Molecular insights on CALX-CBD12 interdomain dynamics from MD simulations, RDCs, and SAXS

Abstract

Na⁺/Ca²⁺ exchangers (NCXs) are secondary active transporters that couple the translocation of Na⁺ with the transport of Ca²⁺ in the opposite direction. The exchanger is an essential Ca²⁺ extrusion mechanism in excitable cells. It consists of a transmembrane domain and a large intracellular loop that contains two Ca²⁺-binding domains, CBD1 and CBD2. The two CBDs are adjacent to each other and form a two-domain Ca²⁺ sensor called CBD12. Binding of intracellular Ca²⁺ to CBD12 activates the NCX but inhibits the NCX of Drosophila, CALX. NMR spectroscopy and SAXS studies showed that CALX and NCX CBD12 constructs display significant interdomain flexibility in the apo state but assume rigid interdomain arrangements in the Ca²⁺-bound state. However, detailed structure information on CBD12 in the apo state is missing. Structural characterization of proteins formed by two or more domains connected by flexible linkers is notoriously challenging and requires the combination of orthogonal information from multiple sources. As an attempt to characterize the conformational ensemble of CALX-CBD12 in the apo state, we applied molecular dynamics (MD) simulations, NMR (¹H-¹⁵N residual dipolar couplings), and small-angle x-ray scattering (SAXS) data in a combined strategy to select an ensemble of conformations in agreement with the experimental data. This joint approach demonstrated that CALX-CBD12 preferentially samples closed conformations, whereas the wide-open interdomain arrangement characteristic of the Ca²⁺-bound state is less frequently sampled. These results are consistent with the view that Ca²⁺ binding shifts the CBD12 conformational ensemble toward extended conformers, which could be a key step in the NCXs’ allosteric regulation mechanism. This strategy, combining MD with NMR and SAXS, provides a powerful approach to select ensembles of conformations that could be applied to other flexible multidomain systems.

Significance

The conformational ensemble of CALX-CBD12, the main Ca²⁺ sensor of Drosophila’s Na⁺/Ca²⁺ exchanger, was characterized by a combination of MD simulations with small-angle x-ray scattering and NMR data using the ensemble optimization method approach. This analysis showed that this two-domain construct experiences opening-closing motions, providing molecular information about CALX-CBD12 in the apo state. Ca²⁺ binding shifts the conformational ensemble toward extended conformers. These findings are consistent with a model according to which Ca²⁺ modulation of CBD12 plasticity is a key step in the Ca²⁺-regulation mechanism of the full-length exchanger.

Introduction

High-resolution NMR spectroscopy is a well-established method to investigate structures of small proteins or protein domains in solution at atomic resolution. The major type of structural information obtained from NMR is short ¹H-¹H internuclear distances (<6 Å) derived from the analysis of nuclear Overhauser effects in NOESY experiments (1,2). Additional sources of structural information, such as residual dipolar couplings (RDCs) measured on weakly aligned samples, rotational diffusion anisotropy determined from the analysis of ¹⁵N R₂ and R₁ relaxation rates, and paramagnetic relaxation enhancements measured in samples labeled with a paramagnetic center, are particularly useful to the structural characterization of complexes and multidomain proteins in solution (3, 4, 5, 6, 7, 8). Small-angle x-ray scattering (SAXS), on the other hand, is a low-resolution method and cannot provide information at atomic resolution (9). From the SAXS scattering profile, it is possible to extract accurate structural parameters such as the average radius of gyration (R_g), the degree of protein folding (Kratky plot), and the interdomain orientation (“finger print”) from the pair-distance distribution function, p(r), which is characteristic of the particle’s shape (10). Therefore, the information derived from SAXS is quite complementary to that obtained from NMR because they provide information in different length scales. Indeed, there are several examples of the simultaneous application of SAXS and NMR data to resolve the structure of large protein-protein complexes or multidomain proteins (11, 12, 13, 14, 15, 16, 17).

Protein motions are essential for function (7,18,19). However, the structural characterization of flexible modular proteins imposes additional challenges. Under these conditions, a unique molecular envelope is not appropriate to describe SAXS data because different protein conformations may exist in solution (10,20). The same is valid for NMR restraints such as RDCs, which are subjected to dynamic averaging because of motions up to the millisecond timescale (21,22). In these cases, one possible approach is to build a large ensemble of different domain orientations representative of the protein dynamics and use the experimental data as a refinement filter of the ensemble (23,24). In this strategy, the principal concern is to avoid overfitting, especially when an ensemble of structures is selected based on a single type of experimental data (23,25,26). The complementarity of NMR and SAXS data can be explored to break the degeneracy of the fitted parameters and prevent overfitting (26,27). Indeed, efforts have been made to calculate structural ensembles of multidomain proteins when different interdomain orientations coexist in solution (5,28), and many of them explore the synergy between NMR and SAXS data (16,27,29, 30, 31, 32). One of the challenges in these approaches is to determine the right ensemble size and to find the appropriate fractions of each model within the ensemble. A minimal representative ensemble may be obtained by optimization of the number of representative models and statistical weights using Bayesian inference (33,34) or genetic algorithms (20,35,36). Alternatively, large ensembles may be calculated using clustering strategies followed by maximal entropy refinement of the statistical weights of each cluster (37).

Na⁺/Ca²⁺ exchangers (NCXs) are secondary active transporters that couple the import of Na⁺ to the extrusion of intracellular Ca²⁺. The NCXs are essential for the maintenance of intracellular Ca²⁺ homeostasis, especially in excitable cells (38). They consist of a transmembrane domain, involved in ion translocation across the lipid bilayer, and a large cytosolic loop that is responsible for regulation of the exchanger activity by its substrates (39, 40, 41). The large intracellular loop contains a Ca²⁺ sensor, CBD12, which consists of two adjacent Ca²⁺-binding domains, CBD1 and CBD2, separated by a highly conserved linker of only three amino acids (Fig. 1) (42,43). The CBDs are β-sandwich motifs, whose Ca²⁺-binding sites are located at the interstrand distal loops (44, 45, 46, 47). Therefore, the Ca²⁺-binding sites of CBD1 are located near the interface with CBD2 (Fig. 1).

Figure 1.

