Ca2+-dependent regulation of sodium channels NaV1.4 and NaV1.5 is controlled by the post-IQ motif

Skeletal muscle voltage-gated Na+ channel (NaV1.4) activity is subject to calmodulin (CaM) mediated Ca2+-dependent inactivation; no such inactivation is observed in the cardiac Na+ channel (NaV1.5). Taken together, the crystal structures of the NaV1.4 C-terminal domain relevant complexes and thermodynamic binding data presented here provide a rationale for this isoform difference. A Ca2+-dependent CaM N-lobe binding site previously identified in NaV1.5 is not present in NaV1.4 allowing the N-lobe to signal other regions of the NaV1.4 channel. Consistent with this mechanism, removing this binding site in NaV1.5 unveils robust Ca2+-dependent inactivation in the previously insensitive isoform. These findings suggest that Ca2+-dependent inactivation is effected by CaM’s N-lobe binding outside the NaV C-terminal while CaM’s C-lobe remains bound to the NaV C-terminal. As the N-lobe binding motif of NaV1.5 is a mutational hotspot for inherited arrhythmias, the contributions of mutation-induced changes in CDI to arrhythmia generation is an intriguing possibility.

V oltage-gated Na + channels (Na V s) rapidly activate upon membrane depolarization to allow passage of Na + ions into cells. Of the nine human isoforms of Na V , the two isoforms studied here are predominantly expressed in skeletal muscle (Na V 1.4) and cardiac tissue (Na V 1.5).
Structurally, Na V s are large (~2000 residues) transmembrane proteins composed of four homologous domains (DI-DIV; each containing six transmembrane helices) that form a highly selective Na + pore. 1,2 DIV is followed by a C-terminal tail which contains a structural domain (CTerm, Na V 1.4 residues 1599-1754) consisting of a five-helix EF hand-like motif (EFL, helices αI-αV) followed by a long α-helix (helix αVI). Helix αVI contains an IQ (isoleucine-glutamine) motif ([I,L,V]Q---R----[R,K]), a high-affinity binding domain for calmodulin (CaM) in both its Ca 2+ -free (apo) and Ca 2+ -saturated form 3 CaM is a small (148 residue) ubiquitous eukaryotic Ca 2+ -sensing regulatory protein. CaM has two homologous lobes (N-lobe, helices A-D, residues 1-76; and C-lobe, helices E-H, residues 81-148) connected by a flexible linker; each lobe is capable of binding 2 Ca 2+ ions cooperatively. Strong intra-lobe cooperativity means that CaM exists primarily in four states of Ca 2+ -saturation: apo, (Ca 2+ ) 2 open state has a solventexposed hydrophobic cleft that may bind target peptides, such as the Na V IQ motif, with high affinity.
Three crystal structures of Na V 1.5 CTerm/CaM complexes have been reported, each representing a distinct biological state: (1) Na V 1.5 CTerm in complex with apo CaM (PDB ID: 4OVN 4 ), (2) Na V 1.5 CTerm in complex with apoCaM plus fibroblast growth factor homologous factor (FHF; a Na V -inactivating protein, PDB ID: 4DCK 5 ), and (3) Na V 1.5 CTerm in complex with (Ca 2+ ) 4 -CaM and FHF (PDB ID: 4JQ0 6 ). These structures provide snapshots of the interactions of Na V 1.5 CTerm and CaM as well as clues to possible CaM binding domains in Na V 1.4 CTerm; all show the C-lobe bound to the IQ-motif, with the N-lobe in varied configurations. Notably, structure 3 identifies a Ca 2+ -Nlobe binding motif (NLBM) in helix αVI, i.e., a post IQ-motif located past where the C-lobe is bound.
Information regarding the global topology of Na V s has been provided by three recent cryo-EM structures of eukaryotic voltagegated sodium channels: cockroach NavPaS (P. americana, PDB ID: 5 × 0 M; 37% identity to H. sapiens Na V 1.4) 7 , eel EeNa V 1.4 (E. electricus, PDB ID: 5XSY; 60% identity to H. sapiens Na V 1.4) 8 and H. Sapiens Na V 1.4 (PDB ID: 6AGF) 9 . One cytosolic region, the linker between domain DIII and DVI (DIII-DIV linker), has already been implicated in channel regulation. In NavPaS the DIII-DIV linker passes between the CTerm of the channel and the membrane, while in the other two full Na V structures the DIII-DIV linker is visible in a different orientation and no CTerm structure is observed. Previous studies have suggested that an IFM (Ile-Phe-Met) motif in the DIII-DIV linker is the putative fast inactivation gate. Studies have also suggested that the DIII-DIV linker interacts with CaM 10,11 or Na V CTerm 12 and the possibility of DIII-DIV linker involvement in Na V 1.4 Ca 2+ regulation merits consideration. Na V 1.4 and Na V 1.5 have distinct responses to increases in the Ca 2+ concentration. Na V 1.4 exhibits a unique CaM mediated Ca 2+ -dependent inactivation (CDI) which results in a reduction of bulk Na + current by approximately 30% after the elevation of cellular Ca 2+ levels to~10 µM. 13 In contrast, Na V 1.5 exhibits no CDI even at elevated Ca 2+ levels. It is still not known what are the structural and thermodynamic mechanisms responsible for this difference in behavior are, given the high overall homology between the two Na V s (65% identity, 1196 of 1836 residues), especially in the regulatory and CaM-binding CTerm (Na V 1.4 residues 1599-1754; 78% identity to Na V 1.5 CTerm).
