I from the open channels is extremely slow and can be considered negligible. Incorporation of the resultant two discrete time constants for recovery from channel modification produced the estimated values (between -100 and 0 mV) given in Fig. 4B (open circles). Thus, it can be concluded that GTX was only able to dissociate from the closed modified sodium channel, and rate constants for unbinding of GTX from this closed state were independent of membrane potential. Therefore, the membrane potential affected the dissociation or association rate of GTX only by changing the open probability of the channel.

Mechanisms for slowing Na⁺ channel deactivation

As shown in Fig. 2, GTX I prolonged the time course of tail currents. Because both veratridine and BTX have been reported to slow deactivation of Na⁺ channels (Khodorov, 1985; Sutro, 1986; Zong et al. 1992; Ulbricht, 1998), such an effect has been considered to be a common characteristic of Site 2 toxins. If the prolongation of tail currents were due to occlusion of the activation gate by GTX, as observed with polycyclic cations (pancuronium, N-methylstrychnine) that sterically hinder channel deactivation (Yeh & Narahashi, 1977; Cahalan & Almers, 1979), the decay of tail currents should represent the time course of unbinding of GTX I from channels. However, time constants for the tail currents actually observed were three orders of magnitude smaller than those for GTX I unbinding. Thus, it is reasonable to speculate that GTX I does not function as a plug for the activation gate, but rather interferes in the interaction of the activation gate with the voltage sensor, for example by reducing the order of activation kinetics from three to one.

Reconstruction of the development of GTX modification during prepulses and kinetic characteristics of GTX modification

The running time integral of Na⁺ channel conductance (T_oNa) is a function of available unmodified channels so that it can be influenced by the rate of GTX modification and inactivation of unmodified channels. In the presence of GTX I, since both modification by GTX and inactivation of unmodified channels should have occurred during a prepulse of 20 ms, we did not know how exactly both processes contribute to a change in T_oNa. Especially in giving long trains of conditioning pulses, slow inactivation could also reduce T_oNa. Therefore, we estimated the number of unmodified Na⁺ channels in the open state during a long train of prepulses, by independently collecting a series of records of the Na⁺ current during a train of conditioning prepulses without GTX I. Figure 8B shows original records with various prepulse protocols. To facilitate comparison with the integrated channel conductance T_oNa, these current records were divided by the driving force for Na⁺ ions. Although the interval (100 ms) between prepulses was long enough for Na⁺ channels to recover from fast inactivation (Miyoshi et al. 1988), peak amplitude of I_Na was gradually attenuated (upper most and lower most records in Fig. 8B). In frog ventricular myocytes, this decrease in amplitude was considered to be due to slow inactivation of Na⁺ channels (Furue et al. 1998). Slow inactivation has been reported to develop exponentially with time constants, at -40 and -20 mV, of 4 and 7 s for the slow component, and 500 and 550 s for the ultraslow component. By contrast, as interpulse intervals were shortened, peak I_Na was rapidly attenuated (middle records in Fig. 8B) due to fast inactivation.

From the results in Fig. 4B and Fig. 5, we postulate, as a full description of the association and dissociation of GTX I with the Na⁺ channel, the state diagram given in Fig. 8A. Using the state diagram with model parameters obtained empirically (including activation parameters for both modified and unmodified Na⁺ channels shown in Table 2), we have calculated the distribution of the five postulated states of the sodium channel during a train of repetitive pulses. The slow inactivation process was accounted for in the calculations, using the experimental data in Fig. 8B. From the same cell represented in Fig. 8B, the I-V curve for unmodified Na⁺ channels was obtained, which provided the absolute values of ionic currents used in the simulation. The estimated time course for development of I_GTX was simulated in Fig. 8C (thick lines) as a function of the number of prepulses applied. Simulated I_GTX, following 300 conditioning pulses to -30 mV (interpulse interval, 100 ms; pulse duration, 20 ms), had a peak value of 685 pA at -80 mV. The I-V curve for the modified Na⁺ channels was estimated with the aid of the activation curve for I_GTX (see Fig. 1E). The relationship between unmodified and modified I-V curves obtained here is quite unique and consistent with the experimental data. To estimate this relationship, we used the normalized chord conductance, i.e. the ratio of chord conductances for I_GTX (E_m≥ -30 mV):I_Na(E_m≥ 10 mV). The simulated value of 0.111 is comparable with the experimentally observed ratio, 0.123 ± 0.031 (n = 10).

