Revealing a hidden conducting state by manipulating the intracellular domains in KV10.1 exposes the coupling between two gating mechanisms

The KCNH family of potassium channels serves relevant physiological functions in both excitable and non-excitable cells, reflected in the massive consequences of mutations or pharmacological manipulation of their function. This group of channels shares structural homology with other voltage-gated K+ channels, but the mechanisms of gating in this family show significant differences with respect to the canonical electromechanical coupling in these molecules. In particular, the large intracellular domains of KCNH channels play a crucial role in gating that is still only partly understood. Using KCNH1(KV10.1) as a model, we have characterized the behavior of a series of modified channels that could not be explained by the current models. With electrophysiological and biochemical methods combined with mathematical modeling, we show that the uncovering of an open state can explain the behavior of the mutants. This open state, which is not detectable in wild-type channels, appears to lack the rapid flicker block of the conventional open state. Because it is accessed from deep closed states, it elucidates intermediate gating events well ahead of channel opening in the wild type. This allowed us to study gating steps prior to opening, which, for example, explain the mechanism of gating inhibition by Ca2+-Calmodulin and generate a model that describes the characteristic features of KCNH channels gating.


Introduction
Voltage-gated potassium channels constitute a large family of proteins that allow K + flow upon changes in the membrane potential. Their general architecture consists of a tetrameric complex with six transmembrane segments (S1-S6) in each subunit to form a central pore with four voltage sensors at the periphery. S1 to S4 segments constitute the sensor domain, while S5 and S6 segments and the loop between them line the pore. The mechanism of voltage-dependent gating is well understood for several subfamilies, namely those closely related to the Drosophila Shaker channel (KCNA and KCNB). In this subset of families, the linker between the sensor and pore domains (S4-S5 linker) acts as a mechanical lever transferring the movement of the voltage sensor to the gate at the bottom of S6 in a neighboring subunit through physical interaction (Barros et al., 2020). Such trans-subunit interaction is commonly denoted "domain swapping." In other families, gating mechanics must be different because there is no domain swapping in the transmembrane regions. Such is the case of the EAG family (KCNH) (Tomczak et al., 2017;Malak et al., 2019;Whicher and MacKinnon, 2019), whose members are implicated in many pathological conditions (Bauer and Schwarz, 2018;Toplak et al., 2022), which makes them attractive therapeutic targets.
In the KCNH channel family, sensor-to-pore coupling does not follow the conventional model; KCNH channels do not display domain-swapping in the transmembrane domains, the S4-S5 segment is very short and does not form a helix (Whicher and MacKinnon, 2016;Wang and MacKinnon, 2017) and voltagedependent gating in KV10.1 (Lörinczi et al., 2015) or KV11.1 (de la Pena et al., 2018) occurs even when the S4-S5 linker is severed or removed. KCNH channels show extensive conserved intracellular domains. The eag domain in the N-terminus, formed by the PAS domain and PAS-Cap, interacts with the CNBHD (cyclic nucleotide-binding homology domain) of the neighboring subunit, which is connected to the S6 through the C-linker, see Fig. S1A). The four eag-CNBHD complexes form a ring in the intracellular side of the channel, connected to the gate via the C-linkers (Whicher and MacKinnon, 2016;Whicher and MacKinnon, 2019). Thus, there is domain-swapping within intracellular domains instead of the transmembrane segments (reviewed e.g., in (Barros et al., 2020;Codding et al., 2020)). This arrangement makes the intracellular ring an excellent candidate to participate in the gating process, as it has been demonstrated for other channels, e.g. (James and Zagotta, 2017;Codding et al., 2020;Nunez et al., 2020;Verkest et al., 2022). Indeed, gating of KCNH channels is affected by manipulations of either the eag domain, the CNBHD, or the interaction between them (Terlau et al., 1997;Ju and Wray, 2006;Sahoo et al., 2012;Gianulis et al., 2013;Dai and Zagotta, 2017;Dai et al., 2018;Codding and Trudeau, 2019;Malak et al., 2019;Whicher and MacKinnon, 2019;Codding et al., 2020). Furthermore, the stability of the interaction between PAS domain and Cterminus is altered by gating in KCNH2 channels (Harley et al., 2021). Recent Cryo-EM work revealed that the position of the voltage sensor in an electric field would preclude the opening of the gate (Mandala and

Disrupting the interaction between PASCap and CNBHD reveals a biphasic gating behavior.
