A new structural paradigm in copper resistance in Streptococcus pneumoniae

Abstract

Copper resistance has emerged as an important virulence determinant of microbial pathogens. In Streptococcus pneumoniae, copper resistance is mediated by the copper-responsive repressor CopY, CupA, and CopA, a copper effluxing P_1B-type ATPase. We show here that CupA is a novel cell membrane-anchored Cu(I) chaperone, and that a Cu(I)-binding competent, membrane-localized CupA is obligatory for copper resistance. The crystal structures of the soluble domain of CupA (sCupA) and the N-terminal metal binding domain (MBD) of CopA (CopA^MBD) reveal isostructural cupredoxin-like folds each harboring a binuclear Cu(I) cluster unprecedented in bacterial copper trafficking. NMR studies reveal unidirectional Cu(I) transfer from the low-affinity site on sCupA to the high-affinity site of CopA^MBD. However, copper binding by CopA^MBD is not essential for cellular copper resistance, consistent with a primary role of CupA in cytoplasmic Cu(I) sequestration and/or direct delivery to the transmembrane site of CopA for cellular efflux.

Copper (Cu) is an essential transition metal in living organisms that functions as a catalytic cofactor in electron transfer reactions, aerobic respiration, photosynthesis, oxidative stress resistance, and in a number of metabolic enzymes by virtue of its ability to undergo reversible oxidation from Cu(I) to Cu(II)¹. This crucial characteristic of Cu chemistry also makes Cu highly toxic since Cu(I), like ferrous iron, catalyzes the production of hydroxyl radical (OH•) from endogenous hydrogen peroxide (H₂O₂) in the presence cellular reductants, which is highly damaging to cellular lipids, proteins and nucleic acids². As such, the Cu supply in mammals is tightly regulated.

Cu is also essential for proper development and functioning of the immune system³. An established feature of innate immunity to bacterial infection is host control of transition metal availability. This has long been recognized for iron⁴, and only recently has control of manganese and zinc availability been linked to the host-pathogen interface⁵. In contrast, emerging evidence suggests that Cu may be used to kill microbial pathogens⁶ by inducing oxidative stress or in the absence of oxygen, mediating disassembly of enzyme-bound Fe-S clusters⁷. Cu(I) is also a highly competitive metal ion and will out-compete most other divalent metal ion binding sites in proteins⁸. In Mycobacterium tuberculosis and Staphylococcus aureus, copper stress is a global stress response that mitigates the effects of thiol oxidation, which disrupts the redox status of the cell^9,10. E. coli and Salmonella strains lacking the ability to efflux Cu are more susceptible to Cu toxicity^11,12. Bacterial pathogens have evolved multiple strategies to quickly mitigate the effects of Cu toxicity with the same mechanisms likely used to maintain the cytoplasmic availability of weakly complexed or “free” Cu to low, near undetectable, levels^6,13–16.

Copper resistance in the Gram-positive respiratory pathogen Streptococcus pneumoniae (Spn) is mediated by a single operon encoding the Cu(I)-dependent repressor, CopY¹⁷, CupA, of unknown function, and a Cu(I)-effluxing P_1B-type ATPase, CopA¹⁸. Although the intracellular requirement for Cu(I) in S. pneumoniae is unknown¹⁹, S. pneumoniae contains significant cell-associated copper²⁰, and adaptation to a high Cu(I) environment may be important for invasive disease. Total Cu(I) is replete in the nasopharynx and in lung tissues and copA expression is induced in these tissues in intranasally infected mice¹⁸. Deletion of copA leads to poor kinetics of colonization in the nasopharynx and delayed appearance and reduced bacterial loads in the lung¹⁸; consistent with this, signature-tagged mutagenesis reveals ΔcupA and ΔcopA strains are attenuated in a murine model of lung infection and pneumonia²¹.

Bacterial copper chaperones are thought to function in Cu resistance by sequestering Cu(I) and buffering the metal to a very low level^8,22. This function is enabled by a high affinity for Cu(I)²³, and/or as articulated in the copper trafficking hypothesis, the ability to donate copper to apo-forms of copper-requiring proteins or to membrane transporters that efflux the metal across the cell membrane²⁴. Copper transfer is facilitated by transient and specific protein-protein interactions between often isostructural donor and target proteins via a metal-ligand exchange reaction without dissociation of the metal into bulk solvent^25–27. S. pneumoniae lacks the major characterized class of Cu(I) chaperone ubiquitous in eukaryotes and some bacterial systems, exemplified by S. cerevisiae or Synechocystis Atx1²⁷ and B. subtilis CopZ²⁸.