Table 2.

Estimated parameters for Na⁺ channel kinetics

	Non-modified Na+ channel (n = 13)				GTX-modified Na+ channel (n = 10)
	αmNa (s−1)	βmNa (s−1)	αhNa (s−1)	βhNa (s−1)	αmGTX (s−1)	βmGTX (s−1)
−80 mV	—	—	—	—	15*	68.3*
−30 mV	1250 ± 350	800 ± 220	3.55 ± 3.12	124 ± 36	76.4 ± 21.8	41.2 ± 11.7
−20 mV	2280 ± 620	542 ± 240	7.04 ± 4.85	432 ± 107	302 ± 50	162 ± 27
−10 mV	3770 ± 1050	7.78 ± 6.00	6.63 ± 5.03	970 ± 300	548 ± 136	311 ± 87
0 mV	5900 ± 1480	3.80 ± 3.38	6.53 ± 5.32	1260 ± 260	2240 ± 890	1070 ± 540

^*Values are obtained from dissociation time constant = 1/(α_mGTX+β_mGTX) (at −80 mV) from the experiment in Fig. 2 and estimated P_oGTX =α_mGTX/(α_mGTX+β_mGTX) from the activation curve shown in Fig. 1E.

Next, we compared the calculated time course for development of I_GTX with increasing numbers of prepulses with experimental data (see Fig. 3). These experimental data (normalized to maximum current) were scaled to the value of simulated I_GTX (685 pA) at the conditioning period of 36 s (equivalent to 300 prepulses). The simulated time course closely fits the experimental data (filled squares), and even reproduces the gradual decrease in I_GTX beyond 40 s (Fig. 3). This decrease is indeed due to slow inactivation, because without slow inactivation the estimated I_GTX time course showed an increase rather than a decrease with time (Fig. 8C, dashed line), which is contrary to what we observed. The simulated I_GTX time course was also in close agreement with experimental observation for prepulses to membrane potentials more positive than -30 mV or interpulse intervals shorter than 100 ms. These results indicate that voltage dependency and frequency dependency of modification by GTX are all explained by a simple hypothesis that GTX binds to only unmodified open channels and unbinds from modified closed channels.

Differences of GTX action from other lipid-soluble toxins

Sutro (1986) has reported that, in the case of veratridine, the cumulative time integral of the Na⁺ channel conductance during conditioning prepulses is proportional to the amplitude of the sustained tail current obtained immediately after the termination of a test pulse, suggesting that veratridine binds to the Na⁺ channel in its open state. However, he also showed that, at membrane potentials more positive than -35 mV, the modification rate was increased with regard to the integral of the Na⁺ channel conductance. This result implies that veratridine binding is accelerated by the two processes, i.e. a process leading to open state conformation of unmodified sodium channels and another process that requires potential energy to further stabilize the bound conformation. On the other hand, the rate constant for GTX binding was found to be independent of the membrane potential of conditioning pulses; I_GTX was solely dependent on the running integral of the Na⁺ channel conductance during conditioning pulses (T_oNa), whatever the amplitude of membrane potentials (Fig. 5B).

Slow inactivation disturbed GTX modification in this study as shown in Fig. 7 and Fig. 8. This result was quite distinct from that with BTX reported by Tanguy & Yeh (1991). In their report, BTX could modify virtually all the Na⁺ channels of pronase-treated squid axons in the slow inactivated state, but much more slowly than in the open channel state.

Unbinding processes of GTX and veratridine are much faster than that of BTX, so that we need to give repetitive conditioning pulses to elicit modified currents every time several seconds after cessation of stimuli. However, the voltage dependency of unbinding rate may be more complicated with veratridine compared with GTX, because reported rate constants did not simply follow the activation kinetics of the modified channel (Leibowitz et al. 1986), as seen in those of GTX in this study.

Both veratridine- (Sutro, 1986) and BTX-modified channels (Wang & Wang, 1992) are reported to be subject to inactivation. However, neither lengthening nor increasing the amplitudes of conditioning pulses produced any trace of inactivation in GTX-modified currents. In fact, either increases in the amplitude or increases in the frequency of repetitive stimuli could induce suppression of I_GTX, but here it was actually found to be due to suppression of unmodified currents caused by fast and slow inactivation of Na⁺ channels.