Ca2+-saturated calmodulin binds tightly to the N-terminal domain of A-type fibroblast growth factor homologous factors

Voltage-gated sodium channels (Navs) are tightly regulated by multiple conserved auxiliary proteins, including the four fibroblast growth factor homologous factors (FGFs), which bind the Nav EF-hand like domain (EFL), and calmodulin (CaM), a multifunctional messenger protein that binds the NaV IQ motif. The EFL domain and IQ motif are contiguous regions of NaV cytosolic C-terminal domains (CTD), placing CaM and FGF in close proximity. However, whether the FGFs and CaM act independently, directly associate, or operate through allosteric interactions to regulate channel function is unknown. Titrations monitored by steady-state fluorescence spectroscopy, structural studies with solution NMR, and computational modeling demonstrated for the first time that both domains of (Ca2+)4-CaM (but not apo CaM) directly bind two sites in the N-terminal domain (NTD) of A-type FGF splice variants (FGF11A, FGF12A, FGF13A, and FGF14A) with high affinity. The weaker of the (Ca2+)4-CaM-binding sites was known via electrophysiology to have a role in long-term inactivation of the channel but not known to bind CaM. FGF12A binding to a complex of CaM associated with a fragment of the NaV1.2 CTD increased the Ca2+-binding affinity of both CaM domains, consistent with (Ca2+)4-CaM interacting preferentially with its higher-affinity site in the FGF12A NTD. Thus, A-type FGFs can compete with NaV IQ motifs for (Ca2+)4-CaM. During spikes in the cytosolic Ca2+ concentration that accompany an action potential, CaM may translocate from the NaV IQ motif to the FGF NTD, or the A-type FGF NTD may recruit a second molecule of CaM to the channel.

The human voltage-gated sodium channels (Na V ) are a family of nine proteins (Na V 1.1-Na V 1.9) that are responsible for the generation and propagation of action potentials in excitable tissues throughout the human body. The functional core of each Na V is a single transmembrane pore-forming α-subunit that interacts with one or more auxiliary β-subunits (Fig. 1, A and B) (1). The physiological function of Na V s requires the α-subunit to rapidly transition among closed, opened, and inactivated states. The importance of rapidly cycling among these functional states is highlighted by the identification of disease-causing mutations throughout the sequences of the Na V isoforms that disrupt this process to cause debilitating conditions including epileptic disorders (2)(3)(4)(5)(6), cardiomyopathies (7)(8)(9)(10), and chronic pain (11)(12)(13).
CaM is composed of two four-helix bundle domains (CaM N and CaM C ). They are connected by a flexible linker that allows the domains to move independently in solution. Both CaM N and CaM C contain a pair of EF-hands that bind Ca 2+ cooperatively. In free CaM, CaM C has an affinity for Ca 2+ that is approximately tenfold higher than that of CaM N (29)(30)(31) resulting in sequential occupancy of the domains. In eukaryotes, CaM regulates many proteins in a Ca 2+ -dependent manner (32)(33)(34)(35)(36). Binding these targets selectively increases or decreases the Ca 2+ -binding affinity of one or both domains of CaM, making CaM an effective Ca 2+ sensor over a wide range (10 3 ) of Ca 2+ concentrations (37).
Ca 2+ -depleted (apo) CaM and (Ca 2+ ) 4 -CaM bind tightly to many IQ motifs. These basic amphipathic α-helix (BAA) CaM binding domains (CaMBDs) are found in all human Na V isoforms, and CaM-Na V interactions have been especially well studied in Na V 1.2 and Na V 1.5 (23)(24)(25)(26)(27). Despite both apo and (Ca 2+ ) 4 -CaM having a high affinity for these IQ motifs, how CaM acts as a Ca 2+ sensor to modulate Na V function is poorly understood. Ca 2+ binding to CaM C induces a 180 rotation of CaM C on the Na V 1.2 IQ motif (25). This rotation may require transient release and reassociation of CaM C with the IQ motif, which could also allow CaM to translocate to a different high-affinity CaMBD.
The four FGF isoforms (FGF11-FGF14) that bind the EFL domain of Na V s are a subgroup of the fibroblast growth factor superfamily (38). Crystallographic structures (39,40) showed that they contain a well-folded β-trefoil core that is nearly identical to that of canonical fibroblast growth factors (41). However, unlike most members of the FGF family, these FGFs are not secreted (38,42). Rather, they remain in the cytosol and have been implicated in trafficking and modulating Na V channel properties including persistent current (17,19,21,43,44).
Multiple splice variants have been identified for each of the four FGF isoforms (Fig. 1C). These arise primarily from differential splicing of the first exon and result in sequences that vary in the length and composition of the NTD (42,45). The effect of FGFs on Na V function depends on the splice variant bound (21,43,46,47). The B-type splice variants typically have a shorter NTD and are associated with changing current density. The A-type splice variants typically have a longer NTD and are specifically associated with an increased rate of inactivation and long-term inactivation of the Na V α-subunit, which has been proposed to result from an interaction between a region in the NTD and the channel (43). The differences suggest important roles for the distinct NTD sequence of each FGF splice variant.
Colocalization experiments have found that CaM and the FGFs interact with multiple Na V isoforms within cells (47)(48)(49)(50). Proteomics studies have shown that CaM and FGF12 interact with Na V 1.2 in neurons (16). Crystallographic structures of a B-type FGF (FGF12B and FGF13U) and CaM bound to Na V CTD fragments that contain both the EFL and IQ motif (26,51) showed that CaM and FGFs are bound near each other. Recently, an indirect allosteric interaction has been proposed to occur between CaM and FGF12B on Na V 1.4 (52). However, there has been no evidence supporting CaM directly binding any splice variant of an FGF isoform.
Here we report for the first time that CaM binds the NTD of each A-type FGF (FGF11A, FGF12A, FGF13A, and FGF14A) in a Ca 2+ -dependent manner. Using steady-state fluorescence spectroscopy, copurification, and solution NMR, we show that CaM binds two sequences in the NTD of each A-type FGF with high affinity and that both domains of (Ca 2+ ) 4 -CaM mediate this interaction. Focusing on FGF12 because of the cellular and structural studies cited above, we demonstrate that binding of full-length FGF12A to a fragment of the Na V 1.2 CTD (Na V 1.2 CTD , residues 1777-1937) containing the EFL and IQ motif increases the Ca 2+ affinity of both CaM domains. Because the IQ motif is known to lower Ca 2+ affinity of CaM C , this new finding is consistent with (Ca 2+ ) 4 -CaM interacting favorably with the NTD of FGF12A in this ternary complex. These results support a model in which the A-type FGFs compete with Na V IQ motifs for (Ca 2+ ) 4 -CaM and suggest that, during spikes in the local cytosolic Ca 2+ concentration, CaM may translocate from an Na V IQ motif to an A-type FGF NTD or that the NTD may recruit an additional CaM molecule to the ternary complex.

