Electromechanical coupling mechanism for activation and inactivation of an HCN channel

Pacemaker hyperpolarization-activated cyclic nucleotide-gated (HCN) ion channels exhibit a reversed voltage-dependent gating, activating by membrane hyperpolarization instead of depolarization. Sea urchin HCN (spHCN) channels also undergo inactivation with hyperpolarization which occurs only in the absence of cyclic nucleotide. Here we applied transition metal ion FRET, patch-clamp fluorometry and Rosetta modeling to measure differences in the structural rearrangements between activation and inactivation of spHCN channels. We found that removing cAMP produced a largely rigid-body rotation of the C-linker relative to the transmembrane domain, bringing the A’ helix of the C-linker in close proximity to the voltage-sensing S4 helix. In addition, rotation of the C-linker was elicited by hyperpolarization in the absence but not the presence of cAMP. These results suggest that — in contrast to electromechanical coupling for channel activation — the A’ helix serves to couple the S4-helix movement for channel inactivation, which is likely a conserved mechanism for CNBD-family channels. Sea urchin hyperpolarization-activated cyclic nucleotide-gated (spHCN) ion channels channels are activated by membrane hyperpolarization instead of depolarization and undergo inactivation with hyperpolarization. Here authors apply transition metal ion FRET, patch-clamp fluorometry and Rosetta modeling to measure differences in the structural rearrangements between activation and inactivation of spHCN channels.

H yperpolarization-activated cyclic nucleotide-gated (HCN) ion channels are opened by membrane hyperpolarization, a phenomenon important for pacemaking in the heart as well as for spontaneous neuronal firing, oscillatory activity, and synaptic transmission in the brain [1][2][3] . This type of electromechanical coupling is reversed compared to most other voltagegated ion channels (VGICs), which are activated by membrane depolarization 4,5 . Paradoxically, HCN channels share a common architecture with other VGICs-particularly cyclic nucleotidegated (CNG) and KCNH channels-with four similar or identical subunits around a centrally-located pore. Each subunit consists of a voltage-sensing domain (VSD) with four (S1-S4) transmembrane helices, a pore domain (PD) with S5-S6 transmembrane helices, an amino-terminal HCN domain (HCND), a carboxyterminal C-linker domain, and a carboxy-terminal cyclic nucleotide-binding domain (CNBD) (Fig. 1a) 3,6,7 . Distinct from the "domain-swapped" VSD-PD architecture of canonical VGICs 8 , however, the VSD and PD of CNBD-family channels, including HCN, CNG, and KCNH channels, are not domain swapped (Fig. 1b) [9][10][11] . The VSD of "non-domain-swapped" channels is adjacent to the PD of the same subunit so that the S4 helix is closely packed to the S5 helix of the same subunit but also in close proximity to the S6 helix and the C-linker region of the neighboring subunit (Fig. 1a, b). Interestingly, CNBD family channels, like HCN and KCNH channels, the VSD and C-linker are in a VSD/C-linker domain-swapped configuration (Fig. 1b). Despite these structural similarities between HCN channels and KCNH channels (e.g., EAG1 and hERG1) ( Supplementary  Fig. 1a), HCN channels are activated by membrane hyperpolarization whereas KCNH channels are activated by depolarization ( Supplementary Fig. 1b). Sea urchin sperm HCN (spHCN) channels also undergo a voltage-dependent inactivation process with hyperpolarization, making the channels opened by both hyperpolarization (activation) and depolarization (recovery from inactivation) [12][13][14] .
The detailed movement of the S4 helix of spHCN has been characterized using transition metal ion Förster resonance energy transfer (tmFRET) combined with Rosetta modeling 15 . Upon hyperpolarization, the S4 helix exhibits an~10 Å downward translation and a tilting/bending motion in the C-terminal portion of the helix 15 . Two voltage-sensing arginines in the S4 move from above the hydrophobic constriction site (HCS), a narrow region in the center of the VSD characterized by a conserved hydrophobic residue (phenylalanine in spHCN) 5 , to below the HCS in response to −100 mV hyperpolarization. This movement likely underlies the voltage-dependence of the hyperpolarizationdependent activation 15 . This rearrangement is consistent with a recent cryo-electron microscopy (cryo-EM) structure of HCN1 locked in the activated position by a metal bridge 16 , as well as molecular dynamics simulations 17 .
Electromechanical coupling is the process by which changes in membrane voltage produce a rearrangement of the VSD that is coupled to a rearrangement of the PD. The polarity of voltagedependent gating is likely determined by the direction of the coupling between the VSD and the PD. The rearrangement of the VSD of HCN channels in response to voltage is generally similar to that in other depolarization-activated channels, with the positively-charged S4 helix moving downward upon hyperpolarization (upward upon depolarization) [15][16][17][18][19][20] . Interestingly, minimal mutations in the intracellular sides of the S4 and S5 helices could reverse the gating polarity of HCN channels, making them depolarization activated 14,21,22 . Some mutations produce channels that are both hyperpolarization activated and depolarization activated 14,22 , suggesting that the coupling pathways for hyperpolarization and depolarization activation are distinct.
The mechanism of electromechanical coupling is thought to differ between the domain-swapped VGICs and the non-domainswapped CNBD channels. For these domain-swapped channels, the coupling is thought to occur primarily through the covalent linkage between the S4 helix of the VSD and the S5 helix of the PD, the S4-S5 linker 5,20,23 . This S4-S5 linker-dependent pathway is considered the canonical electromechanical coupling for VGICs. However, a covalent linkage between the S4 and S5 segment is not required for the voltage-dependent gating of the non-domainswapped channels EAG1, hERG1, and spHCN 14,24,25 . For these non-domain-swapped channels, the electromechanical coupling has been proposed to involve either a noncovalent interaction between the S4 and S5 helices of the same subunit or via the Clinker in the adjacent subunit 22,26 .
