The first N-terminal residues of K_V10.1 (PASCap Morais Cabral et al., 1998) are prime candidates for transmitting voltage sensor motion to the intracellular domain based on crystal structures and interactions inferred from mutagenesis experiments. In particular, two residues at the bottom of S4 –H343 (Terlau et al., 1997) and D342 (Tomczak et al., 2017)– functionally interact with the initial N-terminus. The N-terminal PAS domain can then transmit mechanical cues to its C-terminal interaction partner CNBHD (Whicher and MacKinnon, 2019; Whicher and MacKinnon, 2016; Codding et al., 2020; Codding and Trudeau, 2019; Mandala and MacKinnon, 2022; Wang et al., 2020). To study K_V10.1 gating under perturbed intramolecular interaction, we deleted the PASCap domain (residues 2–25) and, in a more conservative approach, we examined the impact of a point mutation (E600R, Figure 1—figure supplement 1B) reported to disrupt the PASCap-CNBHD interaction (Haitin et al., 2013) and which shows a behavior reminiscent of the PASCap deletion in its response to calmodulin (see below; Lörinczi et al., 2016). We then obtained the response of the mutants to discrete depolarizations to different potentials (–100 to +120 mV for 300ms) in Xenopus oocytes in the presence of 60 mM K⁺ in the extracellular solution to follow deactivation behavior through tail currents.

Figure 1A displays representative current traces of WT and the mutant channels. The threshold for activation was shifted towards hyperpolarizing values in both mutants, giving rise to inward currents at potentials that do not lead to the opening of WT channels. This shift is most evident in the biphasic conductance-voltage (GV) plots (Figure 1B; Figure 1—source data 1). The kinetics of activation (Figure 1C) and deactivation (Figure 1E) of the mutants were also clearly distinguishable from WT. To facilitate the description of the results, we classified the responses into three categories depending on the stimulus amplitude: weak (–90 mV to − 20 mV), moderate (–10 mV to +40 mV), and strong (+50 to+120 mV).

While the activation of WT currents does not accelerate dramatically with increasing depolarizations in the voltage range tested, the mutants activated much slower than the WT upon weak and moderate depolarizations, reaching activation kinetics similar to WT with strong ones, as can be observed in normalized traces (Figure 1C). To obtain a more quantitative estimation of the changes in activation velocity, we used the time required to reach 80% of the maximum current amplitude plotted against the stimulus voltage (Figure 1D; Figure 1—source data 2). ∆PASCap and E600R needed a much longer time than WT to activate at weak depolarizing potentials but were equally fast at membrane potentials larger than +50 mV.

The deactivation (tail) kinetics changes with increasing depolarizations were more evident and more complex than changes in activation kinetics (Figure 1E and F). For increasing test pulse potentials, the peak amplitude of ∆PASCap tail currents first increased progressively, then decreased at moderate values, and rose again in the range of strong depolarizations. E600R showed a similar pattern of tail amplitude, while the increase at strong potentials was less pronounced although still evident. Remarkably, both the tail amplitude and its decay kinetics underwent profound changes depending on the stimulus. While the kinetics of WT tail currents was the same across different potentials, showing the characteristically fast deactivation of K_V10.1, ∆PASCap deactivated slow- and monotonically at weak depolarizations, but a fast component started to become evident after moderate stimuli. The fast component dominated the process at strong depolarizations. For E600R, the deactivation after weak stimuli was also slow and accelerated after a rising phase in the moderate and strong depolarization range.

Due to the complex behavior of the tail currents, different equations would be needed to fit the tails of the various channels to extrapolate the amplitude to time zero. Hence, to calculate the macroscopic conductance, we simply used the current amplitude at the end of the depolarizing stimulus and divided it by the driving force calculated from the measured reversal potential (Figure 1B). As already observed in the raw traces, the threshold for activation for both mutants was strongly shifted in the hyperpolarizing direction with respect to WT (–80 mV vs. –40 mV). Still, the most evident change was that both ∆PASCap and E600R displayed a biphasic GV in contrast to WT. Weak depolarizing pulses increased the macroscopic conductance of both mutants until a maximum at approximately +10 mV. With further depolarizations, the conductance initially declined to rise again in response to strong depolarizations. This finding matches the changes in amplitude of the tail currents, which, therefore, probably reflect a true change in overall conductance. A similar behavior has been mentioned for related (Whicher and MacKinnon, 2019) or unrelated mutations (Zhao et al., 2017) affecting the intracellular domains. However, the reasons for this phenomenon have not been investigated. We thus aimed to understand the molecular mechanisms underlying the biphasic GV.

One possible explanation for the biphasic behavior could be the coexistence of two separate channel populations with different kinetics, amplitude, and voltage dependence. This seems unlikely because the shape of the GVs was consistent in all our recordings, as evidenced by the small error bars (Figure 1B) despite the variability intrinsic to the oocyte system. Alternatively, each channel could have two open states, and the rectification observed between the two components could represent a transition from one state to the other. Indeed, an equation that reflects the two components and a transition between them (Equation 3b; see Materials and methods) described the behavior of the GV of both mutants accurately (Figure 2A; Figure 2—source data 1). Representative current traces are shown in (Figure 1A and Figure 2A and C).

