Charybdotoxin binding to Shaker K⁺ channels is temperature sensitive in high external K⁺ but not in high external Na⁺

Protein–protein interactions are fundamental to numerous biological processes, ranging from enzymatic catalysis to signal transduction. The lifespan of these complexes can vary significantly, from milliseconds to years, depending on the binding energy involved. The association and dissociation pathways of protein complexes often involve the formation of high-energy transient intermediate states, collectively referred to as encounter complexes. These complexes are ruled by the activation energy barriers that determine the temperature sensitivity of reaction rates, as described by Arrhenius’ principles (Dill and Bromberg, 2011). However, despite the valuable insights provided by MD simulations, the ephemeral nature of the encounter complex makes it difficult to capture molecular details through in vitro experiments. Here, we tested the temperature dependence of the association and dissociation kinetics of charybdotoxin (CTX) binding to voltage-gated potassium channels (VGKCs) in vitro to determine the Arrhenius parameters of the encounter/exit complex. This was assessed in the presence of K⁺, a permeant ion, and Na⁺, an impermeant one, to investigate the role of pore occupancy in shaping the energy landscape.

CTX, a neurotoxic peptide derived from the venom of Leiurus quinquestriatus, blocks potassium channels and represents a mechanistically simple yet highly informative model for studying protein–protein interactions. This interaction produces robust electrophysiological signals that can be monitored at both macroscopic and single-molecule levels. The Chris Miller group showed first that CTX blocks potassium ion permeation by physically occluding the external pore entrance of large conductance calcium-activated potassium channel (BK), then they showed an identical mechanism for the blockade of VGKC (MacKinnon and Miller, 1988; Goldstein and Miller, 1993).

Structurally, VGKCs consist of homotetrameric α-subunits that form a central potassium-selective conduction pore surrounded by voltage-sensing domains (MacKinnon, 1991; Long et al., 2005). The selectivity filter, near the extracellular end of the pore, interacts with CTX via key residues such as Lys27, which mimics potassium ions by binding to site S1 in the permeation selectivity filter (Ranganathan et al., 1996; Banerjee et al., 2013). Underscoring its mechanistic simplicity, crystallographic studies have revealed no discernible structural changes in the putative open conformation of VGKC upon CTX binding (Banerjee et al., 2013). In addition, pore-occluding scorpion toxin binding seems to be diffusion limited and electrostatically facilitated (Anderson et al., 1988; Miller, 1990; Escobar et al., 1993). These characteristics make CTX–VGKC an ideal model for exploring molecular pathways underlying protein complex association and dissociation.

An intriguing aspect of CTX–VGKC interaction is that the unbinding rate is sensitive to the K⁺ concentration added at the external side, the same side from where the toxin acts. This outcome is incompatible with either a static toxin–channel interaction or total pore closure. We have known for some time that external potassium ions can access the selectivity filter while CTX remains bound. In fact, the location of the selectivity filter was deduced because permeant ions destabilize, from the external side, AgTx-2, a CTX isoform (Ranganathan et al., 1996). This destabilization occurs with a relative effectiveness that mirrors the ion permeation selectivity sequence (Moldenhauer et al., 2019). Since the structure of K⁺ channels does not reveal any direct routes or fenestrations connecting the extracellular space to the selectivity filter, alternative pathways seem unlikely. A more intuitive explanation is that thermal motion induces dynamic behavior in the bound toxin, resulting in transient external accessibility that allows permeant ions to reach the selectivity filter. We refer to these dynamic partial detachments as “wobble.” Supporting this hypothesis, the crystal structure of the CTX–VGKC complex in a Cs⁺-rich solution shows the Lys27 amino group retracted into CTX, with site S1 occupied by a Cs⁺ ion, suggesting alternative, possibly dynamic, binding arrangements (Banerjee et al., 2013). Given its ephemeral nature (see Discussion), wobbling may represent a transition state that contributes to the activation energy of CTX association and dissociation. To test this hypothesis, we examined how external ions, K⁺, a permeant ion, and Na⁺, an impermeant one, influence temperature dependence to assess the activation energies of CTX binding and unbinding to Shaker VGKC channels. We found (1) potassium-specific enthalpy and entropy components in both association and dissociation rate constants, and (2) the association rate in high external K⁺ can be larger than that in high external Na⁺. We propose that the dissociation and association pathways contain wobbling intermediates. In the association, it may increase the fraction of productive collisions between CTX and VGKC, being an evolutionary advantage in a neurotoxin.

Our Shaker construct was derived from the Shaker H4 Δ(6–46) variant, inserted into the pBlueSK vector, and placed under the control of the T7 promoter (Agilent Technologies). The Shaker-K427E mutant was generated as previously described (Goldstein and Miller, 1992). Capped cRNAs were synthesized from a Not I-linearized template using the mMESSAGE mMACHINE T7 transcription kit (Ambion, Life Technologies), resuspended in 10 μl of water, and stored at −80°C. Female Xenopus laevis frogs were obtained from local suppliers and kept in captivity for several months. Typically, 0.03–0.3 ng of cRNA was injected into each Xenopus oocyte for heterologous expression, following protocols and guidelines described previously (Oliva et al., 2005; González-Pérez et al., 2008; Moscoso et al., 2012).