Cyclic nucleotide monophosphates (cNMPs) directly bind and potentiate the activity of HCN channels, an important pathway for regulating HCN channels during cell signaling 4,27 . For most HCN channels, cyclic adenosine monophosphate (cAMP) is a full agonist for the CNBD and promotes channel opening 28 , causing a depolarizing shift in the voltage dependence of activation. In spHCN channels, however, cAMP also eliminates the voltagedependent inactivation that occurs in the absence of cyclic nucleotide. Binding of cAMP to the CNBD induces a conformational change that is relayed to the transmembrane regions of HCN channels via the C-linker 3,29,30 . The C-linker region is comprised of six helices: A′-F′ helices, with the A′ helix immediately following the S6 transmembrane helix and running nearly parallel to the membrane 6,27 . The A′ and B′ helices form a helixturn-helix motif that interacts with the C′ and D′ helices of the neighboring subunit. This intersubunit "elbow-on-the-shoulder" interaction forms a gating ring immediately below the transmembrane region and is involved in the cyclic nucleotidedependent regulation of HCN and CNG channels 29 .
Here we used tmFRET to determine the conformational changes of spHCN channels in response to membrane hyperpolarization and cyclic-nucleotide binding. Distances measured with tmFRET under different conditions-in the presence and absence of cAMP, and at different voltages (0 or −100 mV)were used as constraints for Rosetta-based structural modeling. The changes in distance could be accounted for by a largely rigidbody rotation of the C-linker relative to the transmembrane domain, putting the A′ helix in close proximity to the S4 helix in the absence of cyclic nucleotide. We propose a mechanism where a rearrangement of the A′ helix in the C-linker could help to translate the downward movement of the S4 into closure of the channel pore (inactivation). In the presence of cAMP, the A′ helix moves further away from the S4 helix, permitting the hyperpolarization-dependent activation mediated by the S5 helix.

Results
Inactivation of spHCN channels in the absence of cyclic nucleotide. Cyclic nucleotides are required to maintain the hyperpolarization-dependent opening of spHCN channels 12 . In the presence of 1 mM cAMP, spHCN channels were activated by hyperpolarizing voltage pulses, similar to mammalian HCN channels (Fig. 1c). However, in the absence of cyclic nucleotide, the spHCN channels rapidly inactivated and exhibited much smaller peak currents compared to those in the presence of cAMP 13 (Fig. 1c). Previously it has been shown that this inactivation process is primarily from closed states and appears to be voltage dependent, occurring more rapidly and completely at hyperpolarized voltages 13,14,31 . In addition, removing the carboxy-terminal region of spHCN channels, including the CNBD and C-linker, eliminates this inactivation 32,33 . The findings that inactivation is voltage dependent and eliminated by cAMP or carboxy-terminal deletion suggest that the spHCN inactivation is tightly coupled to voltage-sensor movement and involves the carboxy-terminal region, particularly the C-linker.
Voltage-sensor movement in the absence of cyclic nucleotide. To understand the structural mechanism of the inactivation of spHCN channels, we asked whether the S4 helix in the VSD still moved with hyperpolarization in the absence of cyclic nucleotide when the channels are largely inactivated. As we previously showed 15 , the fluorescent noncanonical amino acid L-Anap, with its environmentally-sensitive fluorescence emission, allows us to observe the movement of the S4 by measuring the change in  environment of S4 residues upon hyperpolarization. We introduced L-Anap at Ser 346 , in the middle of the S4 helix of a spHCN-YFP fusion construct, using the amber stop-codon (TAG) suppression strategy in Xenopus oocytes 15 (Supplementary Fig. 2a). Patch-clamp fluorometry (PCF) was used to simultaneously measure the fluorescence and ionic current from giant inside-out patches from oocytes, while controlling membrane voltage and rapidly applying intracellular ligands (e.g., cAMP and transition metals) 34,35 . Specific L-Anap incorporation and full-length channel expression were confirmed by the correlation of the magnitude of Anap fluorescence with both the YFP fluorescence and spHCN ionic currents (see 15 ). As we reported previously, there was a substantial increase in the Anap fluorescence in spHCN-S346Anap during hyperpolarizing voltage pulses of −100 mV in the presence of a saturating concentration (1 mM) of the full agonist cAMP (ΔF/F = 61.2 ± 3.3%) ( Supplementary Fig. 2b) 15 . The partial agonist cyclic guanosine monophosphate (cGMP) produced much smaller ionic current, and the absence of cyclic nucleotide generated negligible current, with steps to −100 mV; however, the Anap fluorescence still elevated considerably (ΔF/F = 46.3 ± 2.2% in cGMP and ΔF/ F = 26.0 ± 3.3% in the absence of cyclic nucleotide) (Supplementary Fig. 2b). These results suggest that the S4 helix moved with hyperpolarizing voltage regardless of whether the channel is inactivated (in the absence of cyclic nucleotide) or activated (in the presence of cAMP). Nevertheless, use of the environmental sensitivity of L-Anap provided limited structural information about the size of the S4 movement.
To measure the voltage-sensor movement more quantitatively, we used tmFRET 36,37 . tmFRET measures the distance between a donor fluorophore and an acceptor non-fluorescent transition metal ion, such as Ni 2+ , Co 2+ , and Cu 2+ , bound to minimal transition metal ion binding sites introduced into the protein.
Transition metals such as Ni 2+ , Co 2+ , and Cu 2+ have absorption spectra that overlap with the emission spectrum of L-Anap and hence can serve as nonfluorescent FRET acceptors that quench the donor's fluorescence in a highly distance-dependent manner. Because the absorption of most transition metals is low, with multiple transition dipoles, tmFRET can measure short distances (10-25 Å) with little or no orientation dependence. L-Anap and metal bound to an introduced di-histidine motif are closely associated with the protein backbone and well suited as a tmFRET pair for measuring the backbone distances and changes in distance associated with protein conformational changes.