With the available structural information in mind, the two components could represent sequential access to two open states (from here on, O₁ and O₂) through separate gating steps that differentially involve the sensor movement and ring rotation (Tomczak et al., 2017; Whicher and MacKinnon, 2019; Mandala and MacKinnon, 2022).

To test if the ring underlies one of the two gating steps, we tested the behavior of additional N-terminal deletions of increasing length (∆2–10, 2–25 for ∆PASCap, and 2–135 for ∆eag), expected to disrupt the ring integrity more and more. A biphasic GV was observed in all these mutants (Figure 2A). The V_half value of the first component was very similar across mutants. In contrast, the second component showed different thresholds. We then performed a global fit using Equation 3b, where we linked the parameters of the first components (Vh₁, K₁) across mutants and allowed the parameters for the second component (Vh₂, K₂, A₂) and the transition (Vh_3, K₃) to vary (Supplementary file 1, Figure 2B; Figure 2—source data 2). The global fit accurately described the behavior of the GV in all mutants (Figure 2A).

The global fit results indicate that the first component is conserved across mutants. In contrast, the second component occurs at progressively more depolarized potentials for increasingly larger N-terminal deletions and when the structure of the ring is altered through disruption of the interaction between N- and C-termini (E600R). Thus, the underlying gating events can be separated into two steps: The first gating step involves only the voltage sensor without engaging the ring and leads to a pre-open state, which is non-conducting in the WT but conducting in our mutants. The second gating event operates at higher depolarizations, involves a change in the ring, and leads to an open state both in WT and in the mutants.

To test this hypothesis, we compared the behavior of ∆2–10 and ∆2–10.L341Split, a channel lacking a covalent connection between the sensor and the pore domain (Tomczak et al., 2017), hence decoupling residues downstream S4 (in this case starting from 342) from the movement of the sensor. This decoupling would minimize the action of the displacement of the voltage sensor on the pore domain but would not necessarily affect the subsequent ring rotation. As predicted, compared to ∆2–10, ∆2–10.L341Split showed a significant reduction in the first component of the biphasic GV (Figure 2C and D). This indicates that the coupling of the voltage sensor motion to the entry into O₂ does not require a continuous S4-S5 linker. If, in non-split mutants, the upward transition of S4 allows entry to O₁, it is reasonable to assume that the movement is not transmitted the same way in the split and the transition into O₁ is less probable. The observation that, in the split, entry into O₁ requires higher depolarization and appears to be less likely, suggests that downstream of S4 (beyond position 342), there is a mechanism to convey S4 motion to the gate of the mutants.

Activation of WT K_V10.1 channels (best studied for the Drosophila form eag) drastically slows down in the presence of extracellular divalent cations that bind to the voltage sensor (Silverman et al., 2000; Tang et al., 2000), for example Mg²⁺, Ni²⁺, Co²⁺, and Mn²⁺, but not Ca²⁺. Strikingly, the degree of deceleration correlates with the ions' hydration enthalpy, suggesting that the ion might unbind during activation (Terlau et al., 1996). We chose to study the impact of Mg²⁺ on the kinetics and voltage dependence of activation (Figure 3; Figure 3—source data 1&2) in the mutant ∆eag, which shows the most significant separation between the two conductance components. Mg²⁺ slowed the activation of the channel at all depolarizations, affecting entry to both open states. This result suggests that Mg²⁺ also slows the voltage sensor motion that controls access into the second open state. In addition, the voltage dependence of activation was shifted by approximately 25 mV to more depolarized voltages. This is in line with deep deactivated states bound to Mg²⁺ and requiring stronger depolarization to exit them. Interestingly, the transition from the first to the second component of the GV plot seems unaffected by the extracellular divalent binding, which could be expected if the transition occurs in the cytoplasm.

Thus far, our results are compatible with two different open states in the mutants. The first open state, the mutant-specific O₁, would dominate at weak depolarizations and deactivate slowly, with tail current decay time constants of tens of milliseconds. In contrast, mutant and WT channels would reach the second open state (O₂) at strong depolarizations and deactivate more rapidly, with a few milliseconds or less time constants. A critical test of this hypothesis is the application of more complex voltage stimuli that drive the system to a non-equilibrium state of high O₁ occupancy. This might be achieved by deactivation periods of around 10ms, just long enough to remove most channels from O₂ but sufficiently brief to maintain the occupancy of O₁. For simplicity, we used depolarization periods of the same duration and tested whether a 300ms series of activating and deactivating 10ms pulses could accumulate channels in a high conducting state O₁.

For WT (Figure 4A), alternating between –80 and +80 mV resulted in a smaller amplitude than a constant stimulus to +80 mV, just as expected for a system with a single open state and a monotonic voltage dependence of activation. Moreover, WT’s rapid deactivation resulted in near-complete deactivation during every cycle.

In E600R, in contrast, the current amplitude during activating pulses increased steadily from cycle to cycle. Ultimately, the current amplitude exceeds that obtained with a constant +80 mV pulse (Figure 4A). Because the deactivation of this mutant is much slower and occurs at more negative potentials than that of WT (see Figures 1 and 2B), there was no noticeable deactivation during the –80 mV episodes. In addition, the tail current after the alternating stimuli had a larger amplitude than the one after a continuous pulse and decayed mostly as one component. All those observations are consistent with an accumulation of channels in O₁. A similar behavior was detected with ∆PASCap (Figure 4B), albeit within a different voltage range, as could be predicted from the different voltage dependence of the transition between states (Figure 2B). Again, alternating pulses resulted in larger current amplitudes and less complex tail current as compared to a single long pulse (Figure 4B).