X-ray structure of the two-domain CALX-CBD12 construct (PDB: 3RB5) in the Ca²⁺-bound state (42). Four Ca²⁺ ions at sites Ca1–Ca4 in CBD1 are shown as black spheres. Segments with missing coordinates in the crystallographic structure are represented by segmented lines. The Ca²⁺-binding region of CBD1 corresponds to loops AB, CD, and EF and the interdomain linker. The interdomain interface consists of loops FG of CBD2 and EF of CBD1. The β-strands are indicated according to the color legend. To see this figure in color, go online.

CALX-CBD12 is the cytosolic Ca²⁺ sensor of the Na⁺/Ca²⁺ exchanger from Drosophila, CALX (48). Whereas Ca²⁺ binding to CBD12 activates the mammalian exchangers, CALX is unusual because Ca²⁺ binding to CBD12 inhibits this exchanger (49). Studies of NMR spectroscopy of the CALX and the NCX-CBD12 constructs showed that the two CBDs are flexibly linked to each other in the apo state, whereas binding of Ca²⁺ to CBD1 stabilizes a rigid and elongated interdomain arrangement between CBD1 and CBD2 (50,51). The flexibility of different NCX-CBD12 isoforms (NCX1-CBD12, NCX2-CBD12, NCX3-CBD12-AC, and NCX3-CBD12-B) was characterized by SAXS using the ensemble optimization method (EOM) (20,43,52). It was found that a dynamic regime with a wide R_g distribution describes the apo state SAXS profiles, whereas a narrower R_g distribution was selected in the presence of Ca²⁺. These observations are consistent with the greater interdomain flexibility of the apo state as indicated by NMR (50,51). The same analysis has not been reported for CALX-CBD12.

Despite SAXS and NMR data indicating that CBD12 displays interdomain flexibility (50,51), an atomistic view of the dynamics of the apo state, i.e., the various conformations and interdomain arrangements that CBD12 adopts in solution, is still missing. Considering that an ensemble description of CBD12 in the apo state could give additional insights on the Ca²⁺ allosteric regulation mechanism of the CALX and the NCX exchangers, this question was addressed in this work using molecular dynamics (MD) simulations to generate an initial CALX-CBD12 ensemble and the EOM approach (20) to select a subensemble that agrees with SAXS and RDC data. In the absence of additional experimental data, it is hard to tell that the selected conformations correspond to the native ensemble; however, they do offer insights on large-scale motions experienced by CALX-CBD12 before Ca²⁺-binding. The strategy proposed here, combining MD simulations with SAXS and RDC data, might be useful for the analysis of other multidomain systems that also experience significant interdomain flexibility.

Materials and methods

CALX-CBD12 expression and purification

A DNA fragment corresponding to CALX1.1 residues 434–697 was PCR amplified from the CALX1.1 cDNA and cloned in fusion with a N-terminal six-histidine tag in the pAE vector (53) using XhoI and EcoRI restriction sites. Protein expression was performed in Escherichia coli BL21-CodonPlus(DE3)-RIL (Agilent, Santa Clara, CA). Bacterial cell cultures were grown in LB at 37°C to an OD600 of 0.6; then the temperature was reduced to 18°C, and protein expression was induced by the addition of 0.4 mM of isopropyl-β-D-thiogalactopyranosid for 18 h. Cells were harvested by centrifugation, and cell pellets stored at −20°C. Approximately 10 g of cells were suspended in 200 mL of lysis buffer (20 mM Tris (pH 7.0), 200 mM NaCl, 5 mM β-mercaptoetanol, 0.1 μg/mL of pepstatin and aprotinin, 1.0 mM phenylmethanesulfonyl fluoride, and 1 mg/mL lysozyme), and subsequently lysed by sonication using a VCX 500 (Sonics, Newton, CT) instrument. The cell lysate was clarified by centrifugation at 21,000 × g for 1 h, the supernatant was applied into a 5 mL HisTrap affinity column (GE Healthcare, Chicago, IL) pre-equilibrated with buffer A (20 mM sodium phosphate (pH 7.4), 300 mM NaCl, 5 mM β-mercaptoethanol, 10 mM imidazole), washed with 50 mL of buffer A, and eluted during a gradient of 0.01 up to 0.5 M of imidazole. Fractions containing CALX-CBD12 were combined, concentrated to 2 mL using an Amicon concentrator with a 3 kDa cutoff (Millipore, Burlington, MA), and applied into a Superdex 75 (16/600) gel filtration column (GE Healthcare) pre-equilibrated with the gel filtration buffer (20 mM Tris (pH 8.0), 200 mM NaCl, 5 mM β-mercaptoethanol, 1% (V/V) glycerol). Fractions containing CALX-CBD12 were combined and applied into a MonoQ 10/100 (GE Healthcare) ion-exchange column pre-equilibrated with the gel filtration buffer and eluted in a gradient of 1.0 M of NaCl. Subsequently, fractions containing CALX-CBD12 were combined and buffer exchanged to 20 mM Tris (pH 7.4), containing 5 mM of β-mercaptoethanol, 200 mM of NaCl, 1% (V/V) of glycerol, and 20 mM of EDTA. To prepare the SAXS samples, the EDTA was removed by buffer exchange using a 3 kDa Amicon centrifugation device. In the case of the Ca²⁺-bound sample, a suitable aliquot of a CaCl₂ stock solution prepared in the same buffer as the protein was added just before the SAXS measurements. Protein concentration was determined by measuring the absorbance at 280 nm assuming ε₂₈₀ = 25,900 M¹ cm¹.