To quantify the downward movement of the S4 helix, we measured tmFRET between S346Anap in the S4 and Co 2+ bound to a di-histidine motif (L182H-L186H) introduced into an α helix of the amino-terminal HCND directly below the S4, as previously described (Fig. 1d) 15 . Upon application of 1 mM Co 2+ , there was substantial quenching of Anap fluorescence indicative of FRET between S346Anap and Co 2+ bound to the di-histidine site in the HCND. In the presence of 1 mM Co 2+ , the Anap fluorescence was decreased by the −100 mV hyperpolarization, instead of increased in the absence of Co 2+ , indicating that the quenching (and therefore FRET efficiency) was greater at −100 mV than at 0 mV (Fig. 1e). We quantified the apparent tmFRET efficiency at each voltage by calculating the fractional decrease in Anap fluorescence produced by 1 mM Co 2+ and correcting for the solution quenching in spHCN-S346Anap channels lacking the dihistidine site 15 . In the absence of cyclic nucleotide, FRET efficiency increased substantially at −100 mV, similar to the increase seen in cAMP and cGMP (Fig. 1f). These results indicate that the Ser 346 position in the S4 helix moved downward-closer to the HCND-with hyperpolarization in the absence of cyclic nucleotide, similar to the movement with cAMP or cGMP. These data suggest that inactivation of spHCN channels in the absence of cyclic nucleotide does not arise from immobilization or a fundamentally different movement of the S4 helix.
Rearrangement of the C-linker relative to the S4 helix. How does the spHCN channel inactivate in the absence of cyclic nucleotide? The C-linker is situated just below the transmembrane domain and directly communicates cAMP binding to the CNBD to the transmembrane domain. Therefore, we studied the movement of the C-linker relative to the transmembrane domain using tmFRET 15,36,38,39 . For these and subsequent experiments in this study, we used a variation of tmFRET called ACCuRET (Anap Cyclen-Cu 2+ resonance energy transfer) 15,36,38,39 . ACCuRET measures the FRET efficiency between a donor fluorophore (L-Anap) and an acceptor Cu 2+ chelated by TETAC (1-(2-pyridin-2-yldisulfanyl) ethyl)-1,4,7,10-tetraazacyclododecane) 15,39 . TETAC is a cysteine-reactive compound with a short linker to a cyclen ring that binds transition metal ions with subnanomolar affinity. Single cysteines introduced into the protein react with Cu 2+ -TETAC to introduce a transition metal ion acceptor closely associated with the protein backbone. This configuration of tmFRET allowed us to measure the FRET efficiency as the fractional quenching of Anap fluorescence upon modification by Cu 2+ -TETAC. The distance between Anap and Cu 2+ -TETAC could then be calculated from the FRET efficiency.
ACCuRET was used to measure distances between the transmembrane domain and the C-linker of spHCN channels in the presence and absence of cAMP, at 0 and −100 mV. For the tmFRET donor, L-Anap was incorporated into a cysteine-reduced spHCN-YFP construct at Trp 355 (spHCN-W355Anap), near the intracellular end of the S4 helix, using amber stop-codon suppression 15 . This cysteine-reduced spHCN channel behaved similarly to wild-type channels as previously reported 15 . In addition, we have previously demonstrated efficient and specific L-Anap labeling at the W355 position in spHCN 15 . For the tmFRET acceptors, single cysteines were introduced into the Clinker at two different sites, L481C in the A′ helix ( Fig. 2a) and E506C in the B′ helix (Fig. 2b). Distances between the donor and acceptor were predicted to be much shorter for adjacent subunits (22.1 Å for L481 and 18.8 Å for E506) than for the same subunit (41 Å for L481 and 44.8 Å for E506) or between diagonal subunits (28.1 Å for L481 and 35.4 Å for E506) based on the β-carbon distances in the solved hHCN1 structure (PDB code: 5U6P) 9 . Therefore, considering the R 0 is around 13 Å for W355Anap (see methods), tmFRET is expected to occur primarily between donors and acceptors in adjacent subunits for these sites (also see Supplementary Table 1 summarizing the distance measurements of final structural models). These channels, with W355Anap and Cu 2+ -TETAC modification of the C-linker sites, exhibited hyperpolarization-dependent activation in the presence of cAMP and inactivation in the absence of cAMP similar to the wild-type channel ( Supplementary Fig 3a, c).
As above, PCF was used to simultaneously measure the tmFRET and ionic current while controlling membrane voltage and intracellular ligands (cAMP and Cu 2+ -TETAC) 34,35 (Supplementary Fig. 3). For spHCN-W355Anap, L481C, the Anap fluorescence was significantly quenched after 1-min application of 20 µM Cu 2+ -TETAC to the intracellular side of the patch. The degree of quenching (1 -F Cys ) was considerably higher than the nonspecific quenching (1 -F no Cys ) seen for spHCN-W355Anap without L481C (Fig. 2c). At 0 mV, the Cu 2+ -TETAC quenching of Anap fluorescence was greater in the absence of cyclic nucleotide than in the presence of cAMP ( Fig. 2c and Supplementary Fig. 4a). With voltage steps to −100 mV, Anap fluorescence decreased even in the control condition (in the absence of Cu 2+ -TETAC) due to the environmental change associated with the movement of W355Anap, as we previously reported 15 (Supplementary Fig. 4a). However, at −100 mV, Cu 2 + -TETAC produced an additional decrease in fluorescence, greater than that at 0 mV, and again greater in the absence of cyclic nucleotide than in the presence of cAMP. FRET efficiencies were calculated from the fractional quenching in Anap fluorescence after application of Cu 2+ -TETAC for each condition (0 and −100 mV, in the presence and absence of cAMP) and corrected for the small Cu 2+ -TETAC-dependent quenching in the control lacking L481C. Since the FRET efficiency was measured independently at 0 and −100 mV, the measurement was not affected by the environmental change in Anap fluorescence. Accordingly, at both 0 and −100 mV, the absence of cyclic nucleotide yielded a higher FRET efficiency than the presence of cAMP, indicating a shorter distance between Trp 355 in the S4 and Leu 481 in the A′ helix in the absence of cyclic nucleotide. At −100 mV, the FRET efficiencies all increased significantly relative to 0 mV, consistent with the downward movement of S4 helix with hyperpolarization (Fig. 2c, d and Supplementary Fig. 4a).