A larger current amplitude in O₁ can be due to a larger single-channel conductance or a different open probability. We performed single-channel recordings in membrane patches excised from oocytes expressing the ΔPASCap mutant to distinguish between these two possibilities. To limit the possible contamination by other channels, we measured the activity in outside-out patches with K⁺ as the only cationic charge carrier on the cytoplasmic side (see Materials and methods), rendering a theoretical Nernst equilibrium potential for K⁺ of –93.77 mV and –4.69 mV for Cl^-. We only considered channels producing outward currents at –60 mV, ruling out Cl^- contamination. In such patches, we detected K⁺ current during single-channel openings that typically lasted several milliseconds upon weak depolarizations but could rarely be resolved at strong depolarizations (Figure 5A). Such behavior was never detected in uninjected oocytes. The activity in the patches was silenced by the addition of 100 µM astemizole (Figure 5—figure supplement 1), providing robust evidence that the activity is the result of the expression of ΔPASCap.

To characterize the activity in a quantitative way, we performed series of sweeps where the patch was held at –100 mV for 10 s, depolarized to +10 mV for 2.5 s, held again at –100 mV for 5 s, and finally depolarized to +40 mV for 2.5 s. The procedure was repeated tens of times on each patch, and representative traces are shown in Figure 5B. At +10 mV, we detected openings lasting up to hundreds of milliseconds, while the dwell times were much shorter at +40 mV. In some cases, openings of the two classes were observed in the same sweep, with the long openings preferentially preceding the shorter ones. Any transition from short openings to long openings (or back) always involved a longer intermediate close time, indicating that the channel travels between the two states through one or more closed states without a direct link between the two open states.

A hallmark of K_V10.1 gating is the change in activation kinetics in dependence on the pre-pulse potential reminiscent of (and commonly named) the Cole-Moore Shift (Cole and Moore, 1960; Hoshi and Armstrong, 2015). Hyperpolarized potentials drive the channel into deep closed states, which delays and decelerates activation (Ludwig et al., 1994). This is well described by a model with four identical, independent transitions of the voltage sensor (Schönherr et al., 1999) and is compromised by N-terminal deletions (Whicher and MacKinnon, 2019). To test the behavior of our mutants concerning this property, we applied a series of 5s-long conditioning pulses with voltages ranging from –160 mV to –20 mV, followed by a test pulse to +40 mV in the absence of external Cl^-. The activation kinetics, quantified by the time to 80% of the maximum current, showed a strong pre-pulse dependence in WT, ∆PASCap, and E600R, with much larger rise times in both mutants (Figure 6B; Figure 6—source data 1).

In the mutants, not only activation kinetics but also current amplitude was substantially affected by hyperpolarizing pre-pulses. With respect to the –100 mV pre-pulse potential, the current starting from a –160 mV pre-pulse increased in ∆PASCap by a factor of 3.93±0.36 and in E600R by a factor of 2.65±0.54. In contrast, WT current amplitude was not significantly affected (Figure 6A and C; Figure 6—source data 2). Such increases in amplitude are often related to augmented channel availability due to voltage-dependent recovery from inactivation. Still, although under some conditions, a decrease in outward current can be observed during the stimulus (see, e.g. traces of E600R in Figure 1 and traces in Figure 6), we never detected in any mutants cumulative inactivation after repeated depolarization, as depicted, e.g., in Figure 4. Transition from a conducting to a non-conducting state while the depolarization persists is the definition of inactivation. We nevertheless prefer to refer to the non-conducting states as "closed" rather than "inactivated", because O₁ is non-conducting (or not accessed) in the WT, and therefore, the subsequent states cannot be considered inactivated. The state resulting from the flickering block from O₂ is arguably inactivated, but such events are commonly not defined as inactivated because of their unstable nature.

In the absence of canonical inactivation, the prepulse-dependent current increase at +40 mV could be related to changes in the relative occupancy of the open states. We hypothesized that the open state O₁, which produces larger macroscopic currents, might be more accessible after a hyperpolarization. The current decay after the peak (Figure 6A), especially in ∆PASCap, also indicates a transient phenomenon. To map the voltage dependence of this effect more comprehensively, we next compared the effect of hyperpolarized pre-pulse on currents elicited at different test potentials.

We tested the effect of pre-pulse potentials (–160 and –100 mV) on IV protocols in the absence of Cl^-. Compared to a –100 mV pre-pulse, –160 mV clearly potentiated the first component of ∆PASCap and E600R biphasic IV (Figure 7A and B; Figure 7—source data 1; Figure 7—source data 2).

If the hyperpolarizing potentials facilitate the access to O₁ by driving the channel into deep closed states, then impairing the access to these states will reduce the component corresponding to O₁ in the GV. The mutation L322H, located in the S4 segment, limits access to deep closed states in WT channels (Schönherr et al., 1999). We introduced this mutation in the context of ∆PASCap and E600R. Representative current traces obtained from ∆PASCap^L322H and E600R^L322H are shown in Figure 7C and D; Figure 7—source data 3; Figure 7—source data 4. Both mutants showed drastic attenuation in the first component of the biphasic GV compared to the parental channels. The tail currents of ∆PASCap^L322H and E600R^L322H did not show rectification. They presented homogenous kinetics at all potentials, indicating that reducing the access to deep closed states also reduces the occupancy of O₁.