SAXS experiment

SAXS experiments were performed on Xenocs-Xeuss laboratory SAXS equipment (Sassenage, France) placed at the Institute of Physics of the University of São Paulo. This machine uses a microfocus source GENIX 3D with CuKα radiation, wavelength λ = 1.5418 Å, Fox3D focusing mirrors, and two sets of scatterless slits (Xenocs 2.0) for beam collimation. The scattering x ray resulting from the sample-primary beam interaction was recorded on a two-dimensional photon-counting Pilatus 300k detector at a sample-to-detector distance of 0.83 m. The scattering intensity was described as a function of the momentum transfer vector modulus (q) defined by q = 4 πsinθ/λ, where 2 θ is the scattering angle. In the used setup, the typical q range was 0.01 < q < 0.4 Å⁻¹. SAXS data were collected on samples of CALX-CBD12 at a concentration of 5.3 mg ⋅ mL⁻¹ (158 μM) in the absence (apo state) or in the presence of CaCl₂ at a molar ratio of 6:1 (Ca²⁺/CBD12). Under these conditions, the four Ca²⁺-binding sites in the CBD1 domain must be fully occupied because the total protein concentration is significantly greater than the CALX-CBD12 Ca²⁺ dissociation constant measured by calorimetry, K_d = 1.6 μM (42). CALX-CBD12 samples were injected in a Xenocs low-noise flow cell, and 900 s of exposures were recorded, generating a total of 20 frames. Pairwise comparison of the collected frames indicated no radiation damage on the samples. The same arrangement was performed for an identically prepared sample but without the protein as a background and a scattering reference (plain water) sample to obtain the final intensity in an absolute scale. The subtraction of the blank, normalization, and absolute scaling were performed over all data using the SUPERSAXS package (C.L.P.O. and J. S. Pedersen, unpublished data). After that, all frames were averaged to obtain the final SAXS profiles. Fitting of the SAXS profile was carried out with GNOM (54) using the indirect Fourier transform (IFT) method to monodisperse systems. From this procedure the pair-distance distribution function p(r), the maximal diameter (D_max), the radius of gyration (R_g), and the intensity on q = 0 (I(0)) were determined. I(0) was used to calculate the protein molecular weight in solution (55). The R_g of the scattering molecule was determined also by linear fitting of the Guinier region (56) to the following intensity function: ln(I(q)) = ln(I(0) − $R_g^2$/3)q². The calculation of the theoretical SAXS profile from known protein three-dimensional coordinates was carried out using CRYSOL (57). A first assessment of CALX-CBD12 flexibility was performed applying the EOM (20,36). RANCH (36) was used to build the initial CALX-CBD12 pool based on the crystal structure of the Ca²⁺-bound state (Protein Data Bank, PDB: 3RB5) (42) (Fig. 1) and the protein amino acid sequence. Residues D550–G555, in the linker between CALX-CBD1 and CALX-CBD2, were treated as flexible to generate a random pool of models, and the CBDs were treated as independent rigid bodies. A total of 10,000 models were built without symmetry or distance restraints. After the initial pool generation with RANCH, a total of 100 genetic algorithm (GA) cycles was performed with 1000 generations to select the optimal ensemble as implemented in GAJOE. As many as 50 ensembles were selected by GAJOE, each of them containing 20 or fewer models. Multiple copies of the same conformer in each ensemble were allowed during the optimization. The experimental SAXS data and analysis were deposited in the Small Angle Scattering Biological Data Bank under the accession codes SASBDB: SASDL26 (apo state) and SASBDB: SASDL36 (Ca²⁺-bound state).

MD simulation

MD trajectories of 3.4 μs were calculated using the AMBER18 software package (58) at the target temperature of 300.0 K using the Berendsen weak coupling thermostat with 5 ps coupling time constant, pressure of 1.0 bar maintained with the Monte Carlo barostat, and the AMBER ff14SB force field (59). Starting structures for the simulations were taken from the crystallographic coordinates of CALX-CBD12 in the Ca²⁺-bound state (PDB: 3RB5, chain A) (42). The four Ca²⁺ ions present at the CALX-CBD1 Ca²⁺-binding sites were removed to build the starting configuration for the apo state. The missing coordinates in the crystallographic models were set up using the LEaP program utility from the AMBER-PDB preparation topology functions (60,61). The two CALX-CBD12 initial structures (with and without the four Ca²⁺ ions) were solvated in an explicit TIP3P water model using 10 Å dimension water layer around the protein in an octahedral box. To neutralize the box, Na⁺ and Cl⁻ ions were added as counterions; additional Na⁺ and Cl⁻ ions were added to create a low salt concentration condition. First, energy minimization was performed during 2000 gradient steps, followed by heating up the system from 100 K up to 300 K within 50 ps in three stages with 25,000 steps of 2 fs time step. All the analyses of structural parameters were carried out using CPPTRAJ routines (62). The interdomain angle between CALX-CBD1 and CALX-CBD2 was measured considering three residues located near the centers of mass of CBD1 (A544), CBD12 (D551), and CBD2 (A688), and then the angle between the inter-residue vectors A554-D551 and D551-A688 was calculated for each MD trajectory snapshot. Structures were visualized with VMD (63).

RDC analysis

Experimental ¹H-¹⁵N RDCs measured on ²H/¹⁵N-labeled CALX-CBD12 samples weakly aligned with Pf1 phages or mixtures of C12E5/n-hexanol (apo state) and with Pf1 phages or compressed polyacrylamide gels (Ca²⁺-bound state) were previously reported (51). Fittings of the individual MD snapshots to the experimental ¹H-¹⁵N RDCs were carried out using singular value decomposition implemented in an in-house Python routine using NumPy (64,65). Briefly, each snapshot was aligned applying CPPTRAJ routine (62), with respect to a reference frame taken at 400 ns using all nonhydrogen atoms, after stabilization of the simulation. The Cartesian coordinates of the N-H bond vectors were extracted, normalized, and used to calculate matrix C:

$$C=\left[\begin{array}{lllll}{y}_1^2-x_1^2\hfill & z_1^2-x_1^2\hfill & 2x_1{y}_1\hfill & 2x_1{z}_1\hfill & 2y_1{z}_1\hfill \\ y_2^2-x_2^2\hfill & z_2^2-x_2^2\hfill & 2x_2{y}_2\hfill & 2x_2{z}_2\hfill & 2y_2{z}_2\hfill \\ .\hfill & .\hfill & .\hfill & .\hfill & .\hfill \\ .\hfill & .\hfill & .\hfill & .\hfill & .\hfill \\ y_{n-1}^2-x_{n-1}^2\hfill & z_{n-1}^2-x_{n-1}^2\hfill & 2x_{n-1}{y}_{n-1}\hfill & 2x_{n-1}{z}_{n-1}\hfill & 2y_{n-1}{z}_{n-1}\hfill \\ y_n^2-x_n^2\hfill & z_n^2-x_n^2\hfill & 2x_n{y}_n\hfill & 2x_n{z}_n\hfill & 2y_n{z}_n\hfill \end{array}\right].$$ (1)