Similar experiments were done on spHCN-W355Anap, E506C with the Cu 2+ -TETAC site relocated to the B′ helix in the C-linker (Fig. 2c, e). As above, the channel without the introduced cysteine (spHCN-W355Anap) was used as the control for correcting for any nonspecific quenching to calculate FRET efficiency. Surprisingly, with the acceptor at the B′ helix site, at both 0 and −100 mV, the FRET efficiency was less in the absence of cyclic nucleotide than in the presence of cAMP, opposite to what we observed at the A′ helix site (Supplementary Fig. 4b). Furthermore, as expected, the FRET efficiency increased with hyperpolarization due to the downward movement of the S4 helix. Together, these results reveal a rearrangement of the C-linker in the absence of cyclic nucleotide, moving the A′ helix closer to the S4 helix and the B′ helix further from the S4 helix. As we discuss below, this rearrangement may permit the inactivation process observed, in the absence of cyclic nucleotide, in spHCN channels.
Rearrangement of the A′ helix of the C-linker relative to the S5 helix. Next, we studied the movement of the C-linker relative to the S5 helix by incorporating L-Anap into position Cys 369 near the intracellular end of the S5 helix. The spHCN-C369Anap channel expressed well, produced a considerable amount of current in the presence of cAMP ( Supplementary Fig. 5a), and exhibited a strong correlation between the fluorescence intensities of L-Anap emission and the ionic current and emission of the Cterminal YFP (Supplementary Fig. 5b). In contrast to channels with L-Anap incorporated into the S4 helix, the spHCN-C369Anap channels did not exhibit a noticeable environmental change of Anap fluorescence between 0 and −100 mV (Supplementary Fig. 5c).
We then measured tmFRET between Anap on the S5 helix (C369Anap) and Cu 2+ -TETAC on a site in the A′ helix (Y477C) (Fig. 3a) and compared it to the tmFRET between Anap on the S4 helix (W355Anap) and Cu 2+ -TETAC on the same A′ helix site (Y477C) (Fig. 3b). The spHCN-C369Anap, Y477C channels show similar cAMP modulation, inactivation in the absence of cyclic nucleotide, and voltage dependence of activation, before and after applying Cu 2+ -TETAC, to the wild-type channels (Supplementary Fig. 6). Note that in these experiments, Y477C was used on the A′ helix instead of L481C (one helix turn away) because Y477C is closer to the Cys 369 position of the S5 helix. Indeed, for spHCN-W355Anap, Y477C channels, the results for tmFRET were quite similar to those from spHCN-W355Anap, L481C channels (Fig. 3d).
For these two tmFRET pairs with donor sites on the S5 and S4 helices, cAMP produced opposite effects at 0 mV. When L-Anap was located in the S5 helix, the FRET efficiency was lower in the absence of cyclic nucleotide than in the presence of cAMP (Fig. 3c). Conversely, when L-Anap was in the S4 helix, the FRET efficiency was higher in the absence of cyclic nucleotide than in the presence of cAMP (Fig. 3d). These results suggest that the absence of cyclic nucleotide produced a rearrangement of the A′ helix at 0 mV, bringing the A′ helix closer to the S4 helix and further away from the S5 helix.
In the presence of cAMP, applying the −100 mV hyperpolarizing pulse produced a strikingly lower FRET efficiency for spHCN-C369Anap, Y477C (Cu 2+ -TETAC) channels (Fig. 3c). This increase in distance likely results from a movement of S5 helix coupled to the movement of the S4 at −100 mV. Such a movement of the S5 has recently been demonstrated in a cryo-EM structure of the down state of HCN1 16 and can quantitatively account for our observed decrease in FRET efficiency (see modeling below). Interestingly, in the absence of cyclic nucleotide, −100 mV pulses failed to produce this decrease in FRET (Fig. 3c); instead, increased FRET efficiency slightly. This difference in voltage-dependence of the S5-A′ helix distance in the presence and absence of cAMP is likely related to the inactivation of spHCN in the absence of cAMP. It could result from either a lack of S5 helix movement in the inactivated state, or a difference in the movement of the A′ helix in the inactivated state, or both (see modeling below).
Rosetta models for the cAMP-and hyperpolarizationdependent gating. To perform a more comprehensive structural analysis of our FRET data in various states, we used our FRET efficiencies to determine the distances between donor and acceptor sites for each FRET pair in the presence and absence of cAMP, at 0 and −100 mV. The distance dependence of our tmFRET was estimated by plotting our FRET efficiencies at 0 and −100 mV in the presence of cAMP versus the corresponding βcarbon distances (in distance/R 0 units) from cryo-EM structures of hHCN1 bound to cAMP (in the up and down states of the S4, respectively) (Fig. 4). This strategy is based on the assumption that spHCN in the presence of cAMP shares structural similarity with hHCN1 based on similarities in their sequence and hyperpolarization-dependent activation 12 . For each donor site, W355Anap or C369Anap, we determined the R 0 using the emission spectra and quantum yields of Anap at each site at 0 and −100 mV, and the absorption spectrum of Cu 2+ -TETAC (see Supplementary Fig. 5d and Methods) 15 . As previously observed 15,39 , the relationship between FRET efficiency and distance was somewhat shallower than predicted by the Förster equation, likely due to heterogeneity of the interatomic distances in proteins (Fig. 4b).