Potential CaM-binding sites in NTDs of A-type FGFs
CaM is known to bind tightly to sequences that are intrinsically disordered but that adopt helical geometry when bound by CaM. The NTD sequences of A-type splice variants of intracellular FGFs are thought to be disordered. However, an analysis of the FGF11A, FGF12A, FGF13A, and FGF14A sequences with the Protein Disorder Prediction System (53) showed two minima in the NTD of each FGF isoform (Fig. 1, C and D) suggesting that two segments are capable of adopting ordered secondary structure and might be CaM-binding sites.
One sequence is near the N terminus of the NTD (referred to as the long-term inactivation particle or LTP). It is highly conserved among the four human FGF isoforms (Fig. 1E) and across species (Fig. S1, A-D, Table S1-S4) and was shown to contribute functionally to long-term inactivation of Na V s mediated by A-type FGFs (43). The other sequence is C terminal to the LTP (referred to hereafter as the CaM-binding domain (CaMBD)). Although the CaMBD has a more variable sequence among the four human FGF isoforms (Fig. 1F), the CaMBD sequence of each isoform is highly conserved across species (Fig. S1, E-H, Table S5-S8). Currently it has no known function.
To explore whether the FGF LTP and CaMBD regions might function as CaM-binding sites, α-helical models were made with PyMOL and helical wheels were generated based on the sequence of the FGF12A LTP and CaMBD (Fig. S2, A-F). The sequences each contained an aliphatic patch bracketed by basic residues consistent with other BAA motifs that are known to bind tightly to CaM.
To understand whether these putative sites in the FGF NTD would be accessible to CaM, it would be helpful to have an experimentally determined structure; however, none are available for any of the full-length A-type FGFs. Therefore, structural models of full-length FGF12A were generated with Robetta (54). Each model in the ensemble had a well-folded β-trefoil core that was nearly identical to that of a crystallographically determined structure of FGF12B (Fig. S3, A and B) (39). New insights came from modeling of the FGF12A NTD that included the LTP and CaMBD. Both potential CaM-binding sites were predicted to adopt α-helical secondary structure (Fig. S3B). They were connected by a disordered linker (aa , and the CaMBD region was connected to the β-trefoil core by another disordered linker (aa 52-69). These linkers would allow the LTP and CaMBD to sample many orientations relative to each other and relative to the β-trefoil core as shown in the set of five lowest-energy (most favorable) conformations (Fig. S3, C-H). The predicted secondary structure and BAA motif sequences of the FGF12A LTP and CaMBD suggested that both were strong candidates for CaM binding.

-saturated CaM tightly binds two sites in the A-type FGFs
To determine whether CaM binds the FGF LTP or CaMBD, apo or (Ca 2+ ) 4 -CaM was added to biosensors in which the EDITORS' PICK: (Ca 2+ ) 4 (Fig. 2, A and B). However, after addition of saturating Ca 2+ , reciprocal changes were observed in the intensities of YFP (reduced by 50%) and CFP (increased by 52%) (Fig. 2B). This indicated that (Ca 2+ ) 4 -CaM, but not apo CaM, bound to FGF12A LTP . Equilibrium titrations of the FGF12A LTP biosensor with (Ca 2+ ) 4 -CaM showed that the K d was 576 nM (Fig. 2C 4 -CaM induced robust reciprocal changes in the intensities of YFP (-21%-33%) and CFP (18%-32%) (Fig. 2, D-H). Equilibrium titrations with (Ca 2+ ) 4 -CaM showed that CaM bound the CaMBD of each FGF isoform with a different affinity (Fig. 2, I-L, Table 1), with FGF13A being most favorable (K d = 13 nM) and FGF12A least favorable (K d = 107 nM). The small difference in the affinity of (Ca 2+ ) 4 -CaM for the CaMBD of FGF11A and FGF13A (0.18 kcal/mol) was statistically significant (p value 0.02358) but would have a very small effect on saturation.
These affinities were 5-44-fold more favorable than the affinity of (Ca 2+ ) 4 -CaM for the FGF12A LTP (Fig. 2, C and I-L, Table 1). Based on the high degree of conservation in the LTP sequence of all four FGFs, these findings suggest that when a single (Ca 2+ ) 4 -CaM is bound to a full-length A-type FGF, it would occupy the putative CaMBD rather than the LTP.

Both CaM N and CaM C are required for tight binding to FGF CaMBDs
We assessed the energetic contributions of CaM N and CaM C to the binding of FGF12A CaMBD and FGF13A CaMBD . Initial titrations with isolated CaM N (aa 1-80) or CaM C (aa  showed no evidence of binding at a concentration of 1 μM (data not shown). Because the interaction of CaM with FGF12A CaMBD and FGF13A CaMBD is Ca 2+ -dependent, the energetic contributions of CaM N and CaM C within full-length CaM were explored by determining their affinity for "knockout mutants" of CaM engineered to significantly reduce Ca 2+ -binding to one domain. In these mutants the bidentate  Glu (position 12) in sites I and II (E31Q/E67Q) or sites III and IV (E104Q/E140Q) was replaced with Gln ( Fig. 3, A and B) (31). In these mutants with one domain mutated, the other domain retains a high Ca 2+ -binding affinity (31). Equilibrium titrations of FGF12A CaMBD with these mutants showed that E31Q/E67Q CaM bound to the CaMBD with a K d of 6.74 μM, a 63-fold lower affinity than WT CaM, while E104Q/E140Q CaM bound with a K d of 4.73 μM, a 44-fold lower affinity (Fig. 3, C-E, Table 2). The affinities of the knockout mutants were very close (Fig. 3F), suggesting that CaM N and CaM C contribute similarly to binding FGF12A CaMBD . Compared with the pattern observed for FGF12A CaMBD , the threefold difference in the affinity of E31Q/ E67Q CaM (K d = 1.59 μM, 122-fold weaker than WT) and E104Q/E140Q CaM (K d = 4.73 μM, 363-fold weaker than WT) (Fig. 3, G-I, Table 2) for FGF13A CaMBD indicated that CaM C EDITORS' PICK: (Ca 2+ ) 4 -CaM tightly binds the NTD of A-type FGFs makes an energetic contribution to binding FGF13A CaMBD that is larger than that made by CaM N . The mutant E104Q/E140Q CaM contains only a functional CaM N . Given that its affinity for FGF13A CaMBD and FGF12A CaMBD was identical (Fig. 3, F and J, Table 2), this suggests that the separation in the affinity of WT CaM for the CaMBD of FGF12A and FGF13A may result from differences in the interface between CaM C and the CaMBD.
In rpHPLC chromatograms (Fig. S4B) of the copurified complexes, the ratio of the integrated area under the absorbance peaks corresponding to the FGF NTD and (Ca 2+ ) 4 -CaM showed that each sample contained a 1:1 M ratio of (Ca 2+ ) 4 -CaM to FGF NTD (Fig. S4C). This is consistent with the isolated NTD fragment of each A-type FGF binding a single molecule of (Ca 2+ ) 4 -CaM following copurification. However, these results do not indicate the location(s) of CaM and do not discriminate among the possibilities of having a single (Ca 2+ ) 4 -CaM bound to an LTP or CaMBD site alone, or possibly bridging these two sites with one CaM domain bound to each. Furthermore, these results do not preclude the possibility that a second molecule of (Ca 2+ ) 4 -CaM may bind the NTD if the local CaM concentration was sufficiently high.
CaM N and CaM C bind identically to FGF12A CaMBDp and FGF12A NTD Solution NMR is uniquely capable of monitoring changes in the local environment of individual residues within a protein.
To determine how the two domains of (Ca 2+ ) 4 -CaM rearrange and interact with an FGF NTD at a one-to-one molar ratio, solution NMR was used to monitor FGF12A CaMBD and FGF12A NTD -induced changes in the local environment of residues in labeled (Ca 2+ ) 4 -CaM.
We first sought to determine how binding of the isolated CaMBD of FGF12A (Fig. 4A) changed CaM N and CaM C within (Ca 2+ ) 4 -CaM. To do this we compared the 15 N-HSQC spectrum of 15 N-(Ca 2+ ) 4 -CaM bound to an unlabeled C-terminal fragment of the FGF12A NTD ( 14 N-FGF12A CaMBDp , residues 41-70), corresponding to roughly half of the FGF12A NTD , to spectra of isolated (Ca 2+ ) 2 -CaM N (Fig. 4B) and (Ca 2+ ) 2 -CaM C (Fig. 4C). These showed that FGF12A CaMBDp binding induced changes in the chemical shifts of residues throughout CaM N and CaM C , which is consistent with both domains of (Ca 2+ ) 4 -CaM interacting directly with FGF12A CaMBDp .
To determine how (Ca 2+ ) 4 -CaM interacts with the full NTD that contains both the LTP and CaMBD sequences (  4 -CaM+ 14 N-FGF12A NTD revealed that peaks corresponding to (Ca 2+ ) 4 -CaM residues were in nearly identical positions in both spectra (Fig. 4E). This indicated that residues in (Ca 2+ ) 4 -CaM have equivalent local environments when bound to the FGF12A CaMBDp or FGF12A NTD , suggesting that the interface between (Ca 2+ ) 4 -CaM and the FGF12A NTD is identical to that of (Ca 2+ ) 4 -CaM+FGF12A CaMBDp (Fig. 4F). The simplest explanation is that (Ca 2+ ) 4 -CaM binds the FGF12A NTD exclusively through the CaMBD, with neither domain of CaM making persistent contacts with the LTP. There was no evidence for more than one conformation though we cannot exclude the possibility that some additional conformations were populated in low abundance.