The available cryo-EM structures show K_V10.1 in a complex with Ca²⁺-CaM and therefore in a non-conducting state, as it is well established that binding a single Ca²⁺-CaM inhibits the current through WT channels (Schönherr et al., 2000; Ziechner et al., 2006). In stark contrast, increasing intracellular Ca²⁺ has been reported to potentiate ∆PASCap and E600R current amplitudes (Lörinczi et al., 2016). In the light of the results described above, this seemingly paradoxical behavior of mutants could be explained if Ca²⁺-CaM binding restricts the access to the WT-like open state O₂ while facilitating access to O₁, which gives rise to larger currents and is not visible in WT channels. Therefore, we predicted that Ca²⁺-CaM binding would potentiate the first component of the biphasic IV in the mutants.

To test this, we induced a rise in cytosolic Ca²⁺ using the ionophore ionomycin and inducing release from the stores with thapsigargin (both 5 µM) (Lörinczi et al., 2016). Because the increase in intracellular Ca²⁺ is transient and reverts after approximately 150 s (see Figure 8—figure supplement 1), and our protocols with discrete voltage pulses require a long time to complete, we used a 5 s voltage ramp from –120 to +100 mV repeated every 30 s for 300 s. The currents were recorded in Cl^--free extracellular solution to avoid confounding effects of the endogenous Ca²⁺-dependent Cl^- channels. The results of representative experiments on ∆PASCap and E600R are shown in the upper left panels of Figure 8A and B, respectively. Sixty seconds after ionomycin/thapsigargin application, a marked potentiation of the current amplitude was observed, and the response to the ramp became linear. The current amplitude declined over the following 300 s, and the biphasic IV characteristics partly recovered. The speed and extent of recovery were higher for ∆PASCap than E600R; after 150 s, the first component recovered by 39.84 ± 6.35% for ∆PASCap and 11.84 ± 3.07% for E600R. This recovery time course matches that of the changes in cytoplasmic Ca²⁺ and agrees with the results obtained by Lörinzi et al. for constant pulses (Lörinczi et al., 2016). The magnitude of potentiation and change in IV shape was homogeneous enough among oocytes to allow averaging of the normalized current in all experiments (Figure 8A and B, lower panel). The changes in slope can be easily observed in the corresponding first derivative of the normalized IV as a function of voltage shown in Figure 8—figure supplement 2.

The changes in amplitude and kinetics in response to rising intracellular Ca²⁺ support our hypothesis that Ca²⁺-CaM stabilizes O₁, possibly by driving the channels to deep closed states (Figures 7 and 8), which would result in smaller currents in WT and larger currents in mutants with access to O₁. We, therefore, predicted that forcing the channels to deep closed states using Ca²⁺-CaM could restore access to O₁ in the channels with restricted access to deep closed sates ∆PASCap^L322H and E600R^L322H. This was tested with the approach described above, increasing intracellular Ca²⁺ while recording a repeated ramp protocol in ∆PASCap^L322H and E600R^L322H. As seen in the representative traces in the upper right panels in Figure 8A and B, we observed a notable increase in current 60 s after Ca²⁺ rise, limited to moderate potentials, which results in a biphasic behavior resembling that of the ramps in the parental mutants in the absence of Ca²⁺. For both mutants, the IV returned to a linear shape after 300 s. Consistent with the observations for ∆PASCap and E600R, ∆PASCap^L322H exhibited faster recovery than E600R^L322H. Traces normalized to the maximum current and averaged are shown in Figure 8A and B (lower panel). The respective first derivatives are shown in Figure 8—figure supplement 3.

To further explore the role of CaM, we introduced mutations to preclude CaM binding at the N-terminal (F151N L154N) and C-terminal (F714S F717S) binding sites. We tested the behavior of these mutants (termed BDN and BDC2) in the context of ∆PASCap and E600R constructs (Figure 8C and D; Figure 8—source data 1&2) under conditions of basal intracellular Ca²⁺ concentration. ∆PASCap^BDN showed a GV relationship like ∆PASCap. In contrast, ∆PASCap^BDC2 lost its biphasic behavior. In the case of E600R, mutation of the C-terminal binding site (E600R^BDC2) showed attenuation of the first component of the GV, although not complete. The attenuation of the first component when binding of CaM to its C-terminal binding site is disrupted supports our hypothesis that Ca²⁺-CaM stabilizes O₁. The significance of CaM for the mutants seems different. CaM might be crucial for stabilizing O₁ in ∆PASCap while less critical in E600R.

These results opened the possibility that the biphasic behavior is due to two coexisting populations of channels, depending on CaM binding at rest. We considered this possibility, but we find it is unlikely because (i) the behavior of the mutants is very homogeneous among oocytes, in which resting Ca²⁺ is very variable; it can be as high as 400 nM (Busa and Nuccitelli, 1985), although ten times lower concentrations have also been reported (Parker et al., 1996) and (ii) two independent populations of channels would not explain the rectification or the voltage-dependent transitions during short repeated alternating stimuli.