Order matrices, A, defined in an arbitrary Cartesian reference system were determined by solving a system of n linear equations (64,65):

$$\left[\begin{array}{lllll}{y}_1^2-x_1^2\hfill & z_1^2-x_1^2\hfill & 2x_1{y}_1\hfill & 2x_1{z}_1\hfill & 2y_1{z}_1\hfill \\ y_2^2-x_2^2\hfill & z_2^2-x_2^2\hfill & 2x_2{y}_2\hfill & 2x_2{z}_2\hfill & 2y_2{z}_2\hfill \\ .\hfill & .\hfill & .\hfill & .\hfill & .\hfill \\ .\hfill & .\hfill & .\hfill & .\hfill & .\hfill \\ y_{n-1}^2-x_{n-1}^2\hfill & z_{n-1}^2-x_{n-1}^2\hfill & 2x_{n-1}{y}_{n-1}\hfill & 2x_{n-1}{z}_{n-1}\hfill & 2y_{n-1}{z}_{n-1}\hfill \\ y_n^2-x_n^2\hfill & z_n^2-x_n^2\hfill & 2x_n{y}_n\hfill & 2x_n{z}_n\hfill & 2y_n{z}_n\hfill \end{array}\right]\left[\begin{array}{l}{A}_{yy}\hfill \\ A_{zz}\hfill \\ A_{xy}\hfill \\ A_{xz}\hfill \\ A_{yz}\hfill \end{array}\right]=\left[\begin{array}{l}{D}_1\hfill \\ D_2\hfill \\ .\hfill \\ .\hfill \\ D_{n-1}\hfill \\ D_n\hfill \end{array}\right],$$ (2)

where n is the number of dipolar couplings, $\overrightarrow{D}$ is the vector containing the experimental RDC values (D_exp^NH), and A_ij are the five elements of the traceless order matrix, A. Once A was determined, RDC values $\left({\overrightarrow{D}}_{calc}\right)$ were back calculated according to ${\overrightarrow{D}}_{calc}$ = CAC^T (64,65). The agreement between $\overrightarrow{D}$ and ${\overrightarrow{D}}_{calc}$ was evaluated using an R-factor (66). The smaller the R-factor, the better the correlation between ${\overrightarrow{D}}_{calc}$ and ${\overrightarrow{D}}_{exp}$, i.e., R = 0 means ${\overrightarrow{D}}_{calc}$ = $\overrightarrow{D}$. Alternatively, experimental ¹H-¹⁵N RDCs were fitted to an ensemble of conformations as described by Niu and co-workers (67). In this analysis, population averaged N-H vector coordinates were calculated assuming m different conformations of CALX-CBD12 to build the new coordinate matrix C (Eq. 1) and an average alignment tensor for the ensemble. The six calculated terms $⟨x^2⟩$, $⟨y^2⟩$, $⟨z^2⟩$, $⟨xy⟩$, $⟨xz⟩$, and $⟨yz⟩$ now correspond to population averages defined as

$$\begin{array}{l}⟨x^2⟩=w_1{x}_1^2+w_2{x}_2^2+\dots +w_m{x}_m^2\\ ⟨y^2⟩=w_1{y}_1^2+w_2{y}_2^2+\dots +w_m{y}_m^2\\ ⟨z^2⟩=w_1{z}_1^2+w_2{z}_2^2+\dots +w_m{z}_m^2\\ ⟨xy⟩=w_1{x}_1{y}_1+w_2{x}_2{y}_2+\dots +w_m{x}_m{y}_m\\ ⟨xz⟩=w_1{x}_1{z}_1+w_2{x}_2{z}_2+\dots +w_m{x}_m{z}_m\\ ⟨yz⟩=w_1{y}_z{y}_1+w_2{y}_2{z}_2+\dots +w_m{y}_m{z}_m,\end{array}$$ (3)

where w_i is the population weight of model i with ${\sum }_i^m{w}_i=1$. The fractions of the different models, w_i, were allowed to fluctuate to minimize the R-factor using a Levenberg-Marquart algorithm implemented using in-house Python scripts and the Scipy library (68).

Ensemble analysis combining MD with SAXS and NMR data

Two strategies were implemented to build a minimal structural ensemble of CALX-CBD12 using a Python routine (Fig. S1). In the first approach, snapshots in the production phase of the MD trajectory (from 0.4 μs up to 3.4 μs) were saved every 0.2 ns, resulting in a pool of 15,000 models, which is considered a reasonable sampling size (36,69) (step 1A; first approach) (Fig. S1). This pool was used as an external library to SAXS-EOM (step 2A; first approach), and the agreement of the EOM-selected representative conformers with experimental ¹H-¹⁵N RDCs was evaluated by averaging the individual conformer coordinates (step 3A, first approach) (Fig. S1). In the second approach, a larger pool of 54,000 models was built saving MD snapshots from the production phase of the trajectory every 60 ps (step 1B; second approach) (Fig. S1). The consistency of each snapshot with experimental ¹H-¹⁵N RDCs was first evaluated by singular value decomposition, generating an R-factor distribution of the MD trajectory (step 2B; second approach) (Fig. S1). All models with R-factors lower than given thresholds were selected to form external pools to SAXS-EOM (step 3B, second approach) (Fig. S1). A total of six R-factor limits were tested for the apo state (Pf1 data set): 0.54 (15,000 models), 0.53 (10,000 models), 0.52 (5000 models), 0.47 (1000 models), 0.43 (100 models), and 0.42 (50 models). Finally, the SAXS-EOM analysis (step 4B, second approach, Fig. S1) was carried out to select a minimal structural ensemble. CRYSOL (57) was used to compute the theoretical SAXS intensity of each individual model in the pool and GAJOE, using the GA algorithm, to select the optimal ensemble that best describes the SAXS data (36). Briefly, a total of 100 GA cycles were performed with 1000 generations to select the optimal ensemble, as implemented in GAJOE. As many as 50 ensembles were selected by GAJOE, each of them containing 20 or fewer models. Multiple copies of the same conformer in each ensemble were allowed during the ensemble optimization.