-CaM binding
To probe the interface between (Ca 2+ ) 4 -CaM and the FGF12A NTD from the FGF side, we used solution NMR to examine the effect of unlabeled (Ca 2+ ) 4 -CaM ( 14 N-(Ca 2+ ) 4 -CaM) binding on the local chemical environment of residues in the labeled FGF12A CaMBDp ( 15 N-FGF12A CaMBDp ) and    (Fig. 4G), which was likely due to the small size of this peptide (30 FGF12A residues with a four-residue tag). In contrast, the spectrum of 14 N-(Ca 2+ ) 4 -CaM+ 15 N-FGF12A NTD was more crowded, as expected for a larger fragment (70 FGF12A residues with a four-residue tag) (Fig. 4H). The higher degree of overlap in that spectrum likely reflects the presence of a disordered linker between the LTP and CaMBD, as predicted in the Robetta models of full-length FGF12A (Fig. S3, To assess whether the pattern of peaks in the 15 N-HSQC spectra of 14 N-(Ca 2+ ) 4 -CaM+ 15 N-FGF12A CaMBDp and 14 N-(Ca 2+ ) 4 -CaM+ 15 N-FGF12A NTD were consistent with the predicted α-helical secondary structure of the FGF12A LTP and CaMBD, the observed peak positions were compared with those predicted with SPARTA+ (55) for residues 41-70  (Fig. 4H) showed that a subset of peaks in the 14 N-(Ca 2+ ) 4 -CaM+ 15 N-FGF12A NTD spectrum were located at positions essentially equivalent to those of peaks in the 14 N-(Ca 2+ ) 4 -CaM+ 15 N-FGF12A CaMBDp spectrum (Fig. 4I). This suggests that these peaks correspond to the same residues in the FGF12A CaMBDp and FGF12A NTD and that they have an essentially identical local chemical environment when bound by (Ca 2+ ) 4 -CaM. That supports a model where (Ca 2+ ) 4 -CaM is anchored to the FGF12A NTD via the CaMBD sequence when in a one-to-one complex as shown schematically in Figure 4F.   To quantitatively assess the allosteric effect of FGF12A NTD and FGF12A CaMBDp on the Ca 2+ -binding affinity of CaM N and CaM C , we conducted equilibrium Ca 2+ titrations of CaM in the presence of the FGF12A NTD or FGF12A CaMBDp by monitoring changes in the steady-state fluorescence intensity of endogenous Phe and Tyr residues to detect Ca 2+ binding by CaM N and CaM C , respectively (31).
Equilibrium Ca 2+ titrations of CaM bound to FGF12A NTD showed it increased the Ca 2+ -binding affinity of sites I and II in CaM N (K d-app = 0.81 μM) by 20-fold (Fig. 5A, Table 3) and sites III and IV in CaM C (K d-app = 0.45 μM) by approximately fivefold (Fig. 5B, Table 3) relative to free CaM. In a similar pattern, FGF12A CaMBDp increased the affinity of sites I and II (K d-app = 0.79 μM) by 20-fold relative to CaM alone (Fig. 5C, Table 3), while sites III and IV (K d-app = 0.56 μM) (Fig. 5D, Table 3) bound Ca 2+ with an approximately fivefold higher affinity. Thus, FGF12A NTD and FGF12A CaMBDp increased the Ca 2+ -binding affinity of CaM N (Fig. 5E, no statistically significant difference between the effect of NTD and CaMBD) and CaM C (Fig. 5F, with CaMBD having a larger effect by 0.25 kcal/mol). This is consistent with both domains of (Ca 2+ ) 4 -CaM binding FGF12A NTD exclusively through the CaMBD region and having an identical interface with both (Fig. 5G). This supports the interpretation of NMR data presented in Figure 4, A-I and the conclusion that the LTP does not participate in the CaM-FGF12A NTD interaction in a 1:1 complex.
FGF12B and FGF12A differ in effects on Ca 2+ binding by CaM+Na V 1.2 CTD In isolation, both FGF12A NTD and FGF12A CaMBDp increased the Ca 2+ -binding affinity of CaM N and CaM C (Fig. 5, A-D). This suggests that the allosteric regulatory roles of FGF12A, which includes the NTD and FGF12B, will not differ because only the A-type splice variant will be capable of binding CaM. Currently there is no evidence of CaM binding to FGF12B.
To understand the complementary roles of CaM and FGF bound to Na V channels, it would be ideal to determine the Ca 2+ affinity of CaM in a ternary complex with FGF12A bound to a full-length Na V 1.2 channel in a plasma membrane and compare that with the Ca 2+ affinity of CaM in a complex with FGF12B bound to an identical full-length Na V 1.2. However, no currently available method is capable of measuring this property in these large transmembrane complexes. Therefore, we investigated Ca 2+ binding to CaM in soluble ternary complexes containing either full-length FGF12A or FGF12B bound to the Na V 1.2 CTD that contains both the EFL domain and IQ motif.
Unlike the FGF12A NTD fragments, which had a low abundance of naturally occurring fluorophores (2 Phe, 0 Tyr, 0 Trp), FGF12B (8 Phe, 10 Tyr, 1 Trp), FGF12A (10 Phe, 10 Tyr, 1, Trp), and Na V 1.2 CTD (9 Phe, 4 Tyr, 1 Trp) all contain multiple aromatic residues (Fig. S7A) that could quench or overwhelm signals coming from CaM. There is also a controversial report that the EFL of Na V 1.5 binds Ca 2+ (56), and that phenomenon could contribute a Ca 2+ -dependent change in fluorescence intensity coincident with that of the changes in CaM.
To determine whether the intrinsic fluorescence of FGF12B and Na V 1.2 CTD was Ca 2+ -dependent, titrations of the FGF12B+Na V 1.2 CTD complex were conducted. Its signal was essentially flat (Ca 2+ -independent) (Fig. S7, B and C), and its excitation (Fig. S7, D and E) and emission (Fig. S7, F and G) spectra were essentially identical under Ca 2+ -depleted conditions and in excess Ca 2+ ([Ca 2+ ] Total = 10 mM). Similarly, Ca 2+ titrations of the FGF12A+Na V 1.2 CTD complex (Fig. S8A) showed that its fluorescence intensity was essentially flat (Fig. S8, B and C), consistent with a lack of intrinsic Ca 2+ binding by these FGF-Na V complexes. Thus, in the Ca 2+ titrations of CaM bound to FGF12B+Na V 1.2 CTD or FGF12A+-Na V 1.2 CTD , the change in fluorescence intensity was interpreted as reporting solely on Ca 2+ binding to CaM.
To understand the effect of full-length FGF12B or FGF12A on Ca 2+ binding by CaM bound to the Na V 1.2 CTD , we compared the equilibrium Ca 2+ titrations of the ternary complexes to those of the binary CaM+Na V 1.2 CTD complex (Fig. 6, A and B). In CaM+Na V 1.2 CTD the Ca 2+ affinity of CaM sites I and II (K d-app = 7.91 μM, Fig. 6A, Table 4) increased approximately twofold compared with free CaM. This change was nearly identical to the difference observed between sites I and II in a CaM N fragment (residues 1-75) and in full-length CaM and was shown to reflect the release of anticooperative interactions between CaM N and residues in the linker between CaM domains (30,57). This indicates that Na V 1.2 CTD binding perturbs the thermodynamic linkage between CaM N and CaM C .
In the CaM+Na V 1.2 CTD complex, the Ca 2+ affinity of sites III and IV decreased by 12-fold (K d-app = 33.42 μM, Fig. 6B, Table 4) relative to free CaM, consistent with preferential binding of the Na V 1.2 IQ motif by apo versus (Ca 2+ ) 4 -CaM (22)(23)(24)(25). Comparing the two domains of CaM to each other in the CaM+Na V 1.2 CTD complex, CaM N binds Ca 2+ with a approximately fourfold higher affinity than CaM C , indicating that Na V 1.2 CTD binding reverses the sequential occupancy of the CaM domains observed in CaM alone (gray curves in Fig. 6, A and B).
In the ternary CaM+FGF12B+Na V 1.2 CTD complex, a slight additional increase (approximately twofold) was observed in the Ca 2+ affinity of sites I and II (K d-app = 4.51 μM) relative to CaM bound to the Na V 1.2 CTD (Fig. 6C, Table 4). Inclusion of FGF12B decreased the Ca 2+ -binding affinity of sites III and IV (K d-app = 157.67 μM) by approximately fivefold relative to CaM in the CaM+Na V 1.2 CTD complex (Fig. 6D, Table 4). Thus, FGF12B binding to the Na V 1.   EDITORS' PICK: (Ca 2+ ) 4 -CaM tightly binds the NTD of A-type FGFs shorter FGF12 splice variant that consists primarily of the folded β-trefoil core (Fig. 1C). For CaM in CaM+FGF12A+Na V 1.2 CTD , the Ca 2+ affinity of sites I and II (K d-app = 2.82 μM) was more favorable than those sites in CaM+Na V 1.2 CTD (approximately threefold) or CaM+FGF12B+Na V 1.2 CTD (approximately twofold) (Fig. 6, C and E, Table 4). The binding of FGF12A also increased the Ca 2+ affinity of sites III and IV (K d-app = 16.61 μM) relative to CaM in both the CaM+Na V 1.2 CTD (approximately twofold) and CaM+FGF12B+Na V 1.2 CTD (approximately tenfold) complexes. The increased Ca 2+ -binding affinity of both CaM domains in the CaM+FGF12A+Na V 1.2 CTD complex is consistent with (Ca 2+ ) 4 -CaM interacting favorably with the NTD of fulllength FGF12A when bound to the Na V 1.2 CTD .