The first N-terminal residues of KV10.1 are prime candidates for the transmission of voltage sensor motion to the intracellular domain based on crystal structures and interactions inferred from mutant function. 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, 2016;Codding and Trudeau, 2019;Whicher and MacKinnon, 2019;Codding et al., 2020;Wang et al., 2020;Mandala and MacKinnon, 2022). To study KV10.1 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) reported to disrupt the PASCap-CNBHD interaction (Haitin et al., 2013). 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. 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 is most obvious in the biphasic conductance-voltage (GV) plots (Fig. 1B). The kinetics of activation (Fig. 1C) and deactivation (Fig 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 (-90mV to -20mV), moderate (-10mV to +40mV), and strong (+50 to +120mV).
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 (Fig 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 (Fig. 1D). ∆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 ( Fig. 1E and 1F). For increasing test pulse potentials, the peak amplitude of ∆PASCap tail currents first increased progressively, then decreased at moderate values, and rose again after the range of strong depolarizations. E600R showed a similar pattern of tail amplitude, although the increase at strong potentials was less pronounced. Remarkably, both the tail amplitude and its Figure 1. Characterization of ΔPASCap and E600R mutants. A. Raw current traces resulting from depolarizations between -100 and +120mV in WT (black), ΔPASCap (orange) and E600R (blue). B. GV plots corresponding to the three channel variants (colors as in A). (N: WT = 6, ∆PASCap = 7, E600R = 11; mean±SEM) C. Normalized traces to the indicated voltages to reveal the acceleration of activation with depolarization in the mutants. WT does not activate at -60mV type. D. Rise time of ΔPASCap (up) and E600R (down) as a function of voltage. The activation is much slower than in WT up to +50mV but reaches the speed of WT with stronger stimuli. E. Tail currents at -100 mV after depolarizations to potentials in the weak, medium, or strong range (up to down, see text for details). The arrows indicate the direction of the change in tail peak amplitude with increasing voltage. F. Normalized tail currents at -100 mV after depolarizations to the indicated voltages. 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 KV10.1, ∆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 conductance, we simply used the current amplitude at the end of the stimulus and divided it by the driving force calculated from the reversal potential (Fig. 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 . Still, the most evident change was that both ∆PASCap and E600R displayed a biphasic GV in contrast to WT.
Weak depolarizing pulses increased the conductance of both mutants until a maximum at approximately +10mV. 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 conductance. A similar behavior had 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 had not been investigated. We thus aimed to understand the molecular mechanisms underlying the biphasic GV.
The biphasic GV is described by two sigmoidal components corresponding to a two-step gating mechanism.
One possible explanation for the biphasic behavior could be the coexistence of two separate channel populations with different kinetics, conductance, 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 (Fig. 1B) despite the variability intrinsic to the oocyte system. Alternatively, each channel could have two open states, and the rectification observed between the two conductance components represents a transition from one state to the other. Indeed, an equation that reflects the two components and a transition between them (see Methods) described the behavior of the GV of both mutants accurately ( Fig. 2A).
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 two 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 ( Fig. 2A). The Vhalf 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 4, 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 (Vh3, K3) to vary (Table S1, Fig. 2B). The global fit accurately described the behavior of the GV in all mutants ( Fig. 2A).  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. As predicted, compared to ∆2-10, ∆2-10.L341Split showed a significant reduction in the first component of the biphasic GV ( Fig. 2C, D).