In this report, we show that a structurally novel copper chaperone-copper effluxer pair jointly mediates resistance to copper toxicity in S. pneumoniae D39 strain. We show that CupA is a plasma membrane-anchored copper binding protein whose membrane localization and high Cu(I) binding affinity are required for cellular copper resistance. The crystallographic structures of sCupA and CopA^MBD reveal a new functional twist on the common cupredoxin fold long associated with iron import, cytochrome oxidase assembly and electron transfer^29–31. Although we establish that the soluble domain of CupA (sCupA) is capable of transferring bound Cu(I) to N-terminal metal binding domain of CopA (CopA^MBD) in a thermodynamically favorable and kinetically facile reaction, it is not required for cellular copper resistance under conditions of copper stress. These findings suggest that the primary function of membrane anchored CupA under these conditions is to chelate Cu(I) as soon as it enters the cytoplasm, rather than function as an obligatory chaperone to the MBD of CopA.

RESULTS

Both CupA and CopA localize to the plasma membrane

A transcriptomic analysis of wild-type S. pneumoniae D39 and an isogenic markerless deletion strain, ΔcopY, reveals massive upregulation of the expression of downstream genes cupA and copA with the expression of virtually no other genes significantly affected upon copY deletion (Supplementary Results, Supplementary Fig. 1). This finding, coupled with a previous report of copper-induced expression of copY-cupA-copA, reveals that the cellular response to Cu stress is mediated solely by the cop operon¹⁸.

Although the core domain of CopA looks to be a prototypical bacterial Cu(I)-effluxing CopA of known structure³², a ≈100 residue domain that exhibits high sequence similarity to CupA is found at the N-terminus of CopA. Notably, both domains contain four conserved candidate ligands for Cu(I), arranged in a Cys….Cys-x-Met-x-Met (where×is any amino acid) sequence (Supplementary Fig. 2). Furthermore, the N-terminus of CupA is predicted to contain a single transmembrane helix. The high sequence similarity of CupA and the N-terminal region of CopA is a hallmark of a cognate copper chaperone-metal binding domain (MBD) pair found in other bacterial species³³. S. pneumoniae does not encode an Atx1 or a CopZ and a bioinformatics analysis reveals that CupA is nearly always found in genomes that lack a recognizable gene encoding CopZ or Atx1. Furthermore, CupA is widely distributed, perhaps more so than CopZ/Atx1, but clearly clustered in Lactobacillus and Streptococcus (Supplementary Fig. 3).

All CupAs are predicted to harbor a single transmembrane helix that anchors CupA to the plasma membrane. To test this, we created ΔcupA and ΔcopA Spn D39 deletion strains and tested growth on a rich (BHI) medium under microaerophilic conditions in the presence of 0.2 or 0.5 mM added Cu(II) (Supplementary Table 1). Both strains show a marked growth inhibition phenotype relative to the wild-type strain (Fig. 1a and Supplementary Fig. 4a,b), which can be rescued by ectopic expression of CupA from a heterologous promoter (Fig. 1b). This result rules out any unintended polar effect on the expression of the downstream copA gene due to deletion of cupA; in fact, the ΔcupA strain accumulates CopA protein to high levels (Supplementary Fig. 5b). Strains expressing C-terminally FLAG-tagged CupA or CopA are characterized by a wild-type growth in the presence of 0.2 or 0.5 mM Cu (Supplementary Fig. 4c,d). In contrast, a strain expressing a D442A CopA, which ablates the catalytic Asp residue in the ATPase domain of CopA (based on an alignment with Legionella CopA³²), is indistinguishable from the ΔcopA strain (Supplementary Fig. 4d). More importantly, a strain expressing CupA lacking the N-terminal transmembrane domain, Δ(2–28) CupA (denoted hereafter sCupA; Fig. 1c and Supplementary Fig. 5a), is also unable to grow under these conditions. These experiments establish that a C-terminal FLAG-tag does not interfere with CupA or CopA function thus allowing us to determine the subcellular localization of both CopA and CupA using a standard fractionation scheme followed by western blotting with anti-FLAG antibody (Fig. 1d and Supplementary Fig. 6). These data reveal that both full-length CupA and CopA localize exclusively to the plasma membrane in S. pneumoniae; furthermore, plasma membrane localization of CupA is required for full copper resistance.

