Main

Compared with other P-type ATPases, calmodulin-stimulated calcium pumps contain an additional autoinhibitory or regulatory (R) domain at the N terminus9 (in plants) or C terminus10,11,12 (in mammals) (Supplementary Fig. 1). Pump activity is stimulated by binding of calcium-loaded calmodulin (Ca2+-CaM) to the regulatory domain, thereby inducing a conformational change that displaces the autoinhibitory domain from the pump core structure13,14. Calmodulin (CaM) substantially increases both Ca2+ affinity and pump rate in PMCAs1. To investigate the mechanism of CaM-mediated PMCA regulation, we have determined the structure of an intact regulatory domain (residues 40–95) of the Arabidopsis thaliana PMCA (we denote this domain Aca8R) in a homologous complex with A. thaliana Cam7 and characterized it in vivo and in vitro.

The crystal structure of this complex, determined at a resolution of 1.95 Å, shows an overall dumbbell shape and reveals an unexpected 2:1 stoichiometry (Fig. 1a and Supplementary Table 1): Aca8R forms a 56-residue-long α-helix with two Ca2+-Cam7 molecules bound at two distinct CaM-binding sites within the autoinhibitory domain in a pseudo-symmetrically ‘inverted’ arrangement. Given this structure, we denote the complex (Cam7)2–Aca8R. The two binding sites are separated in space by eight residues with no interaction between the two CaM molecules. Although the first binding site (CaMBS1) had been previously mapped by mutational studies15, the second binding site (CaMBS2) was unknown and unexpected.

Figure 1: Overall structure of the A. thaliana (Cam7) 2–Aca8R complex.
figure 1

a, Representation with CaM molecules in dark green (CaMBS1) and dark blue (CaMBS2), and Aca8R in orange, light green (CaMBS1) and cyan (CaMBS2). Ca2+ is shown in magenta. b, c, Detailed view of hydrophobic anchor residues involved in CaM-binding in CaMBS1 (b) and CaMBS2 (c). Cam7 is shown as ribbon. Residues in Cam7 that are within van der Waals bonding distance of the Aca8R anchor residues (red sticks) are shown as sticks with yellow surfaces. d, Electron density illustrating the extended α-helix (containing both CaM-binding sites) formed by the autoinhibitory region. e–g, Binding of CaM to the autoinhibitory domain of Aca8, examined by ITC. Typical ITC data are shown for the binding of Cam7 to 24-mer peptides corresponding to CaMBS1 (e) and CaMBS2 (f) of Aca8 and to Aca8(40–126) containing both CaM-binding sites (g). Upper panels: raw heat pulse data. Lower panels: integrated heat pulses, normalized per mole of injectant, giving differential binding curves that are adequately described by a one-site (e and f) or two-site (g) binding model with Kd = 13 nM for CaMBS1 and Kd = 500 nM for CaMBS2.

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Both sites show typical structural characteristics of CaM-target recognition16. The hydrophobic anchor points are Trp 47 and Phe 60 in CaMBS1 and Ile 79 and Phe 92 in CaMBS2. Each anchor residue is docked in a hydrophobic cage formed in each lobe of Cam7 (Fig. 1b–d and Supplementary Figs 2 and 3). In both of the binding sites the anchor points show a 1–14 spacing, whereas in CaM complexes of human PMCA4b17 and plant BCA118 a 1–18 spacing of anchor residues has been observed. A superimposition of the two bound CaM molecules reveals that the molecule bound to CaMBS1 has a slightly more closed conformation. The long α-helix formed by the regulatory domain of Aca8 shows a minor bending in CaMBS1.

Small-angle X-ray scattering (SAXS) data of the purified Cam7–Aca8R complex in solution agree with the crystal structure of the 2:1 complex. The distance distribution function shows two separated peaks indicating the presence of two subdomains (Supplementary Fig. 4), and the ab initio SAXS model superimposes with the crystal structure (Supplementary Fig. 4). In contrast, a putative 1:1 Cam7–Aca8R binding model does not fit the experimental SAXS data, indicating that the 2:1 (Cam7)2–Aca8R complex is indeed the favoured, stable complex in solution.