Activation of WT KV10.1 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;, e.g., Mg 2+ , Ni 2+ , Co 2+ , and Mn 2+ , but not Ca 2+ . Strikingly, the degree of deceleration correlates with the ions' hydration enthalpy, suggesting that the ion might unbind during activation (Terlau et al., 1996). In addition, deep deactivated states are accessed with less hyperpolarization when these divalents are present. We chose to study the impact of Mg 2+ on the kinetics and voltage dependence of activation ( Fig. 3)    Alternating potential between -80 and 80 mV in the WT results in current amplitudes that are smaller than those during a sustained stimulus (Upper left traces). In contrast, E600R gave rise to larger currents when the stimulus was intermittent and too short to allow occupancy of O2 (upper right). B. The effect was qualitatively similar for ΔPASCap, which consistently gave rise to larger current upon oscillating stimuli between -20 and +50 mV than during a constant pulse to +50 mV. 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 10 ms, 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 300 ms series of activating and deactivating 10 ms pulses could accumulate channels in a high conductance state O1.
For WT (Fig. 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. What is more, the rapid deactivation of WT 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 +80mV pulse (Fig. 4A). Because the deactivation of this mutant is much slower and occurs at more negative potentials than that of WT (see

Deep-closed states favor access to O1
A hallmark of KV10.1 gating is the Cole-Moore shift, the change in activation kinetics in dependence on the pre-pulse potential (Cole and Moore, 1960). Hyperpolarized potentials drive the channel into deep closed states, which delays and decelerates activation (Ludwig et al., 1994;Hoshi and Armstrong, 2015). This is well described by a model with four identical, independent transitions of the voltage sensor (Schonherr 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 -160mV to -20mV, followed by a test pulse to +40mV in the absence of external Cl -. The activation kinetics, quantified by the time to 80% of the maximum current, showed a strong prepulse dependence in WT, ∆PASCap, and E600R, with much larger rise times in both mutants (Fig. 5B).
In the mutants, not only activation kinetics but also current amplitude was substantially affected by hyperpolarizing pre-pulses. With respect to the -100mV pre-pulse potential, the current starting from a -160mV 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 ( Fig. 5A, 5C). Such increases in amplitude are often related to augmented channel availability due to voltage-dependent de-inactivation.
Still, conventional inactivation was never detected in any mutants after repeated or prolonged depolarization. In the absence of 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 higher conductance open state O1 might be more accessible after hyperpolarization. The current decay after the peak (Fig. 5A), 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. Although the activation is much slower for both mutants (note the different y axis for the mutants), they retain a strong dependence on the prepulse potential. C. Normalized end-pulse current (I/I-20) is plotted vs. prepulse voltage (N: WT = 10, ∆PASCap = 8, E600R = 8; mean±SEM). The amplitude of the current at +40 mV increased markedly when the holding potential was below -100 mV in the mutants, while the amplitude in WT changed only marginally.
We tested the effect of pre-pulse potentials (-160 and -100 mV) on IV protocols in the absence of Cl -.
Compared to a -100mV pre-pulse, -160mV clearly potentiated the first component of ∆PASCap and E600R biphasic IV ( Fig. 6A and 6B). 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 S3-S4 linker, limits access to deep closed states in WT channels (Schonherr 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 Fig. 6 C and D. 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.

Ca 2+ Calmodulin stabilizes O1
The available Cryo-EM structure shows KV10.1 in a complex with Ca 2+ -CaM. It is well established that the binding of a single Ca 2+ -CaM inhibits the current through WT channels (Schonherr et al., 2000;Ziechner et al., 2006). In stark contrast, increasing intracellular Ca 2+ has been reported to potentiate ∆PASCap and E600R current amplitudes (Lörinczi et al., 2016). This seemingly paradoxical behavior of mutants could be explained by the differential effects of Ca To test this, we induced a rise in cytosolic Ca 2+ using the ionophore ionomycin and inducing release from the stores with thapsigargin (both 5µM) (Lörinczi et al., 2016). Because changes in intracellular Ca 2+ are very dynamic (see Supp. 1 to Fig. 7) and our protocols with discrete voltage pulses require a long time to complete, we used a 5s voltage ramp from -120 to +100mV repeated every 30s for 300s. The currents were recorded in Cl --free extracellular solution to avoid confounding effects of the endogenous Ca 2+ -dependent  (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 ( Fig. 7A 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 Supp. 2 to Fig. 7.