Results and discussion

CALX-CBD12 displays conformational heterogeneity in the absence of Ca²⁺

To investigate whether CALX-CBD12 SAXS scattering profiles are sensitive to the differential interdomain dynamics exhibited by the apo and the Ca²⁺-bound states, we recorded SAXS intensities of CALX-CBD12 samples prepared in the absence and in the presence of CaCl₂ at a molar ratio of 1:6 (CBD12/CaCl₂) (Fig. 2 A). The radii of gyration (R_g) obtained from IFT analysis or via Guinier plot are 26.1 ± 0.1 or 25.3 ± 0.2 Å and 28.3 ± 0.1 or 27.1 ± 0.3 Å for the apo and the Ca²⁺-bound states, respectively (Table 1). These results indicate the predominance of slightly fewer open structures in the apo state, whereas extended conformations are predominant in the Ca²⁺-bound state. Because a crystal structure of CALX-CBD12 in the Ca²⁺-bound state is available (PDB: 3RB5) (42) (Fig. 1), we compared the theoretical SAXS intensities with the experimental data using CRYSOL (57). The calculated SAXS intensities showed good agreement with the experimental data obtained in the presence of Ca²⁺ (χ² = 2.3) (Fig. 2 D), whereas a poorer agreement was observed in its absence, particularly at low q-values indicating a more compact arrangement for the apo state and at the intermediate q range (χ² = 10.2). The pair-distance distribution function p(r) observed for the apo state is characteristic of a slightly elongated molecule. In contrast, the p(r) obtained for the Ca²⁺-bound state shows an additional shoulder at ∼55 Å, which is characteristic of a two-domain protein with larger D_max relative to the apo state (Fig. 2 B). Further analysis with the Kratky plot suggested that CALX-CBD12 behaves as a rigid body in the Ca²⁺-bound state, whereas the presence of a broad second shoulder at the q = 0.15–0.20 Å⁻¹ region suggests that it behaves as two domains connected by a flexible linker in the absence of Ca²⁺ (Fig. 2 C) (70). To provide further evidence for flexibility in the apo state, we built CALX-CBD12 models displaying interdomain angles in the range of 63–145° and computed their SAXS intensities using CRYSOL and GNOM (Fig. S2). These calculations showed that the CALX-CBD12 pair distribution function, p(r), is highly affected by the interdomain angle. The p(r) functions of extended conformers (interdomain angles of 116–145°) display a smaller shoulder at ∼55 Å, which increases in intensity followed by a decrease in D_max in the case of compact interdomain arrangements (Fig. S2). The p(r) distribution function exhibited by CALX-CBD12 in the apo state displays similar D_max as the bound state (Table 1), whereas it loses the second maximal correlation at 55 Å, suggesting the presence of conformational heterogeneity (Fig. 2). Altogether, the data are consistent with the view that CALX-CBD12 is best described by an ensemble of conformations in the apo state as previously indicated by NMR (51), but it also suggests that compact interdomain arrangements are sampled more frequently than extended ones.

Figure 2.

SAXS data analysis. (A) Experimental SAXS profiles of CALX-CBD12 in the absence (apo) and presence (Ca²⁺ bound) of Ca²⁺ (symbols) and IFT fits to the experimental data (solid lines). Inset: Guinier region showing the fitting to a linear function and extraction of the radius of gyration, R_g. (B) Pair-distance distribution function, p(r), obtained for the apo (red) and Ca²⁺-bound (blue) samples. (C) Kratky plot (I(q) × q² vs. q) of CALX-CBD12 in the absence (apo, red) and presence of Ca²⁺ (Ca²⁺ bound, blue). (D) Theoretical SAXS profiles calculated using CRYSOL based on the CALX-CBD12 crystallographic coordinates (PDB: 3RB5) (42) (solid line), overlaid on the experimental SAXS profiles of the apo and the Ca²⁺-bound states. Bottom panel: fit residuals calculated using (I(q)^exp − I(q)^calc)/σ_q. χ²- and CorMap p-values are χ² = 10.1 and p < 10⁻⁵ or χ² = 2.4 and p = 0.0342, for the apo and Ca²⁺-bound states, respectively. To see this figure in color, go online.

Table 1.

CALX-CBD12 structural parameters obtained from the analysis of SAXS data recorded in the absence and in the presence of Ca²⁺ at 6:1 molar ratio of CBD12/CaCl₂

Sample	Apo	Ca2+	3RB5a
Guinier analysis
Rg (Å)	25.3 ± 0.2	27.1 ± 0.3	28
I(0) (cm−1)	0.118 ± 5 × 10−3	0.114 ± 4 × 10−3	0.121462
p(r) analysis
Rg (Å)	26.1 ± 0.1	28.3 ± 0.1	28
Dmax (Å)	87	93	93
I(0) (cm−1)	0.1175 ± 4 × 10−3	0.1143 ± 3 × 10−3	N/A
MW (kDa)	33 ± 3	33 ± 3	30

apo, absence of Ca²⁺; Ca²⁺, Ca²⁺-bound state; N/A, not applicable.

^aCalculated values using CRYSOL (57) and the CALX-CBD12 crystal structure (PDB: 3RB5, chain A).

Analysis of the SAXS intensity profiles by rigid body modeling using the EOM approach (20) showed that two R_g distributions consisting of relatively compact models describe the apo state SAXS intensities, whereas a single narrower R_g distribution with the CBDs in extended arrangements was selected for the Ca²⁺-bound state (Fig. S3). However, the agreement between calculated and experimental SAXS intensities in the apo state remained poor (χ² = 10.3), suggesting that the experimental data were not fully described by the EOM-selected ensemble (Fig. S3 B). This observation may be rationalized considering that the initial pool of CALX-CBD12 conformers was built using RANCH by randomization of the short interdomain linker, whereas CALX-CBD1 and CALX-CBD2 were treated as rigid bodies. Hence, this initial pool may not capture the complexity of the conformational energy landscape of the two-domain construct. To start from a more realistic library of conformers, we carried out atomistic MD simulations of CALX-CBD12 in the apo and in the Ca²⁺-bound states and used the MD ensemble as input for EOM.