Figure 1. Copper sensitivity phenotypes of mutant S. pneumoniae D39 strains.

ΔcupA and ΔcopA Spn strains are highly sensitive to copper toxicity (a) which can be reversed by expression of cupA from a heterologous promoter (b). (c) Deletion of the single putative transmembrane helix abrogates copper resistance to an extent comparable to inactivation of CopA(D442A) (compare to Supplementary Fig. 4d). In all cases, two independent isolates of the same strain designation were constructed and duplicate (or more) growth experiments were carried out with each of the two strains. (d) Both CopA and CupA localize to the cell membrane fraction. The results of a subcellular fractionation of copA-(C)-FLAG (IU6044) (top) and cupA-(C)-FLAG (IU6041) (bottom) with visualization by anti-FLAG western blotting. Supernatants (S) or pellets (P) are marked for centrifugation steps, and cell fractions are indicated below the blots. See Supplementary Figure 6 for additional experimental details and the full blot and Supplementary Tables 1 and 2 for strain details.

Copper binding by sCupA and CopA^MBD

The experiments described above suggest that sCupA and CopA^MBD bind Cu(I) directly as a means to effect copper resistance. To test this, we carried out anaerobic titration experiments in which Cu(I) was added to apo-sCupA or apo-CopA^MBD in the absence and presence of one of two specific Cu(I) chelators, bathocuprione disulfonate (BCS) (log β2=19.8 for Cu^I:BCS₂) or bicinchoninic acid (BCA) (log β2=17.2 for Cu^I:BCA₂), thus allowing us to access a range of K_Cu between 10¹² and 10¹⁹ M⁻¹³⁴. A global analysis of two representative titrations at two protein concentrations is shown (Supplementary Figs. 7 and 8) with parameter values compiled in Table 1. Titrations in which apo-sCupA was titrated into a solution of Cu^I:BCS₂ or Cu^I:BCA₂ returned identical parameter values (Supplementary Fig. 9). These titrations reveal that the stoichiometry of Cu(I) binding in both cases is ≈2 per monomer. sCupA is characterized by stepwise affinity constants (K_Cu1, K_Cu2) of 7.4 × 10¹⁷ M⁻¹ and 6.2 × 10¹⁴ M⁻¹, compared to 2.1 × 10¹⁶ M⁻¹ and 2.7 × 10¹³ M⁻¹ for CopA^MBD (Table 1). Thus, the putative chaperone sCupA binds Cu(I) 20- to 30-fold more tightly than the putative Cu acceptor CopA^MBD to each of the high affinity and low affinity sites.

Table 1.

Cu(I) binding affinities for sCupA and CopA^MBD

Protein	log KCu1 (M−1)	log KCu2 (M−1)	log β2,Cu (M−2)
sCupA	17.9 (±0.3)	14.8 (±0.2)2	32.6 (±0.3)
CopAMBD	16.3 (±0.1)	13.4 (±0.3)	29.8 (±0.3)

Parameters (mean values ± s.d.) were measured via global analysis of multiple anaerobic CuCl titrations using BCA or BCS as a competitor Cu chelator (Supplementary Figs. 7–9) using a nonlinear least squares fit to a stepwise two-Cu(I) binding model in both cases.

²Mean value from BCA and BCS titrations. Conditions: 25 mM Hepes, 0.2 M NaCl, pH 7.0, 22 °C.