The changes in amplitude and kinetics in response to rising intracellular Ca 2+ support our hypothesis that Ca 2+ -CaM stabilizes O1, possibly by driving the channels to deep closed states (Figs. 5 and 6). We, therefore, predicted that forcing the channels to deep closed states using Ca 2+ -CaM could restore access to O1 in ∆PASCap L322H and E600R L322H . This was tested with the approach described above, increasing intracellular Ca 2+ while recording a repeated ramp protocol in ∆PASCap L322H and E600R L322H . As seen in the representative traces in the upper right panels in Fig. 7A and B, we observed a notable increase in current 60 s after Ca 2+ rise, limited to moderate potentials, and resembling the first phase of the ramps in the parental mutants. For both mutants, the IV returned to a linear shape after 300s. 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 Fig. 7A  To further explore the role of CaM, we introduced mutations to preclude CaM binding at the N-terminal 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 Ca 2+ 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 Ca 2+ . Although the available literature would not be compatible with this hypothesis (Schonherr et al., 2000;Ziechner et al., 2006), we estimated the fraction of channels (WT or mutant) bound to CaM as a function of free Ca 2+ concentration. We co-expressed Myc- In summary, our results strongly suggest that Ca 2+ -CaM stabilizes O1, possibly by driving the channel to deep closed states.

A two-layer Markov model recapitulates the kinetic features of ∆PASCap.
So far, our experimental results suggest that an additional open state exists in KV10.1 mutants with a compromised intramolecular coupling. This hypothesis can explain the biphasic GV curves, the tail currents' complex shape ( Fig. 1 and 2), the current increase following brief hyperpolarizations (Fig. 4), and even the paradoxical current increase under rising intracellular calcium concentrations ( Fig. 7 and    The early, rapid decrease in current amplitude results from closure of O2. During a delay phase, increasing current through an increasingly populated O1 compensate for this closure, until eventually O1 (dark grey) also closes, but with a much slower kinetics. C. In response to 10 ms pulses alternating between -20 and +50 mV, the model shows currents that exceed the currents obtained with constant pulses to +50 mV (compare Fig. 4 B). Relating the currents during the positive and negative pulses to the concurrent currents elicited by the two constant pulses (brown and orange), the ratio lies by about 1.6 for the period starting 200 ms after the pulse onset. This excess current depends sensitively on the duration and voltage of the two pulse components. The right series of simulations displays the results for 15 ms pulses to -20 mV, alternating with 15 ms pulses to voltages from 15mV to 65 mV. The corresponding responses to the constant pulses are displayed with thin dotted lines. To facilitate perception of the excess current, the five groups of traces are scaled individually, so that the peak amplitude of the dotted response elicited by the stronger depolarizations is displayed at equal size throughout. We first tested whether simple addition of a second open state to the standard model of KV10.1 activation (Schonherr et al., 1999), could replicate the experiments. However, none of these simple models could reproduce the pre-pulse dependence of entering O1. Next, we introduced not only an additional open state, but also an additional gating step that is orthogonal to the standard model's transitions and might be related to a transition of the gating ring. This model successfully captured all the experimental observations ( Figure   8 and supporting figures).