Still, it was possible that CaM is permanently bound to the channel and participates in the gating machinery while only inhibiting the current when bound to Ca²⁺. Although the available literature would not be compatible with this hypothesis (Schönherr et al., 2000; Ziechner et al., 2006), we estimated the fraction of channels (WT or mutant) bound to CaM as a function of free Ca²⁺ concentration. We co-expressed Myc-tagged CaM and K_V10.1, extracted the proteins in different Ca²⁺ concentrations (see Methods), and pulled down the complex through the Myc-tag of CaM. Under these conditions, we could consistently detect a fraction of channels bound to CaM already in 50 and 100 nM Ca²⁺, which increased dramatically in 0.5 and 1 µM, compatible with previous reports, suggesting that, at basal Ca²⁺, only a small and variable fraction of channels are bound to CaM both in the WT and in the mutants (Figure 8—figure supplement 4). The fraction of channels bound to CaM at basal Ca²⁺ (in the range of 4% in 100 nM), even if only one CaM is needed per channel tetramer, is insufficient to explain the prominent and proportionally constant first component observed in the mutants.

In summary, our results strongly suggest that Ca²⁺-CaM stabilizes O₁, possibly by driving the channel to deep closed states.

So far, our experimental results suggest that an additional open state exists in K_V10.1 mutants with a compromised intramolecular coupling. This hypothesis can explain the biphasic GV curves, the tail currents' complex shape (Figures 1 and 2), the current increase following repeated brief hyperpolarizations (Figure 4), and even the paradoxical current increase under rising intracellular Ca²⁺ concentrations (Figure 8 and its supporting figures). However, in each case, there might be alternative explanations, such as two separate channel populations with different properties or voltage-dependent de-inactivation. The ultimate test for the hypothesis is the construction of a single model that consistently and quantitatively captures all these unusual characteristics.

It should be noted that the model structure presented here (Figure 9—figure supplement 1) is not the only one we found to be able to reproduce the data, but it is amongst the simplest that could (see Materials and methods).

Given the large number of model parameters (42+absolute conductance), it might be surprising that all parameters can be constrained. However, the wide range of voltage protocols and the concurrent matching of depolarization and repolarization responses tightly constrains several rate ratios at different voltages and, thereby, ultimately all parameters. This said, the model never fitted all experiments at once very well. Consequently, a global fit proved extremely hard to achieve in an automated way, and we decided to explore the parameter space manually, based on the time constants and rate ratios we could discern from the experiments.

The model parameters are listed in Supplementary file 2. These parameters and the structure in Figure 9—figure supplement 1 jointly define the model that produces all results in Figure 9 and Figure 9—figure supplements 1–5 for ∆PASCap.

Modifications are only necessary to capture the effect of Ca²⁺-CaM-binding and the properties of other channel variants. Suppose the binding influences the interaction between the intracellular modules that stabilize different configurations of the gating ring, e.g., BDC2, CNBHD, BDC1, and PASCap. In that case, the free energy of these states will change upon Ca²⁺-CaM binding. Consequently, the free energy difference between the states, and thereby the apparent voltage sensitivity of the transitions, will change too. Hence, we represented the effect of different degrees of Ca²⁺-CaM binding as different voltage shifts in λ, κ_L, γ, as indicated in Figure 9E.

While the Markov model describes the time and voltage dependence of state occupancies, the experimental observable is current. From the model’s occupancies, current was obtained by application of the GHK flux equation (Equation 4) for both open states. While the single channel conductance of the two open states in the model is identical, the effective occupancy of O₂ and, thereby, its macroscopic conductance is drastically reduced by a flicker block, a rapid transition into C₂, and a slower return to O₂. To match experimental results, in particular the pre-pulse-dependent activation and tail current amplitudes, the flickering kinetics had to be adjusted to achieve a limiting occupancy ratio of 5.5 between C₂ and O₂, i.e. r_close/r_open=4.5. Typically, flicker-closures are thought to result from instabilities of the open state, unrelated to voltage sensor rearrangements. Here, r_close and r_open are constant and voltage-independent. The range of plausible absolute values for r_close and r_open is well constrained by experiments. If, following strong depolarizations, O₂ is populated faster than it is vacating into C₂, a transient overshoot appears shortly after depolarization onset. This is observed in E600R, but not ∆PASCap (Figure 1A and C). We found that the E600R observations can be mimicked with r_open = 30, while mimicking ∆PASCap activation requires at least r_open = 100. Further increases induce only small changes, visible in the triphasic tail current kinetics. In the limit of very fast flickering kinetics, the model becomes indistinguishable from a model without flickering in which O₂ microscopic conductance is reduced to 1/5.5.

To test the model, we focused on the most conspicuous kinetics features observed with ∆PASCap. The first feature was the tail kinetics. In contrast to the slow monophasic deactivation observed in response to weak depolarizing pulses (–20 mV), triphasic tail kinetics was detected in response to strong depolarizing pulses (+80 mV; Figure 1C). The model could replicate the slow deactivation after weak depolarizations, fast after strong depolarizations, and mixed kinetics on moderate stimuli (Figure 9B; Figure 9—figure supplement 2).