Using isothermal titration calorimetry (ITC), we measured CaM binding to the isolated binding sites as well as to a construct containing the entire autoinhibitory/regulatory domain of the protein Aca8. Cam7 binds tightly to peptides corresponding to CaMBS1 (dissociation constant, Kd = 13 nM) and CaMBS2 (Kd = 0.5 μM) of Aca8 (Fig. 1e, f and Supplementary Table 2). When measuring CaM binding to a construct comprising the entire autoinhibitory/regulatory domain (Aca8(40–126)), biphasic binding to two CaM-binding sites was observed with affinities similar to those of binding to individual peptides (Fig. 1g), whereas apo-CaM (stripped using EDTA) did not bind to any construct (data not shown). This indicates that the regulatory domain of Aca8 indeed contains two independent sites that bind Ca2+-CaM with different, but physiologically relevant, affinities.

We performed functional complementation assays using a Ca2+-ATPase-deficient yeast strain (K61619,20). This allowed us to investigate the autoinhibitory function of the R domain from PMCA gain-of-function mutations, because heterologous expression of a constitutively active Ca2+ pump in the endoplasmic reticulum of the yeast is required to maintain internal calcium stores on growth in EGTA-containing medium (see Supplementary Information for a detailed account of this model). Indeed, without galactose-driven expression of Aca8 variants, none of the K616 yeast grows in Ca2+-depleted medium (Fig. 2a, SD medium). However, expression of a constitutively active Ca2+ pump by virtue of truncation of either one or both CaM-binding sites (Δ74Aca8 or Δ100Aca8) complements the lack of endogenous yeast Ca2+-ATPases and allows growth in the Ca2+-depleted medium (Fig. 2a, SG medium), whereas the wild-type autoinhibited Aca8 does not. Yeasts with anchor-point mutations in Aca8 CaMBS1 (Trp47Ala and Phe60Ala) but not in CaMBS2 (Phe92Ala) show moderate growth, indicating that displacement of CaMBS1 alone generates basal pump activity. The Trp47Ala Phe92Ala double mutant with mutation in both CaM-binding sites shows significantly better growth (Fig. 2a) than the Trp47Ala mutant, indicating further involvement of anchor point Phe92Ala (CaMBS2) in autoinhibition. Expression levels were similar for all Aca8 constructs (Supplementary Fig. 5). The results confirm that both CaM-binding sites contribute to autoinhibition of the pump.

Figure 2: Physiological and biochemical characterization of wild-type Aca8 and mutants.
figure 2

a, Functional complementation of the Ca2+-ATPase-deficient yeast strain (K616) expressing wild-type and mutants of Aca8. Yeast strains K601 (wild type) and K616 transformed with empty vector are used as positive and negative controls, respectively. K616 transformed with wild-type and mutants of Aca8 regulated by a galactose-inducible promoter are grown on galactose (SG) or glucose (SD) medium supplemented with either 10 mM CaCl2 (Ca2+) or 10 mM EGTA. Only deregulated pumps are able to complement the lack of endogenous yeast Ca2+-ATPases in Ca2+-depleted medium (SG EGTA). b, Ca2+-stimulated ATPase activity of wild-type Aca8 and truncation variants lacking either CaMBS1 (Δ74Aca8) or both CaM-binding sites (Δ100Aca8) in the presence or absence of 10 μM Cam7. The asterisk denotes the concentration of free Ca2+ measured by the Ca2+-sensitive dye fura-2 (4.80 μM), which gave rise to the greatest difference between the activities with and without CaM and was used for normalization (each construct was normalized separately to allow direct comparison of the effect of CaM) and further characterization. The plot shows the results of one of two independent experiments carried out in triplicate. Errors, s.d. c, Top: ATPase activity of wild-type and mutant Aca8. The ratio of CaM-independent activity (Ca2+ with no Cam7) is given relative to the Ca2+-CaM-dependent activity (Ca2+ with 10 μM Cam7). Errors, s.d. (2–4 independent experiments in triplicate). Bottom: schematic of the two CaM-binding sites; the position of anchor point residues and the parts removed in the truncated versions of Aca8 are indicated.