Binding of multiple CaM molecules to the FGF12A+Na V 1.2 CTD complex
Ca 2+ -saturated CaM can bind two sites in the FGF12A NTD (Fig. 2, A-L) and one site in the Na V 1.2 IQ motif (22)(23)(24)(25). Thus, at high local concentrations of Ca 2+ and CaM, the CTD of Na V 1.2 channels with FGF12A bound might bind up to three molecules of (Ca 2+ ) 4 -CaM. However, (Ca 2+ ) 4 -CaM binds more weakly to the LTP than the CaMBD (Fig. 2, C and J, Table 1), and the solution NMR data were consistent with (Ca 2+ ) 4 -CaM binding the FGF12A NTD exclusively through the CaMBD region in a one-to-one complex (Fig. 4, E and I).
To explore the limits of stoichiometry, we tested whether FGF12A+Na V 1.2 CTD might recruit a total of two molecules of CaM: one at the Na V 1.2 IQ motif and one at the FGF12A CaMBD (Fig. 7A). To do this, Ca 2+ titrations were conducted of the CaM+FGF12A+Na V 1.2 CTD complex at a [CaM]:[FG-F12A]:[Na V 1.2 CTD ] ratio of 2:1:1 (CaM+FGF12A+Na V 1.2 CTD (2:1:1)). In this complex it was anticipated that CaM N would not interact with the IQ motif regardless of the Ca 2+ concentration (25) and that it would bind the FGF CaMBD only under Ca 2+ -saturating conditions. In contrast, CaM C would bind to the Na V 1.2 IQ motif constitutively (±Ca 2+ ), but CaM C of a second -(Ca 2+ ) 4 -CaM molecule might bind at the FGF CaMBD.
The Ca 2+ titrations of CaM C in the CaM+FGF12A+-Na V 1.2 CTD (2:1:1) were biphasic (Fig. 7C, red line), in contrast to the titrations of CaM+FGF NTD (Fig. 5B) and CaM+FG-F12A+Na V 1.2 CTD with a 1:1:1 stoichiometry (Fig. 6F). Fitting these data as a sum of two isotherms (see Experimental procedures), we determined that the dissociation constant of the first phase (K d-app = 1.14 μM) was similar to that of CaM C in CaM+FGF12A NTD (K d-app = 0.45 μM, Fig. 7C, black line) while the dissociation constant of the second phase was similar to that of CaM C in CaM+FGF12B+Na V 1.2 CTD (K d-app = 157.67 μM, Fig. 7C, gray line, Table 4).
Both the shape of the Ca 2+ titration curve of CaM sites III and IV in the 2:1:1 complex and the values of the resolved dissociation constants for each transition suggest that the FGF12A+Na V 1.2 CTD complex can bind two CaM molecules simultaneously. Consistent with this, the change in intensity of both the Phe (Fig. 7D) and Tyr (Fig. 7E) signals observed in titrations of the CaM+FGF12A+Na V 1.2 CTD (2:1:1) complex was approximately twofold larger than in Ca 2+ titrations of CaM+FGF12B+Na V 1.2 CTD or CaM+FGF12A+Na V 1.2 CTD .
The biphasic titration curves of the CaM C sites and the changes in affinity of CaM N and CaM C in the CaM+FG-F12A+Na V 1.2 CTD (2:1:1) complex were consistent with FGF12A+Na V 1.2 CTD binding two molecules of CaM simultaneously with one molecule of CaM bound via the FGF12A CaMBD and the other bound at the Na V 1.2 IQ motif. This suggests that if local concentrations of Ca 2+ and CaM were sufficiently high, Na V 1.2 channels that have FGF12A associated may recruit a second molecule of CaM through the FGF12A CaMBD independent of CaM binding at the Na V 1.2 IQ motif.