Recordings from cRNA-injected oocytes were obtained ∼20–28 h after injection using the two-electrode voltage-clamp (TEVC) technique with a Warner OC-750C amplifier (Warner Instruments). The recording chamber measured 30 mm in length, 4 mm in width, and 3 mm in depth and was mounted in a Warner RC-24N/PM-1 heating/cooling module (Warner Instruments). Continuous perfusion was maintained with either Hi-Na⁺ or Hi-K⁺ recording solutions. The Hi-Na⁺ solution contained (in mM): 96 NaCl, 2 KCl, 2 CaCl₂, 1 MgCl₂, and 10 HEPES (pH 7.4). For the Hi-K⁺ solution, 96 mM NaCl was replaced with 96 mM KCl. CTX (Alomone Labs) was resuspended at 200 μM in Hi-Na⁺ solution containing 25 μg/ml bovine serum albumin.

Electrodes were filled with 3 M KCl, 1 mM EGTA, and 5 mM HEPES (pH 7.0) and had resistances of ∼1 MΩ. The typical holding potential was −80 mV, and 500-ms voltage pulses (from −70 to +80 mV) were applied from a PC running either WinWCP software (University of Strathclyde, Glasgow, UK) or pClamp software (Molecular Devices), using either a PCI-MIO-16XE-10 card (National Instruments) or a Digidata 1440 (Molecular Devices), respectively.

Temperature was controlled using a TC2BIP controller (Cell MicroControls) interfaced with the Warner heating/cooling module. Recorded traces were exported into pClamp format (Molecular Devices) for signal analysis and curve fitting with Clampfit 10 (Molecular Devices). Data are presented as mean ± SD or, for fitted parameters of averaged data, as parameter ± SE of the parameter fit. Error propagation was performed as described by Diaz-Franulic et al. (2018). Data fits, within 95% confidence limit, were carried out using Origin 6.0 (OriginLab) with the Levenberg–Marquardt method. Statistical significance between curves was assessed using a modified χ² method that includes corrections for non-normality and sample size (Hristova and Wimley, 2023). Although some oocytes were used for measurements at different temperatures, most data can be assumed to be taken independently from separated cells.

As observed with κ-conotoxin PVIIA (κ-PVIIA), a pore-blocking peptide toxin, the application of CTX to Shaker-K427E channels results in slow current relaxations upon channel opening. Voltage-dependent gating in the K427E variant is indistinguishable from that of the parent construct (Fig. 1 A; [Stocker and Miller, 1994]). These CTX-induced slow relaxations occur because the same voltage pulse used to open the channels also destabilizes CTX binding in a voltage-dependent manner (García et al., 1999; Terlau et al., 1999; Moldenhauer et al., 2019; Naranjo and Díaz-Franulic, 2020).

The reaction Scheme 1 is the following:

This equation yields a straight line in a 1/τ versus [CTX] plot, where k_on is the slope and k_off is the intercept. The intercept, k_off, changes with the voltage pulse, while the slope remains nearly voltage independent, in good agreement with the results from the analysis using Eq. 2. We chose Eq. 2 over this methodology because with a single CTX concentration we can obtain k_on and k_off at different voltages. However, the single-concentration method becomes unreliable in Hi-K⁺ conditions when the relaxation amplitude is low—e.g., when ss ≈ ssc (near +90 mV), or near the K⁺ reversal potential (∼0 mV; see Fig. 2). Therefore, for temperature dependence of the rate constants, we present temperature dependence data at +60 mV, where the signal-to-noise ratio was maximal.

The English in each paragraph (including this one) was individually checked using ChatGPT with the instruction “check grammar: ‘Text paragraph…’.” The content was then reviewed to ensure that no unintended changes in meaning were introduced.

Fig. S1 shows how the k_on and k_off were estimated using the variant of Eq. 1a. Data S1 contains the original data for the Figs. 1 and S1; Data S2 contains the original data for Fig. 2; Data S3 contains the original experimental traces used for Fig. 2; Data S4 contains a summary of experimental data in open channels for Figs. 3 and 5; Data S5 and Data S6 contain the data for Figs. 4 and 5.

Shaker K channels expressed in Xenopus oocytes were recorded using the TEVC technique. CTX, at concentrations of 2–20 nM, was applied under continuous perfusion with either Hi-K⁺ or Hi-Na⁺ solution (see Materials and methods for details). The application of CTX to Shaker-K427E channels produces voltage-dependent relaxations in the hundreds-of-milliseconds range. Therefore, we chose to assess CTX blockade using 500-ms voltage pulses (compare Fig. 1, A and B).

Fig. 1, A and B, show two families of current traces obtained in Hi-Na⁺ solution in response to voltage steps ranging from −70 to +90 mV (top panels), in the absence (Fig. 1 A) and presence (Fig. 1 B) of 4 nM CTX. CTX induces slowly increasing potassium currents, which correspond to relaxations from a high-affinity, closed-channel toxin-binding state to a lower-affinity, voltage-dependent binding regime in open channel (Scanlon et al., 1997; García et al., 1999; Terlau et al., 1999; Naranjo, 2002; Moldenhauer et al., 2019; Naranjo and Díaz-Franulic, 2020). The amplitude and kinetics of the relaxations increased with the voltage pulse amplitude, indicating that, in open channels, the toxin binding is destabilized by membrane depolarization. Fig. 1 C shows a family of point-by-point current ratios—CTX-modified traces divided by their corresponding control traces—for pulse voltages >0 mV (see Materials and methods). These ratios, plotted with the same color scheme as their parent traces, originate near a common value at the beginning of the pulse (green arrow), indicating the fractional inhibition in closed channels (ssc). As voltage increases, the amplitude and speed of the relaxations increase. These relaxation traces were fitted with Eq. 2 (blue traces), yielding estimates for ssc, the time constant (τ), and the steady-state inhibition at each voltage (ss; see Fig. 1, D and E).

