CALX-CBD1 Ca²⁺-Binding Cooperativity Studied by NMR Spectroscopy and ITC with Bayesian Statistics

Abstract

The Na⁺/Ca²⁺ exchanger of Drosophila melanogaster, CALX, is the main Ca²⁺-extrusion mechanism in olfactory sensory neurons and photoreceptor cells. Na⁺/Ca²⁺ exchangers have two Ca²⁺ sensor domains, CBD1 and CBD2. In contrast to the mammalian homologs, CALX is inhibited by Ca²⁺ binding to CALX-CBD1, whereas CALX-CBD2 does not bind Ca²⁺ at physiological concentrations. CALX-CBD1 consists of a β-sandwich and displays four Ca²⁺-binding sites at the tip of the domain. In this study, we used NMR spectroscopy and isothermal titration calorimetry (ITC) to investigate the cooperativity of Ca²⁺ binding to CALX-CBD1. We observed that this domain binds Ca²⁺ in the slow exchange regime at the NMR chemical shift timescale. Ca²⁺ binding restricts the dynamics in the Ca²⁺-binding region. Experiments of ¹⁵N chemical exchange saturation transfer and ¹⁵N R₂ dispersion allowed the determination of Ca²⁺ dissociation rates (∼30 s⁻¹). NMR titration curves of residues in the Ca²⁺-binding region were sigmoidal because of the contribution of chemical exchange to transverse magnetization relaxation rates, R₂. Hence, a novel, to our knowledge, approach to analyze NMR titration curves was proposed. Ca²⁺-binding cooperativity was examined assuming two different stoichiometric binding models and using a Bayesian approach for data analysis. Fittings of NMR and ITC binding curves to the Hill model yielded n_Hill ∼2.9, near maximal cooperativity (n_Hill = 4). By assuming a stepwise model to interpret the ITC data, we found that the probability of binding from 2 up to 4 Ca²⁺ is approximately three orders of magnitude higher than that of binding a single Ca²⁺. Hence, four Ca²⁺ ions bind almost simultaneously to CALX-CBD1. Cooperative Ca²⁺ binding is key to enable this exchanger to efficiently respond to changes in the intracellular Ca²⁺ concentration in sensory neuronal cells.

Significance

CALX-CBD1 is the Ca²⁺-sensor domain of the Na⁺/Ca²⁺ exchanger of Drosophila melanogaster. It consists of a β-sandwich and contains four Ca²⁺ binding sites at the distal loops. In this study, we examined the cooperative binding of four Ca²⁺ ions to CALX-CBD1 using NMR spectroscopy and isothermal titration calorimetry experiments. NMR and isothermal titration calorimetry data were analyzed using the framework of the binding polynomial formalism and Bayesian statistics. A novel, to our knowledge, approach to analyze NMR titration data in the slow exchange regime was proposed. These results support the view that CALX-CBD1 binds four Ca²⁺ with high cooperativity. The significant ligand binding cooperativity exhibited by this domain is determinant for the efficient allosteric regulation of this exchanger by intracellular Ca²⁺.

Introduction

Ca²⁺ is a key intracellular regulator and an important second messenger (1). Hence, cells developed various mechanisms to control the intracellular Ca²⁺ concentration very precisely (2,3) Among those, the Na⁺/Ca²⁺ exchanger (NCX) is particularly relevant (4) After the Ca²⁺-ATPases, the NCX is one of the most important mechanisms for the extrusion of intracellular Ca²⁺, particularly in excitable cells (5). The NCX couples the translocation of one Ca²⁺ to the countertransport of three Na⁺ across the cell membrane (5,6). It consists of a large transmembrane domain, involved in ion translocation across the lipid bilayer, and a large intracellular loop that connects transmembrane helices 5 and 6 and that is responsible for the regulation of exchanger activity. Binding of Ca²⁺ to two calcium-binding domains (CBD1 and CBD2), located at the NCX cytoplasmic loop, activates the exchanger, enabling the in and out flux of Na⁺ and Ca²⁺. The Na⁺/Ca²⁺ exchanger of Drosophila melanogaster, so-called CALX, is unusual because Ca²⁺ binding to the CBDs inhibits this exchanger (7). This behavior is curious because the CALX and the NCX display ∼44$\text{\%}$ of amino acid sequence identity (8) and are believed to share the same architecture. The CALX Na⁺/Ca²⁺ exchanger is found in Drosophila photoreceptor cells and in olfatory sensory neurons, where it is the main Ca²⁺ extrusion mechanism (9,10). CALX plays an essential role in light-mediated signaling. Mutation of CALX in transgenic flies caused a reduction in light signal response amplification, whereas its overexpression generated significant retinal degeneration (9).

The CBDs are also called CALX-β motifs (8) or CALX-β domains (11). They appear adjacent to each other, separated by a linker of three amino acids that is highly conserved among exchangers of different organisms (12,13). The CALX-CBD2 domain does not bind Ca²⁺ at physiological concentrations (14). Hence, in the CALX exchanger, the regulatory Ca²⁺-binding sites are located only in the CBD1 domain (13). The CALX-CBD1 crystal structure shows four Ca²⁺ in the distal loops of the CBD1 β-sandwich, at the tip of the domain (Fig. 1 A; (15)). The four Ca²⁺-binding sites are located at ∼4 Å from each other. A series of negatively charged residues provides most of the anchoring points for Ca²⁺ coordination. Most of these residues are located in the EF loop and at the C-terminus (Fig. 1 A), near the linker with CBD2. CALX-CBD1 was also crystallized in the apo state and in an intermediate state (15). Although the apo state structure shows no electron density for the EF loop, the crystal structure of the intermediate state shows two Ca²⁺ at sites Ca1 and Ca2. The intermediate state structure is very similar to the fully loaded Ca²⁺-bound state, with a backbone root mean-square deviation of only 0.3 Å. These observations indicate that the binding of Ca²⁺ to sites Ca1 and Ca2 is sufficient to stabilize the structure of the Ca²⁺-binding region of CALX-CBD1 (15). Furthermore, they suggest that the Ca²⁺-binding mechanism is sequential, rather than the simultaneous binding of four Ca²⁺ to sites Ca1–Ca4 in all-or-none fashion (15).

Figure 1.

Binding of Ca²⁺ stabilizes CALX-CBD1. (A) Crystal structure of CALX-CBD1 in the holo state (Protein Data Bank, PDB: 3EAD (15)) is shown. Ca²⁺ ions are shown as green spheres. Residues whose ¹H-¹⁵N crosspeaks appear only in the presence of Ca²⁺ are indicated and shown as gray spheres. The assigned residues in the unbound state are shown in blue. (B) Superposition of ¹H-¹⁵N HSQC spectra of CALX-CBD1 recorded in the absence (blue) and presence (red) of 20 mM of CaCl₂ is shown. (C) DSC experiment showing the thermal denaturation of CALX-CBD1 in the absence (blue), and presence of Ca²⁺ (red) is given. The protein melting temperatures, T_m, under these conditions are 55.3 and 69.6°C for the apo state and Ca²⁺-bound states, respectively. To see this figure in color, go online.