The model also reproduces the effect of a hyperpolarizing prepulse on different test potentials. As described (Figure 6), O₁ is preferentially accessed from deep closed states, which correspond to states towards the left in the lower layer in the model. It is plausible that a hyperpolarizing pre-pulse (–160 mV) drives the channel to occupy the deep closed states (lower layer), while a pre-pulse of –100 mV distributes the channel between both layers. We, therefore, adjusted the parameters accordingly (Supplementary file 2) and simulated the current trace (Figure 9—figure supplement 3). We focused on a test pulse that represents moderate depolarizations (+20 mV), and compared it to a strong depolarizing pulse (+80 mV). Like in the experiment, the more strongly hyperpolarizing prepulse (–160 mV) potentiates the current at +20 mV, as compared to the prepulse to –100 mV (Figure 9—figure supplement 3A). This does not happen for the larger depolarization to +80 mV (Figure 9—figure supplement 3B).

The model also recapitulates the behavior of ∆PASCap during repeated short stimuli between –20 and +50 mV. The current amplitude driven by intermittent stimuli is larger than that driven by a sustained stimulus to the same potential. The model also reproduces the relative size and the kinetics of the tail current (Figure 9C; Figure 9—figure supplement 4).

The effect of a rise in Ca²⁺ can be reproduced by shifting the voltage dependence of just two transitions (γ↔δ and κ). The rationale behind this that Ca²⁺-CaM binding stabilizes the basal configuration of the ring and thereby shifts the activation energy for state transitions that are coupled to ring reconfigurations, i.e. the second VSD displacements (γ↔δ) and the ring gating itself (κ). Shifts in activation energy of voltage-dependent rates correspond to an extra term that can be expressed as voltage offset. When the voltage-dependence of these three rate constants is shifted by 10–120 mV, the occupancy of states in the "lower" layer is increased and thereby the access to O₁ (Figure 9D). The resulting simulated currents reproduce the experimental observations: a linear current response during ramps in high intracellular Ca²⁺.

To describe the behavior of K_V10.1 WT, we only needed to remove the access to O₁ and shift the parameters of the rotation of the ring in the hyperpolarizing direction to reflect the more stable structure resulting from intact interactions among intracellular domains and between these and the core of the channel. The model recapitulated the change in kinetics depending on the pre-pulse potential.

The model structure and the values of its parameters have been developed to reproduce the kinetic features of currents through K_V10.1 ∆PASCap channels. Can it provide insights into specific properties of other genotypes? A very palpable, E600R-specific feature is the transient current peak that occurs within about 30ms after depolarizations above +70 mV (Figure 1A and C). It suggests that O₂, the open state underlying current at these voltages, is populated and vacated with very similar rates. In the model, such a transient peak can indeed be reproduced if the rate constant from O₂ into C₂ (Figure 9—figure supplement 1) is reduced from 100 s^–1 for ∆PASCap to 30 s^–1 for E600R (Figure 9—figure supplement 5). E600R also supports larger tail currents, relative to the test-pulse currents, indicating an even stronger bias away from O₂ into C₂. To replicate this, r_close/r_open was increased to 11 and the rate constant ζ, leading out of O₂ was adjusted to compensate for the lower O₂ occupancy. These few changes, all concerned with O₂ instability, underly the simulations in Figure 9—figure supplement 5 A and B. The corresponding parameters are given in Supplementary file 2.

The tails observed in E600R show a shape reminiscent of that of K_V11.1, where slow deactivation is crucial for its physiological function. Our model can mimic K_V11.1 if the flicker block is biased further towards the closed state, and the transitions between closed states are slowed (Figure 9—figure supplement 5 D and E; Supplementary file 2).

Mutants were generated using K_V10.1 (hEAG1) cloned in pSGEM (M. Hollmann, Bochum University) as a template (Jenke et al., 2003). The deletion mutants, ∆2–10 and ∆PASCap, were generated using In-Fusion HD Cloning kit (Clontech (TaKaRA)) following the supplier’s instructions. For each construct, we designed two primers, each of them with two regions: a 3' region that anneals to the template immediately up- or downstream of the sequence to be deleted and a 5' that does not bind to the template but overlaps with the second primer (Supplementary file 3). The subsequent PCR amplification will then omit the sequence between the hybridization sites for the primers.

To generate the point mutations (∆PASCap^L322H, ∆PASCap^BDN, ∆PASCap^BDC2, E600R^L322H, E600R^BDN, E600R^BDC2), site-directed mutagenesis was performed using Quick Change II XL kit (Agilent Technologies) using the primers listed in Supplementary file 3. E600R.pLeics71 and ∆eag.pLeics71 were a gift from Dr. John Mitcheson, University of Leicester.

The expression construct for 5-myc-calmodulin was obtained by restriction cloning of CALM1 from pKK233-hCaM, which was a gift from Emanuel Strehler (Addgene plasmid # 47598) (Rhyner et al., 1992) into a pSGEM construct with five consecutive repeats of the myc tag (Lörinczi et al., 2015) using NcoI and HindIII (New England Biolabs).

All plasmids were linearized with NheI, and cRNA was synthesized using mMESSAGE mMACHINE T7 Transcription kit (Invitrogen Ambion).