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The Ca2+-stimulated ATPase activity of wild-type Aca8 further shows that the pump encompasses both a high- and a low-affinity sensor for Ca2+ (via Ca2+-CaM; Fig. 2b). Wild-type Aca8 is inactive (autoinhibited) in the absence of CaM and active in its presence. The Δ74Aca8 truncated form, lacking the high-affinity CaM-binding site, shows basal activity and can be further activated twofold by CaM, whereas the Δ100Aca8 form, which lacks both CaM-binding sites, shows CaM-independent activity (Fig. 2b). Furthermore, the characterization of the different Aca8 mutants supports the proposal that both CaM-binding sites contribute to autoinhibition as well as to Ca2+-CaM-mediated activation of the pump (Fig. 2c).

The presence of two CaM-binding sites is, however, not unique to the A. thaliana Aca8 protein. Sequence analysis suggests that both CaM-binding sites are conserved in other Arabidopsis Aca isoforms and plant PMCA homologues (Supplementary Fig. 6). Even more surprisingly, our analysis of mammalian PMCA (PMCA1 to PMCA4) sequences indicates that tandem CaM-binding sites are generated through alternative splicing in several variants (Fig. 3). The autoinhibitory domain of mammalian PMCAs is C-terminal and subject to tissue- and cell-type-specific alternative splicing5,21. PMCA splice variants show not only differences with respect to inhibition and CaM activation but also in response to different Ca2+ signals5, supporting the idea that alternative splicing might be a general mechanism for the fine-tuning of intracellular signalling22,23,24. Binding experiments by ITC using peptides of PMCA splice variants (PMCA1 to PMCA4) confirmed that CaM binds to their second sites with Kd values in the low-micromolar range (Fig. 3a–d and Supplementary Table 2), indicating that several mammalian PMCA variants also interact with two CaM molecules. The spacing between the CaM-binding sites is comparable to that in Aca8, suggesting a similar 2:1 structural arrangement and a similar mechanism of two-step, Ca2+-dependent activation by CaM.

Figure 3: Binding of CaM to the putative second CaM-binding site of PMCA splice variants.
figure 3

a–d, Typical ITC data for the binding of mammalian CaM to 24-mer peptides corresponding to splice variants of PMCA1 (a), PMCA2 (b), PMCA3 (c), and PMCA4 (d). Upper panels: raw heat pulse data. Lower panels: integrated heat pulses, normalized per mole of injectant, giving differential binding curves that are adequately described by a one-site binding model. e, Control peptide lacking the hydrophobic anchor residues of PMCA4d (Val4Ala, Leu6Ala and Phe19Ala), illustrating that CaM binding is specific. f, Alignment of Aca8 and mammalian PMCA splice variants coloured according to the CLUSTAL colouring scheme. The two CaM-binding sites are enclosed with boxes.

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Using mathematical network modelling of two-binding-site Ca2+-CaM activation of PMCA, we find that the pump system is ready for steep activation above a basal Ca2+ concentration, meaning that the enzyme is inactive below this level and rapidly activates as soon as concentrations exceed it (Supplementary Fig. 7). This gives our results particular physiological relevance, because Ca2+ activation through just one or no CaM-binding or autoinhibitory site (assuming otherwise identical conditions) is much less abrupt, meaning that a minimal cellular Ca2+ concentration would be less stable and acceleration of pump activity at increased Ca2+ levels less pronounced.