Here, we present two crystal structures of the Na V 1.4 CTerm, one bound to apo CaM and the other bound to (Ca 2+ ) 4 -CaM, as well as binding data between the CTerm of each isoform and CaM in four states of Ca 2+ -saturation. Comparison of the two crystal structures reveals the Ca 2+ -dependent changes experienced by CaM when bound to the Na V 1.4 CTerm. The binding data were used to model the populations of four CaM states bound to Na V 1.4 and 1.5 CTerm as a function of [Ca 2+ ] and [CaM]. In addition, electrophysiological data show that the CTerm of Na V controls CDI and that deletion of the post-IQ NLBM in Na V 1.5 results in robust CDI. These structural, thermodynamic and electrophysiological data all support a mechanism of CDI in Na V s controlled by the positioning of the N-lobe of CaM. Ca 2+ -N-lobe binding to the post-IQ NLBM (WT Na V 1.5) prevents CDI from occurring at elevated Ca 2+ levels. The absence of a post-IQ NLBM sequence (Na V 1.4, Na V 1.5 with NLBM deleted) leads to CDI when the CaM N-lobe binds Ca 2+ . Thus, we showed that the structural and thermodynamic determinants of CDI reside in the CTerm and determine the physiological differences between the two Na V isoforms' response to Ca 2+ . These findings provide a path to identifying the possibility of Ca 2+ -inactivation in other Na V isoforms.

Results
Na V C-terminal tail and CaM N-lobe control CDI. It was previously shown that Na V 1.4 responds to an increase in the Ca 2+ concentration by reducing the maximum Na + current by approximately 30% (calcium-dependent inactivation, CDI) 13 . This effect was observed in HEK293 cells transfected with Na V 1.4 as well as in skeletal myotubes derived from mouse GLT cells. CDI was not observed in similar experiments involving expressed Na V 1.5. We performed electrophysiology experiments to confirm the Na V -CTerm as the region responsible for the CDI as well as to determine the post-IQ region's role in physiological Na V function. The sequences of the two isoforms in the IQ and post-IQ regions are shown in Fig. 1f.
Electrophysiology experiments in HEK293 cells were performed using a chimera in which the C-terminal tail of Na V 1.5 (aa 1774-2016) was replaced by its Na V 1.4 counterpart (aa 1599-1836). Ca 2+ was delivered using voltage pulses that selectively activate voltage-gated Ca 2+ -channel Ca V 2.1 which was co-expressed with the Na V channels. The chimeric protein (Na V 1.5-CTail1.4; Na V 1.5 1-1773 with Na V 1.4 1599-1836) shows CDI, in presence of CaM ( Fig. 1a-d). The opposite experiment, Na V 1.4-CTail1.5, was reported previously and does not show CDI 13 . The participation of CaM as the Ca 2+ sensor for CDI was confirmed using two engineered CaM mutants with Ca 2+ binding sites binding disabled in either the N or the C lobe: CaM 12 (D20A, D56A; N lobe Ca 2+ binding disabled) or CaM 34 (D93A, D129A; C lobe Ca 2+ binding disabled). Only WT CaM and CaM 34 were capable of inducing CDI (Fig. 1e). These experiments show that CDI is dependent on the Na V C-terminal tail and CaM. Furthermore, the C-lobe of CaM is not required to bind Ca 2+ ; the N-lobe binding Ca 2+ is sufficient to cause CDI.
Crystal structures of the Na V 1.4 CTerm-CaM complexes. The structure of the Na V 1.4 CTerm-CaM complex was determined in the absence and in the presence of 10 mM Ca 2+ . Extensive crystallization trials using two different Na V 1.4 CTerm constructs -Long (residues 1599-1764) and Short (residues 1599-1754)produced the crystals used in the structure determinations.
Crystal structure of Na V 1.4 CTerm bound to apoCaM. The 1.8 Å resolution structure of Na V 1.4 CTerm Long in complex with apo CaM (R work /R free = 20.3/23.4) contains one complex in the asymmetric unit (ASU) of the cell (Fig. 2a, Table 1, Supplementary Fig. 1). The Na V 1.4 CTerm contains the 5-helix globular EFL (αI-αV, residues Glu1614-Met1706; residues 1599-1613 not observed) followed by a long helix (αVI, residues Leu1722-Lys1748). Helix αVI is in the same orientation relative to the EFL as seen in Na V 1.5 CTerm in complex with apo CaM (PDB ID: 4OVN) 4 . In contrast, there is a rotation of~90°of helix αVI relative to the EFL in the structure of Na V 1.5 CTerm, apo CaM and FHF (PDB ID: 4DCK) 5 . The apo CaM C-lobe is in a semi-open configuration, and bound to the IQ-motif of helix αVI with a buried surface area (BSA) of 872 Å 2 (Fig. 2b) 14 . The apo Clobe contacts appear to be anchored by two Na V residues which are in the C-lobe's hydrophobic pocket: Ile1734 (120 Å 2 BSA) and Tyr1738 (119 Å 2 BSA). The CaM C-lobe also forms four Glu-Arg -20mV Na V 1.
Tyr1738 Arg1739 Arg1740 Arg1736 Asp80 Glu84 salt-bridges with helix αVI: Glu114-Arg1736, Glu120-Arg1739, Glu123-Arg1745, and Glu127-Arg1745. As expected, in the absence of Ca 2+ the CaM N-lobe is in a closed conformation. Its surface contacts the CTerm in such a way that CaM helices A and B of the N-lobe contact helices αIII and αVI of the CTerm burying 495 Å 2 (Fig. 2c). The apo N-lobe contacts are anchored by EFL residue Ile1659 (100 Å 2 BSA). The CaM N-lobe residue Glu11 is involved in salt-bridges with Na V 1.4 CTerm: one with Lys1658 and another with Lys1725.