To account for this heterogeneity, the data were fit by the convolution of the Förster equation with a Gaussian function (Förster Convolved Gaussian (FCG)) as previously described 15,39 . In this case, when FRET donors were in the transmembrane segments and acceptors were in the C-linker, a Gaussian distribution of distances with a standard deviation of 5 Å could fit the distance dependence of the FRET efficiency we observed at 0 and −100 mV in the presence of cAMP (Fig. 4b).
This relationship also assumes similar heterogeneity in our different transmembrane segment-C-linker distances and provides a standard curve to convert our measured FRET efficiencies to βcarbon distances for each of the conditions in our experiment. While the distances may also reflect the rotameric states of L-Anap and Cu 2+ -TETAC-modified cysteines, previous experiments have suggested that this effect is minimal with the short linkers of our donor and acceptor 15,39 . Figure 5 shows the distances for each FRET pair in four conditions: cAMP bound at 0 mV, "resting-cAMP state"; apo at 0 mV, "resting-apo state"; cAMP bound at −100 mV, "activated state"; and apo at −100 mV, "inactivated state". To interpret our measured distances in the context of the channel structure, we used Rosetta-based structural modeling 15,40,41 . The Rosetta software suite is a powerful set of programs for predicting the structure of proteins based on known high-resolution structures, experimental constraints, and empirical rules for protein folding. It allowed us to combine known cryo-EM structures of HCN channels with our measured distances to identify rearrangements of the channel that are consistent with each of our four distances in each state. We began by generating starting models of the spHCN channel for each of the four states: resting-cAMP, resting-apo, activated, and inactivated. The starting models for resting-cAMP and restingapo states were based on the cryo-EM structures of hHCN1 in the presence (PDB: 5U6P) and absence (PDB: 5U6O) of cAMP, respectively. The starting model for the activated state was based on the hHCN1 cyro-EM structure with its S4 trapped in the down state by a metal bridge. Because of the lack of a decrease in FRET efficiency between the S5 helix and the A′ helix with voltage steps to −100 mV in the absence of cAMP (Fig. 4d), the starting model for the inactivated state was a chimeric homology model with the amino terminus and VSD from the S4 helix-down structure (PDB code: 6UQF) and the S5-S6 and the carboxy-terminal region from the apo structure of hHCN1 (PDB code: 5U6O). We then imposed our distance measurements as constraints in the βcarbon distances in the Rosetta modeling. The modeling assumed fourfold symmetry and primarily rigid-body movements between the transmembrane domain and carboxy-terminal region (see Methods). With the above assumptions and constraints, the modeling in each state converged, with the top 17 highest scoring models for each state nearly identical (Cα RMSD <1 Å ( Supplementary Fig. 7). Furthermore, the Rosetta models accurately reproduced the distances measured from our tmFRET experiments for each of the four states (Fig. 5).
cAMP-induced rearrangement of the C-linker region of spHCN channels. The resting-cAMP model was quite similar to  Fig. 4. However, the resting-apo model exhibited a noticeable rearrangement of the carboxy-terminal C-linker and CNBD. These models suggest a largely rigid-body clockwise rotation of the Clinker in spHCN channel in the absence of cyclic nucleotide at 0 mV as viewed from the intracellular side (Fig. 6, Supplementary  Fig. 8, and Supplementary Movie 1). This rotation causes the A′ helix to move closer to the S4 helix and further from the S5 helix, and the B′ helix to move further from the S4 helix, as predicted from the FRET measurements alone (Fig. 5a, c). In addition, in the absence of cyclic nucleotide, the C-linker moved slightly downward relative to the transmembrane domain (Fig. 6, Supplementary Fig. 8, and Supplementary Movie 1). This new position of the A′ helix in the absence of cyclic nucleotide could provide a possible link between the S4 helix and the A′ helix and might be critical for the inactivation observed in spHCN channels in the absence of cyclic nucleotide.
Comparing the inactivated to the activated models at −100 mV, the absence of cAMP in the inactivated model produced a qualitatively similar rearrangement of the C-linker as seen in the resting models, despite the S4 helix of the VSD being in the down position. Like the resting models, the C-linker undergoes a clockwise rotation around the central axis of the pore and small downward movement in the absence of cAMP (Fig. 6, Supplementary Fig. 8, and Supplementary Movie 2). The rotation, however, is somewhat smaller at −100 mV than observed at 0 mV. As discussed below, this smaller rotation appears to be due to the downward and tilted position of the carboxy-terminal region of the S4 and may underlie the inactivation of spHCN seen at −100 mV.
Hyperpolarization-induced activation and inactivation of spHCN. The resting-cAMP and activated models largely reflect the starting models used in the Rosetta modeling based on known HCN1 cryo-EM structures, as expected from Fig. 4. Compared to the resting-cAMP model, the activated model displays a large (~10 Å) downward movement of the S4 with a tilting motion below residue Ser 346 (Fig. 6, Supplementary Fig. 8, and Supplementary Movie 3). This rearrangement is also consistent with previous tmFRET measurements of the movement of the S4 and molecular dynamics simulations [15][16][17] . In addition, the activated model showed a significant bending movement of the S5, consistent with the cryo-EM structure of the hHCN1 channel with its S4 helix trapped in the downward position 16 (Fig. 6, Supplementary Fig. 8, and Supplementary Movie 3). These features were present in the starting models and were largely constrained during the modeling. Nevertheless, this movement of the S5 could almost completely account for the decrease in FRET efficiency between the S5 helix and the A′ helix with hyperpolarizing steps to −100 mV in the presence of cAMP (Fig. 3d). Like the hHCN1 structure 16 , the activated model displayed little change in the relative orientation of the transmembrane domain and Clinker relative to the resting-cAMP model ( Supplementary  Movie 3). Indeed, the activated spHCN model and the hHCN1 model with the S4 helix trapped in the down position had an RMSD of only 1.91 Å. These results suggest that the hHCN1 S4down structure 16 also well represents the spHCN activated structure (at −100 mV in the presence of cAMP), and the mechanism of hyperpolarization-dependent activation of spHCN channels is likely to be similar to that of mammalian HCN channels. The conformational rearrangements between the resting-apo and inactivated models showed features distinct from those in the presence of cAMP (Fig. 6, Supplementary Fig. 8, and Supplementary Movie 4). Unlike the models in the presence of cAMP, the inactivated model displayed a considerable rotation of the Clinker relative to the resting-apo model (compare Supplementary  Movies 3 and 4). The rotation appears to result from an interaction between the carboxy-terminal region of the S4 helix and the A′ helix, causing the downward and tilting motion of the S4 to be translated into a rotation of the C-linker (Supplementary Movie 4). The counterclockwise rotation of the C-linker at −100 mV in the absence of cyclic nucleotide is in the direction expected to wind the S6 bundle and might be responsible, at least in part, for pore closure (inactivation). These models, therefore, provide a potential molecular mechanism for how hyperpolarization causes activation in the presence of cAMP and inactivation in the absence of cAMP for spHCN channels.