The Ca²⁺-binding cooperativity exihibited by the CBDs is critical to enable them to function as efficient allosteric switches of the Na⁺/Ca²⁺ exchangers. Therefore, in this work, we used NMR spectroscopy and isothermal titration calorimetry (ITC) experiments to investigate the Ca²⁺-binding properties of CALX-CBD1. Consistent with the crystallographic data, we observed that CALX-CBD1 displays substantial backbone flexibility near the Ca²⁺-binding sites. Experiments of ¹⁵N chemical exchange saturation transfer (CEST) and of ¹⁵N Carr-Purcell-Meiboom-Gill (CPMG) relaxation dispersion, recorded at the Ca²⁺/CALX-CBD1 stoichiometric molar ratio, allowed the determination of Ca²⁺ dissociation rates. Ca²⁺-binding cooperativity was examined by ITC and NMR titration experiments, assuming different stoichiometric binding models and using a Bayesian approach for data analysis. The NMR titration curves obtained for residues near the Ca²⁺-binding sites displayed an accentuated sigmoidal behavior, which could be accounted for by calculating the effective transverse magnetization relaxation rates, R₂^eff, at each titration point, using the exact solution of the Bloch-McConnell equation (16). In summary, this study sheds new, to our knowledge, light on the Ca²⁺-binding cooperativity of CALX-CBD1.

NMR titration theoretical framework

In an NMR titration experiment, in which the protein-ligand binding equilibrium follows the slow exchange regime, a titration curve may be built by computing the variable η, the intensity ratio of the protein NMR signal in the bound state at a given ligand concentration, I, and at saturating conditions, I_max:

$$\eta \equiv \frac{I}{I_{\text{max}}}.$$ (1)

Assuming a Lorentzian lineshape, the maximal intensity of a ¹H-¹⁵N HSQC (Heteronuclear Single Quantum Coherence) crosspeak may be written as

$$I=C\frac{\text{exp}\left(-2{\text{R}}_2^{\text{INEPT}}\Delta \right)}{{\text{R}}_{2,\text{N}}^{\text{eff}}{\text{R}}_{2,\text{H}}^{\text{eff}}}{p}_B,$$ (2)

where C is a constant that takes into account the physical dimensions of the equilibrium magnetization; ${\text{R}}_{2,\text{N}}^{\text{eff}}$ and ${\text{R}}_{2,\text{H}}^{\text{eff}}$ are the effective transverse relaxation rates for the ¹⁵N and ¹H nuclei, respectively; p_B is the population of protein molecules in the bound state; and R₂^INEPT is the relaxation rate during the INEPT magnetization transfer period of duration Δ. The latter is also affected by chemical exchange between the apo and bound states.

The relaxation of transverse magnetization during the INEPT period may be estimated at every titration point using the Bloch-McConnell matrix $\hat{\mathbf{B}}$ (Eq. S35) as follows:

$${\text{R}}_2^{\text{INEPT}}=-\frac{1}{\Delta }\text{ln}\left(\frac{M_{f,y}^B}{M_{0,y}^B}\right),{\mathbf{M}}_f=\text{exp}\left(\frac{\Delta }{2}\hat{\mathbf{B}}\right){\hat{\mathbf{R}}}_y\text{exp}\left(\frac{\Delta }{2}\hat{\mathbf{B}}\right){\mathbf{M}}_0,$$ (3)

where ${\hat{\mathbf{R}}}_y$ is a 180° rotation matrix, M₀ = ${\left[M_{0,x}^A{M}_{0,y}^A{M}_{0,x}^B{M}_{0,y}^B\right]}^{\text{T}}$ is the initial magnetization, and the final magnetization is given by M_f = ${\left[M_{f,x}^A{M}_{f,y}^A{M}_{f,x}^B{M}_{f,y}^B\right]}^{\text{T}}$. Without loss of generality, in the slow exchange regime, the initial magnetization may be written as M₀ = M₀([0 p_A 0 p_B]^T), where M₀ is a constant and p_A is the population of the protein in the apo state.

R^eff_2,H and R^eff_2,N may be calculated using the exact solution for R₂ in chemically exchanging systems derived by Leigh (16). For this analysis, we considered the lowest eigenvalue of the characteristic matrix of the Bloch-McConnell equation because in our case, the NMR signal of the bound state must be sharper than that of the apo state. Therefore, R^eff₂ was written as

$${\text{R}}_2^{\text{eff}}=A_2-{\left(\frac{G+{\left(G^2+H^2\right)}^{1/2}}{2}\right)}^{1/2},$$ (4)

where

$$A_2=\frac{1}{2}\left(R_{2,A}^{\text{o}}+R_{2,B}^{\text{o}}+k_{\text{on}}+k_{\text{off}}\right),$$ (5)

$$G=\frac{1}{4}\left({\left(R_{2,A}^{\text{o}}-R_{2,B}^{\text{o}}+k_{\text{on}}-k_{\text{off}}\right)}^2+k_{\text{on}}{k}_{\text{off}}-\Delta {\Omega }^2\right)$$

$$H=\frac{\Delta \Omega }{2}\left(R_{2,A}^{\text{o}}-R_{2,B}^{\text{o}}+k_{\text{on}}-k_{\text{off}}\right)$$

ΔΩ is the chemical shift difference between the apo and bound states, k_off is the complex dissociation rate constant, and k_on is the pseudo-first-order association rate constant. ${\text{R}}_{2,A}^{\text{o}}$ and ${\text{R}}_{2,B}^{\text{o}}$ are the transverse relaxation rates of the apo and the bound states, respectively.

Under conditions of saturation, i.e., when all ligand binding sites are occupied, ${\text{R}}_2^{\text{eff}}$ tends to ${\text{R}}_{2,B}^{\text{o}}$, and ${\text{R}}_2^{\text{INEPT}}$ tends to the average transverse relaxation rates of in-phase and antiphase coherences, R′₂; hence, the exchange contribution to the effective transverse relaxation rates is negligible, and the crosspeak intensity is given by

$$I_{\text{max}}=\frac{C\text{exp}\left(-2{\text{R}}_2\text{'}\Delta \right)}{{\text{R}}_{2,\text{N},B}^{\text{o}}{\text{R}}_{2,\text{H},B}^{\text{o}}}.$$ (6)

Therefore, it is convenient to rewrite the variable η as

$$\eta =\frac{{\text{R}}_{2,\text{N},B}^{\text{o}}{\text{R}}_{2,\text{H},B}^{\text{o}}}{{\text{R}}_{2,\text{N}}^{\text{eff}}{\text{R}}_{2,\text{H}}^{\text{eff}}}\text{exp}\left(-2{\text{R}}_{\text{ex}}^{\text{INEPT}}\Delta \right)p_B,$$ (7)

where ${\text{R}}_{\text{ex}}^{\text{INEPT}}=\left({\text{R}}_2^{\text{INEPT}}-\text{R}{\text{'}}_2\right)$. In this work, as an approximation, we assumed that R′₂ is equal to ${\text{R}}_{2,\text{H}}^{\text{o}}$. The population of protein molecules in the apo and in the bound states may be written in terms of the binding polynomial (Eq. S6):

$$p_A=\frac{1}{Z},p_B=1-p_A=1-\frac{1}{Z}.$$ (8)

One should note that the population p_B, as defined here, contains the contribution of all protein bound states. By substituting Eq. 8 into Eq. 7, we may restate η as

$$\eta =f_{\text{ex}}\left(1-\frac{1}{Z}\right),f_{\text{ex}}=\frac{{\text{R}}_{2,\text{N},B}^{\text{o}}{\text{R}}_{2,\text{H},B}^{\text{o}}}{{\text{R}}_{2,\text{N}}^{\text{eff}}{\text{R}}_{2,\text{H}}^{\text{eff}}}\text{exp}\left(-2{\text{R}}_{\text{ex}}^{\text{INEPT}}\Delta \right).$$ (9)

An analogous binding curve could be derived by monitoring the intensity decrease of the protein NMR signals of the apo state.