Using Eq. 1a and 1b, we solved for the association and dissociation rates, k_on and k_off, for each voltage (Fig. 1 F). Consistent with a diffusion-limited association process, k_on values are high and only weakly voltage dependent (Miller, 1990; Goldstein and Miller, 1993). In contrast, k_off accounted for most of the voltage dependency of CTX binding, increasing approximately e-fold for every 40–50 mV of depolarization. The continuous lines in Fig. 1 F represent fits of Eq. 4 to the data. A summary of the fit parameters for CTX binding to Shaker-K427E in Hi-Na⁺ at 20°C is as follows: k_offo = 0.22 ± 0.03 s⁻¹$$⁠, zδ = +0.55 ± 0.05 (n = 10) and k_ono = 0.12 ± 0.01 nM⁻¹s⁻¹, zδ = −0.05 ± 0.06 (n = 10).

To assess the contribution of potassium to the activation energy of CTX binding to Shaker channels, we compared kinetics in Hi-K⁺ and Hi-Na⁺ solutions at different temperatures. We measured the association and dissociation rates between ∼10°C and ∼30°C (see Materials and methods for details). Fig. 2 illustrates two representative temperature comparisons (Δt ≈ 20°C) in Hi-Na⁺ (Fig. 2 A) and Hi-K⁺ (Fig. 2 A′). The “Control” panels show current traces elicited by voltage pulses in the absence of toxin at 12°C and 30°C for Hi-Na⁺ and at 14°C and 33°C for Hi-K⁺. As previously reported, temperature increases both activation and inactivation kinetics (Meyer and Heinemann, 1997). The “10 nM CTX” panels display the corresponding currents in the presence of CTX (see Fig. 1), where inhibition in Hi-Na⁺ appears stronger. The “Fractional current” panels show point-by-point current ratios in Hi-Na⁺ and Hi-K⁺; blue traces represent fits to Eq. 2. In this representation, CTX inhibition behaves very differently between solutions. First, in Hi-K⁺, inhibition of closed channels is much weaker than in Hi-Na⁺ (green arrows; ssc ∼0.60–0.85 versus ∼0.20–0.25, respectively). Second, the relaxation direction differs: in Hi-K⁺, relaxations are downward rather than upward, indicating that, unlike in Hi-Na⁺, CTX inhibition is stronger in open channels for most tested voltages. Thus, in Hi-Na⁺, closed-channel inhibition resembles that of open channels at approximately +20 mV, while in Hi-K⁺, it corresponds more closely to open-channel inhibition at approximately +90 mV. Third, relaxation kinetics remain voltage dependent in both conditions, becoming faster at more positive voltages. Fourth, in both Hi-Na⁺ and Hi-K⁺, toxin affinity for closed channels increases with temperature. In Hi-Na⁺, ssc decreases from ∼0.25 at 12°C to ∼0.20 at 30°C, while in Hi-K⁺, it drops from ∼0.85 at 14°C to ∼0.60 at 33°C. Fifth, the similarity in upward relaxations at 12°C and 30°C in Hi-Na⁺ suggests that CTX inhibition of open channels is only modestly affected by temperature. In contrast, in Hi-K⁺, temperature has a much more pronounced effect, as indicated by the larger amplitude of downward relaxations observed at 33°C. In summary, CTX displays higher affinity at elevated temperatures, and its binding kinetics to open channels in Hi-K⁺ are more temperature sensitive than in Hi-Na⁺.

The point-by-point current ratios shown in the Fractional current panels of Fig. 2, A and A′, were fit to Eq. 2 to obtain the parameters τ (the time constant), ss (the fractional inhibition at equilibrium), and ssc (the fractional inhibition of closed channels). Fig. 2, B–E and B′–E′, presents a comparative analysis based on several experiments similar to those in Fig. 2, A and A′, conducted at 11.8 ± 1.5°C (n = 5) and 30.7 ± 0.4°C (n = 3) in Hi-Na⁺ and at 12.9 ± 0.9°C (n = 6) and 32.4 ± 2.3°C (n = 5) in Hi-K⁺. Fig. 2, B and B′ show the temperature sensitivity of the average τ. A temperature increase resulted in a statistically significant ∼20% acceleration of relaxation in Hi-Na⁺ (χ² = 58.1; P < 10⁻⁵), while in Hi-K⁺, the relaxation became approximately twofold faster (χ² = 200; P < 10⁻⁵; Fig. 2 B′). Fig. 2, C and C′, displays the averages of ss and ssc, representing the equilibrium inhibition of open and closed channels (shown with open and filled symbols, respectively). A comparison of Fig. 2, C and C′, reveals that in both conditions, binding to closed and open channels increases with temperature. However, the increase is significantly more pronounced in Hi-K⁺ (χ² = 106; P < 10⁻⁵ for ss and χ² = 102; P < 10⁻⁵ for ssc), whereas in Hi-Na⁺, the changes in ss and ssc are not statistically significant (χ² = 7.28; P = 0.507 for ss and χ² = 8.41; P = 0.395 for ssc).