Discussion
All HCN channels are activated by membrane hyperpolarization. However, unlike mammalian HCN channels, spHCN channels also undergo hyperpolarization-dependent inactivation in the absence of cyclic nucleotide which is eliminated in the presence of cAMP. Using tmFRET, we show that the movement of the S4 is similar in the presence and absence of cAMP, suggesting that the inactivation does not result from a change in the S4 movement, but from a conformational change that is coupled to the S4 movement, exclusively in the absence of cAMP. Furthermore, we show that, in the absence of cyclic nucleotide, there is a substantial repositioning of the A′ helix of the C-linker region closer to the S4 segment. Using Rosetta modeling of our tmFRET results, we show how the close proximity between the S4 helix and the A′ helix might allow the downward movement of the S4 helix with hyperpolarization to be coupled to the pore via the A′ helix ( Fig. 6 and Supplementary Movie 4). This coupling could make opening of the channel less favorable, leading to inactivation. We therefore propose that the A′ helix may mediate the coupling between the S4 segment and the PD during voltagedependent inactivation.
This hypothesis for inactivation is consistent with a number of previous observations in CNBD-family channels. It has previously been shown that, unlike the N-type or C-type inactivation in voltage-dependent potassium (Kv) channels 42 , the inactivation in spHCN channels involves the same gate as activation, the bundle crossing at the bottom of the S6 13 . This idea of using the same gate for both activation and inactivation of spHCN is compatible with our proposed mechanism for inactivation. While the mechanism for inactivation was originally proposed to involve a loss of coupling between the VSD and the pore (also referred to as desensitization to voltage or "slippage") 13 , that mechanism cannot account for the constitutive opening produced by many mutations that disrupt electromechanical coupling of spHCN channels 14 . Our Rosetta model suggests that a separate new coupling pathway contributes to the inactivation rather than a simple loss of coupling for activation. Perhaps most importantly, in spHCN channels, deletion of the carboxy-terminal domain, including the A′ helix, eliminates the inactivation process while leaving the hyperpolarization-dependent activation intact 32,33 . Similarly, removing the S4-S5 linker, which generates a split channel with a break in the backbone between the VSD and the PD, attenuates the inactivation 14 . In addition, crosslinking the A′ helix to the S4-S5 linker with a Cd 2+ bridge can produce channels that are closed at hyperpolarized voltages but open at depolarized voltage (depolarization-activated) 43 . All of these observations are consistent with the A′ helix mediating the coupling between the S4 segment and the pore during voltagedependent inactivation.
The C-linker, including the A′ helix, is common to all CNBD family channels 6 . The A′ helix has been shown to rearrange after cyclic-nucleotide binding to promote the pore opening, which was further corroborated in the new cryo-EM structures of a eukaryotic CNG channel TAX-4 and a human rod photoreceptor CNGA1 channel 11,30,[44][45][46][47] . Our models display an upward movement of the C-linker after cyclic nucleotide binding similar to other CNBD family channels 44,46,48,49 . However, a counterclockwise rotation of the A′-B′ helix around the central axis of the pore after cAMP binding ( Supplementary Movies 1 and 2) a b Resting-cAMP Activated was also revealed in our tmFRET measurements and modeling. This movement has not been observed in other CNBD family channels, including the rearrangement between the open and closed conformations of TAX4 44 or human CNGA1 47 , and may underlie why this type of inactivation is only observed in spHCN channels but not in other HCN or CNG channels.

Resting-apo Inactivated
The hyperpolarization-dependent activation of HCN channels involves a different coupling pathway, independent of the A′ helix or the short S4-S5 linker. HCN channels with a deletion of either the A′ helix or the S4-S5 linker maintain their hyperpolarizationdependent activation 14,32,33,50 . Instead, mutations of the S4 and S5 segments can eliminate the hyperpolarization-dependent activation and uncover depolarization-dependent activation 14,21,22 . This depolarization-dependent activation is eliminated by the addition of cAMP, reminiscent of the hyperpolarization-dependent inactivation in spHCN channels 14 .
Collectively, it appears that there are two separate coupling pathways for voltage-dependent regulation of spHCN channels. The hyperpolarization-dependent activation seems to involve a stabilization of the closed conformation of the pore by the "up state" of the S4 helix via the S5 helix, while the hyperpolarizationdependent inactivation seems to involve stabilization of the closed (inactivated) state via the A′ helix. A mixture of these two pathways could explain the "bell-shaped" and "U-shaped" G-V relationships often observed in the CNBD-family channels 14,22,51 .