Methods

CALX-CBD1 expression and purification

A DNA fragment corresponding to residues 434–555 from the Drosophila melanogaster CALX 1.1 was PCR amplified from the CALX1.1 cDNA and cloned in fusion with an N-terminal six-histidine tag in the vector pET-28a (Novagen, Gibbstown, NJ), using NdeI and XhoI restriction sites. Protein expression was carried out in Escherichia coli BL21-CodonPlus (DE3)-RIL (Agilent, Santa Clara, CA). Uniform labeling with ¹⁵N or with ¹⁵N and ¹³C was achieved by overexpression in M9 supplemented with 1.0 g/L of ¹⁵NH₄Cl (Cambridge Isotopes Laboratories, Tewksbury, MA) and/or 4.0 g/L of ¹³C-labeled glucose (Cambridge Isotopes Laboratories). Bacterial cultures were grown at 37°C to an OD600 of 0.7, at which point the temperature was decreased to 18°C and protein overexpression was induced by the addition of 0.4 mM of isopropyl-β-D-thiogalactopyranoside (Thermo Fisher Scientific, Waltham, MA) overnight. Cells were harvested by centrifugation and the cell pellets stored at −20°C. Approximately 10 g of cells was suspended in 100 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 phenylmethylsulfonyl 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, and the supernatant was applied into a 5 mL Ni²⁺ column (HisTrap; 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 five column volumes of buffer A, and eluted with 0.5 M of imidazole. Fractions containing CALX-CBD1 were combined, concentrated to 2 mL using an Amicon concentrator with a 3 kDa cutoff (Millipore, Burlington, MA), and applied into a gel filtration Superdex 75 (16/600) 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). Finally, the desired fractions were combined and applied into a MonoQ 10/100 (GE Healthcare) column, pre-equilibrated with the gel filtration buffer, and eluted with a gradient of 1.0 M of NaCl. To prepare NMR samples, the eluted CALX-CBD1 was concentrated and buffer exchanged to 20 mM Tris-HCl (pH 7.4), containing 5 mM β-mercaptoethanol, 200 mM NaCl, 1% (V/V) of glycerol, and 10% of D₂O. Protein concentration was determined by measuring the absorbance at 280 nm, assuming ε₂₈₀ = 7575 M⁻¹ cm⁻¹. The molecular weight of CALX-CBD1 was confirmed as being 16.025 kDa using mass spectrometry using MALDI (Matrix Assisted Laser Desortion Ionization) in TOF/TOF (Time of Flight) mode recorded on a MALDi Ultraflextreme instrument (Bruker, Billerica, MA). Unless otherwise mentioned all chemicals were purchased from Merck KGaA, Darmstadt, Germany.

NMR spectroscopy

All NMR spectra were recorded on a Bruker AVANCE III spectrometer (Bruker) equipped with a TCI CryoProbe and operating at 800 MHz (¹H frequency). CPMG-based ¹⁵N relaxation dispersion experiments were additionally recorded on a Bruker Avance III-HD spectrometer operating at 600 MHz (¹H frequency) and equipped with a TCI cryoprobe. NMR experiments were carried out at 308 K unless otherwise stated. All NMR data were processed with NMRPipe (17) and analyzed using the CcpNmr Analysis software (18). Protein samples used for backbone resonance assignment consisted of ∼200 μM of ¹⁵N/¹³C double-labeled CALX-CBD1. The apo state sample contained 2 mM of EDTA, whereas the Ca²⁺-bound sample contained 20 mM of CaCl2. Backbone (¹HN, ¹⁵N, ¹³Cα, ¹³CO) and side-chain (¹³Cβ) resonance assignments for CALX-CBD1 were obtained from the analysis of three-dimensional HNCA, HN(CO)CA, HNCO, HN(CA)CO, CBCA(CO)NH, and HNCACB experiments. The assigned chemical shifts for CALX-CBD1 in the Ca²⁺-bound state were deposited in the Biological Magnetic Resonance Data Bank under the accession code BMRB: 27787.

Longitudinal R₁ and rotating-frame (R_1ρ) relaxation rates and the [¹H]-¹⁵N heteronuclear Nuclear Overhauser Effect (NOE) were measured using standard ¹⁵N relaxation methods recorded as pseudo-three-dimensional or interleaved experiments (19,20). Protein samples consisted of 380 μM of $15$N-labeled CALX-CBD1 containing CaCl₂ at a molar ratio of 16:1 (CaCl₂/protein). The R_1ρ experiment was recorded using spin-lock field strength γB₁/2π = 1013 Hz. Rotating-frame R_1ρ relaxation was sampled at 4, 8, 16, 24, 35, 44, 58, 66, 80, 92, 104, and 115 ms, whereas longitudinal R₁ relaxation was sampled at 150, 300, 450, 600, 900, 1250, 1500, 1800, 2000, 2250, and 2500 ms. The heteronuclear NOE was recorded using a saturation time of 3.0 s. The recycle delay was set to 4.0 s for the R₁ and R_1ρ experiments, whereas a delay of 5.0 s was used for the heteronuclear NOE experiment. R₁ and R_1ρ relaxation rates were determined by fitting the crosspeak intensity decays to an exponential decay function consisting of two parameters, the intensity at time zero and a decay rate. The uncertainties of the peak heights were taken from the noise level in each spectrum, whereas the uncertainties of the fitted parameters were estimated using Monte Carlo (at least 1000 iterations). R_1ρ relaxation rates were measured at two different ¹⁵N carrier frequencies, 123.942 and 110.942 ppm, satisfying the conditions presented by Massi et al. (20). The chosen R_1ρ-values corresponded to the smallest Ω/(γB₁) ratio, in which Ω is the resonance offset in hertz, indicating best alignment of the magnetization with the spin-lock field. R₂-values were obtained by correcting R_1ρ for off-resonance effects using the following relation: R₂ = R_1ρ/sin²θ − R₁(cosθ/sinθ)², where θ = arctan(γ B₁/Ω).