Crystallographic structures of sCupA and CopA^MBD

In order to understand the structural basis for the Cu(I) binding stoichiometry, affinity and resistance, we solved the X-ray crystallographic structures of sCupA and CopA^MBD to 1.45 Å and 1.50 Å resolution, respectively (Fig. 2a–f and Supplementary Table 3). Each structure reveals an eight-stranded β-barrel harboring a binuclear Cu(I) cluster with a single Cys from the β2-β3 loop (Cys49 in CopA^MBD and Cys74 in sCupA) functioning as a bridging ligand to each Cu site, denoted S1 and S2. The S1 Cu site is digonal bis-thiolato while the more solvent-exposed S2 site is best described as distorted trigonal planar coordination by the three protein-derived ligands, with a long axial coordination bond to a Cl⁻ anion from solution (or distorted trigonal pyramidal; Supplementary Fig. 10 and Supplementary Table 4). A conserved Cys-gly-Met-asp/asn-Met motif position in the β7-β8 loop in each protein provides three of the four donor atoms to the Cu(I) ions. The Cu-Cu distance is 3.15 Å in each case. Both sCupA and CopA^MBD adopt a well-known cupredoxin fold, with Dali z-scores ranging from 10–12 for cupredoxins of known structure (Supplementary Fig. 11). However, the metal-ligand disposition (Supplementary Table 4) is completely novel, evidence that nature has adapted this ancient fold³⁵ to perform Cu(I) trafficking rather than electron transfer.

Figure 2. Crystallographic structures of sCupA and CopA^MBD.

Structure representations of sCupA (a–c) and CopA^MBD (d–f). Close-up views of the Cu(I) coordination geometries of each protein are shown (b, e) as are solvent-accessible surface areas (arbitrarily colored according to residue type) (c, f) around each binuclear Cu(I) chelate. Electrostatic surface potentials (painted based on surface potentials) of sCupA (g) and CopA^MBD (h). Structure statistics compiled in Supplementary Table 3.

Despite adopting identical folds with identical Cu(I) coordination chemistries, sCupA and CopA^MBD possess contrasting electrostatic surface potentials around the Cu(I) binding sites, with the sCupA largely negatively charged and the CopA^MBD largely positively charged in the vicinity of the Cu(I)-binding sites (Fig. 2g–h). Electrostatic complementarity is an established feature of copper chaperone-MBD pairs, which would allow the Cu(I) chelates of each protein to transiently dock and undergo ligand exchange and Cu transfer, without dissociation of bound Cu(I) into solvent^8,36.

The high and low affinity Cu sites in sCupA and CopA^MBD

The copper trafficking hypothesis²⁴ states the copper transfer moves from donor chaperone to target protein with or against a relatively shallow thermodynamic gradient as defined by K_Cu measured with purified proteins^37,38. For sCupA and the CopA MBD, the situation is complicated by the presence of two bound Cu(I) ions in each case, with no insight as to which site defines the high and low affinity Cu(I) sites in each case. We therefore used X-ray absorption spectroscopy (XAS) and NMR spectroscopy to define the sequence of Cu(I) binding, exploiting the fact that the stepwise Cu(I) affinities differ by about ≈1000-fold for both sCupA and CopA^MBD (Table 1).

The addition of substoichiometric Cu(I) to sCupA and CopA^MBD gives rise to Cu(I) near-edge feature in the XANES spectrum whose intensity is consistent with a low-coordination number complex, either n=2 or n=3 (Fig. 3). For Cu₁ CopA^MBD, the EXAFS spectrum is best-described by a model corresponding to a digonal bis-thiolato (2S) complex or a trigonal 2S, 1Br⁻ complex in NaBr; in NaCl, a three-coordinate 2S-Cl⁻ fit with a long Cu-Cl⁻ bond (2.42 Å) is the best fit. These data and accompanying Cu(I)-S⁻ bond distances (2.18 Å) are consistent with Cu(I) binding to the two S1 site thiolate ligands Cys49 and Cys86 (Supplementary Fig. 12 and Supplementary Table 5). For Cu₁ sCupA, the spectra in both NaBr and NaCl are consistent with an n=3 complex, with a best fit 2S, 1N/O complex, consistent, for example, with recruitment of a solvent molecule into the anticipated 2S (Cys74, Cys111) complex (Supplementary Table 6). As expected, XAS analysis of a Cu₂ sCupA sample in NaBr gives rise to an average Cu(I) coordination environment that is consistent with the crystal structure, including the presence of bound Br⁻ anion (Supplementary Table 7, Supplementary Fig. 12).

Figure 3. The Met-rich S2 site is the low-affinity site on both CopA^MBD and sCupA and Cu(I) is transferred only from the S2 site of sCupA to the S1 site of apo-MBD.