How might the position of the A′ helix in the absence of cyclic nucleotide couple the downward movement of the S4 to channel closing (inactivation)? Morphs between our proposed resting-apo and inactivated structures suggest that hyperpolarizing voltage steps elicit a counterclockwise rotation of the A′ helix of the Clinker around the pore central axis (Supplementary Movie 4) which could twist the bundle crossing closed. In contrast, in the presence of cAMP, there is no rotation (Supplementary Movie 3). The inactivation, therefore, might result from an interaction between the S4 or S4-S5 linker and the A′ helix in the absence of cyclic nucleotide so that the tilting motion of the S4 essentially drags the A′ helix in a counterclockwise direction (Supplementary Movie 4). In the presence of cAMP, the S4 is further from the A′ helix and might interact more weakly or differently with the A′ helix. In this sense, the A′ helix seems to function as a clutch for inactivation. In the absence of cyclic nucleotide, the clutch is engaged allowing the downward movement of the S4 to close (inactivate) the pore. Like pushing the clutch pedal on a car, cAMP disengages the clutch and the downward movement of the S4 no longer causes channel closure. For mammalian HCN channels, it is likely that this A′ helix clutch is mostly disengaged so that they do not inactivate even in the absence of cyclic nucleotide. We speculate that the A′ helix of mammalian channels might rotate differently in the absence of cAMP, so that it is not positioned to couple the movement of the S4 to channel inactivation. In general, coupling is an inherently energetic phenomenon, and it is currently very difficult to estimate energetics from structures alone.
The mechanism we propose might be relevant to other channels in the CNBD family. KCNH channels have an overall architecture similar to HCN channels, including a non-domainswapped VSD, a C-linker, and a cyclic nucleotide-binding homology domain (CNBHD) 52 . However, KCNH channels are activated by membrane depolarization instead of by membrane hyperpolarization. It is worth noting that the hyperpolarizationdependent inactivation in spHCN can also be viewed as a depolarization-dependent activation. Indeed, we found the Clinker movement of spHCN in the absence of cAMP in response to depolarizing voltage steps resembles that postulated for KCNH channels by morphing the closed EAG structure and the open hERG structure [53][54][55] (Supplementary Movie 5). We postulate that the A′ helix may function similarly for the depolarizationdependent activation of KCNH channels and the hyperpolarization-dependent inactivation of spHCN channels. This A′ helix-mediated pathway has also been proposed to underlie the calmodulin modulation and "Cole-Moore" effect of KCNH (EAG) channels 55 . Furthermore, a role for the A′ helix in hyperpolarization-dependent activation has also been proposed for KAT1 channels, a plant CNBD channel 26 . Interestingly, in the canonical domain-swapped VGICs, the S4-S5 linker forms a long helix that is in a structurally-similar position to the A′ helix of CNBD channels, and has been proposed to have a similar functional role, to couple the downward movement of the S4 to closure of the channel 20,23,56 .
In conclusion, the CNBD family channels could have evolved two noncanonical coupling pathways between the VSD and the PD: hyperpolarization-dependent stabilization of the open state that involves the amino-terminal part of S5 helix and depolarization-dependent stabilization of the open state that involves the A′ helix of the C-linker. These two pathways for VSD-PD coupling might act nearly simultaneously to affect the overall energetics of channel opening and can explain the diverse voltage-dependent gating behaviors of the CNBD family of channels. Oocyte expression and electrophysiology. The animal-use protocols were consistent with the recommendations of the American Veterinary Medical Association and were approved by the Institutional Animal Care and Use Committee (IACUC) of the University of Washington. L-Anap (free-acid form, AsisChem, Waltham, MA) was made as a 1 mM stock in water at a high pH by adding NaOH as previously published 15 . The pANAP plasmid (purchased from Addgene, Cambridge, MA) contained the orthogonal tRNA/aminoacyl-tRNA synthetase specific to L-Anap 57 . Inside-out configuration of the patch-clamp technique was implemented with an EPC-10 (HEKA Elektronik, Germany) or Axopatch 200B (Axon Instruments, Union City, CA) patch-clamp amplifier and PATCHMASTER software (HEKA Elektronik) 15 . Solution changing was done using a µFlow microvolume perfusion system (ALA Scientific Instruments, Farmingdale, NY). For oocyte patch-clamp recording and Co 2+ -HH tmFRET experiments, the standard bath and pipette saline solutions contained 130 mM KCl, 10 mM HEPES, 0.2 mM EDTA (pH 7.2). 1 mM CoSO 4 was added to the perfusion solution with EDTA eliminated. For ACCuRET experiments, stabilization buffer (SBT) contained 130 mM KCl, 30 mM TRIS, 0.2 mM EDTA (pH 7.4) and was used for both the pipette and the bath solution. A + 40 mV voltage was used to facilitate tail-current measurements. The Cu 2+ -TETAC (used at a final concentration of 20 µM) was prepared as previously described 39 .

Methods
Fluorescence measurements. PCF and spectral measurements were done similar to previously published 15 . Our PCF experiments used a Nikon Eclipse TE2000-E inverted microscope with a 60 × 1.2 NA water immersion objective. Epifluorescence recording of L-Anap was performed with wide-field excitation using a Lambda LS Xenon Arc lamp (Sutter Instruments) and a filter cube containing a 376/30 nm excitation filter and a 460/50 nm emission filter. A 425 nm long-pass emission filter was used for the spectral measurement of L-Anap. YFP was measured with a filter cube containing a 490/10 nm excitation filter and a 535/30 nm emission filter. Images were collected with a 200 ms exposure using an Evolve 512 EMCCD camera (Photometrics, Tucson, AZ) and MetaMorph software (Molecular Devices, Sunnyvale, CA). For spectral measurements, images were collected by a spectrograph (Model: 2150i, 300 g/mm grating, blaze = 500 nm; Acton research, Acton, MA) mounted between the Nikon microscope and the Evolve 512 EMCCD camera.
Data analysis. Data were analyzed using IgorPro (Wavemetrics) and Image J (NIH), similar to previously published 15 .