The standard model for KV10.1 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, which is characteristic for KV10.1 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) from the conventional open state. Otherwise, the transition from "O1 preferred" to "O2 preferred" is very gradual and never produces the biphasic GV curves. Second, we found that the first gating transition in the standard model (left to right) can either produce a sigmoidal current onset or bias the model for occupancy of state O1 over O2. However, in the latter case, opening occurs without sigmoidal onset. Waveforms such as the dark orange trace in figure 5 A, in response to a -160 mV pre-pulse and a 20mV 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, which is 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 ground floor to 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 lead us to attach the mutant-specific O1 to the basal level, and the conventional O2 to the upper level. To explain the experiments, O1 had to be accessible to states on the right of the ground floor, and not too far towards the bottom. Eventually, we decided to attach O1 only to the state that corresponds to completion of the first gating step in all for subunits, but no other gating step, neither the second voltage-sensor transition, nor the gating ring transition. In contrast, to enter O2, all subunits must complete both voltage sensor transitions and also the collective gating ring transition.
It should be noted that the model structure presented here is not the only one we found to be able to reproduce the data, but it is amongst the simplest that could. 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 conductances. 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.
We have extensively tested variants with this symmetric structure, with a broken symmetry in the gating kinetics. In these models, the conventional gating steps (left -right, top -bottom) differed between the ground floor and the newly introduced top floor states, e.g. by introduction of factors to the α, β, γ, δ values.
Under these conditions, local balance was achieved by corresponding inverse factors to the local κ and λ.
Given the large number of model parameters (41+absolute conductance), it might be surprising that the 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. Because the model does never fit all experiments very well, a global fit proved extremely hard to balance and we decided to explore the parameter space manually, based on the time constants and rate ratios we could discern from the experiments.  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 (-20mV), triphasic tail kinetics was detected in response to strong depolarizing pulses (+80mV) (Fig. 8B; Supp. 2 to Fig. 8). The model could replicate the slow deactivation after weak depolarizations, fast after strong depolarizations, and mixed kinetics on moderate stimuli. Figure 8. Current simulations for ∆PASCap upon depolarization to -20 or +80 mV in the presence of high extracellular K + . A. The triphasic current kinetics (see Fig. 1E) observed experimentally at +80 mV (insert) is predicted by the model. B. Occupancy of State_4 (state closest to O1), O1 and O2 as a function of time during a depolarization to +80 mV. Figure 8. Current simulations for ∆PASCap upon depolarization to +20 and +80 mV after a conditioning pulse to -160 or -120 mV. The current at +20 mV is larger after -160 mV, while the current at +80 mV is unaffected by the conditioning pulse (see Fig. 6A)

Supplement 3 to
The model also reproduces the effect of a hyperpolarizing pulse on different test potentials. As described ( Fig. 6), O1 is preferentially accessed from deep closed states, which correspond to states in the lower layer in the model. It is plausible that a hyperpolarizing pre-pulse (-160mV), drives the channel to occupy the deep closed states (lower layer), while a pre-pulse of -100mV distributes the channel between both layers.
We, therefore, adjusted the parameters accordingly (Table S2) and simulated the current trace (Supp. 2 to Fig. 8) We focused on a test pulse that represents moderate depolarizations (+20mV), and compared it to a strong depolarizing pulse (+80mV). Like in the experiment, -160mV potentiates the current at +20mV, without impacting the current at +80mV (Supplement 2 to Fig. 8, A). This does not happen with -100mV pre-pulse (Supp. 2 to Fig. 8, B).
The model also recapitulates the behavior of ∆PASCap during repeated short stimuli between -20 and +50 mV. The amplitude of the intermittent stimuli is larger than that of a sustained stimulus to the same potential. It also reproduces the relative size and the kinetics of the tail current (Fig. 8C.; Supp. 4 to Fig. 8).