In terms of binding affinity, these differences translated into K_D calculated using Eq. 4 (Fig. 2, D and D′; open and filled symbols depict open and closed channels, respectively). For both experimental conditions, the effect of the temperature on K_D in open and closed channels is similar but more pronounced in Hi-K⁺. After fitting Eq. 4 to K_D data (solid lines in Fig. 2, D and D′), we observed the following: in Hi-Na⁺, the K_D for open channels decreased from K_D0 = 2.32 ± 0.058 nM with zδ = 0.62 ± 0.01 to K_D0 = 1.78 ± 0.07 nM with zδ = 0.59 ± 0.01 (values are fit parameter ± SE of the fit). Meanwhile, in Hi-K⁺, the K_D for open channels decreased from K_D0 = 6.33 ± 0.53 nM with zδ = 0.45 ± 0.03 to K_D0 = 2.2 ± 0.5 nM with zδ = 0.57 ± 0.08. Similar changes were observed in closed channels: in Hi-Na⁺, the K_D decreased from K_D = 3.57 ± 0.12 nM to K_D = 2.51 ± 0.13 nM. Meanwhile, in Hi-K⁺, the K_D decreased from K_D = 48.03 ± 0.85 nM to K_D = 17.91 ± 0.95 nM. These results indicate that, under both ionic conditions, increasing the temperature enhances the binding affinity of CTX.

Fig. 2, E and E′, shows a comparison of the resulting kinetic rate constants in Hi-Na⁺ and Hi-K⁺ solutions, respectively. In both experimental conditions, k_on is more temperature sensitive. Notably, k_on in Hi-K⁺ (orange open circles in Fig. 2 E′) seems to be the most temperature-sensitive rate constant, showing a three- to fourfold increase, compared with less than twofold increase in Hi-Na⁺. The dissociation rate in Hi-K⁺ also increased significantly at all voltages tested, whereas in Hi-Na⁺, the differences between the two temperatures were not statistically significant (χ² = 10.6; P value = 0.16). In summary, only k_off in Hi-Na⁺ appears temperature insensitive.

Fig. 3 summarizes the temperature dependence of CTX binding to open Shaker channels in Hi-Na⁺ and Hi-K⁺. Fig. 3 A plots the K_D at zero voltage, K_Do, obtained from fits of Eq. 4 to data as shown in Fig. 2, D and D′. K_Do is reduced to a half in Hi-K⁺, while the changes in Hi-Na⁺ remain within the range of data dispersion. Such a temperature dependence in Hi-K⁺ points to an additional ΔΔG = ∼24 kJ/mol when K⁺ replaces external Na⁺, corresponding to an ∼20,000-fold difference in affinity at room temperature (20°C). The effective valence of the voltage dependency, zδ, the other parameter of Eq. 4, shows negligible variation in Hi-Na⁺. In contrast, in Hi-K⁺, zδ increases by ∼0.2e with temperature (Fig. 3 B). Since this additional voltage dependence could be artifactual (see Materials and methods), we used the average association and dissociation rates measured at +60 mV, where the signal-to-noise ratio is highest, to calculate enthalpies (50–70 mV; Fig. 3, C–D). Fig. 3 C shows that at ∼13°C, the dissociation rates constants, k_off, are similar in both ionic conditions. However, at ∼30°C, k_off in Hi-K⁺ is approximately twofold larger than in Hi-Na⁺. In this later ionic condition, k_off is not temperature sensitive. In contrast, the association rate shows more dramatic temperature dependence (Fig. 3 D): it increases three- to fourfold in Hi-K⁺, compared with only ∼50% in Hi-Na⁺. Interestingly, this greater temperature sensitivity causes k_on in Hi-K⁺ to surpass that in Hi-Na⁺ at temperatures above ∼20°C. While surprising, similar observations have been reported for Shaker: the CTX-R25Q variant showed a twofold higher association rate in high external K⁺; and low ionic strength experiments revealed an approximately fourfold higher association rate in K⁺ solutions compared with Na⁺ solutions (Goldstein and Miller, 1993; Moldenhauer et al., 2019). Binding to BK channels has also been observed to occur about twice as fast in K⁺ compared with Na⁺ solutions (Anderson et al., 1988). In summary, we found that CTX binding to open Shaker K channels in Hi-K⁺ exhibits greater temperature sensitivity in both association and dissociation rate constants than in Hi-Na⁺. This enhanced sensitivity suggests the presence of K⁺-dependent enthalpic components in both the association and dissociation pathways of CTX binding.