X-ray absorption near-edge spectra (XANES) of Cu₁ CopA^MBD (a) and Cu₁ sCupA (b) in the presence of 0.2 M NaBr (red) or 0.2 M NaCl (blue). Overlay of the Met thioether methyl (¹³Cε-¹Hε) region of an ¹H,¹³C-HSQC spectrum for CopA^MBD (c) and sCupA (d) acquired in the apo-state (magenta), Cu₁ state (green) and Cu₂ states (blue). Cyan crosspeaks result when apo-MBD is mixed with 2.0 mol equiv of Cu₂ sCupA (c) or 1.0 mol equiv of Cu₂ sCupA (d). Overlay of the backbone ¹H,¹⁵N-HSQC spectra of CopA^MBD (e) and sCupA (f), with the same crosspeak color pattern as in panels c,d.

We next examined Cu(I) binding to the apoproteins by monitoring perturbations in the amide chemical shifts of uniformly ¹⁵N, ¹³C-labeled samples of sCupA and CopA^MBD upon sequential filling each of the two Cu(I) sites (Supplementary Fig. 13). In each case (but more so in CopA^MBD) the β3-β4 and β7-β8 metal binding loops in the apoproteins are conformationally exchange broadened indicative of substantial µs-ms dynamics in this region (Fig. 4), as recently found for another apo-cupredoxin involved in electron transfer³⁹. Stepwise addition of Cu(I) quenches this line broadening with the addition of the first Cu(I) inducing measurable perturbations beyond these loops and into nearby β-strands, e.g., the β7 strand; addition of the second Cu(I) gives rise to significant perturbations in the metal binding loops only (Fig. 4). These perturbation maps are fully consistent with C49 (CopA^MBD) and C74 (sCupA) functioning as a bridging ligand since filling of both S1 and S2 Cu sites in each induces backbone perturbations in both β3-β4 and β7-β8 loops.

Figure 4. NMR chemical shift perturbation analysis of sCupA and CopA^MBD induced by Cu(I) binding.

Ribbon representation of the changes in backbone amide chemical shift upon Cu(I) binding by sCupA (a,b) and CopA^MBD (c,d). Panels a and c represent Δppm (Cu₁–apo) while panels b and d represent Δppm (Cu₂–Cu₁). The ribbon is painted white for Pro residues and black for those resonances broadened beyond detection in the apo-state in each case.

Although the Cu₁ and Cu₂ states of both sCupA and CopA^MBD are readily distinguished from one another (Supplementary Fig. 13) they cannot be used to assign the high- and low-affinity sites. We therefore assigned the methionine ¹³Cε–Hε groups of both sCupA and CopA^MBD by ¹³C-edited NOESY spectroscopy, with direct Met-Cu(I) coordination expected to induce a strong downfield shift of the ¹³Cε chemical shift as revealed by a ¹H, ¹³C-HSQC spectrum (Fig. 3c)⁴⁰. Consistent with XAS, only upon addition of the second mol•equiv Cu(I) is there a strong downfield shift of the ¹³Cε-¹Hε methyl crosspeaks of M88 and M90 of CopA^MBD indicative of direct ligation (Fig. 3c). For sCupA, addition of the first mol•equiv of Cu(I) results in a slight upfield shift of the M116 ¹³Cε–Hε with few other changes in the spectrum; only upon addition of the second mol•equiv of Cu(I) is there a strong downfield shift of the methyl resonances of M113 and M115. Inspection of the sCupA structure reveals that M116 is quite close to the S1 Cu ion, and thus reports on filling the digonal bis-thiolato S1 site (Fig. 3d). We conclude that the high affinity Cu(I) site on both CopA^MBD and sCupA is the bis-thiolato S1 site, with the more solvent-exposed Met-rich S2 site the low affinity Cu(I) site in each protein.