A relaxation-compensated Bruker pulse sequence (hsqcrexetf3gpsitc3d) was used for all CPMG-based ¹⁵N relaxation dispersion experiments, using constant relaxation times of 40 or 50 ms. The experiments were recorded as a series of two-dimensional (2D) planes with CPMG field strengths of 50, 100, 150, 200, 250, 300, 350, 400, 500, 600, 700, 800, and 900 Hz, and a reference spectrum measured by omitting the CPMG period. The crosspeak intensities were converted into effective transverse relaxation rates doing R₂^eff = −1/T_exln(I/I₀), where I₀ is the crosspeak intensity in the reference spectrum. Uncertainties of R₂^eff were calculated by error propagation, assuming the noise level as the uncertainty in the crosspeak heights in each spectrum. CPMG relaxation dispersion curves recorded at 600 and 800 MHz were simultaneously fitted to the Bloch-McConnell equation assuming a two-site chemical exchange model (Eq. S35) through the calculation of the following equation using a home-made python script:

$${\mathbf{M}}_{\text{tot}}={\hat{\mathbf{\Gamma }}}^{2n}{\mathbf{M}}_0,$$ (10)

where M₀ is the initial transverse magnetization aligned with the y axis, n is the number of CPMG periods, and $\hat{\mathbf{\Gamma }}$ is given by

$$\hat{\mathbf{\Gamma }}=\text{exp}\left(\hat{\mathbf{B}}{\tau }_{cp}\right){\hat{\mathbf{R}}}_y\text{exp}\left(\hat{\mathbf{B}}{\tau }_{cp}\right),$$ (11)

where $\hat{\mathbf{B}}$ is the Bloch-McConnell equation for the transverse magnetization and ${\hat{\mathbf{R}}}_y$ is a 180° rotation matrix. The python functions matrix_power from the numpy package and expm from the scipy package were used to calculate M_tot. CEST experiments were recorded using a Bruker implementation of the CEST experiment described by Vallurupalli and co-workers (21). A weak ¹⁵N radio frequency field of γB₁/2π = 25 Hz and a CEST exchange period T_ex of 400 ms were used. The power level for the saturation radio frequency field was calculated from the calibrated ¹⁵N hard pulse assuming linear amplifiers. The saturation field offset was varied from −1250 to 1250 Hz in intervals of 25 Hz, covering the entire ¹⁵N spectral width. A reference spectrum was recorded with T_ex set to 0. CEST profiles were fitted to the Bloch-McConnell equation (Eq. S33), assuming a two-site exchange model, or to the Bloch equation, using a similar strategy as that used to compute the evolution of the magnetization during the CPMG period. The exchange rate k_ex, the population of the apo state p_A, the offset difference between the apo and the bound states ΔΩ, and the ¹⁵N R₁ and R₂ rates for the apo and the bound states were treated as free parameters. Ca²⁺ dissociation rates were obtained by doing k_off = k_ex × p_A, where p_A = 1 − p_B, with A referring to the population of the apo state and B to the fully Ca²⁺-bound state.

The NMR titration was carried out using a sample of 180 μM of CALX-CBD1 in 10 mM Tris (pH 7.4), containing 200 mM NaCl, 1 mM phenylmethylsulfonyl fluoride as protease inhibitor, and 10% of D₂O. This preparation was previously incubated with 10 mM EDTA to remove residual Ca²⁺. The EDTA was removed by a series of concentration and dilutions using an Amicon (Millipore) with a cutoff of 3 kDa at 4°C. A series of ¹H-¹⁵N HSQC spectra were recorded at 308 K as matrices of 1024 × 128 complex points. The NMR data was processed without apodization to apply the theoretical model outlined in the previous section. The data set was zero filled up to 4096 × 2048 points before Fourier transformation. Aliquots from a 5 M CaCl₂ stock solution, prepared in the same buffer, were added to the NMR sample up to final Ca²⁺ concentrations of 5, 15, 25, 50, 70, 90, 190, 340, 490, 740, 990, 1490, 1990, or 3990 μM. Only well-isolated ¹H-¹⁵N HSQC crosspeaks belonging to residues 452–456, 458–460, 479, 481, 483, 486–491, 512, 514–516, 518–520, 523, 525, 549, 550–552, and 555 of CALX-CBD1 in the Ca²⁺-bound form were considered for the analysis. Crosspeak intensities were determined from interpolation of a 2D numerical function (2D spline) as detailed in Fig. S1. The factor η was calculated according to Eq. 1 for each crosspeak along the titration. Only intensities above the noise level of each spectrum were considered for the analysis. The baseline threshold was determined by calculating the absolute intensity at 1σ of the baseline distribution (68%). The intensity level at the plateau of the binding curve, I_max, was determined as the mean intensity value of the three greatest Ca²⁺ concentrations: 1490, 1990, and 3990 μM of CaCl₂. The NMR titration curves were fitted to Eq. 9. The protein population in the apo state, p_A, was calculated according to the Hill model. The dissociation constant (K_d) and the Hill coefficient (n_Hill) were treated as free parameters. The ¹H and ¹⁵N chemical shift differences between the apo and the Ca²⁺-saturated states (ΔΩ_N and ΔΩ_H); the Ca²⁺ dissociation rates (k_off); and the transverse relaxation rates of apo ${\text{R}}_{2,\text{N},A}^{\text{o}}$, ${\text{R}}_{2,\text{H},A}^{\text{o}}$ and bound state ${\text{R}}_{2,\text{N},B}^{\text{o}}$, ${\text{R}}_{2,\text{H},B}^{\text{o}}$ were considered as nuisance parameters. We used a Gaussian distribution as prior information for the dissociation rate, for the ¹⁵N transverse relaxation rates of the bound state, and for the dissociation constant. The distributions were centered at k_off = 30 s⁻¹, ${\text{R}}_{2,\text{N},B}^{\text{o}}$ = 14 s⁻¹, and K_d = 2.52 μM and displayed σ = 10 and 20% for the first two parameters and for the last parameter, respectively. This prior information was based on the results obtained from the CPMG relaxation dispersion experiment, the ¹⁵N transverse relaxation rates determined for CALX-CBD1 in the bound state, and ITC experiments. The protein NMR concentration used for the NMR titration experiment was set to 180 μM using a narrow Gaussian prior with a σ equal to 10% of this value.