CTX-binding equilibrium to the closed BK and VGKC is voltage independent (Anderson et al., 1988; Goldstein and Miller, 1993; Moldenhauer et al., 2019). This property allows for a clear separation of voltage dependence from potassium dependence. To evaluate CTX-binding kinetics to closed channels, we used a two-pulse protocol previously developed for κ-PVIIA (Terlau et al., 1999; Naranjo and Díaz-Franulic, 2020). In this protocol, a first conditioning voltage pulse significantly alters the CTX-binding equilibrium (Fig. 4, A and B, top). Then, after a variable inter-pulse interval at the holding voltage, a second (test) pulse is applied to assess the time course of the return to the closed-channel CTX-binding equilibrium. Fig. 4, A and B, shows 10 current traces obtained using this two-pulse protocol in Hi-Na⁺ (Fig. 4 A) and Hi-K⁺ (Fig. 4 B) at 25°C. The blue dots in Fig. 4, A and B, represents isochronal current amplitudes measured 5–10 ms after the onset of the test pulse. A single-exponential function was fitted to the data (solid lines) to determine the time constant (τ) for closed-channel binding. Fig. 4 C shows that the time constants in Hi-K⁺ exhibit greater temperature sensitivity over the tested range (∼15 to ∼32°C; green and pink symbols represent Hi-Na⁺ and Hi-K⁺, respectively). For the closed-channel equilibrium blockade (ssc) at various temperatures (Fig. 4 D), we used the average of the convergence points from the point-by-point ratios shown in Fig. 2, C and C′ (see Naranjo and Díaz-Franuli [2020]). Applying the equation system 1 to these data allowed us to calculate k_on and k_off for closed channels at different temperatures (open and filled symbols, respectively) in Hi-Na⁺ and Hi-K⁺ (Fig. 4 E). As with open channels, both association and dissociation rates in Hi-K⁺ showed greater temperature sensitivity than in Hi-Na⁺. Interestingly, at lower temperatures, the association rate in Hi-Na⁺ is threefold higher than in Hi-K⁺; however, near 35°C, as observed in open channels, the association rate in Hi-K⁺ surpassed that in Hi-Na⁺. Thus, the temperature-dependent behavior of CTX binding is similar in both open and closed channel conformations.

The solid lines in Fig. 3, C and D; and Fig. 4 E correspond to fits of Eq. 5 to the temperature dependence of the rate constants. Fig. 5 summarizes the estimated activation enthalpies (ΔH^≠) derived from the temperature dependence of the rate constants for both open and closed channels in Hi-Na⁺ and Hi-K⁺ solutions (in cyan and pink bars, association [open bars] and dissociation [filled bars], respectively). In both channel conformations, k_on in Hi-K⁺ shows the largest contribution to temperature dependence, with ΔH^≠ ≈ 45 kJ/mol. In contrast, ΔH^≠ for k_off ranges between 17 and 27 kJ/mol and is consistently higher in Hi-K⁺ than in Hi-Na⁺ (filled bars). Despite the use of different experimental methodologies used to estimate k_on and k_off (single-pulse for open channels versus multiple-pulse in closed channels), the consistency of the results supports a specific effect of K⁺ ions on the ΔH^≠ of association and dissociation in open and closed channels. Interestingly, although the activation enthalpy of k_off is ∼24 kJ/mol larger in Hi-K⁺ than in Hi-Na⁺, the association rates are nearly identical at 20°C, suggesting the presence of a K⁺-specific activation entropy (ΔS^≠) of about 82 J/mol∙K, which compensates for the potassium-dependent increase in enthalpy.

The most prominent and surprising finding of this study is that, in high external K⁺ solutions, the activation enthalpy of CTX association and dissociation from the Shaker K channel is greater than in high external Na⁺ solutions (Fig. 5). Considering that k_on is expected to be diffusion limited in both Hi-K⁺ or in Hi-Na⁺ solutions, this K⁺-dependent increase in activation enthalpy is unexpectedly high (Escobar et al., 1993). Moreover, at temperatures above 20°C, the association rate in high external K⁺ surpasses that observed in high external Na⁺ (Fig. 3 C and Fig. 4 E)—a counterintuitive result, as potassium competes with CTX for binding to the pore (see, for example, Ranganathan et al., 1996; Moldenhauer et al., 2019). In the following paragraphs, we discuss why these two findings, along with the external K⁺ sensitivity of the dissociation rate, represent unexpected results.

The toxin dissociation rate in Hi-K⁺ is approximately twice as high as in Hi-Na⁺, as shown in Fig. 3 C. This result is consistent with earlier electrophysiological findings indicating that high external K⁺ reduces toxin affinity (Ranganathan et al., 1996). Additional support for this idea comes from two observations: (1) the CTX K_D follows the same selectivity sequence as permeation and (2) the external ion selectivity of the dissociation rate enhancement in Shaker mirrors the internal ion selectivity observed in BK channels (Anderson et al., 1988; Moldenhauer et al., 2019). Access to the selectivity filter during CTX binding could be explained in two ways: either CTX transiently unbinds from the pore, or—similar to the μ-conotoxin blockade of the SCN4A Na⁺ channel—the toxin only partially occludes the pore (French et al., 1996). Gating current measurements of Shaker K channels blocked with AgTx-2 offer insight into this distinction. Aggarwal and MacKinnon (1996) using TEVC in Xenopus oocytes, observed that ∼10¹⁰ toxin-blocked Shaker channels produced <1 µA of ionic current at +50 mV. From this, we estimate that the residual unitary current of blocked channels must be < 0.1 fA—that is, <0.01% of the current from unblocked channels. If the toxin only partially blocks the pore, it would leave a clearance with an effective radius of about 10 fm, assuming that the radius of capture for K⁺ ions in Shaker channels is ∼0.8 Å (Díaz-Franulic et al., 2015; Moldenhauer et al., 2016). This dimension is implausibly small at the molecular scale unless we consider that the interaction between CTX and the channel is dynamic. Thus, this external accessibility likely results from transient fluctuations of the bound toxin caused by thermal motion. Consequently, the idea that the toxin briefly unbinds, allowing the pore to be accessible for <0.01% of the time, is both simpler and more intuitive. Furthermore, since the pore is formed by the close apposition of all four subunits, a partial occlusion model cannot easily account for the observation that AgTx-2 simultaneously contacts all four residue-449 positions around the Shaker pore (Gross and MacKinnon, 1996). Therefore, to permit access of external ions to the selectivity filter, one or more of these 449-residue contacts must intermittently separate from the toxin. This implies that the bound CTX undergoes dynamic movement, trembling, or wobbling, which could be facilitated by potassium ions occupying the S1 site in the selectivity filter.