Discussion
Under resting conditions, the cytosolic CTD of Na V channels binds one FGF and one CaM (16,17,22,48); however, the mechanism by which these two auxiliary proteins modulate channel function is poorly understood. The thermodynamic and structural studies presented here show a direct, Ca 2+ -dependent interaction between (Ca 2+ ) 4 -CaM and the NTD of the four A-type FGF splice variants. We found that (a) (Ca 2+ ) 4 -CaM preferentially binds a CaMBD in the NTD with a dissociation constant in the low nM range but can bind the LTP with weaker affinity, and (b) both domains of (Ca 2+ ) 4 -CaM bind the CaMBD. These results suggest that at elevated cytosolic Ca 2+ concentrations reached during an action potential, CaM may translocate from the Na V IQ motif to the FGF CaMBD and participate in regulatory functions previously identified as requiring FGF binding to Na V s.

Discovery of novel (Ca 2+ ) 4 -CaM-binding sites
Members of the intracellular FGF subfamily were reported to directly bind Na V isoforms (17,18), voltage-gated potassium channels (58), and islet brain protein 2 (59). A recent report proposed an interaction between CaM and FGF12B when bound to Na V 1.4 (52); however, there has been no evidence for a direct interaction between CaM and any FGF isoform. Using multiple spectroscopic methods, we have demonstrated that the isolated LTP (Fig. 2, B and C) and CaMBD (Fig. 2, E-L) sequences of A-type FGFs bind (Ca 2+ ) 4 -CaM but not apo CaM (Fig. 2, B and E-H), mirroring the selectivity of CaMBD sequences in targets such as CaMKII (60), myosin light chain kinase (61), and calcineurin (62).
Robetta models of all four full-length A-type FGFs (Fig. 8A) predicted that segments of both LTP and CaMBD sequences would adopt α-helical structure. For FGF12A, this was supported by the 15 N-HSQC spectra of 15 N-FGF12A CaMBDp and 15 N-FGF12A NTD with one bound (Ca 2+ ) 4 -CaM (Fig. 4, G-I, Fig  S6, C and D). The energetically similar models for each FGF show an ensemble of positions for the LTP and CaMBD separated by a disordered linker. The full NTD is tethered to the β-trefoil core with a disordered linker (Fig. 8A). In solution, this would allow the LTP and CaMBD to move independently relative to each other and the β-trefoil core. This flexibility and range of motion may facilitate (Ca 2+ ) 4 -CaM binding the FGF NTD when the β-trefoil core is bound to a Na V EFL.
(Ca 2+ ) 4 -CaM is known to bridge noncontiguous sites as observed in structures of CaM bound to the STRA6 retinol receptor (63) and the SK channel (64)., However, comparison of NMR spectra (Fig. 4E) and effects of FGF12A CaMBDp and FGF12A NTD on Ca 2+ binding by CaM (Fig. 5, A-F, Table 3) were consistent with (Ca 2+ ) 4 -CaM binding the FGF12A NTD exclusively at the CaMBD site. This suggests that (Ca 2+ ) 4 -CaM would bind the NTD of the other A-type FGF isoforms (11A, 13A, and 14A) exclusively through the CaMBD in a one-toone complex. However, the ability of (Ca 2+ ) 4 -CaM to bind the isolated FGF12A LTP (and its nearly identical sequence in all four A-type FGFs) suggests that if the local CaM concentration is high, the LTP site could recruit a second molecule of CaM to an A-type FGF. Although (Ca 2+ ) 4 -CaM binds to CaMBD with higher affinity than to LTP, CaM might interact transiently with LTP before binding to CaMBD. The reported thermodynamic studies were conducted under equilibrium conditions and did not address kinetics or explore possible translocation between the sites.