Calorimetry

ITC experiments were carried out using a Malvern VP-ITC instrument (Malvern Panalytical, Malvern, UK) at 35°C. Samples of CALX-CBD1 of nominal concentrations 2, 5, 10, 15, 20, and 229 μM in 20 mM Tris-HCl (pH 7.4), 200 mM NaCl, 5 mM β-mercaptoethanol, and 1% (V/V) glycerol were treated with 10 mM of EDTA. The EDTA was removed by buffer exchange using an Amicon centrifugation device (Millipore), and the sample was transferred to the calorimeter cell. The injection syringe was filled with a solution of CaCl2 at 300, 500, or 7600 μM in the same buffer. The experiments consisted of a first injection of CaCl₂ of 2 μL, followed by 28 injections of 10 μL of CaCl₂. Peak integration was carried out using the instrument software, providing the heat energy released in each Ca²⁺ injection. The ITC binding curves were fitted to Eq. S28 assuming different stoichiometric binding models, as described in the Supporting Materials and Methods. The Bayesian approach used to fit the ITC data was based on Nguyen and co-workers (22). Fits to the Hill model considered the dissociation constant K_d, the Hill coefficient (n_Hill), and the molar binding enthalpy (ΔH_bind) as free parameters, whereas fits to the stepwise model treated K_d,1, K_d,2, K_d,3, K_d,4, and ΔH_bind as free parameters. As proposed by Nguyen and co-workers (22), we included a set of nuisance parameters involved in the theory, among which are the ligand concentration in the syringe [L]_o, the protein concentration in the cell [P]_tot, the heat offset Q_o, and the Gaussian error of the ITC data σ for each ITC curve. The latter was considered the same for all data points. Therefore, in total, there were 16 nuisance parameters for each stoichiometric model. In the case of the stepwise model, the protein concentration in the calorimeter cell was taken from a Gaussian distribution centered at calibrated values. The calibration of the protein concentration values was done by a global fitting of the ITC binding curves to a model of n independent binding sites with the same affinity, in which n was constrained to 4 using a narrow Gaussian prior with $\sigma =0.01$. This calibration was important because of the inaccuracy in the determination of the active protein concentration, which was ∼10–15% far from the nominal value in all experiments except for that performed with the lowest protein concentration (2 μM), where it was ∼50% off (Fig. S2). The script implemented to globally fit ITC data using Bayesian statistics may be obtained upon request or in the GitHub (https://github.com/jodarie/CalBayS_v1).

Micro-differential scanning calorimetry (DSC) experiments were performed on a VP-DSC (MicroCal, Northampton, MA) instrument. The CALX-CBD1 concentration used in the DSC experiments was ∼100 μM with or without CaCl₂ at a molar ratio of 10:1 (Ca²⁺/CBD1).

Results

CALX-CBD1 displays significant backbone flexibility in the apo state

The ¹H-¹⁵N HSQC spectrum of the CALX-CBD1 domain recorded in the absence of Ca²⁺ displayed well-dispersed crosspeaks, which are indicative of a well-folded protein. However, ∼23 of the expected ¹H-¹⁵N correlations were missing. All apo state residues that could be assigned are located at the bottom of the domain, opposite to the four Ca²⁺-binding sites (Fig. 1). In contrast, in the presence of 20 mM of CaCl₂, all the expected ¹H-¹⁵N crosspeaks were observed (Fig. 1; Fig. S3), and 111 out of 121 backbone resonances were successfully assigned through the analysis of triple-resonance NMR experiments. These observations suggest that the tip of the domain, near the Ca²⁺-binding sites, experiences flexibility at the NMR chemical shift timescale but becomes rigid upon Ca²⁺-binding. Consistent with this observation, the crystal structure of CALX-CBD1 in the apo state does not show electron density for residues 516–522 at the EF loop, indicating flexibility at the Ca²⁺-binding region (15). The EF loop contains six negatively charged residues. It is, therefore, not surprising that it exhibits flexibility in the apo state. Micro-DSC experiments showed that the binding of Ca²⁺ leads to an increase of CALX-CBD1 thermal stability by ∼15°C (Fig. 1). A similar increment in thermal stability upon Ca²⁺-binding was observed for classical C2 domains belonging to PKC isoenzymes (23). Measurements of ¹⁵N relaxation rates, R₁ and R₂, and the heteronuclear NOE, carried out in the presence of excess of Ca²⁺, confirmed that CALX-CBD1 behaves as a rigid protein in the Ca²⁺-bound state (Fig. S4). An analysis of the overall tumbling rate based on ¹⁵N R₂/R₁ ratios for all ¹H-¹⁵N spin pairs, assuming isotropic tumbling, yielded τ_c = 9.5 ns under our NMR conditions. Larger ¹⁵N transverse relaxation rates were detected for residues 539–546, at β-strand G, near the β-bulge, far away from the Ca²⁺-binding sites (Fig. S4). These larger R₂ rates could be due to a conformation exchange process on a slow (microsecond to millisecond) timescale or to transient oligomerization of the domain involving the β-bulge. Consistent with the latter hypothesis, we observed that the NMR sample tends to aggregate with time.

CALX-CBD1 Ca²⁺-binding affinity determined by NMR

To investigate the mechanism of Ca²⁺-binding to CALX-CBD1, we carried out NMR titration experiments. ¹H-¹⁵N HSQC spectra of CALX-CBD1 recorded in the absence and presence of increasing Ca²⁺ concentrations showed that Ca²⁺ binding occurs in slow exchange at the NMR chemical shift timescale. Furthermore, only crosspeaks for the apo and the Ca²⁺-saturated states were observed as reported before for the mammalian ortholog NCX-CBD1 (24). Considering that crosspeaks due to intermediate Ca²⁺-bound states were not detected, this scenario is consistent with the cooperative binding of four Ca²⁺ to CALX-CBD1. Ca²⁺-binding curves were calculated by monitoring the intensity increase of well-isolated NMR signals of the protein in the bound state according to Eq. 1. To avoid bias in the determination of the crosspeak intensities, a 2D cubic spline function was maximized for each crosspeak, as shown in Fig. S1. Interestingly, all residues located at the tip of the domain, near the Ca²⁺-binding sites, or involved in Ca²⁺ coordination such as D552 displayed sigmoidal Ca²⁺-binding curves. In contrast, crosspeaks of residues located further away from the Ca²⁺-binding sites, such as A487, displayed nearly hyperbolic binding curves (Fig. 2; Fig. S5). As shown in (Fig. 2 A), the accentuated sigmoidal Ca²⁺-binding curves did not agree with the Hill model, even when maximal cooperativity, n_Hill = 4, was assumed. Therefore, the accentuated sigmoidal profile of some of the Ca²⁺-binding curves is not due to ligand binding cooperativity. Because CALX-CBD1 experiences significant backbone flexibility in the apo state, the binding of Ca²⁺ must be accompanied by conformational changes at the Ca²⁺-binding sites. Therefore, we examined the possibility that conformational selection or induced-fit contributions to the Ca²⁺-binding equilibrium would lead to highly sigmoidal Ca²⁺-binding curves. These possibilities were discarded because simulations of the stepwise model, considering four binding events and an induced-fit or conformational selection step, did not lead to binding curves displaying sigmoidal behavior.

Figure 2.

NMR titration. (A) Typical examples of NMR titration curves are shown. Residue D552 displays an accentuated sigmoidal behavior (top left) in comparison with A487 (bottom left). Red lines are fits to the Hill model, and black lines are fits to Eq. 9 using the binding polynomial for the Hill model. Error bars were computed from the noise level in the spectra. (B) Histograms of the obtained values for the Hill coefficient (n_Hill) and affinity (K_d) for all analyzed residues are given. The red line indicates the median of the distribution. (C) Quantitative analysis of the magnitude of exchange contribution to the NMR titration curve is shown as a function of the residue number and mapped on the crystal structure of CALX-CBD1 (PDB: 3EAD). The G_ex parameter is defined in Fig. S6. Residues indicated in red (left) are involved in Ca²⁺ coordination. To see this figure in color, go online.