CTX binds to the open VGKCs with a simple 1:1 lock and key mechanism (Goldstein and Miller, 1993; Banerjee et al., 2013). The structure of the CTX/Kv1.2 channel complex reveals a tightly complementary interaction surface, with only minor structural differences compared with the toxin-free, presumably open, Kv channel structure (PDB ID 4JTA and PDB ID 2R9R for the complex and channel alone, respectively [Banerjee et al., 2013]). In the toxin–channel complex, S1, the outermost K⁺-binding site in the selectivity filter, lacks K⁺ electron density. Instead, the amino group of Lys27 in CTX occupies this site, effectively mimicking a K⁺ ion (Banerjee et al., 2013). Supporting this interpretation, a cryo-EM structure of the sea anemone toxin ShK bound to the Kv1.3 channel also shows a lysine amino group mimicking a K⁺ ion at S1 (Selvakumar et al., 2022).

These structural features strongly support the most prominent functional effect of CTX binding: the physical occlusion of the pore, which blocks ionic current (Figs. 1 and 2). As shown in Figs. 1 and 2, increasing the internal voltage accelerates the dissociation rate, k_off, with an effective electrical valence of zδ ∼0.5 e_o (see Fig. 3 B). This voltage effect likely reflects the outward movement of K⁺ ions in the selectivity filter, destabilizing CTX (MacKinnon and Miller, 1988). While this model, originally proposed for BK channels, explains part of the Shaker K channel behavior, it does not fully account for it. In Shaker channels, removing internal K⁺ reduces the effective valence of the voltage sensitivity by half, rather than eliminating it, as observed in BK channels. This suggests a weaker coupling between pore occupancy and CTX voltage sensitivity (Goldstein and Miller, 1993).

Compared with experiments in Hi-Na⁺, potassium contributes ∼25 kJ/mol to the activation enthalpy of association and 10–20 kJ/mol to the dissociation enthalpy in Hi-K⁺ for both open and closed channels. These values are in line with prior estimates of the 20–25 kJ/mol energy difference in Na⁺ versus K⁺ permeation, derived from energy calculations and electrophysiological evaluations of KcsA, a structurally well-characterized K⁺ channel (Aqvist and Luzhkov, 2000; Bernèche and Roux, 2001; LeMasurier et al., 2001). This figure is consistent with the selectivity ratio P_Na+/P_K+ < 0.01 estimated from reversal potential measurements in Shaker channels (Heginbotham and MacKinnon, 1993; Díaz-Franulic et al., 2015; Naranjo et al., 2016) and with an affinity ratio of ∼0.001 estimated for the outer binding site, likely S1, of the BK channels in the presence of Ba²⁺ in the pore (Neyton and Miller, 1988). Thus, the additional activation enthalpy observed in the toxin rate constants may reflect the differing occupancy of the selectivity filter by Na⁺ versus K⁺ ions. In this context, it is reasonable to expect a K⁺-specific enthalpic penalty for CTX binding, since in Hi-K⁺, the S1 site would be occupied more frequently by K⁺, thereby hindering binding of the Lys27 side chain (Ranganathan et al., 1996; Banerjee et al., 2013; Moldenhauer et al., 2019).

CTX is a positively charged peptide (+5), then its association rate can be shaped by the electrostatic attraction to the negatively charged mouth of the channel. This kind of attraction occurs through an electrostatically transparent environment that is screened by a fog of dissolved ions (or ionic strength). The ionic strength interferes with the association rate according to the Brønsted–Bjerrum equation (Castaneda-Agullo et al., 1961). In fact, in κ-PVIIA (charge +4), the electrostatically assisted rate decreases exponentially with the square root of the ionic strength if a charge of −2.5 is assigned to the Shaker vestibule (Naranjo and Díaz-Franulic, 2020). While this model can approximate the magnitude of the association rate enhancement, it oversimplifies the interaction by treating it as the collision of two point charges. In reality, the CTX molecule is over 8 Å in diameter, comparable with the Debye length at 0.15-M ionic strength, and probably must align precisely with the receptor for binding to be productive.

Thus, a very large association rate likely arises from a combination of factors, all with weak temperature dependence, such as local concentration increases, electrostatic attraction, and steering into the correct orientation for productive binding (Miller, 1990; Volkov et al., 2006; Harel et al., 2009; Schreiber et al., 2009). Therefore, the high activation enthalpy must originate from a postbinding step.