Differences in (Ca 2+ ) 4 -CaM-FGF CaMBD interface
The two-domain architecture of CaM allows it to recognize target sequences in a variety of ways, with some targets such as Na V and myosin IQ motifs (65), binding a single domain of CaM (CaM C ) while others, such as CaMKII (66), bind both. Titrations of the FGF12A and FGF13A CaMBD with E31Q/ E67Q CaM (Fig. 3, D and H) and E104Q/E140Q CaM (Fig. 3, E and I), and the 15 N-HSQC spectra of labeled (Ca 2+ ) 4 -CaM bound to the unlabeled FGF12A CaMBDp (Fig. 4, B and C) or FGF12A NTD (Fig. 4E, and Fig. S5, A-D) were consistent with both CaM domains recognizing FGF CaMBD sequences. However, the approximately tenfold difference in the affinity between FGF13A and FGF12A indicates that their CaM-FGF interfaces differ.
To explore possible structural sources for this disparity, we modeled the (Ca 2+ ) 4 -CaM-FGF12A CaMBD interface on a high-resolution structure (2HQW.pdb) of (Ca 2+ ) 4 -CaM bound to the NR1C1 site of the N-methyl-D-aspartate (NMDA) receptor (67,68). In 2HQW, F880 binds the hydrophobic cleft of CaM C while T886 is the primary contact in the cleft of CaM N (Fig. 8, B and C). An alignment of NR1C1 with the CaMBDs of FGF12A and FGF13A (Fig. 8D) suggested that CaM C would bind a Phe in each FGF CaMBD (F49 in FGF12A or F46 in FGF13A) (Fig. 8, B-E). However, CaM N would contact a Cys (C55) in FGF12A (Fig. 8D) and a Phe (F52) in FGF13A (Fig. 8E). In homology models of (Ca 2+ ) 4 -CaM bound to the FGF12A (Fig. 8D) and FGF13A CaMBD (Fig. 8E), based on 2HQW and minimized using YASARA, the hydrophobic pocket of CaM N would make more favorable close contacts with the bulkier F52 in FGF13A than with the smaller polar C55 of FGF12A. This may explain the approximately tenfold higher affinity of (Ca 2+ ) 4 -CaM for FGF13A CaMBD.
The structural models shown in Figure 8, D and E were simulated assuming that CaM binds to both FGF12A and FGF13A in an antiparallel arrangement (i.e., CaM N binds the C-terminal half of the CaMBD) that is observed for the majority of CaM-target interactions. However, the binding of knockout mutants having only one functional domain suggests another possible arrangement. We found that Ca 2+ -saturated E104Q/E140Q CaM (functionally equivalent to apo CaM C tethered to (Ca 2+ ) 2 -CaM N ) bound the FGF12A and FGF13A CaMBDs with nearly identical affinity (Fig. 3, E, F, I, and J). A simple interpretation would be that those titrations represent binding of (Ca 2+ ) 2 -CaM N to a similar half-site in each FGF CaMBD. Thus, the disparity in the affinity might arise from differences in the interface between CaM C and FGF CaMBDs.
The ability of CaM N and CaM C to recognize a variety of target sequences (68) makes it extremely difficult to predict their orientation on a CaMBD. There are high-resolution structures of some peptides bound to (Ca 2+ ) 4 -CaM in a parallel orientation. The ability of the hydrophobic clefts of CaM N and CaM C to form more favorable interactions with a Phe versus Cys may cause the functional domain in each CaM knockout mutant to compete for the same sequence in the FGF12A CaMBD, as was previously observed in the binding of (Ca 2+ ) 4 -CaM to melittin (69). In that complex, the single Trp residue of melittin preferentially binds to CaM C in full-length CaM, and CaM N interacts elsewhere; however, CaM N as an isolated fragment will bind to the Trp residue that is available because CaM C is absent.
In the titrations of the FGF12A CaMBD biosensor with E104Q/E140Q CaM, the functional CaM N may interact with F49 in the FGF12A CaMBD. This would make the interface between E104Q/E140Q CaM with the CaMBD of either FGF12A or FGF13A similar, which could explain the nearly identical affinity of E104Q/E140Q CaM for these sequences.
Although (Ca 2+ ) 4 -CaM was modeled according to the more common antiparallel orientation, CaM could recognize the FGF12A and FGF13A CaMBD in a parallel orientation as seen in structures of (Ca 2+ ) 4 -CaM bound to IQ motif peptides from Ca V 1.2, Ca V 2.2, and Ca V 2.3 (70, 71) and a CaMBD from CaMdependent kinase kinase (72). Alternatively, (Ca 2+ ) 4 -CaM might bind the CaMBD of FGF12A in an orientation opposite from that adopted when binding to FGF13A. Crystal structures have shown a Ca V target peptide bound to CaM in both parallel and antiparallel orientations (71,73) and TFP, an antipsychotic drug that binds (Ca 2+ ) 4 -CaM, has also been found in opposing orientations (74)(75)(76).
In the future, high-resolution structures of (Ca 2+ ) 4 -CaM bound to the FGF12A and FGF13A CaMBD will be required to determine the positions of CaM N and CaM C and how differences in the interface between CaM and these FGF CaMBDs contribute to free energies of binding.
EDITORS' PICK: (Ca 2+ ) 4 -CaM tightly binds the NTD of A-type FGFs FGF12B lowers Ca 2+ affinity of CaM C bound to Na V 1.2 CTD In high-resolution structures of apo CaM bound to Na V 1.5 CTD fragments in the presence or absence of a B-type FGF, the interface between apo CaM C and the Na V IQ motif is essentially identical (28,51). Although two residues (Y98 and K144) in the β-trefoil core of the B-type splice variant of FGF13 (FGF13U) are within 5 Å of residues K95 and N111 in CaM C in a crystallographic structure of apo CaM bound to the Na V 1.5 CTD with FGF13U (51), no interface is observed between CaM C and FGF13U in this structure. The simplest conclusion is that the interaction of CaM C at the Na V IQ motif is independent of B-type FGF binding to Na V EFL. However, binding of FGF12B to CaM+Na V 1.2 CTD decreased the Ca 2+ affinity of sites III and IV in CaM C (Fig. 6D, Table 4). Thermodynamic linkage requires that FGF12B allosterically alters the energy of CaM binding to Na V 1.2 CTD .
Because CaM is a highly acidic protein (pI 4) and FGF12B is basic (pI 9), we hypothesized that FGF12B may increase the affinity of apo CaM for the Na V 1.2 CTD through favorable electrostatic interactions. However, in superpositions of apo and (Ca 2+ ) 4 -CaM bound to the Na V 1.2 CTD with either FGF12B or FGF12A (Fig. 9C and Fig. S9, A-D), the nearest residues in apo CaM C (K94) or (Ca 2+ ) 2 -CaM C (I130 and R126) and the large basic patch in the β-trefoil core of FGF12B (K117) or FGF12A (K193) are separated by > 13 Å. Thus, it is unlikely that electrostatic interactions between CaM C and FGF12B are sufficient to explain the FGF12B-induced changes in the energetics of CaM association with the Na V 1.2 CTD .
Ca 2+ binding to CaM C induces a 180 rotation of CaM C on the Na V 1.2 IQ motif (25). This may require transient release and reassociation of CaM C with the Na V 1.2 IQ motif, which in turn might be facilitated by conformational flexibility (i.e., a hinge) between the EFL and IQ motif of Na V 1.2. In crystallographic structures containing an Na V CTD bound by FGF12B or FGF13U, the FGF contacts both the Na V EFL and residues that precede the IQ motif (26,51). This suggests that the binding of FGF12B may alter the dynamics between the Na V 1.2 EFL and IQ motif, which could perturb the ability of CaM C to reassociate with the Na V 1.2 IQ motif following a Ca 2+ -induced release.
Ca 2+ ligation states of CaM bound to Na V 1.2 Based on the Ca 2+ affinities of the CaM domains when bound to FGF12B+Na V 1.2 CTD or FGF12A+Na V 1.2 CTD , we predict that, at high cytosolic Ca 2+ concentrations (10 μM (77)), Na V 1.2 associated with FGF12B will have either apo CaM or half-saturated ((Ca 2+ ) 2 -CaM N , apo CaM C ) CaM bound (Fig. 9A). In contrast, channels bound to FGF12A are expected to be populated by apo, half ((Ca 2+ ) 2 -CaM N , apo CaM C ), and fully Ca 2+ -saturated CaM (Fig. 9B). Thus, Na V 1.2 with either FGF12 splice variant bound could undergo regulatory processes requiring only apo CaM or Ca 2+ binding solely to the sites in CaM N . However, only Na V 1.2 bound to FGF12A would support modulation requiring Ca 2+ -induced rotation or release of CaM from the Na V 1.2 IQ motif.
The effect of FGF binding on Na V function has been shown to depend upon the FGF splice variant bound (21,43,46,47). Multiple splice variants of a particular FGF isoform have been found to be expressed simultaneously (38,78), suggesting that within a cell, Na V s would be associated with more than one. Their unique effects on Na V function have been proposed to correlate with variations in their NTD sequences. While it is unclear how CaM and the FGFs modulate Na V function, the FGF splice variant-dependent differences in the available states of CaM during a spike in the local Ca 2+ concentration could contribute to their unique effects on the functional states of Na V .