Sampling CALX-CBD12 energy landscape by atomistic MD simulations

Long 3.4 μs MD trajectories of CALX-CBD12 in the Ca²⁺-bound and in the apo states were calculated in explicit water starting from the CALX-CBD12 crystal structure as described in the Materials and methods. Analysis of the backbone root mean-square deviation (RMSD) relative to the first frame indicated that the simulations took ∼0.4 μs to equilibrate (Fig. 3, A and B). The Ca²⁺-bound form deviated from the starting x-ray structure and was confined into a major conformational state characterized by RMSD of ∼5 Å  and interdomain angle $⟨\theta ⟩$ = 81 ± 7° during most of the trajectory, experiencing frequent jumps to other conformations with RMSDs in the range of 3.5–7 Å (Figs. 3, A and B and S4). In contrast, the apo form visited three major conformational states characterized by averaged RMSDs of ∼3.5, 5.0, and 8.5 Å  from the initial structure and mean interdomain angles $⟨\theta ⟩$ = 116 ± 8, 87 ± 6, and 81 ± 5° (Figs. 3, A and B and S4).

Figure 3.

Analysis of molecular dynamics trajectories of CAXL-CBD12 in the apo (red) and in the Ca²⁺-bound (blue) states. (A) RMSD of CALX-CBD12 backbone atoms with respect to the first frame, (B) relative angle between CBD1 and CBD2, and (C) backbone root-mean-square fluctuation (RMSF of CALX-CBD12 in the apo (red) and Ca²⁺-bound states (blue) calculated over 0.4 μs up to 3.4 μs. The gray shaded areas correspond to the loops of the β-sandwich: (I) AB loop, (II) BC loop, (III) CD loop, (IV) DE loop, (V) EF loop, and (VI) FG loop. (D) Crystallographic model of CALX-CBD12 (PDB: 3RB5) colored according to the relative RMSF between apo and Ca²⁺-bound states (RMSF_apo − RMSF_bound/RMSF_apo), for which red and blue correspond to regions displaying decreased or increased fluctuations in the Ca²⁺-bound states relative to the apo state, respectively. To see this figure in color, go online.

Comparison of the backbone root mean-square fluctuation (RMSF) along the two trajectories indicated that Ca²⁺ binding to CALX-CBD1 restricted the backbone motions in the Ca²⁺-binding region corresponding to the AB, CD, and EF loops of CBD1 and the linker between the two domains (Fig. 3, C and D). Particularly, larger fluctuations were observed at the interstrand loops located opposite to the interdomain interface, AB, CD, and EF in CBD2 and BC, DE, and FG in CBD1. The only exception is the FG loop in CBD2, which displayed large fluctuations despite being located near the interdomain interface. Fluctuations of the EF and FG loops in CBD2 were not affected by occupation of the Ca²⁺-binding sites in CBD1 (Fig. 3, C and D). However, the CBD2 CD loop, despite of its location opposite to the Ca²⁺-binding sites, displayed increased flexibility in the Ca²⁺-bound state than in the apo state. We attempted to investigate whether this observation could be in agreement with previously published NMR data for CALX-CBD12 (51); however, NMR signals in this region were broad, and relaxation rates could not be measured in the Ca²⁺-bound state. These observations are consistent with the presence of dynamics at the microsecond-to-millisecond timescale in the CBD2 CD loop. Indeed, this loop does not show electron density in the crystallographic model of CALX-CBD12 (Fig. 3 D).

Residues E455 and D552, which coordinate Ca²⁺ at sites Ca1, Ca2, and Ca3 in CBD1 (42), remained ∼4.3 Å apart during most of the trajectory in the Ca²⁺-bound state (Fig. 4). Furthermore, the orientations of D552 and D550 side chains, which coordinate Ca²⁺ at sites Ca1 and Ca2, also remained stable (Fig. S5). These observations indicate that the Ca²⁺ coordination geometry was preserved during the simulation. In contrast, in the apo state simulation, E455 and D552 became further apart and sampled two major conformational states, indicating that the Ca²⁺-coordination geometry was disrupted and suggesting greater flexibility at the Ca²⁺-binding sites (Figs. 4 and S5). This conclusion is consistent with the observation that R584 was more mobile in the apo state than in the Ca²⁺-bound state simulation (Fig. S6). R584 could play a pivotal role in the stabilization of the extended interdomain arrangement seen in the x-ray structure, as it participates in a hydrogen-bonding network with N615 in CBD2 and D552 that coordinates Ca²⁺ at sites Ca1 and Ca2 in CBD1 (Fig. 4). Furthermore, the formation of a salt bridge between R584 and D517 in the CBD1 EF loop and a hydrogen bond between D521 in the CBD1 EF loop and R673 in α-helix H2 (Figs. 4 and S6) may help stabilize the extended arrangement between CALX-CBD1 and CALX-CBD2. These two interactions break in more compact interdomain arrangements, in which E521 makes a new hydrogen bond with R681 in the C-terminal end of α-helix H2 (Figs. 4 and S6). Indeed, these analyses are consistent with the observation that CALX-CBD12 deviated from the initial structure and sampled compact interdomain arrangements during most of the trajectory in the Ca²⁺-bound state (Fig. 3). The crystallographic structure of CALX-CBD12 shows hydrophobic contacts (<4 Å) between F519 in the EF loop with L677 and S678 in α-helix H2 (Fig. 4) (42). When these contacts were examined during the course of the MD simulations, it was found that the distance between F519 and S678 displayed broader bimodal distribution in the apo state relative to the Ca²⁺-bound state (Fig. 4), consistent with the fact that CALX-CBD12 more frequently sampled a wider range of different interdomain arrangements in the former state.

Figure 4.

CALX-CBD12 interdomain contacts during the MD trajectories of the apo (red) and the Ca²⁺-bound (blue) states. (A) (Top) Crystal structure (PDB: 3RB5) of CALX-CBD12 showing the hydrogen-bonding network formed between N615, R584, and D552, and the hydrogen bond formed between E521 and R673. Hydrogen bonds are indicated by dashed lines. D552 and D455 coordinate Ca²⁺ ions at Ca1 and Ca2. A possible salt bridge between D517 and R584 and a hydrophobic contact between S678 in the FG loop of CBD2 and F519 in the EF loop of CBD1 are also shown. (B) MD snapshot of the apo state simulation showing the formation of hydrogen bonds between R681 and E521. (Bottom) Pair distribution functions and fluctuation over time of the distances between E455-D552 (left), F519-S678 (middle), and E521-R681 (right). Distances were computed in the interval between 0.13 and 3.4 μs. As a reference, distances observed in the crystal structure and in the apo state representative snapshot are indicated by 3RB5 and “closed,” respectively. To see this figure in color, go online.