Oocyte preparation and injection were performed as described (Stühmer, 1992). The amount of cRNA injected depended on the current amplitude obtained with each construct: 0.075–0.5 ng/oocyte (WT and point mutation), 0.075–5 ng/oocyte (deletion mutants), and 8–10 ng/oocyte (split channels). Oocytes were maintained at 18 °C in ND96 buffer (in mM: 96 NaCl, 2 KCl, 1.8 CaCl₂, 1 MgCl₂, 5 HEPES, 2.5 Na-pyruvate, 0.5 Theophylline, pH 7.55). Tetracycline (USB) (50 µg/ml), Amikacin (Enzo) (100 µg/ml), and Ciprofloxacin (Enzo) (100 µg/ml) were added as recommended in O’Connell et al., 2011.

Two-electrode voltage-clamp (TEVC) recordings were performed 1–5 days after oocyte injection. The intracellular electrodes had a resistance of 0.4–1.5 MΩ when filled with 2 M KCl. Normal Frog Ringer solution (NFR): (in mM: 115 NaCl, 2.5 KCl, 10 HEPES, 1.8 CaCl₂, pH 7.2), was used as external solution. Higher K⁺ concentration (mM: 60 KCl, 57.5 NaCl, 10 HEPES, 1.8 CaCl₂, pH 7.4), was used instead to examine tail currents. Cl^--free NFR (in mM: 115 Na-methanesulfonate, 2.5 KOH, 10 HEPES, 1.8 Ca(OH)₂, pH 7.2), was used to limit current contamination with Cl^- current; in this case, agar bridges (2% agar in 3 M NaCl) were used for the reference electrodes. To raise the intracellular Ca²⁺ concentration (Lörinczi et al., 2016), 5 µM ionomycin (Abcam) and 5 µM Thapsigargin (Abcam) were added to the bath. Ionomycin and Thapsigargin 5 mM stocks were prepared using DMSO and diluted in the recording medium (Cl^--free NFR) immediately before recording. The final concentration of DMSO was thus 0.1%.

Data acquisition was performed using a TurboTEC 10 CD amplifier (npi Electronics) and the ITC-16 interface of an EPC9 patch-clamp amplifier (HEKA Elektronik). The current was filtered at 1.3 KHz and sampled at 10 KHz. Patchmaster software (HEKA Elektronik) was used to design and apply the stimulus protocols applied. Because of the profound effects of hyperpolarization on channel kinetics, leak subtraction was avoided except when explicitly indicated. Linear leak was subtracted offline assuming a reversal potential of 0 mV. Fitmaster (HEKA Elektronik) and IgorPro (WaveMetrics) were then used to analyze the recordings.

Most conductance-voltage plots were obtained for recordings with [K⁺]_ext =60 mM. In this condition, tail currents are large and allow precise estimation of the reversal potential V_eq. Under this condition, the difference between intra- and extracellular potassium concentration is small and the Goldman-Hodgkin-Katz flux equation predicts a nearly linear relation. In these cases, overall conductance was calculated from the end-pulse current after measuring the reversal potential (V_eq) using:(1)G=I/(Vm−Veq)

where I is the current amplitude and V_m the stimulus. Reversal potential was calculated using the end pulse current for mutant channels activating below the equilibrium potential for potassium, or instantaneous IV using tail currents for channels opening at more depolarized potentials. Conductance was then normalized to the maximum value and plotted against voltage stimulus. For WT recordings (Figure 1B), a sigmoidal response was then fitted with a Boltzmann equation:(2)f(V)=(1+exp((Vh −Vm)/K))−1

With V_h being the voltage for half-maximal activation, K the slope factor and V_m the membrane potential as above.

The biphasic response we observed in the mutants was described with two sigmoidal components and a weight W to represent the transition between the two components. The equation used was as follows:(3a)f(V)=Ao+(1−W(V))⋅A1⋅(1+e(Vh1−Vm)/K1)−1+W(V)⋅A2⋅(1+e(Vh2−Vm)/K2)−1(3b)W(V)=(1+e(Vh3−Vm)/K3)−1

If the currents were recorded in [K⁺]_ext=2.5 mM, the driving force for currents becomes considerably non-linear (Kotler et al., 2022) and we estimated the conductance based on the full Goldman-Hodgkin-Katz flux equation for a current surface density Φ.Φ=P⋅Popen⋅zF⋅VmVT([K+]in−[K+]out ⋅ e−Vm/VT1− e−Vm/VT),

where VT=RTzF ,with the gas constant R, the Faraday constant F, the absolute temperature T, the potassium channel open probability P^open, and the maximum permeability P. The ion’s valence z equals 1. Because we only work with normalized conductances, the following relation can be used to determine the voltage-dependent conductance:(4)GV∝I∙1-e-Vm/VTK+in-K+oute-Vm/VT∙VTzFVm

The vitelline membrane of oocytes expressing ∆PASCap cRNA, as described for two-electrode experiments, was mechanically removed after osmotic shock (Stühmer, 1992) to expose the plasma membrane. Patch pipettes were pulled from thick-wall (0.5 mm) borosilicate capillaries to obtain a resistance of 7–12 MΩ when filled with the intracellular solution, which contained (mM) 100 KCl, 10 EGTA, 10 HEPES pH 7.2 (KOH). Recordings on outside-out patches were acquired using an EPC10 Plus amplifier and PatchMaster software (HEKA Elektronik). Currents were digitized at 10 kHz and filtered at 2 kHz. Analysis was performed using FitMaster. For presentation, the traces were digitally filtered at 100 Hz.