The CTX-binding process may involve a two-step mechanism in which a relatively long-lived encounter (or intermediate) complex is formed (Escobar et al., 1993; Schreiber et al., 2009). Before reaching the final Shaker–CTX-blocked conformation, the toxin likely diffuses into the channel vestibule, where short- and long-range contact rearrangements occur before CTX finally “clicks” into the S1 site. For dissociation, the toxin must retrace this path, breaking weak and strong bonds, disengaging contact surfaces, and detaching from the receptor. We can represent this with the following reaction in Scheme 2:

If k₂ and k₋₂ are temperature-dependent, both k_a and k_-a would contribute significantly to the enthalpy of activation. We assume that Scheme 2 holds under both Hi-K⁺ and Hi-Na⁺ experimental conditions. However, the high enthalpy observed in Hi-K⁺ (Fig. 5) likely results from a K⁺-dependent reduction of k₂ and possibly an acceleration of k₋₂. Interestingly, if the association rate is limited by the number of effective collisions, the rate remains diffusion controlled.

The interaction interface between the toxin and the Shaker channel is large (∼50–100 Ų), with many residues on both surfaces contributing sticky contacts. We propose that the formation of the Ch*Tx intermediate is facilitated by complementary electrostatics, which play a key role in attracting and steering the toxin into a favorable orientation. As a result, the complex likely explores several contact geometries before achieving full binding, with the ε-amino group of Lys27 ultimately clicking into the S1 site. This scenario implies that a large fraction of protein–protein encounters are productive, provided that electrostatically aided collisions are followed by a stochastic search for the correct configuration. In fact, this mechanism appears to be general. Other well-studied protein–protein systems, such as barnase–barstar, cytochrome c and its oxidase, and trypsin with its inhibitor BPTI, also exhibit steering and reaccommodation of binding peptides, allowing a large fraction of collisions to be effective (Schreiber and Fersht, 1995; Frisch et al., 2001; Volkov et al., 2006; Kahler et al., 2020).

Despite the large K⁺-dependent activation enthalpy (∼25 kJ/mol), both kinetic rate constants (k_a and k_-a) are similar in Hi-K⁺ and Hi-Na⁺ at 20°C (Fig. 3 C and Fig. 4 E). If the difference between Na⁺ and K⁺ binding were solely due to the enthalpy of the transition state, CTX binding in high Na⁺ solutions would be predicted to be ∼20,000-fold faster. However, the observed similarity in association rates implies that the excess K⁺-dependent ΔH^≠ is offset by a compensating K⁺-dependent ΔS^≠ of ∼82 J/mol·K. A simplistic interpretation of these thermodynamic parameters is that, despite the enthalpic penalty imposed by K⁺, the Ch*Tx intermediate exhibits a large gain in conformational entropy, suggesting ∼20,000 more accessible pathways to reach the fully bound state at 20°C.

In addition to the large K⁺-specific ΔH^≠, we identified a notable inconsistency with the classical model of diffusion-controlled CTX binding to Shaker. At temperatures above 20°C, and despite the competitive relationship between K⁺ and CTX, the toxin’s association rate in Hi-K⁺ can surpass that in Hi-Na⁺ (Fig. 3 C). Since K⁺ is a competitor, one would intuitively expect the CTX-binding rate in high K⁺ to be at most equal to that in high Na⁺, but not greater. Nevertheless, this counterintuitive result has precedents. The CTX-R25Q variant binds Shaker two to three times faster in high external K⁺ than in Na⁺ Additionally, at 20 mM ionic strength, CTX exhibits a fourfold higher association rate in K⁺ compared with Na⁺ solutions (Moldenhauer et al., 2019). Similarly, across a wide range of ionic concentrations, CTX binds BK channels approximately twofold faster in K⁺ versus Na⁺ (Anderson et al., 1988). These observations point to a complex binding mechanism—potentially consistent with Scheme 2.

In this framework, the conceptual separation between the initial binding event and the formation of the fully bound complex could help explain the anomaly. We may speculate that while the absolute collision frequency (k₁) remains similar under both ionic conditions, the fraction of effective collisions—given by $k2/(k−1+k2)$⁠, remains constant in high Na⁺ but increases with temperature in high K⁺. Thus, CTX and K⁺ may not directly compete for binding the channel. Instead, once CTX is bound, its Lys27 amino group competes with K⁺ for occupancy of the S1 site. This leads to a configurational search phase that ends when S1 becomes available and Lys27 locks in. All steps in this exploration are accelerated at higher temperatures, shortening the lifetime of the intermediate Ch*Tx. At 20°C, this intermediate is sufficiently long-lived to equalize the association rates in Hi-K⁺ and Hi-Na⁺ conditions.