The sigmoidal behavior of the Ca²⁺-binding curves can be explained by considering the existence of chemical exchange contributions to the NMR lineshapes. Simulations of binding curves computed with Eq. 9 and using the exact solution for ${\text{R}}_2^{\text{eff}}$, Eq. 4, in the case of a two-site chemical exchange model (16) showed that deviations from the usual behavior of the Hill model might be significant outside the extreme limits of the titration curve (Ca²⁺/CBD1 ≈ 0 or Ca²⁺/CBD1 ≈ 4), i.e., when ${\text{R}}_2^{\text{eff}}>{\text{R}}_{2,\text{B}}^{\text{o}}$ (Fig. 3). In the absence of chemical exchange, i.e., when k_off = 0, η is equivalent to p_B, and the Ca²⁺-binding curve follows the Hill model (Fig. 3). In contrast, when the chemical exchange contributions to R₂ increase, the binding curve may deviate from the expected behavior, as observed in our experimental data (Fig. 2). It is worth noting that the existence of undetectable intermediate Ca²⁺-bound states, displaying large R₂ rates, could provide an alternative explanation for the observed sigmoidal Ca²⁺-binding curves. This hypothesis is consistent with the approach proposed here; however, the inclusion of additional binding constants and relaxation rates because of a more complex stoichiometric model would make the data analysis rather more complicated.

Figure 3.

Contributions of chemical exchange to NMR titration curves. Simulation of η (bottom) and f_ex (top) as a function of the ligand/protein molar ratio is shown. (A) k_off = 40 s⁻¹ was kept constant while ΔΩ was varied from 0 to 120 Hz. (B) ΔΩ = 80 Hz was left constant while k_off was varied from 0 to 100 s⁻¹. (C) k_off = 40 s⁻¹ was kept constant and R_2,A = R_2,B for both ¹⁵N and ¹H nuclei while ΔΩ was varied from 0 to 120 Hz. η and f_ex were calculated according to Eq. 9 assuming the Hill model (Eq. S25) and the following relaxation rates: ${\text{R}}_{2,\text{H},A}^{\text{o}}$ = 150, ${\text{R}}_{2,\text{H},B}^{\text{o}}$ = 50, ${\text{R}}_{2,\text{N},A}^{\text{o}}$ = 42, and ${\text{R}}_{2,\text{N},B}^{\text{o}}$ = 14 s⁻¹ for the ¹H and ¹⁵N spins. The relaxation rate during the INEPT transfer periods was calculated numerically assuming Δ = 5.2 ms. The total protein concentration was 180 μM, dissociation constant K_d = 4 μm, n_Hill = 4, and ΔΩ_H = 0 Hz. To see this figure in color, go online.

Analysis of the probability distribution functions of the free parameters indicated that K_d and n_Hill are well defined for most residues. The representative values obtained from the median of the distributions of all analyzed residues are shown in Fig. 2 B and indicate that n_Hill = 2.93 and K_d = 2.29 μM. The determined Hill coefficient (n_Hill = 2.93) indicates that Ca²⁺ binds cooperatively to CALX-CBD1. Importantly, this analysis did not include prior information for the following parameters: ${\text{R}}_{2,\text{N},\text{A}}^{\text{o}},{\text{R}}_{2,\text{H},A}^{\text{o}},{\text{R}}_{2,\text{H},B}^{\text{o}}$, ΔΩ_N, and ΔΩ_H. The extent of deviation from the profile expected for each binding curve in the absence of exchange was estimated through an empirical parameter G_ex. The latter was defined as the ratio of the area of the experimental binding curve relative/the area of a rectangle from molar ratios 0 to 4 (Fig. S6). This analysis does not depend on the convergence of the fitted parameters, but rather depends on the shape of the binding curve. G_ex may be qualitatively associated to the degree of chemical exchange contribution to the transverse relaxation rates at a specific HN site. As shown in Fig. 2 C, all residues involved in Ca²⁺ coordination in the crystal structure displayed the largest deviations and hence the largest G_ex-values.

Determination of Ca²⁺ dissociation rates (k_off) by ¹⁵N relaxation experiments

CEST experiments are informative about dynamic processes that occur in the slow exchange regime, at the millisecond timescale (21). Therefore, we investigated whether ¹⁵N CEST experiments could reveal information on the kinetics of Ca²⁺ binding to CALX-CBD1. The observed CEST effects were interpreted assuming a two-site exchange model, corresponding to CALX-CBD1 in equilibrium between the apo and the fully Ca²⁺-saturated states. To take advantage of all backbone resonance assignments available for CALX-CBD1 in the Ca²⁺-bound state, we recorded ¹⁵N-CEST experiments on samples prepared in the presence of CaCl₂ at the stoichiometric 4:1 molar ratio (Ca²⁺/CALX-CBD1). Under this condition, crosspeaks due to the apo state are not detected. As shown in Fig. 4, three different CEST profiles were observed. Residues located at the bottom of the domain, i.e., far away from the Ca²⁺-binding sites, displayed a single and narrow CEST dip, which did not change upon the addition of an excess of Ca²⁺ (Fig. 4). In contrast, residues at the tip of the domain or involved in Ca²⁺ coordination displayed broadened CEST dips, which became significantly narrower upon the addition of an excess of Ca²⁺. A total of four residues located at or near the Ca²⁺-binding sites, N456, V518, F519, and L549, displayed a single CEST dip and a shoulder, whereas only G550, which coordinates Ca²⁺ at Ca3, displayed two well-separated CEST dips. Residues that displayed the greatest broadening effects are the ones closer to the Ca²⁺-binding sites and are expected to experience the largest chemical shift changes upon Ca²⁺-binding (Fig. 4). The absence of two well-separated CEST dips precluded a quantitative analysis of the ¹⁵N-CEST profiles for most CALX-CBD1 residues, with the exception of N456, V518, F519, and G550. Their ¹⁵N-CEST profiles were fitted to the Bloch-McConnell equation assuming a two-site exchange model. It was found that the population of the apo state, p_A, was in the range of 5–8%, whereas k_ex was in the range of 310–521 s⁻¹ (Fig. S7).

Figure 4.

Representative ¹⁵N CEST profiles. Peaks that show no evidence of chemical exchange (Narrow) at the molar ratio of 4:1 (Ca²⁺/CALX-CBD1) and that show nearly two CEST dips (Broad) or eventually two dips (Split) are color coded on the crystal structure of CALX-CBD1 (PDB: 3EAD (15)). The color coding was based on the ratios of ¹⁵N R₂/R₁ obtained at 4:1 molar ratio (Ca²⁺/CBD1) relative to 16:1. The relaxation rates were obtained by fitting the CEST profiles to the Bloch equation. Residues 530, 488, and 518 are shown as spheres. To see this figure in color, go online.