By combining structural, physiological and biochemical data with modelling, we also derive a structural model for Aca8 in its autoinhibited state. Aca8 homology models in Ca2+-bound (E1) and Ca2+-free (E2) conformations reveal the presence of a highly conserved cleft, situated between the A domain and the N and P domains, that is fully exposed in the E2 conformation and buried in the E1 conformation (Supplementary Video 1 and Supplementary Figs 8 and 9). Several acidic residues previously reported to be involved in autoinhibition (Glu 252, Asp 303 and Asp 332) cluster along this region25 (Supplementary Fig. 9). The N-terminal autoinhibitory domain of Aca8, however, contains several conserved basic residues15 (Arg 58, Arg 61, Lys 67 and Lys 68), which are of critical importance for autoinhibition and could potentially interact with the acidic residues mentioned above (Supplementary Fig. 8). We suggest that as the Ca2+ concentration increases, Ca2+-CaM first binds to and displaces the high-affinity CaMBS1 in the region between the A and N domains, and that further Ca2+-CaM activation leads to displacement of CaMBS2 from the linker regions between the transmembrane domain and the mobile A domain (Fig. 4 and Supplementary Fig. 8). Displacement of CaMBS1 allows free movement of the cytoplasmic domains as required for ion pumping at basal levels, and the additional displacement of CaMBS2 by higher Ca2+-CaM concentrations or the presence of acidic phospholipids26 results in further activity. This model provides a conceptual framework for a bimodular, Ca2+-mediated CaM-activation mechanism that allows regulation of intracellular Ca2+ concentration over a broad range of physiological conditions, ready to respond promptly at increased Ca2+ levels and setting the basal Ca2+ level in the cell. Such a mechanism seems to be well suited to the fine-tuning of calcium homeostasis and intracellular signalling in eukaryotes.

Figure 4: Schematic of the proposed two-step, Ca 2+-mediated CaM-activation mechanism.
figure 4

With increasing Ca2+ concentration, Ca2+-CaM first binds to and displaces high-affinity CaMBS1 before even higher Ca2+ concentration leads to displacement of CaMBS2 from the catalytic core, allowing free movement of the A domain as required for ion pumping. Actuator (A), nucleotide-binding (N) and phosphorylation (P) domains and the transmembrane region are indicated. Aca8R is shown as cylinder with the CaM-binding site colour-coded as in Fig. 1.

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Methods Summary

Procedures for the expression, purification and crystallization of the (Cam7)2–Aca8R complex were similar to those described in ref. 27. The complex was crystallized at 4 °C using sitting-drop vapour diffusion against a reservoir containing 1.9 M (NH4)2SO4, 0.1 M CAPS (pH 10.5) and 0.2 M Li2SO4. The crystals have space group P41212 and unit-cell parameters a = b = 71.25 Å, c = 163.28 Å and α = β = γ = 90°. Diffraction data were collected to a resolution limit of 1.95 Å at the ID23-2 beamline of the European Synchrotron Radiation Facility (France). The structure was determined by molecular replacement followed by iterative model building and refinement. The final model yielded a crystallographic R-factor of 22.1% and a free R-factor of 25.3%. Evaluation of the Ramachandran plot showed all residues except one (99.7%) in allowed regions (97.0% in favoured regions). SAXS data were collected at the X33 beamline at EMBL/DESY (Germany), following standard procedures. Heterologous expression, yeast complementation tests, membrane purification and activity assays of full-length Aca8, N-terminal truncation and single-point-mutation constructs were performed essentially as previously described15,28. More detailed methods can be found in Method and Supplementary Information.