The crystal structure of Na V 1.4 CTerm Short (residues 1599-1754) in complex with (Ca 2+ ) 4 -CaM was determined to a resolution of 3.30 Å (R work /R free = 24.0/28.5). Crystals belong to the space group P4 3 2 1 2 and contain one complex in the ASU (Fig. 2d, Table 1). The Na V 1.4 CTerm shows the same fold observed in the higher resolution structure with apo-CaM with helix α VI in the same orientation which indicates that this helical rotation is insensitive to CaM's Ca 2+ state. The (Ca 2+ )-saturated CaM C-lobe bound to the IQ-motif adopts a semi-open 15 configuration and buries 745 Å 2 (Fig. 2e), anchored by Ile1734 (103 Å BSA,) and Tyr1738 (123 Å 2 BSA) as well as Gln1735 (110 Å 2 BSA). Unlike in the complex with the apo-CaM, in this complex the C-lobe does not form any salt bridges with the Na V 1.4 CTerm although two residues in the CaM lobe linker are involved in salt bridges: Asp78 and Asp80, both with Arg1740. The N-lobe and EFL interface involves the external regions of the N-lobe, not the hydrophobic cleft, and buries 334 Å 2 of total area. This interface involves CaM residues Leu18 (84 Å 2 BSA) and Leu39 (95 Å 2 BSA) and Na V residues Ile1659 (83 Å 2 BSA) and Leu1722 (72 Å 2 BSA).
The Ca 2+ -saturated CaM N-lobe conformation differs significantly from the one seen in the apo-CaM complex (Fig. 2f). The N-lobe's hydrophobic cleft, formed between helices A-E 16 , is now open and solvent exposed but despite having a 12-residue DIII-DIV linker peptide in the crystallization media, no peptide is observed bound inside the cleft. In contrast, no large conformational change is observed in the CaM C-lobe bound to the Na V 1.4 CTerm upon Ca 2+ addition ( Fig. 3b and Supplementary Fig. 2). Anomalous scattering was used to confirm the presence of bound Ca 2+ ions. The same crystal used for structure determination of Na V 1.4 CTerm bound to (Ca 2+ ) 4 -CaM was used to collect data at a wavelength of 2.515 Å, near the anomalous edge of Ca 2+ (3.070 Å) ( Table 1). These data were used to calculate an anomalous map at 3.9 Å resolution. This map showed five peaks above 4σ contour of the map corresponding to the positions of the 4 Ca 2+ ions, one in each EF-hand loops of CaM (Fig. 3c, d), as well as the sulfur of Met 1668 in the CTerm. This strong anomalous scattering signal confirms the presence of Ca 2+ -with high occupancy in CaM in the crystal and also eliminates the possibility of Ca 2+ -binding sites within the Na V 1.4 EFL itself, in agreement with previous reports of weak or no-binding between Ca 2+ and Na V 1.5 EFL 6,17 .
Inspection of crystal packing in the Na V 1.4 CTerm and (Ca 2+ ) 4 -CaM crystal shows an intermolecular interaction between the CTerms of symmetry-related molecules: the end of helix αVI interacts with a groove in the EFL of a neighboring CTerm ( Supplementary Fig. 3). The EFL's groove is formed by helices αΙ, IV, and V with 841 Å BSA. No salt bridge or hydrogen bond interactions are formed in the CTerm and helix αVI interaction and the complex formation significance score (CSS) is  0.00, which strongly suggests that this interaction is a result of crystal packing 14 . It is possible that this interaction is mimicking physiological DIII-DIV linker and EFL interactions (see Discussion).
Binding measurements of Na V CTerm to CaM. The binding affinities of Na V 1.4 and Na V 1.5 CTerms for CaM were determined using isothermal titration calorimetry (ITC). Titrations were conducted under both Ca 2+ -free (with 50 µM EGTA) and Ca 2+ -saturating conditions (with 1 mM CaCl 2 ). As CaM has two pairs of EF-hands, Ca 2+ -occupancy of CaM sites is more complex than the binary apo or fully Ca 2+ -saturated captured in these two crystal structures. Each CaM EF hand is capable of binding one Ca 2+ ion so there are 16 possible states of Ca 2+ -saturation. However, because of the cooperativity between Ca 2+ binding to the two EF hands in each lobe (i.e., between EF hands 1 and 2 in the N-lobe and between EF hands 3 and 4 in the C-lobe), states in which each lobe is either empty or has 2 Ca 2+ ions will be the most highly populated. These considerations lead to an approximate model with CaM in 4 states of Ca 2+ -saturation: apo,  4 -CaM shows the weakest binding (K d = 275 nM) indicating a general trend: the more Ca 2+ -saturated the species of CaM the more they are (modestly) penalized for Na V 1.4 CTerm binding.
The K d s of CaM binding to the cardiac Na V 1.5 CTerm Long range from 48 to 90 nM for three of the species: apoCaM, (Ca 2+ ) 2-N -CaM, and (Ca 2+ ) 4 -CaM ( Table 2). The fourth CaM species, (Ca 2+ ) 2-C -CaM, binds the Na V 1.5 CTerm with a K d of 3.6 µM, or about 40-fold weaker binding than any other CaM species. The dramatically weakened binding of (Ca 2+ ) 2-C -CaM to Na V 1.5 CTerm contrasts with the trend observed in Na V 1.4, for which (Ca 2+ ) 2-C -CaM binds with high affinity to the CTerm. For the Na V 1.5 CTerm the two tightest binding CaM species are the two physiological endpoint species: apo CaM (K d = 48 nM) and fully saturated (Ca 2+ ) 4 -CaM (K d = 70 nM) which is a trend captured in our thermodynamic model. Thermodynamic analysis of CTerm and CaM binding data. The differences in affinity of the two isoforms' CTerms for the four CaM species must result in different species being present at each Ca 2+ concentrations and determine the different physiological responses to elevated Ca 2+ concentration. We employed a thermodynamic model that provides estimates of the populations of Na V CTerm and CaM species at varying [Ca 2+ ] and [CaM]. To start, the fractions of the CaM species as a function of [Ca 2+ ] can be calculated using the previously reported binding data, which describes Ca 2+ affinities for the N-and C-lobe of full-length mammalian CaM 18,19 (Fig. 4a). These affinities provide the necessary information to compute the fraction (f X ) of all four species as a function of [Ca 2+ ] ( Supplementary Fig. 9).