NMR detection of facile Cu transfer from sCupA to CopA^MBD

We next determined if Cu(I) bound to the putative donor sCupA could be transferred to acceptor CopA^MBD, taking advantage of the distinct spectroscopic signatures of Cu(I) bound to each of the two Cu(I) sites (Fig. 3c,d). We performed this experiment using an NMR-based strategy³¹ by mixing ¹³C,¹⁵N-sCupA with unlabeled CopA^MBD or unlabeled sCupA with ¹³C,¹⁵N-CopA^MBD, with sCupA loaded with two mol•equiv of Cu(I) as copper donor. When unlabeled apo-CopA^MBD is mixed with stoichiometeric Cu₂ ¹³C,¹⁵N-sCupA, one Cu(I) is lost, specifically from the low-affinity Met-rich S2 site as evidenced by a return of the ¹³Cε-¹Hε crosspeaks of M113 and M115 to their positions in Cu₁ sCupA (Fig. 3d); the same is evident on inspection of the ¹H,¹⁵N-HSQC spectrum of sCupA, with the Cu₂ resonances lost, and concomitant superposition of the crosspeaks associated with bona fide Cu₁ sCupA and those that results when Cu₂ sCupA is mixed with apo-CopA^MBD (Fig. 3f). There is no trace of apo-sCupA in these spectra. Monitoring the same reaction with excess (2:1) unlabeled Cu-saturated sCupA and ¹³C,¹⁵N-apo-CopA^MBD reveals formation of only the bona fide Cu₁ CopA^MBD with the S1 sites filled (Fig. 3c), with no evidence of the Cu₂ or apo-MBD in these mixtures (Fig. 3e). Thus, even in the presence of excess Cu bound to sCupA, only the high affinity S1 site on the CopA^MDB is capable of accepting the Cu(I) from sCupA, and that Cu(I) is donated from the more solvent-exposed lower affinity S2 site on sCupA.

The reverse experiment was also done in which stoichiometric ¹³C,¹⁵N-labeled Cu₁ CopA^MBD was mixed with unlabeled apo-sCupA. There is no change in the spectrum (Supplementary Fig. 14), thus revealing that despite the higher affinity, the S1 site on sCupA is unable to strip the MDB of its bound Cu(I) under these conditions. Efficient Cu(I) transfer is therefore preferentially unidirectional, but may depend on the molar ratio of CupA and CopA in the membrane.

Cu resistance requires Cu binding by CupA but not CopA^MBD

In order to further understand the essentiality of CupA for copper resistance we characterized cupA allelic replacement strains using our structure as a guide (Fig. 2). Mutant cupA strains include M113A/M115A (cupA(2A)), which abrogates binding to the S2 site only; a triple Cu-coordinating β7-β8 loop mutant (C111A/M113A/M115A) designated (cupA(3A)); a single bridging ligand substitution of C74 (cupA(C74S)); and a quadruple mutant in which all metal ligands are substituted with nonliganding residues (cupA(C74S,3A)). C74S sCupA binds a single mol•equiv of Cu(I) with a low affinity (K_Cu≈10¹² M⁻¹) but adopts a fold identical to that of wild-type sCupA with only local structural perturbations near the substitution (Supplementary Fig. 15).

In the absence of added copper, all cupA metal-liganding mutant strains grow similarly to the wild-type (WT) strain (Fig. 5a). However, in the presence of 0.2 mM Cu(II), growth of the cupA(3A) strain is inhibited but viable, while the cupA(2A), cupA(C74S) and cupA(C74S,3A) strains all fail to grow significantly (Fig. 5b), despite the fact that these CupAs accumulate to a level greater than that of wild-type CupA (Supplementary Fig. 5a). At 0.5 mM Cu(II), none of the mutant cupA strains is able to grow (Supplementary Fig. 16b). In fact, the behavior of the cupA(C74S) strain is indistinguishable from a copA(D442A) strain expressing a catalytically inactive CopA (Fig. 5c). Interestingly, western blotting reveals that CopA accumulates to very high levels in both strains, as well as in the ΔcupA strain (Supplementary Fig. 5b). Analysis of the total cell-associated metal content of these strains by ICP-MS reveals a substantial increase in total cellular Cu, which reaches a level ≈5-fold higher than WT cells 3 h after addition of 0.2 mM Cu in the ΔcupA and cupA(C74S) strains (Supplementary Table 8).

Figure 5. Mutagenesis of CupA Cu(I) binding residues partly or completely abrogates Cu(I) resistance by S. pneumoniae, but not in CopA^MBD.