To obtain further kinetic information on the binding of Ca²⁺ to CALX-CBD1, we recorded CPMG-based ¹⁵N R₂ dispersion experiments on CALX-CBD1 samples prepared in the presence of CaCl₂ at the stoichiometric 4:1 molar ratio (Fig. 5). As observed in the CEST experiment, residues located near the Ca²⁺-binding sites displayed more dispersion than the ones located further away. The dispersion was significantly reduced or absent in the presence of an excess of Ca²⁺, indicating that the exchange phenomenon was due to the Ca²⁺-binding equilibrium (Fig. 5). Dispersion curves obtained at two spectrometer frequencies (600 and 800 MHz) were fitted simultaneously to a two-site exchange model, yielding the absolute chemical shift difference between the apo and the Ca²⁺-bound states, the exchange rate, and the population of the Ca²⁺-bound state. Prior information on k_ex obtained from the quantitative analysis of the CEST experiment was used to fit the CPMG dispersion curves. Hence, sampled k_ex-values were taken from a Gaussian distribution centered at 454 s⁻¹ with 1σ = 104.5 s⁻¹. The dispersion curves of a total of 12 residues could be analyzed, yielding a representative Ca²⁺ dissociation rate (k_off) of ∼31.2 s⁻¹ and an apo state population of ∼6% (Fig. 5). As much as 42.5% of all analyzed residues displayed k_off in the range of 20–25 s⁻¹, near the Ca²⁺ dissociation rate of 18.5 s⁻¹ measured by stopped flow using a fluorescent Ca²⁺ chelator (13).

Figure 5.

¹⁵N relaxation dispersion experiments. (A) Representative ¹⁵N CPMG relaxation dispersion curves obtained at 4:1 (red) and 16:1 (black) Ca²⁺/CALX-CBD1 molar ratios are shown. The residue number is indicated in the figure, and the location on the structure is shown in Fig. 4. A constant relaxation time of 50 ms was used for these experiments. (B) Fitting of ¹⁵N CPMG relaxation dispersion curves obtained for E521, obtained at 800 and 600 MHz (¹H frequency) using a constant relaxation time of 40 ms, to a two-site exchange model (left) are shown. Histograms of the Ca²⁺ dissociation rates and populations of the apo state determined by fitting the profiles obtained for residues 452, 453, 456, 488, 490, 491, 515, 516, 518, 521, 523, 549, and 552 are given. The red line indicates the median of the distribution, and the representative values are indicated in the figure. To see this figure in color, go online.

Thermodynamics of Ca²⁺-binding

The thermodynamics of Ca²⁺ binding to CALX-CBD1 was investigated by ITC. To have a better statistics for the fitted parameters, four ITC experiments were carried out using different protein concentrations in the calorimeter cell. Global fitting of all ITC binding curves to a stoichiometric model assuming n independent binding sites was carried out as indicated in the Methods, yielding a dissociation constant, K_d = 0.214 ± 0.005 μM, in agreement with previous ITC data reported in the literature (Fig. S2; (14)). However, because CALX-CBD1 binds Ca²⁺ cooperatively, we tested other stoichiometric models. Hence, we fitted the ITC binding curves to the Hill model (Fig. S8), obtaining a dissociation constant of K_d = 2.52 μM and a Hill coefficient n_Hill = 2.99 (Table 1), in agreement with the n_Hill determined independently by NMR titrations (Fig. 2). Because a characteristic of the Hill model is the strong correlation between the Hill coefficient (n_Hill) and the dissociation constant (K_d) (Fig. S8), we tested whether a stepwise model of four binding events was able to capture the Ca²⁺-binding cooperativity of CALX-CBD1. We assumed a mean molar binding enthalpy (ΔH_bind; see Eq. S31) instead of individual binding enthalpies for each Ca²⁺-binding site. This assumption is justified because the four Ca²⁺-binding sites are located at ∼4 Å from each other in the CALX-CBD1 crystallographic structure (15), and each Ca²⁺ ion is coordinated by two or more electron donor groups from different amino acids. Here, the simultaneous fitting of the four ITC binding curves was key to alleviate the degeneracy among the stepwise dissociation constants (Fig. 6). In addition, the application of Bayesian statistics to sample the space of the parameters was critical to make reliable estimations for K_d,1–K_d,4 and to examine the degree of correlation between each of them (Fig. 6). The probability distribution functions indicated that K_d,3 and K_d,4 are well defined and equal to 0.34 and 0.85 μM, respectively (Fig. 6; Table 1). K_d,1 is well defined with a median value of 148 μM, but its distribution is rather wide. Finally, the degeneracy of K_d,2 was only partially resolved. Nevertheless, the trend for K_d,2 is in the nanomolar range (Fig. 6; Table 1). To improve the resolution of K_d,2, two additional ITC experiments were performed at protein concentrations near our instrument detection limit, 2 μM, and closer to K_d,1 at 229 μM. However, the simultaneous fitting of the six ITC curves to the stepwise model did not alleviate the degeneracy on K_d,2 (Fig. S9). The greater degeneracy observed for K_d,2 relative to the other dissociation constants could be related to the fact that the experiments were carried out using protein concentrations well above its value. To test whether the dissociation constants K_d,1–K_d,4 reported in Table 1 are consistent with the saturation being reached near the 4:1 molar ratio as observed in the ITC and NMR titrations (Figs. 2, 6, and S5), we simulated the expected behavior of the binding isotherm for the stepwise model. As shown in Fig. S10, the average number of ligands bound, ν, as defined by Eq. S20, approaches saturation at molar ratios near 4–5, in agreement with our experimental observations. The statistical significance of fitting the four ITC binding curves to the more complex model (stepwise) relative to the simpler models (independent and Hill) was evaluated using the Akaike information criterion (AIC) (25). The AIC is a function of the likelihood penalized by the number of parameters. Fig. S11 shows that the AIC is lowest for the stepwise model, indicating that this model is preferable relative to the other ones.

Table 1.

Thermodynamic Binding Constants Obtained Using ITC

	Kd	nHill	Kd,1 (β1)	Kd,2 (β2)	Kd,3 (β3)	Kd,4 (β4)	ρ2	ρ3	ρ4	ΔHbind
Hill	2.52	2.99	N/A	N/A	N/A	N/A	N/A	N/A	N/A	−5.39
Stepwise	N/A	N/A	148 (0.0068)	0.00023 (29.4)	0.34 (86.4)	0.85 (101.7)	1310	1.26	1.14	−4.99

K_d and K_d,i are in units of micromolars and ΔH_bind in kcal/mol. β_i is in units of 10⁶ⁱ M⁻ⁱ. ρ is a dimensionless factor. N/A, not applicable.

Figure 6.

Ca²⁺-binding cooperativity investigated by ITC. (A) Calorimetric titrations of CALX-CBD1 with CaCl₂ using different total protein concentrations in the calorimeter cell ([P]_tot,0). The thermograms were fitted to the stepwise model assuming four binding events. (B) One-dimensional marginalized parameter distributions and 2D marginalized distributions of pairs of thermodynamic parameters are shown. The 1σ confidence contour region is shown in cyan, and the 2σ confidence contour region is shown in green plus cyan. K_d,i are in units of micromolars and ΔH_bind in kcal/mol. The plots are in logarithmic scale. To see this figure in color, go online.