Since the total number of Na V channels is much smaller than the number of CaM molecules, the CaM populations in Fig. 4a will not be affected by binding to the Na V CTerm. In this case, the fractions of five CTerm-CaM species (including free CTerm) can be calculated as a function of the CaM species, using the binding constants reported here (Table 2) and the equations presented in Fig. 4a, b.
This analysis links the concentrations of CaM species, and their [Ca 2+ ] dependence, to the species in Fig. 4b. By estimating the fractional population of Na V CTerm species we sidestep working with the concentration of transmembrane Na V . This is particularly useful as the 2-D concentration of membrane-bound species is difficult to measure experimentally and the theoretical framework for thermodynamic analysis of 2-D species is less developed. Our model allows the resulting CaM/Ca 2+ /CTerm species populations to be readily calculated from relevant experimental variables and soluble species: [CaM] and [Ca 2+ ] (Fig. 4c-f). The Ca 2+ -dependent trends for each isoform are less sensitive to the  (Fig. 5, Supplementary Fig 10).
The post-IQ region of Na V controls CDI response. To identify specific regions of the CTerm contributing to the CDI we analyzed the available Na V 1.5 CTerm and CaM structures. The structure of Na V 1.5 CTerm in complex with (Ca 2+ ) 4 -CaM and FHF (PDB ID: 4JQ0) 6 identified the post-IQ NLBM as residues 1916-1927 (LLQRSLKHASFL) with the N-lobe binding burying two Na V residues in its hydrophobic cleft: Leu1917 and Leu1921. In contrast, the structures and binding model presented here suggest Na V 1.4 CTerm lacks such an NLBM. Accordingly, a C-terminally truncated Na V 1.5 with the post-IQ NLBM removed (Na V 1.5ΔP-IQ, last residue Ser1920) was used in electrophysiology experiments. This truncation, in the middle of the Ca 2+ -N-lobe binding domain, eliminates the 2 nd anchor Leu and any other subsequent downstream Na V -CaM contacts. Photouncaging Ca 2+ in HEK293 cells expressing the Na V 1.5 ΔP-IQ channel leads to robust CDI not observed in full-length Na V 1.5 (Fig. 6). These experiments are consistent with the Na V 1.5 post-IQ NLBM preventing the development of CDI in this channel.

Discussion
Na V 1.4 exhibits robust regulation by CaM: apo CaM bound to the channel's CTerm causes an increase in channel open probability 20 whereas elevated Ca 2+ (~10 µM) causes the rapid onset of CaMmediated CDI. In contrast, Na V 1.5 which also binds CaM in its CTerm, does not exhibit CDI at elevated Ca 2+13 . This isoformspecific response has been shown to be CTerm controlled and to require bound CaM. The strongest evidence for the localization of this effect is shown in Fig. 1: a chimera containing the Na V 1.5 four transmembrane domains followed by the Na V 1.4 C-terminal tail exhibits robust CDI.
Understanding the different responses of the two isoforms to the increase in the [Ca 2+ ] requires the detailed identification of the structural determinants of the CDI as well as the thermodynamics of binding between the two CTerm regions and CaM at different Ca 2+ concentrations. We carried out binding and structural studies to characterize the interactions of CaM with the Na V 1.4 CTerm. Apo CaM shows high affinity for Na V 1.4 CTerm Long (K d = 17 nM, Table 2), indicating that CaM is likely bound to the CTerm of Na V at resting Ca 2+ levels. The structure of apo CaM bound to the Na V 1.4 CTerm, determined to 1.8 Å resolution, shows that the CaM C-lobe binds to the Na V IQ motif in helix αVI in a semi-open conformation and that the CaM N-lobe makes surface contacts with the CTerm EFL (Fig. 2a-c). This structure is highly similar to that of the complex of Na V 1.5 CTerm and apo CaM (PDB ID: 4OVN, rmsd 2.71 Å, chains D and I). The similarities between the Na V 1.4 and Na V 1.5 CTerm complexes with apo CaM, in both conformation and binding affinities (Na V 1.5-CTerm Long K d = 48 nM, Table 2) and the equivalence of the response of both isoforms to apo CaM binding (i.e., increased activation) suggest that the conformation of the  a Reaction scheme of Ca 2+ ions binding to CaM lobes. Thermodynamic data of these binding reactions were reported previously 18,19 .  4 -CaM in complex with Na V 1.4 CTerm Short shows that the C-lobe of (Ca 2+ ) 4 -CaM binds the IQ motif of helix αVI, in a pose similar to that seen in the apo CaM CTerm complex (Fig. 2a, b). In this complex Ca 2+ binding does not open the C-lobe's hydrophobic cleft; instead, the C-lobe is fully Ca 2+ -saturated and yet maintains a semi-open configuration (Fig. 3b, d; Supplementary Fig. 2). The structure reported here suggests that the C-lobe serves to anchor CaM to the Na V 1.4 IQ motif, both in the presence and absence of Ca 2+ , maintaining the same conformation and the same interface.
The N-lobe of Ca 2+ -CaM is found in an open configuration, in contact with the Na v EFL, with a shifted center of mass (3.6 Å shift) and with a reduced BSA relative to the apo CaM N-lobe EFL interface (334 vs. 495 Å 2 ). The hydrophobic cleft of the Ca 2+ -saturated N-lobe is open, solvent exposed and unoccupied in this structure (Fig. 3a). Even though the Na V 1.4 CTerm construct used here includes the entire post-IQ NLBM previously identified in Na V 1.5 CTerm (Na V 1.4 residues 1742-1753, LLQRSMKQASYM, 67% identity to Na V 1.5), no N-lobe binding post-IQ was observed here. This difference indicates that the post-IQ region is crucial for control of Ca 2+ -CaM N-lobe binding.