Using the MD trajectory as initial pool for SAXS-EOM analysis

We investigated whether refinement of an MD-derived pool against SAXS data could improve the agreement between experimental and calculated SAXS intensities. To this end, an external pool corresponding to 15,000 MD snapshots was selected and refined against SAXS data using EOM. The refined ensemble (MD-EOM) yielded a better agreement with experimental SAXS profiles than the rigid body ensemble (RANCH-EOM) as indicated by the χ², which decreased from 6.6 to 5.2 and from 10.3 to 1.2 for the Ca²⁺-bound and the apo states, respectively (Figs. S3 and S7). The apo state MD-EOM ensemble consisted of four R_g distributions, with representative models displaying R_g-values of 23.7, 24.9, 24.9, and 26.8 Å and interdomain angles of 75, 88, 89, and 127°. With the exception of the latter, all of them are more compact than the x-ray structure that displays R_g = 28 Å and interdomain angle of 131° (Table S1). It is, therefore, clear that a trend toward compact conformations is observed for the apo state (Fig. S7). In the case of the Ca²⁺-bound state, two narrower R_g and D_max distributions were obtained (Fig. S7). The two representative conformers displayed similar interdomain arrangements as indicated by interdomain angles of 126 and 129°, consistent with a relatively rigid two-domain protein in the extended conformation (Fig. S7). It is noteworthy that the apo state SAXS-refined ensemble contained a population of the wide-open conformation characterized by R_g ∼26.7 Å, which is, however, enriched in the Ca²⁺-bound ensemble. Comparison of the initial MD pool with the MD-EOM ensemble shows that CALX-CBD12 became trapped in a local minimum far from the native structure along most of the MD trajectory in the Ca²⁺-bound state (Fig. S7).

RDCs measured on protein samples weakly aligned in the magnetic field report on the average orientation of the internuclear bond vector with respect to an alignment tensor. Hence, RDCs are rich sources of information on structure and dynamics of proteins in solution. It was previously reported that ¹H-¹⁵N RDCs obtained for CALX-CBD12 in the apo state did not agree with the crystallographic structure as indicated by R = 0.57 obtained for RDCs measured in the presence of Pf1 (42,51). However, better agreement was obtained with the coordinates of the separate domains as indicated by R = 0.26 and 0.34 for CALX-CBD1 and CALX-CBD2, respectively (Fig. S8). Fitting the experimental RDCs to the population averaged coordinates of the four apo state MD-EOM representative CALX-CBD12 conformers (Eqs. 2 and 3) improved the R-factor only slightly from 0.57 to 0.44 (Figs. S8 and S9), suggesting that MD sampling of CALX-CBD12 conformational space was not sufficient or that the SAXS data did not contain information on the local geometry of the HN bond vectors. This analysis yielded conformer populations that were highly correlated with each other, indicating that the correct fraction of each model was unreliable. In contrast, RDCs measured for the Ca²⁺-bound state were in reasonable agreement with the crystal structure (R = 0.35) (51), which is consistent with the rigidity of the Ca²⁺-bound state (Fig. S8).

Using RDCs to select native-like conformations sampled during MD

During the MD simulations, CALX-CBD12 eventually visited conformations that are consistent with the ¹H-¹⁵N RDCs. R-factor distributions of all MD conformers were calculated as described in the Materials and methods (Fig. 5). The apo state R-factor distribution was centered at approximately R = 0.6 (Fig. 5, red), indicating that conformational sampling was insufficient to improve the agreement with the experimental RDC data set. However, a few snapshots exhibited R-factors in the range of 0.3–0.4, indicating consistency with the experimental data. The lowest R-factor MD snapshot corresponded to a compact interdomain arrangement (Fig. 5, red), and reproduced well the experimental SAXS curve with χ² = 1.6 using CRYSOL (Fig. S10). However, the calculated pair distribution function p(r) indicated a more compact conformation than the experimental curve (Fig. S10). Furthermore, the CorMap analysis indicated that the calculated and experimental SAXS intensities differ mainly at the low q region (Fig. S12). Therefore, these snapshots possibly represent compact conformers that are substantially populated in the native apo state ensemble, but they do not fully describe the experimental SAXS data. Similarly, the R-factor distribution of the Ca²⁺-bound MD ensemble was centered at R = 0.4 (Fig. 5, blue), larger than that obtained with the crystallographic structure (R = 0.35) and consistent with the fact that CALX-CBD12 deviated from the Ca²⁺-bound native conformation during most of the MD trajectory, visiting more compact interdomain arrangements (Fig. S7). As observed for the apo state, a few MD snapshots displayed improved agreement with the RDCs than the crystal structure, as indicated by R-factors as low as 0.28. The snapshot displaying the lowest R-factor showed an overall agreement with the interdomain arrangement observed in the crystal structure (Fig. 5 B, blue), suggesting that the improved agreement with the experimental RDCs could result from local reorientations of the HN bond vectors rather than changes in the interdomain orientation. Indeed, the local geometry overall quality improved during the simulation as indicated by an increase from 78 to 88% of residues in the most favored regions of the Ramachandran plot in the MD snapshot relative to the x-ray structure. Similar observations were made for RDC data sets measured using either C12E5/n-hexanol mixtures (apo state) or compressed polyacrylamide gels (Ca²⁺-bound state) as the alignment medium and are shown in Fig. S10.

Figure 5.

(A) RDC R-factor distributions for CALX-CBD12 MD ensembles in the apo (red) and in the Ca²⁺-bound states (blue). Experimental ¹⁵N-¹H RDCs were measured using Pf1 as alignment medium (51). MD snapshots were saved every 60 ps along the production phase of the trajectory (from 0.4 to 3.4 μs). The vertical dotted lines indicate the R-factor cutoffs accepted to select the MD subensembles used as input for EOM analyses. Arrows indicate the R-factor values obtained when CALX-CBD12 crystallographic coordinates (PDB: 3RB5) were used for fitting. The star symbols indicate the best MD snapshots. (B) MD snapshots displaying best agreement with the RDCs obtained for the apo (red) and the Ca²⁺-bound states (blue) superimposed on the crystallographic model (PDB: 3RB5) in gray. To see this figure in color, go online.