Online Methods

Purification and crystallization of (Cam7)2–Aca8R

Purification of the complex and initial crystallization was performed as previously described27. In brief, Aca8(40–95) and Cam7 (both from A. thaliana) were co-expressed in Escherichia coli C41 cells29 and purified using standard His-tag purification protocols followed by TEV protease digestion, a second Ni-affinity chromatography step to separate a fusion protein tag and a final gel-filtration step. Initial crystals were obtained using the vapour diffusion technique in sitting drops prepared by mixing 1.5 μl of (Cam7)2–Aca8R solution (16 mg ml−1) with 1 μl of reservoir solution, and equilibrated against reservoir solution containing 2.0 M (NH4)2SO4, 0.1 M CAPS (pH 10.5) and 0.2 M Li2SO4 (final pH 8.2) at room temperature (293 K). These crystals belonged to space group C2 and diffracted to a resolution of 3.0 Å (ref. 27). Better-diffracting crystals belonging to a different space group (P41212) were obtained at 4 °C under slightly modified conditions: 1 μl of (Cam7)2–Aca8R solution (16 mg ml−1) was mixed with 1 μl of reservoir solution and equilibrated against reservoir solution containing 1.9 M (NH4)2SO4, 0.1 M CAPS (pH 10.5) and 0.2 M Li2SO4 at 4 °C (277 K). Crystals appeared after several months, grew to maximum dimensions of 0.7 mm × 0.35 mm × 0.2 mm within weeks (Supplementary Fig. 10) and proved to be superior to the room-temperature crystal with respect to diffraction properties. Crystals were mounted and flash-cooled in liquid nitrogen without additional cryoprotection.

Characterization of CaM-binding sites using complementation tests and activity assays

Cam7 from A. thaliana and mammalian CaM alone were expressed in E. coli C41 and purified using standard His-tag purification protocols. Heterologous expression, yeast complementation tests, membrane purification and activity assays of full-length Aca8, N-terminal truncation and single-point-mutation constructs were performed essentially as previously described15,28. The yeast strain K616 lacks the regulatory subunit B (Cnb1) of calcineurin in addition to the two Ca2+-ATPases (Pmc1 and Pmr1). Under normal conditions, calcineurin inhibits the low-affinity vacuolar Ca2+/H+ antiporter Vcx1. Vcx1 is the only transporter that can fill up the vacuolar Ca2+ store in the mutant lacking the two Ca2+-ATPases. At high Ca2+ concentration in the cytosol, Vcx1 transports Ca2+ into the vacuole. Therefore, to get a viable yeast strain, the cnb1 mutation is required. The mutation of calcineurin activates the antiporter, which then removes Ca2+ from the cytosol. At low Ca2+ concentration, the K616 strain needs an active high-affinity transporter (Ca2+-ATPase) to remove Ca2+ from the cytosol; that is, complementation requires a constitutively active Ca2+ pump in the endoplasmic reticulum/Golgi apparatus apparently to scavenge trace Ca2+ for proper functioning of the secretory pathway. It has previously been shown that only expression of active Ca2+-ATPases can rescue the growth defect in Ca2+-depleted medium15. The growth rate of the mutant in Ca2+-depleted medium thus provides an in vivo assay for functional characterization of overexpressed recombinant Ca2+ pumps from heterologous sources.

The expression level of Aca8 and mutants in yeast microsomal membranes (20 μg) were determined by SDS–polyacrylamide gel electrophoresis. The biochemical characterization was carried out on microsomal membranes (5 μg). ATPase activity was determined with and without 10 μM Cam7 by varying the free Ca2+ concentration. The free Ca2+ concentrations were determined using the Ca2+-sensitive dye fura-2 (ref. 30). Calibration curves were generated using the Calcium Calibration Buffer Kit #1 (zero and 10 mM CaEGTA) and fura-2 pentapotassium salt (Invitrogen/Molecular Probes). Each buffer and ATPase assay sample (prepared as for the ATPase activity assay) was supplemented with 1 μM fura-2. For each calibration buffer and test sample, excitation scans were generated between wavelengths 250 and 450 nm (slit, 5 nm) while detecting the emission at wavelength 510 nm (slit, 5 nm) essentially as described in the provided protocol from Invitrogen. The HORIBA Jobin Yone FluoroMax-4 spectrofluorometer and the software FLUORESSENCE were used for the measurements. For the final calculations, fluorescence at 380 nm (F380) was used. The free Ca2+ concentration in the calibration kit buffer was calculated using the specific Kd (EGTA) values at pH 7.3 (30 °C). The addition of Cam7 in the absence of Ca2+ did not result in any change in ATPase activity. Activity without Ca2+ and Cam7 were subtracted from those with Ca2+ and with and without Cam7 to give the measured Ca2+-ATPase activity.