The largest difference between the affinities of CaM for the Na V 1.4 and 1.5 CTerm is found in the species with Ca 2+ only in the C-lobe ( Table 2). The (Ca 2+ ) 2-C -CaM 12 species binds Na V 1.4 CTerm Long with a K d = 154 nM and Na V 1.5 CTerm Long with a K d = 3.6 μM. With CTerm Short the situation is similar: (Ca 2+ ) 2-C -CaM 12 has a K d = 156 nM for Na V 1.4 and K d = 5.26 μM for Na V 1.5. This large difference may, in part, be responsible for the differences in CDI between the isoforms. Nevertheless, a complete explanation of the differences requires an analysis of all the species contributing to the control of the channel's activity. To this effect, the binding measurements were used to model the populations of Na V CTerm-CaM species as a function of [CaM] and [Ca 2+ ]. Using the experimental affinities, this model provides the relative populations of the five CTerm species in Fig. 2 (Fig. 4) The populations obtained with this model show similar trends for bound-CaM behavior with both Na V isoforms at the extremes of low or high Ca 2+ concentration. These trends are most defined at [CaM] of~10 µM which is near the measured concentration of   Fig. 6 Deletion of Na V 1.5 post-IQ NLBM reveals CDI. a Schematic of the sodium channel Na V 1.5 displaying CTerm and post-IQ NLBM region; currents unaffected by 10 µM Ca 2+ . Gray dots, peak currents before uncaging. Bottom, mean ± ecm for CDI versus Ca 2+ -step amplitude. CDI = 1 −average peak I Na of last three to four responses after Ca 2+ uncaging/peak I Na before uncaging. b Schematic of Na V 1.5 displaying CTerm and the post-IQ deletion; Na + currents reduced strongly at 10 µM Ca 2+ , the envelope of peak currents is outlined in red and the difference in peak current before and after uncaging is shaded. Current measurements of Na V 1.5ΔP-IQ, shown as in (a) CaM in cardiac myocytes 21 and skeletal muscle cells (Fig. 5a). 21,22 For both isoforms, apo CaM bound to Na V CTerm is the dominant species at physiological resting Ca 2+ levels (~100 nM) while (Ca 2+ ) 4 -CaM bound to Na V CTerm is the dominant species at high Ca 2+ levels (~100 µM). The isoform populations are most divergent at 10 µM Ca 2+ at which concentration Na V 1.4 has a high population of half Ca 2+ -saturated CaM, (Ca 2+ ) 2-C -CaM, while Na V 1.5 is switching from bound apo CaM to bound (Ca 2+ ) 4 -CaM with nearly absent intermediate populations.
This isoform-specific tuning of CaM behavior occurs at a Ca 2+ concentration that corresponds to those found in relevant cell Ca 2+ signaling events and which leads to CDI. The half Ca 2+saturated species of CaM, (Ca 2+ ) 2-C -CaM, predicted bound to Na V 1.4 CTerm may then be essential to the molecular mechanism of CDI. However, inspection of the crystal structures presented here shows that Ca 2+ binding to the C-lobe does not have a major effect on its conformation nor CaM interaction with the Na V 1.4 CTerm. Instead, it is the lack of Ca 2+ binding by the Nlobe when the CaM C-lobe is bound to Na V 1.4 CTerm, at 10 µM Ca 2+ that is mechanistically relevant. The affinity of Ca 2+ for the CaM N-lobe is intrinsically low (K d ≈ 20 µM) and Ca 2+ binding is enhanced when bound to a target helix. This lack of Ca 2+ binding is consistent with a mechanism in which the Na V 1.4 CTerm lacks a functional NLBM and the N-lobe is free to bind another region of the channel. In contrast, with the Na V 1.5 CTerm, which does contain the NLBM, the Ca 2+ -N-lobe binds to this motif and is unavailable. This is supported by the thermodynamic binding model which shows that the N-lobe of CaM binds to Na V 1.5 CTerm more readily when it binds Ca 2+ (Fig. 5b). If the Ca 2+ -Nlobe does not bind post-IQ it is free to bind some another cytoplasmic region of the Na V . This is the interaction that results in CDI. One suggested target for CaM binding in Na V regulation is the cytosolic DIII-DIV linker, (residues 1292-1354 in Na V 1.4) 23 . In a recent Na + channel structure, NavPaS (PDB ID: 5 × 0 M) 7 as well as in the Ca V 1.1 structure (PDB ID: 5GJV) 24 , a portion of the DIII-DIV linker makes contact with the EFL in a pocket formed by helices α I, IV, and V, suggesting the DIII-DIV linker would be near to bound CaM in Na V 1.4 ( Supplementary  Fig. 11). Two previous structures, the Na V 1.5 residues Q1491-1501L bound to the Ca 2+ -saturated C-lobe (PDB ID: 4DJC) 11 and Na V 1.5 residues L1514-1522K bound to Ca 2+saturated N-lobe (PDB ID: 5DBR) 25 , show helical portions of the Na V 1.5 DIII-DIV linker (Na V 1.4 residues 1467-1529) bound to (Ca 2+ ) 4 -CaM.
We tested whether the Ca 2+ -N-lobe of CaM attached to the Na V 1.4 CTerm by the Ca 2+ -C-lobe binding to the IQ motif can bind the DIII-DIV linker. However, attempts at co-crystallizing a peptide that spans residues 1316-1327 of the DIII-DIV linker (first helix) and the Na V 1.4 CTerm (Ca 2+ ) 4 -CaM complex produced crystals but showed no density that could be attributed to the peptide. Furthermore, ITC experiments titrating the Na V 1.4 CTerm and (Ca 2+ ) 4 -CaM complex with two DIII-DIV linker peptides (12 or 20 residues) exhibit no binding even at high peptide concentrations (Supplementary Fig. 12). Binding to the DIII-DIV linker, however, cannot be fully ruled out. Binding as a free peptide vis a vis the physiological situation has to overcome two large endergonic processes: (1) stabilization of the helix as required for binding, since the free peptide may not be helical in solution and (2) bringing the peptide and the binder together that in the physiological situation might already be proximal as part of the same complex (chelate effect). Independently of which region is recognized, a proximal binding partner in the Na V 1.4 for the CaM-Ca 2+ N-lobe brings together the known crystal structures, the thermodynamic model and the existing physiological data.