Cellular competition for (Ca 2+ ) 4 -CaM
Both CaM and FGF colocalize with Na V (19,47,50,79,80). Because both apo and (Ca 2+ ) 4 -CaM bind Na V IQ motifs with high affinity (22)(23)(24)(25)(26)(27)(28) and the β-trefoil cores of FGF12 and FGF13 also bind Na V CTD fragments with high affinity (20,40), it is likely that CaM and an FGF are constitutively associated with an Na V (Fig. 9C). Proteomic studies investigating Na V 1.2-associated proteins in rat neurons have found a level of CaM and FGF enrichment in pull-downs of the Na V 1.2 αsubunit similar to other constitutively associated proteins such as the Na V β-subunit β2 (16).
Our thermodynamic and structural studies suggest that at elevated cytosolic Ca 2+ levels, an FGF CaMBD and Na V IQ motif will compete for (Ca 2+ ) 4 -CaM in an isoform-dependent manner (Fig. 9D) due to their proximity and similar affinities for (Ca 2+ ) 4 -CaM. The FGF12A-induced increase in the Ca 2+ affinity of both CaM domains when bound to the Na V 1.2 CTD (Fig. 6, E and F) suggests that CaM translocates from the Na V IQ motif to the FGF CaMBD at elevated cytosolic Ca 2+ concentrations. While the nine Na V and four FGF isoforms have tissuedependent patterns of expression, multiple isoforms of both are expressed in some tissues (38,42,45,81,82), implying that multiple Na V -FGF pairings are present across tissues as well as within a particular cell. The different possible forms of FGF CaMBD and Na V IQ motif recognition by (Ca 2+ ) 4 -CaM may have distinct effects on channel function and could provide a means to elicit unique modulation of Na V by Ca 2+ , CaM, and FGF in different tissues and potentially across channels within a particular cell. Structural and functional studies investigating (Ca 2+ ) 4 -CaM bound to complexes composed of CTD fragments of other Na V isoforms and FGF11A, FGF13A or FGF14A will be needed to determine the generality of the allosteric effects of FGFs on Ca 2+ binding by CaM observed in this study

Stoichiometry of CaM bound to Na V
The Ca 2+ titrations of CaM+FGF12A+Na V 1.2 CTD (2:1:1) were consistent with the FGF12A+Na V 1.2 CTD complex binding one molecule of CaM at the FGF12A CaMBD and one at the Na V 1.2 IQ motif (Fig. 7, B-D, Table 4). This may allow Na V channels to recruit a second molecule of CaM, as has been reported for Ca V 1.2 (50,83). The ability of the FGF CaMBD to anchor a CaM molecule to an Na V may explain the results of a recent report that found FGF13A is sufficient to regulate arrhythmogenic late current in cardiac Na V 1.5 channels with an IQ>AA mutation that blocks CaM binding (44). Although those channels would not have CaM bound at the IQ motif, our findings predict that the NTD of FGF13A would bind (Ca 2+ ) 4 -CaM, which might be sufficient for regulation if the primary role of the IQ motif is to serve as a sink of constitutively bound CaM.
The closely related channel Na V 1.4, primarily found in skeletal muscle, bound only a single molecule of CaM in HEK293 cells under resting conditions and during spikes in cytosolic Ca 2+ (50). That 1:1 stoichiometry may be related to the fact that HEK293 cells do not express any A-type FGF splice variant (42) and may lack (or have a lower expression level of) other auxiliary proteins as well. When present, other auxiliary proteins could enable multiple CaM molecules to be recruited to an Na V in an excitable cell.
The schematic models in Figure 9E show Na V 1.2 CTD with both CaM and FGF12A bound to illustrate how partially ((Ca 2+ ) 2 -CaM N , apo CaM C ) and fully Ca 2+ -saturated CaM may recognize the Na V 1.2 IQ motif and FGF12A CaMBD and how two CaM molecules might bind. The stoichiometry between CaM, Na V 1.2 CTD , and FGF12A and locations of CaM reflect those used in the Ca 2+ titrations of the CaM+FGF12A+-Na V 1.2 CTD complex and the results of those experiments (Fig. 6, E and F, and Fig. 7, A-E). However, the finding that (Ca 2+ ) 4 -CaM binds the isolated FGF12A LTP with a weaker affinity than the CaMBD suggests that at a sufficiently high local CaM concentration a third CaM molecule could also bind to the LTP.
Multiple reports have found that (Ca 2+ ) 4 -CaM binds the highly conserved linker between domains III and IV (DIII-DIV linker) (56,(84)(85)(86)(87). Recently CaM has also been reported to associate with a site in the NTD of Na V 1.5 (88). The direct binding of (Ca 2+ ) 4 -CaM to the LTP and CaMBD in the NTD of the A-type FGFs suggests that, when bound to an A-type FGF, the CTD of an Na V may associate with three molecules of CaM simultaneously. Thus, in the cell an Na V with a bound A-type FGF could potentially bind multiple CaM molecules.
Within the context of a cell, multiple targets compete for CaM, making free CaM a limiting reagent in the cytosol (89,90). However, a number of CaM-binding proteins are found near or within the membrane that may serve as sinks. Among these proteins are ion channels including the Na V , Ca V , SK channels, and NMDA receptor, which can form clusters in the membrane (91)(92)(93) that would have high local CaM concentrations. Additional CaM-binding targets, such as neurogranin (94,95) and neuromodulin (96), constitutively bind apo CaM and release it upon Ca 2+ binding. This may provide a pool of free CaM on the intracellular side of the plasma membrane that could allow recruitment of additional CaM to an Na V associated with an A-type FGF.
Flux of Na 2+ through the pore of the Na V α-subunit is tightly regulated by a network of intramolecular conformational changes and direct interactions with auxiliary proteins that are expressed as different isoforms and splice variants. These may interact with each other as well as with the channel, which could contribute to how they tune Na V function. An understanding of the structural and energetic forces driving direct interactions between individual auxiliary proteins present at an Na V will provide valuable insights into how they work in concert to modulate channel function as well as how mutations within their sequences disrupt regulatory processes.
The thermodynamic and structural studies here are the first to identify a direct Ca 2+ -dependent interaction between CaM and the NTD of A-type FGFs and suggest that Ca 2+ -saturated CaM may translocate from the Na V IQ motif to the FGF CaMBD. These findings lay the groundwork for future studies investigating the consequence of the (Ca 2+ ) 4 -CaM-FGF CaMBD interaction on Na V function.