The effect of a rise in Ca 2+ can be reproduced if the voltage dependence of the rate constants for transitions between the two layers are shifted to hyperpolarized potentials, increasing the probability of states in the "lower" layer and, therefore, of the access to O1 (Fig. 8D; Supp. 5 to Fig. 8). Figure 8. Current simulations for ∆PASCap upon alternating stimuli between -20 and +50 mV, as compared to sustained depolarization to each of the potentials (see Fig. 4B) Supplement 5 to Figure 8. Current simulations for ∆PASCap under ramp depolarization using shifted rate constants (g, d, k) to mimic the effect of CaM binding (see Fig. 7A)

Supplement 4 to
To describe the behavior of KV10.1 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. Figure 8. Side-by-side comparison of experimental data and model prediction during depolarizations between -100 and +100 mV in the presence of high (A) or low extracellular K + (B). the model describes the features of the current except the sustained rising phase during strong depolarizations.

Discussion
The wide diversity of electrical responses in cells relies greatly on subtle differences in the behavior of voltage-gated channels. Despite the many relevant advances in the knowledge of the structure of ion channels, the correlation between the structures and the functional determinants of channel behavior is incompletely understood. In this study, we have combined biophysical, biochemical, and mathematical approaches to understand the complex gating behavior of KV10.1 potassium channels, which is the basis of a group of diseases with devastating consequences (e.g. (Toplak et al., 2022;Tian et al., 2023)).
In KCNH channels, intracellular domains contribute to gating by forming an intracellular ring that rotates in response to depolarizing stimuli (Mandala and MacKinnon, 2022). We have studied a series of mutant channels where the integrity of the intracellular ring is compromised by either deletions or point mutations.
In all the mutants, the G-V relationship shows a biphasic behavior with evident inward rectification at Importantly, this observation is incompatible with two independent populations of channels. Since the two gating steps are sequential (Mandala and MacKinnon, 2022), the displacement of the VSD remains the main factor governing the speed and voltage dependence of the activation. Thus, changes in the extracellular Mg 2+ concentration, which are known to interfere with the movement of the VSD (Silverman et al., 2004;Bannister et al., 2005), cause a shift of the voltage dependence and activation speed that affects both gating components (Fig. 3), but not the transition between them.
The biphasic behavior arises from a different conductance between the two open states, larger for O1, that results in a decrease in current amplitude as the channels leave O1 and transition to O2. Since the time required to access the two states is different, when short alternating stimuli are applied, each with a too short duration to allow entry into O2, the different conductance results in a larger current amplitude than when a single sustained stimulus is used (Fig. 4). The presence of a second state with larger conductance when the integrity of the ring is compromised could explain the larger current amplitudes observed in heteromeric KV11.1 (HERG1a/1b) channels, which lack at least one PAS domain as a result of alternative splicing and are crucial for proper cardiac repolarization (Feng et al., 2021). Thus, the second open state could also have physiological relevance in naturally occurring channel complexes.
Access to O1 is favored from deep deactivated states, which appear important in other aspects of KV10.1 channel function (e.g., Cole-Moore shift). Our conclusion is based on the changes in amplitude observed with different pre-pulse potentials (that is, driving the population to deep closed states, Fig. 6A and B) and on the behavior of a mutant known to hinder access to such deactivated states (L322H), which, when combined with mutations revealing O1, shows limited access to this state ( Fig. 6C and D).
Ca 2+ -CaM is an important modulator of KV10.1 that reduces WT current amplitude in the presence of elevated Ca 2+ levels. A paradoxical current increase had been described for some of the mutants used in this study (Lörinczi et al., 2016), and we speculated that the presence of O1 could be the basis for this phenomenon. Indeed, the elevation of intracellular Ca 2+ leads to a transient loss of the biphasic behavior and larger current amplitude of the mutants compatible with a larger fraction of channels in O1. Because access to O1 occurs from deep closed states, this could be explained by an increased occupancy of such deactivated states in response to CaM binding. This appears to be the case since CaM induces a biphasic behavior in the mutant channels that show reduced access to deep closed states; thus, L322H mutants behave like the parental variants in the presence of Ca 2+ -CaM. This implies a mechanistic explanation for the effect of Ca 2+ -CaM on WT since favoring entry into deep closed states would result in a decrease in current amplitude in the absence of (a permeable) O1.