The structure of the CTX/Kv 1.2/2.1 complex crystallized in Cs⁺ salt may provide a physical picture of some early stage of wobbling (PDB ID 4JTC; [Banerjee et al., 2013]). Unlike the CTX–Kv1.2/2.1 structure obtained in K⁺ salts, where S1 is devoid of K⁺ electron density (Fig. 6 A), the complex crystallized in Cs⁺ shows a Cs⁺ ion occupying S1, while the amino group of Lys27 is retracted ∼2–3-Å back into the CTX body (Fig. 6 B; [Banerjee et al., 2013]). This crystal structure captures a permeant ion residing in S1 while the ε-amino group of Lys27 is displaced. This conformation aligns with MD simulation snapshots of the VGKC–CTX complex in K⁺, taken ∼10 ns after applying a 500-mV transmembrane electric field (Fig. 6 C; Moldenhauer et al. [2019): data available at https://doi.org/10.5061/dryad.0p77qk4). As in the Cs⁺ crystal, Fig. 6, C and D, shows the amino group of the Lys27 side chain retracted >3-Å above S1, which is occupied by a K⁺ ion. This represents the early stage of wobbling, as later in the simulation, the ε-amino group of Lys27 can be found up to 10-Å above its native position (Moldenhauer et al., 2019).

The dynamic behavior of the intermediate complex may resemble what we previously described as wobbling (Moldenhauer et al., 2019). High external potassium concentrations would significantly increase the occupancy of S1, thereby slowing k₂, without affecting the effective collision rate, which remains diffusion controlled (Wobbling: II in Fig. 7). A potential reason for the extended lifetime of the Ch*Tx intermediate complex could be that occupancy of S1 by the Lys27 side chain is antagonized by potassium ions. In contrast, under high external Na⁺ conditions, S1 would remain unoccupied for a greater fraction of time. As a result, wobbling should be briefer and not rate limiting (Wobbling: I in Fig. 7), and thus would not contribute a significant enthalpic component. This separation between CTX binding and Lys27 clicking could explain the high association rate observed in high K⁺. While CTX binding itself may not compete with K⁺, the Lys27 clicking step does. Therefore, the detachment of the Lys27 amino group from S1, the most distinctive feature of wobbling, may be a shared characteristic of the Ch*Tx intermediate complex.

Does wobbling represent the transition state in the CTX-binding reaction pathway? We propose that the specific energetic impact of external K⁺ on toxin binding and unbinding kinetics results from K⁺ competitively preventing the Lys27 ε-amino group from occupying S1 while the toxin is wobbling (Wobbling in Fig. 7). A similar wobbling pattern (I and II) may occur in both directions of the reaction coordinate. In the association pathway, Shaker and CTX form a binding intermediate that explores geometrical complementarity, establishing a series of transient interactions along the reaction trajectory until the Lys27 ε-amino group, competing with external K⁺, clicks into S1 to form the fully bound state. This pathway could account for the larger activation enthalpy and entropy observed for k_on in Hi-K⁺ compared with Hi-Na⁺. As expected for an energy-conservative process, the reverse pathway would be traversed during dissociation (Dill and Bromberg, 2011).

The wobbling behavior of CTX in Shaker K channels permits access to the selectivity filter from the extracellular when the channel is blocked by CTX, favoring permeant ions over non-permeant ones (Moldenhauer et al., 2019). Here, we further propose that wobbling contributes to the increased association and dissociation enthalpies when K⁺ is the main external cation, suggesting that wobbling is briefer and not rate limiting when the external ion is non-permeant. Thus, it remains to be tested whether a relationship exists between ion-binding enthalpy of CTX binding and permeation.

Wobbling can be economically described by a two-step binding mechanism in which a positively charged neurotoxin binds to an oppositely charged molecular receptor, as outlined in Scheme 2. This mechanism may be shared by other neurotoxins that act on the external vestibule of K⁺ channels, such as κ-PVIIA from Conus, ShK from sea anemone, and dendrotoxin from mamba (Kalman et al., 1998; García et al., 1999; Imredy and MacKinnon, 2000). Wobbling has been suggested for κ-PVIIA, as its dissociation rate from the open channel is insensitive to ionic strength, whereas in the closed channel it is highly dependent on it. This observation suggests that in the open channel, ionic strength is buffered by the intracellular environment via the pore, while in closed channels that connection is disrupted by the internal gate (Naranjo and Díaz-Franulic, 2020). Evolution may have favored a binding mechanism that incorporates wobbling because it relaxes the orientation constraints required for productive encounters, thereby increasing the overall fraction of effective collisions. Targeting VGKCs, alongside other neurotoxins in scorpion venom, contributes to a rapid excitotoxic effect that immobilizes the prey (Terlau et al., 1996).

The data underlying all figures are available in the online supplemental material.

Christopher J. Lingle served as editor.

We thank Drs. Ignacio Díaz-Franulic and Antonio Peña for their careful reading and insightful discussions.

This work was funded by Fondo Nacional de Desarrollo Científico y Tecnológico (FONDECYT) 1211366 (to D. Naranjo) and FONDECYT 1211143 (to H. Poblete). F. Salas-Sepulveda acknowledges the Doctoral fellowship ANID-21241753. We are sincerely thankful to the editors and reviewers for their careful and constructive support throughout the process.

Author contributions: N. Navarro-Quezada: formal analysis, investigation, and resources. F. Salas-Sepulveda: formal analysis, investigation, methodology, validation, visualization, and writing—review and editing. H. Poblete: conceptualization, data curation, formal analysis, funding acquisition, investigation, methodology, project administration, resources, software, supervision, validation, visualization, and writing—original draft, review, and editing. D. Naranjo: conceptualization, data curation, formal analysis, funding acquisition, investigation, methodology, project administration, resources, supervision, validation, visualization, and writing—original draft, review, and editing.