Protein expression and purification
Full-length (aa 1-148) and domain fragments (CaM N [aa , CaM C [aa ) of WT or mutant human CaM sequences were bacterially overexpressed and purified (23,98). Genes for full-length or domain fragments of WT or mutant CaM sequences [E31Q/E67Q (E32Q/E68Q) and E104Q/ E140Q (E105Q/E141Q)] were expressed with a pT7-7 vector (23). The standard protein designation for each mutant is given first. The parenthetical notation corresponds to the UniProt convention in which the initial Met is designated as residue 1. The three human genes for CaM (CALM1, CALM2, and CALM3) all code for the same protein sequence that corresponds to the sequence of WT CaM used in this study.
Full-length FGF12A was then refolded by rapid dilution into refolding buffer (100 mM Tris, 200 mM KCl, 100 mM L-arginine, 5% (w/v) sucrose, 0.02% NaN 3 , 2 mM DTT, pH 7.7, 500 ml per L of cell growth) at 4 C stirred at 700 rpm with a Teflon-coated stir bar. Prior to the addition of the denaturated His-GST-FGF12A, the CaM+Na V 1.2 CTD complex (final concentration 0.2 μM) was added to the refolding buffer to assist FGF12A refolding. Twenty-four hours after the addition of His-GST-FGF12A, insoluble material was removed by centrifugation (20,000 rpm, 4 C, 20 min) and the sample was concentrated. The HIS-GST-tag was cleaved with 3C protease and removed by repassing the sample over nickel sepharose resin. Anion exchange chromatography (pH 8.5-7.4, KCl 0-300 mM) separated FGF12A and Na V 1.2 CTD from CaM to make the FGF12A+Na V 1.2 CTD complex. Complex purity (>95%) was assessed by SDS-PAGE, rpHPLC, and UV-Vis spectroscopy.  , 102)). The FGF sequence used in each biosensor is given in Buffer subtracted and dilution-corrected titrations were fit to Equation 1, as described (25).

Affinity of CaM for FGF biosensors
where [CaM] free was calculated using Equation 2, , and the positive value is taken as [CaM] free . The quality of each fit was judged by evaluating the values of the 67% confidence intervals for each parameter, the span and randomness of the residuals, square root of the variance, and the values of the correlation matrix (30). The magnitude of the confidence intervals was typically smaller and within a factor of 2 of the standard deviation of the average determined from the independent replicate titrations. The average ΔG values and standard deviations from three to nine replicate titrations are reported in Tables 1 and 2. Pairwise comparisons were evaluated using the unpaired t-test (GraphPad Prism, StatPlus); all p values were considered to be very (<0.005) or extremely (<0.0001) statistically significant unless noted otherwise.

Molar ratio of CaM to FGF NTD
The molar ratio of CaM to FGF NTD in the copurified complexes of (Ca 2+ ) 4 -CaM bound to the FGF11A NTD , FGF12A NTD , FGF13A NTD , or FGF14A NTD was analyzed chromatographically with rpHPLC. The complexes were separated with a Supelco C-18 column with a binary solvent system of water (A) and acetonitrile (B), both with 0.1% (v/v) TFA, using the following gradients: 20%-70% B from 1 to 10 min, 70% B from 10 to 14 min, 70%-90% B from 14 to 16 min. The molar ratio between CaM and the FGF11A NTD , FGF12A NTD , FGF13A NTD , or FGF14A NTD was determined by comparing the area of the absorbance peaks at 220 nm for CaM and the FGF NTD construct in rpHPLC chromatograms.

Solution NMR
Spectra were collected at 25 C on a Bruker Avance II 500 MHz, Varian Unity Inova 600 MHz, or cryoprobeequipped Bruker Avance NEO 600 MHz spectrometer. Samples were 15

Analysis of Ca 2+ -binding affinity
Each domain of CaM can be considered a two-site macromolecule and the affinities of Ca 2+ binding to sites I and II or sites III and IV can be fit to a two-site Adair equation where K 1 (ΔG 1 = −RTlnK 1 ) is the sum of the intrinsic constants (k 1 + k 2 ) of the two sites in either domain of CaM, K 2 (ΔG 2 = −RTlnK 2 ) is the product of the intrinsic constants and the cooperativity constant (k 1 ⋅k 2 ⋅k c ), and [X] is the free [Ca 2+ ].
To account for variations in intensity between experiments, the low and high endpoints of each titration were fit to the function [f(x)] shown in Equation 4 with nonlinear least squares analysis.
The variable Y [X]low corresponds to the intensity of the Ca 2+ -depleted sample, Y 2 is the average fractional saturation, and Span accounts for the difference in intensity at the highest and lowest ligand concentrations. Ca 2+ titrations of CaM in the presence of the FGF12A CaMBDp , FGF12 NTD , Na V 1.2 CTD , FGF12B and Na V 1.2 CTD , or FGF12A and Na V 1.2 CTD were analyzed assuming that each domain of CaM contained two functional Ca 2+ -binding sites. Pairwise comparisons of ΔG determinations were evaluated using the unpaired t test (GraphPad Prism, StatPlus); all p values were considered to be very (<0.005) or extremely (<0.0001) statistically significant unless noted otherwise. EDITORS' PICK: (Ca 2+ ) 4 -CaM tightly binds the NTD of A-type FGFs ratio of 2:1:1 were fit to Equation 5. Ca 2+ titrations of CaM sites III and IV in the same complex were fit to the biphasic function [f(x)] shown in Equation 5 as previously described (37).

Analysis of Ca
The variables Y 2A and Y 2B are the average fractional saturation of the Ca 2+ -binding sites that correspond to the first and second transitions, respectively. Span A and Span B account for the direction and magnitude of signal change in the first and second transitions, respectively, and Y [X]low is the intensity of the Ca 2+ -depleted sample.

Fractional population of intermediate states
The fractional populations of ligated species shown in Figure 9, A and B were calculated with a standard Boltzmann distribution, where the probability (f s ) of a species (s) is given by Equation 6: where [X] is the free [Ca 2+ ], j is the stoichiometry of Ca 2+ bound by species s, and ΔG s represents the free energy of species s, which includes the intrinsic binding affinity for each site (k I and k II for CaM N , and k III and k IV for CaM C ) and cooperative interactions between the sites (k I-II or k III-IV ). The curves in Figure 9, A and B were simulated using the ΔG 1 values for Ca 2+ binding by CaM in the CaM+FGF12B+Na V 1.2 CTD or CaM+FGF12A+Na V 1.2 CTD complexes reported in Table 4 and assumed that the intrinsic Ca 2+ -binding affinities of both sites in each domain were equal (i.e., k I = k II = k N and k III = k IV = k C ), as described previously (23). For CaM in the CaM+FGF12B+-Na V 1.2 CTD complex k N and k I-II were 1.39 × 10 4 M −1 and 284.3, respectively, and k C and k III-IV were 5.36 × 10 3 M −1 and 1.5, respectively. For CaM in the CaM+FGF12A+Na V 1.2 CTD complex k N and k I-II were 1.04 × 10 5 M −1 and 11.9, respectively, and k C and k III-IV were 4.30 × 10 3 M −1 and 198.1, respectively.

Data availability
Data reported in this publication are shown in the figures and contained within the article or available upon request from the corresponding author (Madeline A. Shea, madeline-shea@ uiowa.edu).
Supporting information-This article contains supporting information.