Data collection and X-ray diffraction analysis

Diffraction data were collected to a resolution limit of 1.95 Å. Two full data sets containing 200 oscillation images each with an interval of 1° were collected using the same crystal at a wavelength of 0.9464 Å at the ID23-2 beamline of the European Synchrotron Radiation Facility (France). Exposure times and crystal-to-detector distances were respectively 0.4 s and 472 mm (set one) and 0.5 s and 245 mm (set two). Low-resolution and high-resolution data sets were merged using XSCALE31.

Reflections were indexed and scaled with XDS31. The crystals belonged to the tetragonal space group P41212 and had unit-cell parameters a = b = 71.25 Å, c = 163.28 Å and α = β = γ = 90°. A summary of the data statistics is given in Supplementary Table 1.

Structure determination

The structure was solved by molecular replacement using PHASER32 with a systematic combination of search models (derived from various CaM complexes) and search parameters. An initial molecular replacement solution contained two molecules of CaM N-terminal domain and one molecule of CaM C-terminal domain and revealed clear extra density that could be unambiguously assigned to Aca8R. Subsequent rounds of manual building using COOT33 and refinement using PHENIX.REFINE34 allowed placement of the second CaM C-terminal domain and led to almost complete model building (five residues (76–80) in a flexible linker connecting Cam7 lobes bound to CaMBS2 could not be traced). The final model yielded a crystallographic R-factor of 22.1% and a free R-factor of 25.3%. The model was validated using MOLPROBITY35,36. Evaluation of the Ramachandran plot showed all residues except one (99.7%) in allowed regions (97.0% in favoured regions), with Ser 82 situated in the flexible loop connecting the N- and C-terminal lobes of Cam7 (CaMBS1) as the single outlier. All figures were prepared using PYMOL37. The data are deposited in the Protein Data Bank.

SAXS — data collection and ab initio modelling

SAXS data were collected at the X33 beamline at EMBL/DESY (Germany), following standard procedures. Repetitive data collection on the same sample was performed and no radiation damage was detected. Samples of (Cam7)2–Aca8R solution were prepared in concentrations ranging from 4.5 to 9.0 mg ml−1 in a buffer containing 40 mM Tris/HCl (pH 7.4), 150 mM NaCl, 5 mM β-mercaptoethanol and 5 mM CaCl2. All SAXS data were analysed using the package ATSAS38. Raw data were processed using PRIMUS39. The radius of gyration (Rg) was evaluated using the Guinier approximation (I(s) = I(0)exp(−s2Rg2/3) for sRg < 1.3, where I denotes intensity and s denotes momentum transfer) and also from the entire scattering curve with the program GNOM40; the latter also provided the distance distribution function, p(r), and the maximum dimension, Dmax. The masses of the solutes were evaluated by comparison of the forward scattering intensity with that from a BSA reference solution (mass, 66 kDa).

Low-resolution SAXS models were obtained using the ab initio simulated annealing program DAMMIN41, which generates models consisting of dummy atoms to fit the experimental data Iexp(s) by minimizing the discrepancy

where N is the number of experimental points, c is a scaling factor, and Icalc(sj) and σ(sj) are the calculated intensity and the experimental error at the momentum transfer sj, respectively. Superimposition of low-resolution dummy atom models was performed using SUPCOMB42.

Isothermal titration calorimetry

The thermodynamic parameters were determined using an isothermal titration calorimeter (MicroCal ITC200, GE Healthcare) at 15 °C in a buffer containing 40 mM Tris/HCl (pH 7.4), 150 mM NaCl, 5 mM β-mercaptoethanol, 5 mM CaCl2. For binding of Cam7 to Aca8(40–126) 400 μM Cam7 was titrated into the sample cell containing 20 μM Aca8(40–126). For binding of Cam7 to peptides corresponding to Aca8 CaMBS1 (residues 42–65) and Aca8 CaMBS2 (residues 74–97) typically 150–400 μM of the peptide was titrated into the sample cell containing 7–40 μM Cam7. Reverse titration yielded identical thermodynamic parameters. For binding of mammalian CaM to peptides corresponding to the putative second CaM-binding site of mammalian PMCA1, PMCA2, PMCA3 and PMCA4 splice variants typically 0.6–1.2 mM CaM was titrated into the sample cell containing 50–100 μM peptide. Injection steps were 1.5 μl (first injection, 0.3 μl) with 150-s spacing. Baseline corrections were performed by titrating protein or peptide into sample buffer and sample buffer into protein or peptide. Further data evaluation (Supplementary Table 2) was done using the MicroCal ORIGIN program. Peptides were purchased from GL Biochem (China; HPLC purified, >90% purity).