Xenopus laevis oocytes were co-injected with RNA coding for 5xmyc-calmodulin (10 ng) and K_V10.1 (0.5 ng). Oocytes were lysed 72 h after injection through mechanical disruption in lysis buffer and incubation for 30 min on ice. The lysis buffer (1% Triton X-100, 150 mM NaCl, 50 mM HEPES pH 7.4, cOmplete EDTA-free protease inhibitor cocktail (Roche)) contained different free Ca²⁺ concentrations (0, 20, 50, 100, 500, and 1000 nM). To obtain accurate Ca²⁺ concentrations, EGTA was titrated with CaCal₂, to prepare 100 mM CaEGTA stock solution as described in Tsien and Pozzan, 1989. CaEGTA and EGTA were then added to the lysis buffer, adjusting EGTA/CaEGTA to control the concentration of free Ca²⁺ taking into account pH, ionic strength and temperature of solution using MaxChelator (Bers et al., 2010). As controls, non-injected oocytes, and oocytes injected with only K_V10.1 or 5xmyc-calmodulin were lysed in a Ca²⁺ free buffer.

The lysate was then centrifuged (20,000 xg) at 4 °C for 3 min to remove debris. 10% of the supernatant was set aside to load on the gel as input control. The lysate was pre-cleared using protein G magnetic beads (New England Biolabs). The cleared supernatant was then incubated with 3 µg anti-myc antibody (SIGMA M4439 monoclonal anti c-myc or Abcam ab206486 rat mAb to myc tag (9E10)) for 1.5 hr at 4 °C. Protein G magnetic beads were then added and incubated for 1.5 hr at 4 °C in rotatio beads were washed three times using 0.1% Triton X-100, 300 mM NaCl, 50 mM HEPES pH 7.4, cOmplete (EDTA-free protease inhibitor cocktail), EGTA and CaEGTA to obtain the corresponding Ca²⁺-free concentrations (see above). Electrophoresis and immunoblotting conditions were as previously described (Lörinczi et al., 2015) using an anti-Myc (Sigma, 1:1000) or an anti-K_V10.1 antibody (Chen et al., 2011) overnight.

The standard model for K_V10.1 gating comprises two gating steps for each of the four subunits' voltage sensors. The first step unfolds in the hyperpolarized voltage range and forms the basis of the Cole-Moore shift, characteristic of K_V10.1 channel gating. The second, faster step readies the channel for opening, and once it is performed in all subunits, a conducting state can be reached (see also Mandala and MacKinnon, 2022). While this model captures the key features of WT activation, we had to extend it to account for the features of mutant gating. Throughout the model development and tuning, we focused on the experiments performed with the ∆PASCap mutant. However, a limited number of tests with other parameters showed that experimental findings with E600R and even with K_V11.1 can also be matched (Supp.5 to Figure 9).

In a first step, we attempted a minimal model extension by attaching an additional open state to some closed state of the standard model. None of the resulting models, for any choice of attachment site and rate voltage dependence, could replicate the multi-phasic tail currents, the pre-pulse dependent activation, and the delayed opening. We came to this conclusion in two steps. First, we could exclude many possible attachment sites because the attachment site must be sufficiently far away from the conventional open state. Otherwise, the transition from ‘O₁ preferred’ to ‘O₂ preferred’ via a few closed intermediate states is very gradual and never produces the biphasic GV curves. Second, we found that the first gating transition in the standard model (along α, left to right) can either produce a sigmoidal current onset or bias the model for occupancy of state O₁ over O₂, but not both. Waveforms such as the dark orange trace in Figure 6A, in response to a –160 mV pre-pulse and a 20 mV test pulse require both a bias towards O₁ and a sigmoidal onset. We found that this can only be accounted for by introducing a third gating step orthogonal to the two transitions in the standard model.

Without a priori information about the new states introduced in this way, we decided to simply add a copy of the standard model as an additional layer, an ‘upper floor’. Crossing from the ground floor to the upper floor was made possible for any state. From a structural view, this newly added transition might be related to a reconfiguration of the gating ring. Considerations as given above led us to attach the mutant-specific O₁ to the basal level and the conventional O₂ to the upper level. The experimental data indicated that O₁ had to be accessible to states ‘on the right of the ground floor’, that is, accessible from deep closed states. Along the same lines, O₁ could not be located ‘too far toward the bottom’ of the scheme, because it is an open state. Eventually, we decided to attach O₁ only to the state that corresponds to the completion of the first gating step with no further transitions (neither the second voltage-sensor transition nor the gating ring transition) in all four voltage sensors. In contrast, to enter O₂, all subunits must complete both voltage sensor transitions and the collective gating ring transition. This model’s structure is displayed in Supp. 1 to Figure 9.

We also tested models in which the upper floor was only accessible from a subset of states and models with O₁ attached to more than a single closed state or even multiple O₁ states with varying conductance. While those more complex models offered a gradual improvement matching experimental traces, they showed no striking advantages over the more symmetric and parsimonious model presented here. Furthermore, we have extensively tested variants with a broken symmetry in the gating kinetics. In these models, the conventional gating steps (rates α, β, γ, δ) differed between the ground floor and the newly introduced top floor states, e.g., by the introduction of factors to the α, β, γ, δ values. Under these conditions, a local balance was achieved by corresponding inverse factors to the local κ and λ. Again, the gradual improvements that could be achieved did not seem to justify the introduction of the additional parameters.