The strongest evidence that Na V CDI is controlled via a distal binding partner of the Ca 2+ -N-lobe is provided by electrophysiology experiments using Na V 1.5. Unlike Na V 1.4, WT Na V 1.5 is insensitive to Ca 2+ concentrations of up to 10 µM and shows no CDI (Fig. 6a). Here we showed that robust CDI may be revealed in Na V 1.5 by a deletion of the post-IQ NLBM (Fig. 6); that is, elimination of the NLBM results in CDI.
Our results, along with other previously published data, strongly suggest a molecular mechanism of CDI in Na V in which the CTerm and CaM interactions play a crucial role. CaM is anchored by its C-lobe binding to the IQ motif of the Na V CTerm and this interaction is independent of [Ca 2+ ]. The N-lobe of CaM acts as a Ca 2+ -dependent switch: it is closed and makes surface contacts with the EFL under apo conditions; upon binding Ca 2+ the N-lobe switches to the open conformation. The N-lobe is then poised to bind a nearby target in the cytoplasmic regions of the channel. In Na V 1.5 the Ca 2+ -N-lobe binds the post-IQ NLBM and no CDI results (Supplementary Fig. 13). In Na V .14 the Nlobe has a much lower affinity for the post-IQ NLBM and binding to another N-lobe partner results in CDI. Differences in the post-IQ motif between Na V 1.4 and Na V 1.5 are likely the cause of this isoform-specific behavior in Ca 2+ -N-lobe binding. Several residues differ between the isoforms in the post-IQ motif (Fig. 1,  Supplementary Fig. 14) including the change of Leu1921of Na V 1.5 to Met (1747) in Na V 1.4. Leu1921 is buried in the Nlobe's hydrophobic pocket and makes a close contact with Met73 in Ca 2+ -CaM (PDB ID: 4JQ0). The change of Leu to Met combined with other differences may lead to steric clashes, resulting in a weaker affinity of the Ca 2+ -N-lobe for the post-IQ motif of Na V 1.4. This proposal identifies a motif that can be used to facilitate the study of Ca 2+ -regulation in other Na V isoforms. Isoform-specific CDI may represent an additional level of regulation of Na V channels reflecting the different characteristics of their currents: periodicity (or not), frequency and duration.
Also, as the post-IQ is a mutational hotspot for inherited arrhythmias, the contributions of mutation-induced changes in CDI to arrhythmia generation is an intriguing possibility 26,27 . The same effects may be operational in neuronal isoforms that mimic the behavior of Na V 1.5 leading to neurological disorders such as seizures or neuropathic pain.
Whole cell I Na and I Ca were recorded under voltage-clamp with an Axopatch 200 A patch-clamp amplifier (Molecular Devices Corp., Sunnyvale, CA) at room temperature (22°C). Voltage command protocols were generated by customwritten software and PCLAMP 10 (Molecular Devices Corp). Briefly the protocol is constituted of three parts: a test pulse P 1 at −20 mV to asses I Na , steps of 10 mV from −60 mV to +50 mV increase to allow Ca 2+ to enter the cell and a final test pulse P 2 at −20 mV to evaluate the effect of Ca 2+ on I Na . The length of P1 and P2 were 15 ms, the steps for Ca 2+ entry were 200 ms in length. The holding potential was −120 mV. Capacitance compensation was optimized and series resistance was compensated by 40-80%. Membrane currents were filtered at 5 kHz and digitized with 12-bit resolution through a DigiData-1200 interface (Molecular Devices Corp.).
Expression and purification of Na V CTerm-CaM complex. The gene for H. sapiens Na V 1.4 CTerm Long (SCN4A; a.a. 1599-1764; ENF…GDD) in a pGEX-6-P1 plasmid with an N-terminal GST tag was purchased from Genscript, together with the gene for full-length mammalian calmodulin (R. norvegicus CALM2; 100% amino acid identity with H. sapiens CaM) cloned into a pET24b plasmid 4 were used to co-transform BL21-CodonPlus RIL E. coli (Agilent) cells. The proteins were co-expressed and purified as a complex, using the purification of Na V 1.5 CTerm and apo CaM as a guide 4 . In brief, the cells were grown overnight at 37°C in 100 ml of LB medium supplemented with 50 µg/mL kanamycin, 20 µg/mL chloramphenicol and 100 µg/mL ampicillin. Ten mL of the overnight culture was used to inoculate 1 L of LB media containing the same antibiotics. The cells were grown at 37°C to an absorbance of 0.8 and protein expression was induced with 0.5 mM isopropyl b-D-1-thiogalactopyranoside (IPTG). The cells were grown overnight at 18°C (approximately 18 h), centrifuged and the cell pellet was frozen at 80°C.