The conductance-voltage (G-V) relationships were measured from the instantaneous tail currents at +40 mV following voltage pulses from 0 mV to between 0 and −110 mV. The relative conductance was plotted as a function of the voltage of the main pulse and fitted with a Boltzmann Eq. (1): where V is the membrane potential, V 1/2 is the potential for half-maximal activation, and V s is the slope factor. Fluorescence images from the membrane patches were imported into ImageJ 58 for analysis. Regions of interest were determined manually around the dome of the patch, excluding any regions of the glass of the pipette (Supplementary Fig. 3b, d).
For each patch, a background subtraction was performed by selecting an area outside of the patch inside the pipette. The mean subtracted fluorescence intensity (fl) was used for the following calculations.
The FRET efficiency was calculated using the following Eq. (2) as previously described 34 : or FRET eff ¼ F no Cys À F Cys F Cys Ã F no Cys þ F no Cys À F Cys Where F HH and F no HH are the fractions of fluorescence that are unquenched by Co 2+ in channels with and without HH sites, respectively; F ¼ fl ðmetalÞ fl ðno metalÞ . Similarly, F Cys and F no Cys are the fractions of fluorescence that are unquenched by Cu 2+ -TETAC in channels with and without cysteines, respectively.
The R 0 values, the distances that predict 50% energy transfer, were calculated using the established Eq. (3) 39 .
Where C is the scaling factor, J is the overlap integral of the donor emission spectrum and the acceptor absorption spectrum, Q is the quantum yield of the donor, η is the index of refraction, and κ 2 is the orientation factor. η was assumed to be 1.33, and κ 2 was assumed to be 2/3, consistent with what was previously reasoned and used 15 . The J values for each L-Anap site at 0 and −100 mV in the presence and absence of cAMP were calculated using the emission spectrum of each site at each voltage and the absorption spectrum of Cu 2+ -TETAC in solution.
The relative quantum yields of L-Anap at each site at 0 and −100 mV were estimated from the slopes of the plots of Anap intensity vs. YFP intensity at 0 mV and the relative brightness at −100 mV vs. 0 mV (fl Anap, −100 mV / fl Anap, 0 mV ) as previously published ( Supplementary Fig. 5) 15 . R 0 values calculated using the estimated spectral overlaps and quantum yields were as follows: 13.3 Å (0 mV) and 13.0 Å (−100 mV) for W355Anap both in the presence and absence of cAMP; and 13.9 Å (0 mV) and 13.9 Å (−100 mV) for C369Anap both in the presence and absence of cAMP. No spectral shifts due to hyperpolarization to −100 mV were observed for either W355Anap or C369Anap emission.
Rosetta modeling. Homology models of the spHCN channel based on the human HCN1 structure 9 were created using RosettaCM without any experimental constraints 40,41 . PDB codes used for the four starting models are: 5U6P for the "resting-cAMP" (cAMP, 0 mV) model, 5U6O for the "resting-apo" (no cyclic nucleotide, 0 mV) model, 6UQF for the "activated" (cAMP, −100 mV) model, and a chimeric combination of 6UQF (amino-terminal end to transmembrane S1-S4) and 5U6O (S5 helix to the carboxy-terminal end) for the "inactivated" (no cyclic nucleotide, −100 mV) model. Four spHCN channel models: resting-cAMP, resting-apo, activated, and inactivated were built and refined using RosettaCM similar to previously published 15 . The structures were refined using RosettaCM with a combination of three types of restraints: (1) coordinate restraints on every non-hydrogen backbone atom tethering the absolute Cartesian coordinates; (2) atom-pair constraints to all backbone atom pairs within some cutoff distance tethering atoms in close proximity to maintain their distance; and (3) reference constraints using experimentally-derived distances based on our tmFRET measurements. Coordinate constraints were applied to the amino-terminal region and S1-S4 transmembrane domain (amino acids 167-362). Atom-pair constraints were applied to the S5-S6 transmembrane domain (amino acids 363-511) without symmetry and the carboxy-terminal domain (amino acids 515-657) with symmetry. This was done to "rigidify" the structure while still allowing for domain movements. All three types of constraints used a harmonic potential.
During refinement, there were four key parameters that controlled refinement behavior: three weights controlling the relative weigh on each of the three constraint types, and the distance cutoff used for the atom-pair constraints. A 4D grid search was carried out where we considered: weights of 1, 2, and 4 kcal/mol/Å 2 for the atom-pair and coordinate restraints; weights of 10, 20, 30, and 40 kcal/mol/ Å 2 for reference model restraints; and 6, 8, and 10 Å for our atom-pair distance cutoff. We then chose the refined structure with strongest "reference model" restraints and weakest experimental restraints that satisfied measured distances to within 1 Å in all four models. This resulting structure had a coordinate constraint weight of 1 kcal/mol/Å 2 , an atom-pair constraint weight of 2 kcal/mol/Å 2 , an atompair-constraint cutoff distance of 6 Å, and experimental constraint weight of 40 kcal/mol/Å 2 . The resulting models were the ones that minimally perturbed local structure while satisfying the experimental data. Structural representations and morphs were created using the PyMOL software (https://pymol.org).
Statistics and Reproducibility. Data parameters were expressed as mean ± s.e.m. of n independent patches. Statistical significance (*p < 0.05; **p < 0.001) was determined using a one-way ANOVA and Tukey's post hoc test. The mean and s.e. m. for the FRET efficiency of TETAC experiments were calculated using the fractional quenching measurements (i.e., F Cys and F no Cys ) in Monte Carlo resampling (NIST Uncertainty Machine v1.3.4; https://uncertainty.nist.gov) as previously published 15 . For their individual data points and statistical tests, FRET efficiencies were calculated with Eq. (2), using F cys from independent experiments and the averaged F no Cys from all experiments under the same condition.
Reporting Summary. Further information on research design is available in the Nature Research Reporting Summary linked to this article.