The peptide sequences were as follows: Aca8-CaMBS1: ERLQQWRKAALVLNASRRFRYTLD; Aca8-CaMBS2: EMRQKIRSHAHALLAANRFMDMGR; PMCA1-CaMBS2: HHDVTNISTPTHIRVVNAFRSSLY; PMCA2-CaMBS2: SQDVANLSSPSRIRVVKAFRSSLY; PMCA3-CaMBS2: LHDVTNLSTPTHIRVVKAFRSSLY; PMCA4-CaMBS2: HLDVKLVPSSSYIKVVKAFHSSLH; PMCA4-CaMBS2-minus-anchor: HLDAKAVPSSSYIKVVKAAHSSLH.

Bioinformatics analysis and homology modelling

Multiple sequence alignments were produced using CLUSTAL W43. A sequence motif was generated using WEBLOGO44. Homology models of Aca8 in the E1 and E2 conformations were computed with MODELLER45 using the SERCA structures (Protein Data Bank IDs, 3N5K and 3N8G) as templates and a manually optimized alignment as input. Conservation scores were calculated with CONSURF46. Docking of the autoinhibitory N terminus onto the Aca8 homology model was performed with HADDOCK47,48 using residues previously observed to be involved in autoinhibition15,25 (Arg 58, Arg 61, Lys 67, Lys 68, Glu 252, Asp 303 and Asp332) as restraints.

Mathematical modelling

We denote free CaM by C0 and CaM in complex with four Ca2+ ions by C4. The autoinhibited wild-type pump is denoted P0, whereas P1 and P2 denote the pumps with one and, respectively, two CaM-binding sites occupied by C4 (X1 and X2 in the Ca2+-bound state). Finally, Pi denotes inorganic phosphorus. The wild-type model is represented by the following set of reactions:

Assuming mass-action kinetics, the reactions give rise to a set of polynomial differential equations. Supplementary Fig. 7 shows a typical output obtained using the reaction rates λ = 10, μ = 5, α0 = 10, β0 = 0.1, α1 = 1, β1 = 0.25, σ1 = 1, τ1 = 0.001, γ1 = 0.01, σ2 = 2, τ2 = 0.001 and γ2 = 0.1 and with total amount of CaM equal to 10 and the total amount of PMCA equal to 1. For varying total amounts of Ca2+, the steady-state concentrations are obtained from numerical simulation of the system of differential equations using MATHEMATICA. The steady-state production rate of inorganic phosphorus

where square brackets denote concentration, is used as a measure of pump activity and plotted as a function of the steady-state concentration of free calcium. The ΔCaMBS1 and ΔCaMBS1+2 models are derived from the wild-type model by leaving out P0 and, respectively, P0 and P1 as well as all reactions in which the omitted pump or pumps participate. All simulations were started with [Ca2+] = Ca2+tot and [C0] = Ctot, and with all PMCAs in the state with no CaM bound. That is, in states P0, P1 and P2 for wild-type, ΔCaMBS1 and ΔCaMBS1+2, respectively.

We note that the models are nested: all parameters in the ΔCaMBS1+2 and ΔCaMBS1 models are also parameters in the ΔCaMBS1 and, respectively, wild-type models. Simulations were made assuming that α0 > α1 and σ2 > σ1, meaning that the binding affinity of CaM to CaMBS1 was higher than that of CaM to CaMBS2 and that the activity of P2 was higher than that of P1, respectively.