After thawing, pellets were re-suspended at 0.2 g/mL with phosphate-buffered saline (PBS). DNAse was added and the cells were lysed using a microfluidizer (Microfluidics Corporation; model 110 Y) and the lysate clarified at 27,500 × g. The supernatant was loaded a 30 ml Glutathione Sepharose 4 Fast Flow resin using gravity flow. The column was washed with 200 mL buffer and protein was eluted in aliquots of 8 ml with an elution buffer containing 154 mg of reduced L-glutathione in 50 mM Tris-HCl at pH 8. Eluted fractions containing protein were pooled and 5 µg of PreScission protease was added per mg of Na V CTerm and CaM complex. Dialysis was performed against 500 mL of 20 mM Tris, 50 mM NaCl, 1 mM DTT, pH 7.4. The buffer was changed 3 times and the final dialysis was allowed to proceed overnight. The dialyzed and Precission-cleaved protein was loaded on a Source Q anion exchange column. Elution was performed using a buffer of 20 mM Tris and 1 mM DTT and a gradient of 50-500 mM NaCl. Free cleaved GST tag eluted at~8 mS/cm and Na V CTerm and CaM in complex eluted at~10 mS/cm. Fractions were judged to be 98% pure by SDS-PAGE gel then pooled and concentrated to~40 mg/mL protein.
The gene for Homo sapiens Na V 1.4 CTerm Short (SCN4A; aa 1599-1754; ENF…YMY) was cloned into a pGEX-6-P1 plasmid with an N-terminal GST tag. This construct contained an additional 7 residues at the C-terminus, LTRAAAS. BL21-CodonPlus RIL E. coli (Agilent) were then co-transformed with Na V 1.4 CTerm Short and CALM2 pET-24b plasmids 4 . The proteins were co-expressed and purified in complex in the same manner as the Na V 1.4 CTerm Long and CaM complex.
Expression and purification of Na V CTerm and CaM. Na V 1.4 CTerm and CaM were co-expressed in BL21-CodonPlus RIL E. coli (Agilent) cells. Cells were grown and lysed as above. The supernatant was loaded onto a Glutathione Sepharose 4 Fast Flow resin using gravity flow column and washed with 1.5 L of low pH PBS buffer with added trifluoroperazine (TFP) and Ca 2+ (10 mM phosphate, 154 mM NaCl, 1 mM of TCEP, 50 µM TFP, 1 mM CaCl 2 , pH 6.4). This TFP wash removed almost 100% of the CaM bound the Na V CTerm. This was followed by a 4 CV wash of the same buffer lacking TFP and Ca 2+ , a 4 CV wash of PBS at pH 8.0 (10 mM phosphate, 154 mM NaCl, 1 mM of DTT, pH 8.0) and elution with PBS at pH 8.0 containing 10 mM L-glutathione (10 mM phosphate, 154 mM NaCl, 1 mM of DTT, 10 mM L-glutathione, pH 8.0). The Na V CTerm was 70% pure as judged by visual estimation of SDS-PAGE electrophoresis.
The gene for full-length mammalian calmodulin (H. sapiens/R. norvegicus CALM2) cloned into a pET24b plasmid 4 was used for CaM expression. Two engineered CaM mutants, CaM 12 (D20A and D56A) and CaM 34 (D93A and D129A), were obtained as a generous gift from the late David Yue lab. CaM 12 and CaM 34 are lobe-specific Ca 2+ -binding knockouts have been shown to calciuminsensitive up to 2 mM CaCl 2 31 . BL21-CodonPlus RIL E. coli (Agilent) were transformed with the individual plasmids. In brief, the cells were grown overnight at 37°C in 100 ml of LB medium supplemented with 50 µg/mL kanamycin and 20 µg/mL chloramphenicol. Ten mL of the overnight culture was used to inoculate 1 L of LB media containing the same antibiotics. The cells were grown at 37°C to an absorbance of 0.8 and protein expression was induced with 0.5 mM IPTG. The cells were grown overnight at 18°C (approximately 18 h), centrifuged and the cell pellet was frozen at 80°C.
After thawing, pellets were re-suspended at 0.2 g/mL with buffer containing 50 mM Tris, 1 mM EDTA, 2 mM DTT, pH 7.4. DNAse was added and the cells were lysed using a microfluidizer (Microfluidics Corporation; model 110 Y) and the lysate clarified at 27,500×g. The supernatant was run through at HiPrep™ Phenyl FF (high sub) 16/10 column (GE Lifesciences) equilibrated in a matched buffer using an ÄKTA FPLC (GE Lifesciences). The eluate was collected and brought up to 10 mM CaCl 2 . This high Ca 2+ -eluate was run through a second HiPrep™ Phenyl FF (high sub) 16/10 column (GE Lifesciences) equilibrated in a match high-Ca 2+ buffer. The column was washed with 200 mL of buffer containing 50 mM Tris, 10 mM CaCl 2 , 2 mM DTT, pH 7.4. Calmodulin was eluted with an elution buffer containing 50 mM Tris, 1 mM EDTA, 2 mM DTT, pH 7.4. Fractions were judged to be 98% pure by SDS-PAGE gel.
Synthesis of DIII-DIV linker peptides. The 12-mer peptide corresponding to Na V 1.4 residues 1316-1327 (100% identity with Na V 1.5 residues 1491-1502) was synthesized with an addition of 2 N-terminal alanines (AAQKKYYNAMKKLG). This peptide has 25% identity with the helical portion of the DIII-DIV linker seen contacting the EFL in NavPaS (PDB ID: 5 × 0 M) 7 . Synthesis was performed by AnaSpec and the peptide was judged to be over 90% pure by HPLC.
The 20-mer peptide corresponding to Na V 1.4 residues 1312-1331 (100% identity with Na V 1.5 residues 1487-1506) was synthesized (MTEEQKKYYNAMKKLGSKKP). This peptide has 30% identity with the DIII-DIV linker seen in NavPaS. Synthesis was performed by Genscript and judged to be over 95% pure.
Structures of Na V 1.4 CTerm-CaM complexes. The Na V 1.4 CTerm Long in complex with apo CaM (50 µM EGTA) was crystallized by hanging drop vapor diffusion at 18°C with a 1:1 ratio of protein to well solution. The well solution contained 0.1 M MES at pH 6.0, 20% PEG 6000 and 1.0 M LiCl. Crystals were flash-frozen in mother liquor prior to data collection. Diffraction data for the crystals were collected on the 17-ID-1 AMX beamline of the NSLS-II (Upton, NY) with a wavelength of 0.918 Å resulting in a 98.0 % complete data set to a resolution of 1.80 Å. Indexing and data reduction were carried out with XDS 32 .