To evaluate the Ca²⁺-binding cooperativity of CALX-CBD1 according to the stepwise model, we calculated the ρ factor as proposed by Wyman and Phillipson (26). The latter is defined as the ratio between the overall association constants β_i (see Eq. S19) normalized by the number of combinations in each binding event (W_n,i) (24,26):

$${\rho }_i={\left(\frac{{\beta }_i}{W_{n,i}}\right)}^{1/i}{\left(\frac{{\beta }_{i-1}}{W_{n,i-1}}\right)}^{-1/\left(i-1\right)},$$ (12)

where i = 2, …, n and n is the total number of binding sites. When ρ_i > 1, the binding sites display positive cooperativity. In contrast, when ρ_i ⩽ 1, the binding sites are anticooperative or independent (26). As shown in Table 1, binding of two, three, or four Ca²⁺ ions to CALX-CBD1 is favored by approximately three orders of magnitude in comparison with the binding of a single Ca²⁺ ion, indicating a large positive cooperativity among the four Ca²⁺-binding sites.

Discussion

In this study, we investigated the Ca²⁺-binding properties of CALX-CBD1 using NMR spectroscopy and ITC experiments, in combination with Bayesian statistics for data analysis. The NMR data indicated that CALX-CBD1 binds four Ca²⁺ in an all-or-none fashion, as observed previously for the NCX-CBD1 (27,28). Furthermore, indirect measurements of Ca²⁺ dissociation rates, obtained from the analysis of ¹⁵N R₂ dispersion and ¹⁵N CEST experiments, are in agreement with the Ca²⁺ off rates determined directly by stopped-flow fluorescence measurements (13). The NMR spectra showed no evidence of the existence of an intermediate state of CALX-CBD1 with Ca²⁺ at sites Ca1 and Ca2, as observed by crystallography (15). A possible explanation for this discrepancy is that in highly cooperative systems, the intermediate states are less populated than the apo and the fully bound states.

It is noteworthy that the n_Hill coefficients determined by the analysis of NMR and ITC binding curves were in very good agreement with each other (Fig. 2; Table 1). The determined n_Hill indicates that the binding of four Ca²⁺ to CALX-CBD1 is a highly cooperative process (Fig. 2). Curiously, the n_Hill coefficient obtained for CALX-CBD1 in this study (n_Hill ∼2.9) is greater than that determined for the NCX-CBD1 from the analysis of equilibrium ⁴⁵Ca²⁺ binding assays (n_Hill = 2.0) (29), suggesting that the CALX-CBD1 binds Ca²⁺ slightly more cooperatively than its mammalian ortholog. Because the two CBDs share the same Ca²⁺-binding mode, the reason for this difference is not clear.

Even though the Hill model captures the binding cooperativity of the system in terms of the Hill coefficient, it represents an extremely limiting situation in which all ligands bind simultaneously. Moreover, the Hill model has the inconvenience that the n_Hill is strongly correlated with the K_d, as indicated by our analysis (Fig. S8). Therefore, to have additional insights on the cooperative binding of Ca²⁺ to CALX-CBD1, we analyzed the ITC binding curves assuming a stepwise model of four binding events. Ca²⁺-binding cooperativity of CALX-CBD1 was evaluated in terms of the ρ factor. According to Wyman and Phillipson (26), the ρ_i factor may be interpreted as the ratio of the arithmetic mean probability of binding i and i + 1 ligands, without distinguishing the binding sites. Then, cooperativity is understood as the excess probability of binding i + 1 ligands over the probability of binding i ligands. This analysis showed that the probability of binding of two, three, or four Ca²⁺ ions to CALX-CBD1 is approximately three orders of magnitude greater than the probability of binding of a single Ca²⁺ (ρ₂ = 1310, whereas ρ_3,4 = 1.1–1.3 (Table 1).

Interestingly, the NMR titration curves of residues located at short distances from the Ca²⁺-binding sites or involved in Ca²⁺ coordination displayed significant deviations from the expected behavior of a typical binding curve following the Hill model (Fig. 2 C). Such deviations were explained by considering chemical exchange contributions to the crosspeak intensities. This interpretation is consistent with the observation that residues whose binding curves are more sigmoidal map to the same region of the structure as the ones displaying the largest ¹⁵N chemical shift differences (ΔΩ_N) between the Ca²⁺-bound and apo states, as determined from the analysis of ¹⁵N R₂ dispersion curves (Fig. 2 C; Fig. S12). It is curious, however, that the NMR titration curves obtained for the NCX-CBD1 domain in the NCX-CBD12 construct were all nearly hyperbolic (28). The explanation for this discrepancy is not clear, but the deviations from the expected behavior display a complex dependence on the exchange rates and on the differences of chemical shifts and relaxation rates between the apo and the bound states, as shown in Fig. 3.

Conclusion

Na⁺/Ca²⁺ exchangers play critical roles for the maintenance of intracellular Ca²⁺ homeostasis. The basal intracellular Ca²⁺ concentration in Drosophila photoreceptor cells is approximately 0.16 μM, but it may be elevated to 200 μM very rapidly after light stimulation (30). In this context, the exchanger activity must be tightly regulated to meet the cell’s needs. Activation of the NCX by intracellular Ca²⁺ is a highly cooperative process (31). The efficient Ca²⁺ regulation of the exchangers must be, at least in part, explained by the cooperative binding of Ca²⁺ to their CBD domains. Therefore, in this study, we revisited the cooperativity of Ca²⁺ binding to CALX-CBD1, the only domain that has binding sites for regulatory Ca²⁺ in the Drosophila Na⁺/Ca²⁺ exchanger. We found that four Ca²⁺ ions bind in a highly cooperative fashion to CALX-CBD1. According to the stepwise model, the dissociation constant of the first Ca²⁺ is on the order of 150 μM, whereas the dissociation constants of the second, third, and fourth Ca²⁺ are in the nanomolar and micromolar ranges, respectively. This observation indicates that the probability of binding of a single Ca²⁺ is significantly lower than that of binding from two up to four Ca²⁺ ions. Ca²⁺ dissociation must also be highly cooperative, as indicated by NMR, with off rates on the order of 30 s⁻¹. These findings provide new, to our knowledge, insights on the Ca²⁺-binding cooperativity of CALX-CBD1, which is key to enable this exchanger to efficiently respond to changes in the intracellular Ca²⁺ concentration in sensory neuronal cells.

Author Contributions

All authors contributed to the study conception and design. P.A.M.V. and L.A.A. prepared protein samples. L.A.A. assigned backbone resonances. P.A.M.V., M.V.C.C., and M.F.S.D. did ITC experiments. Preliminary analysis codes for ITC and NMR titration curves were performed by M.F.S.D.; the final codes for data analysis on NMR and ITC experiments were designed and developed by J.D.R. and R.K.S.; M.V.C.C. and L.A.A. acquired and processed NMR relaxation and titration data. The first draft of the manuscript was written by R.K.S., M.V.C.C., P.A.M.V., and J.D.R.; all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

Editor: Michael Sattler.

Supporting Citations

References (32, 33, 34, 35, 36, 37) appear in the Supporting Material.