Our initial hypothesis that CaM participates constitutively in the gating machinery of the channel, based on the loss of biphasic behavior when the C-terminal binding site for CaM was mutated (Fig. 7D), is unlikely to be correct because although there is a significant binding of CaM to the channel at basal intracellular Ca 2+ , this fraction of channels, combined with the strong increase in bound CaM in the presence of high Ca 2+ and the variable intracellular basal Ca 2+ in oocytes would be insufficient to explain the qualitatively consistent behavior of the current of the different mutants. We speculate that the effects of the mutations in CaM binding sites are more related to their location in the protein than to their ability to bind CaM.
In summary, the gating of KV10.1 (and similar channels) consists of a sequence of events that affect the voltage sensing domain, which moves in two sequential steps (Schonherr et al., 1999) and whose movement is transferred to the pore domain through intramolecular interactions (Bassetto et al., 2023). The voltage sensor maintains the gate closed (Mandala and MacKinnon, 2022), and its displacement has a permissive effect on gate opening. Once this restrictive factor is removed, a second step, most likely corresponding to a rotation of the intracellular ring, occurs and finally allows the gate to relax to the open state (Patlak, 1999).
This final step is the only one directly observed in WT channels.
The presence of O1 allowed us to model the behavior of the mutant channels based on a sequential "standard" Markovian model ( Fig. 8  The model also predicts the behavior of mutant channels under short alternating stimuli between -20 and +50 mV. The current amplitude is larger under these conditions than during constant pulses to +50 mV. Furthermore, it also accounts for the increased current amplitude observed after hyperpolarizing conditioning pulses, that is, when accessing from deep closed states (Suppl 3 to Fig.8).  8).
In summary, this study presents a more complete description of the gating mechanism of KV10.1 channel, which can be extended to other members of the KCNH family. In response to depolarization, the movement of the voltage sensor would have a permissive role for the opening of the gate. The rotation of the intracellular ring would be the effective unlocking mechanism allowing permeation. This has profound implication pertaining the possibilities of fine tuning of gating, since the intracellular ring is more susceptible of posttranslational modifications and protein-protein interactions than the transmembrane domains. Our current knowledge of the physiology and pathophysiology of KV10.1 indicate that the channel is relevant for the regulation of excitability acting at potentials close to the resting, rather than during active electrical signaling. Therefore, sustained modulation of gating, possible through modification of the intracellular ring, would be crucial for channel function. Since they allow dissection of the ring-dependent effect, our mutants will allow for a direct study of such modulation mechanisms,

Constructs
Mutants were generated using KV10.1 (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 (Table S3). The subsequent PCR amplification will then omit the sequence between the hybridization sites for the primers. 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).
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. Fitmaster (HEKA Elektronik) and IgorPro (WaveMetrics) were then used to analyze the recordings.
Most conductance-voltage plots are obtained for recordings with [K + ]ext =60mM. In this condition, tail currents are large and allow precise estimation of the reversal potential Veq. 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, conductance was calculated from the end-pulse current after measuring the reversal potential (Veq) using: = /( 4 − 56 ) Eq.2 where I is the current amplitude and Vm the stimulus. Conductance was then normalized to the maximum value and plotted against voltage stimulus. For WT recordings (Fig. 1B), a sigmoidal response was then fitted with a Boltzmann equation: ( ) = .1 + exp 3( 7 − 4 )/ 56 +# Eq.3 With Vh being the voltage for half-maximal activation, K the slope factor and Vm 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: Eq.5
CaEGTA and EGTA were then added to the lysis buffer, adjusting EGTA/CaEGTA to control the concentration of free Ca 2+ 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 KV10.1 or 5xmyc-calmodulin were lysed in a Ca 2+ 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 1.5h at 4 °C . Protein G magnetic beads were then added and incubated for 1.5h at 4 °C in rotation. After magnetic retrieval, the 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 Ca 2+ -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-KV10.1 antibody (Chen et al., 2011) overnight.