The structure was determined by molecular replacement with Phaser 33 using as a search model the Na V 1.5 CTerm-CaM C complex (PDB ID: 4OVN, chain I and D, CaM residues 82-147) 4 followed by the independent placement of the N-lobe (PDB 1K93, chain D, CaM residues 5-76) 34 . One copy of the CTerm-CaM complex was placed in the asymmetric unit. Model building was completed with iterative cycles of manual rebuilding with Coot 35 and refinement with Phenix Refine 36 . The structure was refined to an R work of 19.9 (R free = 23.2) with excellent geometry (  37 . Crystals were flash-frozen in mother liquor prior to data collection. Diffraction data for the crystal were collected at NSLS-II at the 17-ID-2 FMX beamline at a wavelength of 0.979 Å. Diffraction data were then collected from the same crystal at 2.515 Å, near to the Ca 2+ anomalous edge. Indexing and data reduction were carried out with XDS 32 . The structure was determined by molecular replacement using the program Phaser 33 with CaM lobes as search models. Briefly, the coordinates of individual CaM lobes were extracted from PDB depositions containing CaM (at 3.0 Å resolution or better) resulting in 192 N-lobe and 179 C-lobe search models; PDB ID: 2HQW 38 chain A for the CaM N-Lobe, PDB ID: 3G43 39 chain B for the CaM C-lobe were the most successful. The CTerm of the Na V 1.2 CTerm -FHF-(Ca 2+ ) 4 -CaM complex (PDB ID: 4JPZ) 6 was then placed. The crystal contained one copy of the Na V 1.4 CTerm-CaM complex in the ASU. No density was observed for the DIII-DIV linker peptide. Model building was completed with iterative cycles of manual model building with Coot 35 and refinement with Phenix Refine 36 . The final structure was refined to an R work of 23.8 (R free = 29.7) with excellent geometry (Table 1).
Isothermal calorimetry titration experiments. Titrations were conducted using a VP-ITC MicroCalorimeter (MicroCal Inc.) and data were analyzed with the Origin-5.0 software and fitted to a single binding site per monomer and the error of this fit is reported. The concentration of CTerm used was always between 2 and 25 µM and the concentration of CaM varied from 30 to 1000 µM, depending on the binding affinity. The results of one replicate are reported in Table 2 and Supplementary Table 1. Proteins were prepared for ITC titrations by 3 rounds of dialysis; two of 4-h and one overnight. The buffer used was 20 mM MOPS, 150 mM NaCl, 1 mM MgCl 2 , 50 µM EGTA with 1 mM CaCl 2 added for high calcium titrations.
A thermodynamic model was built consisting of two sequential reaction schemes. The first reaction (Fig. 4a) is the thermodynamic cycle of CaM binding Ca 2+ . The binding of two Ca 2+ ions to either CaM lobe was modeled as a single event and single-ion-bound intermediates were not considered. This model contains four states: apoCaM, (Ca 2+ ) 2-N -CaM, (Ca 2+ ) 2-C -CaM, and (Ca 2+ ) 4 -CaM. The free energy of cooperative two-site binding of Ca 2+ to either lobe in full-length mammalian CaM was reported by Evans and Shea as −12.82 ± 0.09 kcal mol −1 for the N-lobe and −15.06 ± 0.03 kcal mol −1 for the C-lobe and Linse et al. as −12.7 ± 0.6 and −14.9 ± 0.2 kcal mol −118, 19 . Comparing the thermodynamic model results generated with the two sets of binding constants resulted in no discernable difference. The data from Evans and Shea were used in the first binding cycle (Fig. 4a) of the thermodynamic model to match the inclusion of 1 mM MgCl 2 in our experimental buffer.
All Ca 2+ -uncaging experiments were conducted on a Nikon TE2000 inverted microscope with a Plan Fluor Apo 40 × oil objective. Ca 2+ -uncaging was performed using a classic Cairn UV flash photolysis system. UV pulses of~1.5 ms in duration were powered by a capacitor bank of 4000 µF charged to 200-280 V. PMTs were protected during UV pulse to prevent photo-damage. For simultaneous Ca 2+ imaging, Fluo4FF and Alexa568 dyes (in fixed, predetermined ratios) were dialyzed into the cell and then probed with Argon laser excitation (514 nm). Autofluorescence for each cell was obtained prior to pipet dialysis of dyes. A fieldstop aperture was used to isolate fluorescence from a single cell. Two-color fluorescence measurements were attained using a 545DCLP dichroic mirror, paired with a 545/40BP filter for detecting Fluo4FF, and a 580LP filter for detecting Alexa568. Ca 2+ measurements were determined from ratio of Fluo4FF/Alexa fluorescence intensities (R), according to the relation [Ca 2+ ] = K d · (R − R min )/ (R max − R). All three parameters K d , R min , R max were experimentally determined in HEK293 cells dialyzed with reference Ca 2+ solutions. Briefly, R min was determined with internal solution containing 40 mM EGTA, and R max using 4 mM Ca 2+ /1 mM EGTA (~3 mM free Ca 2+ ) solution. An R 20µM measurement was obtained with internal solution containing [Ca 2+ ] = 20 µM (buffered using NTA). K d was experimentally determined by solving the equation above. Calibration measurements were repeated at 1 or 4 mM DMN to account for minor differences in R max . Uncaging experiments were conducted following 2 min of dialysis of internal solution upon reaching stable current levels. In all cases, the steady-state [Ca 2+ ] step amplitude was measured at 150 ms after the instant of uncaging.
Reporting Summary. Further information on experimental design is available in the Nature Research Reporting Summary linked to this article.