Combining SAXS and RDCs to refine the apo state CALX-CBD12 MD ensemble

To select a subensemble that agrees with both low-resolution and high-resolution structural information, we used RDC and SAXS experimental data to refine the MD ensemble of CALX-CBD12. We first filtered the external MD pool based on the R-factor limit of 0.54, corresponding to 15,000 snapshots (Figs. 5 and S1). This RDC-filtered pool was then refined with SAXS data using the EOM approach. The refined MD-RDC-EOM subensemble displayed trimodal R_g and D_max distributions (Figs. 6 and S11). It contains a larger number of compact conformers, whereas those ones characterized by wider interdomain arrangements are less populated (Fig. 6). The selected representative subensemble reproduced the experimental SAXS intensities with χ² = 1.2 and yielded a better agreement with the experimental data at low and midrange q-values (0.1 < q < 0.2 Å⁻¹) according to two-dimensional analysis using CorMap (Fig. S12), representing an improvement with respect to the fittings obtained using single models. The ensemble description for CALX-CBD12 adopted here is further justified by the observation of interdomain dynamics from the analysis of previously published NMR data (51). The three representative conformers display compact (population p₁ = 59%, θ = 79°), semiopen (p₂ = 33%, θ = 85°), and wide-open (p₃ = 8%, θ = 111°) interdomain arrangements, the latter being similar to the Ca²⁺-bound state (Figs. 6 and S11). Additional SAXS-EOM runs carried out starting from smaller apo state external pools by assuming lower R-factor thresholds converged to similar subensembles, predominantly composed of semiopen (R_g = 25.5 Å and θ = 92°) and compact (R_g = 23.4 Å and θ = 73°) models with the advantage of consuming less computer time (Table S1). When the flexibility of CALX-CBD12 was quantified based on SAXS data, values of R_flex = 69% and R_σ = 1.1 were obtained for the apo state (Table S1). Despite the smallest subensembles having a reduced R_flex (R_flex decreases from 78% for the largest pool to 56% for the smallest pool), the ratios of the standard deviations of the selected distributions with respect to the pool, R_σ, remained greater than 0.8, near the maximal expected average of 1.0 for a fully flexible system (36) (Table S1).

Figure 6.

EOM selection of subensembles from a pool of 15,000 MD snapshots previously filtered based on the RDC R-factor distributions. (A and B) Two-dimensional R_g and interdomain angle (θ) distributions calculated for the external pool (gray) and for the SAXS-refined subensemble (colored). The population of each conformer is color coded. 1D projections of R_g and θ distributions are shown on top and at the side for the initial pool (gray) and the EOM-selected subensemble (blue). The representative conformers, their populations, and the MD time interval of each snapshot are indicated. To see this figure in color, go online.

As a control, the same MD-RDC-EOM analysis was carried out for the Ca²⁺-bound state using an R-factor threshold of 0.40 corresponding to a MD ensemble of 15,000 snapshots. When the external ensemble was refined using SAXS data, a single and narrow R_g distribution centered around wide-open conformers, which included the crystalographic structure of CALX-CBD12 in the Ca²⁺-bound state (PDB: 3RB5), was obtained. The representative structure displayed interdomain angle θ = 121°, backbone RMSD of 2.3 Å with respect to 3RB5, and R-factor of 0.37, nearly the same as that displayed by the crystallographic structure (R = 0.35) (Fig. 6). Flexibility analysis based on SAXS data yielded R_flex = 52% and R_σ = 0.12 for the Ca²⁺-bound state, consistent with a rigid system (Table S1). Therefore, the Ca²⁺-bound state is best represented by the 3RB5 structure. Similar conclusions were obtained when other ¹H-¹⁵N RDC data sets, measured either in PEG (apo state) or in compressed polyacrylamide gels (Ca²⁺-bound state), were used for filtering (Fig. S13).

Conclusion

Understanding the CALX Ca²⁺ regulation mechanism in atomic detail requires description of the conformational energy landscape of the two-domain Ca²⁺ sensor, CBD12, in the apo state. Here, this question was addressed using molecular dynamics simulations, SAXS, and RDC experimental data in combination with the EOM approach for the analysis of flexible multidomain proteins. It was found that CALX-CBD12 interconverts between open (130 > θ > 110°) and closed (99 > θ > 70°) interdomain arrangements in the apo state; however, the latter is more frequently sampled. In contrast, a single structure corresponding to the open interdomain arrangement (θ ∼131°) best represents the Ca²⁺-bound state. Although the MD simulations sampled a range of open and closed conformations both in the Ca²⁺-bound and the apo states, a preference for more closed conformations was observed. Especially for the Ca²⁺-bound case, this is not consistent with the experimental result of a dominating extended interdomain orientation. One needs to consider that small inaccuracies of the force field representation by 1–2 kcal/mol are equivalent to relative population changes (e.g., between closed versus open states) of a factor of 10. In summary, these findings highlight the interdomain motions experienced by the apo state. Binding of Ca²⁺ shifts this equilibrium toward the wide-open state (Fig. 7). This observation is in agreement with the previous proposal that this population shift event will trigger a tension on the linker domains that eventually could be relayed to the transmembrane helices, causing CALX inactivation (51). The overall strategy of combining optimized conformational sampling from MD simulations, high-resolution information from NMR-RDC data, and low-resolution information from SAXS data can be a good guide for the investigation of other types of multidomain proteins.

Figure 7.

Large-scale interdomain motions exhibited by CALX-CBD12 in the apo state. The conformational equilibrium is shifted toward extended structures upon Ca²⁺ binding to the CBD1 domain. The apo state ensemble consists of the EOM representative models superimposed on the coordinates of the CBD2 domain, and the Ca²⁺-bound state is represented by the EOM-selected conformer. To see this figure in color, go online.

Author contributions

M.F.d.S.D. collected and analyzed SAXS data and analyzed RDC data. P.A.M.V. prepared protein samples required for SAXS data collection. L.A.A. provided RDC data. M.F.d.S.D. and M.Z. carried out MD simulations and analysis of MD trajectories. M.F.d.S.D., M.Z., M.S., R.K.S., and C.L.P.O. designed the research and wrote the manuscript.

Editor: Jill Trewhella.