Representative growth curves for the indicated S. pneumoniae strains in BHI in the absence (a) or presence (b,c) of 0.2 mM Cu(II) added to the growth medium. In all cases, two independent isolates of the same strain designation were constructed and duplicate (or more) growth experiments were carried out with each of the two strains. See Supplementary Tables 1 and 2 for strain details.

In contrast, when a substitution that is analogous to C74S in CupA is introduced into the CopA^MBD in the copA gene (copA(C49S)), copper resistance is unaffected at both 0.2 mM (Fig. 5c) and 0.5 mM Cu(II) (Supplementary Fig. 16c). Consistent with this, FLAG-tagged C49S CopA accumulates to a level similar to that of wild-type CopA rather than to that of Cu-sensitive mutants (Supplementary Fig. 5b). These experiments thus establish that a major function of CupA in copper stress resistance is likely not to chaperone Cu(I) to the CopA^MBD but instead is required for direct copper delivery to the transmembrane Cu(I) binding sites in CopA for efflux and/or to sequester Cu(I) during copper stress in an effort to mitigate the effects of cellular Cu toxicity.

DISCUSSION

In this work, we define a new structural paradigm for copper trafficking and resistance characterized in the Gram-positive respiratory pathogen S. pneumoniae. Soluble CupA and CopA^MBD are isostructural and of opposite electrostatic surface potentials, and each harbors a binuclear Cu(I) cluster in the context of a novel architecture not previously observed in bacterial copper trafficking. The Cu(I) binding affinities of sCupA and CopA^MBD differ significantly from one another, and although sCupA binds Cu(I) more tightly overall than CopA^MBD, copper transfer is preferentially down a thermodynamic gradient, from the low affinity S2 site of sCupA to the high affinity S1 site of CopA^MBD, as found in many other Cu(I) chaperone systems^23,37,38. CupA therefore satisfies all established criteria for designation as a copper chaperone³³, but is the first one known to be inserted into the plasma membrane which itself is obligatory for copper resistance.

This is the first instance to our knowledge where biological studies establish that deletion or functional inactivation of the copper chaperone reduces copper resistance to a level identical to deletion or inactivation of the copper transporter itself. This requirement of the CupA chaperone in Cu resistance in Spn was missed in the previous report, which suggested that a Spn strain encoding a translationally terminated cupA gene gave rise only to a more modest copper sensitivity phenotype¹⁸. We show here that CupA protein levels in all cupA missense strains that express CupA with diminished Cu(I)-binding affinities accumulate to a level greater than that in a wild-type background. A hyperaccumulation of both CupA and CopA in these cells may be reporting on hypersensitivity or continued derepression of CopY-mediated transcription of the cop operon in a failed effort to resist the effects of increased cytoplasmic copper.

Although Cu transfer from the S2 site of CupA to the S1 site of CopA^MBD occurs spontaneously, we suggest that this may occur only under non-stressed or “housekeeping” conditions since it is not strongly relevant to the cellular Cu toxicity response. In fact, recent studies^32,41 support a model in which the N-terminal MBD (not visualized in the crystallographic structure of Legionella CopA) plays a regulatory role. Here, the MBD is thought to dock against the actuator domain (Supplementary Fig. 17) and inhibit ATP hydrolysis in the absence of Cu(I); metal binding by the MBD then disrupts this interaction, allosterically activating ATP hydrolysis and Cu(I) transport. It is known that the cytoplasmic copper chaperone Atx1 can deliver Cu(I) to either the N-terminal MBD, which is not on-pathway for copper transfer, or the transmembrane site directly⁴², the latter hypothesized to occur via docking to the positively charged platform region that surrounds the putative entry site for Cu transfer³². Thus, the negative electrostatic surface potential of sCupA is complementary to both the MBD and the platform region of CopA, and may facilitate transient docking and direct Cu delivery to either site (Supplementary Fig. 17).

Our data are consistent with recent experiments in Synechocystis and in Listeria monocytogenes which suggest that a primary role of the copper chaperone is to buffer free Cu(I) to a very low level, thus preventing what is a highly competitive, thiophilic metal from binding indiscriminately to other cellular targets^8,22. There is little known about the intracellular cuproproteome of S. pneumoniae and it is unknown how copper enters the cell^15,43,44. In addition, there are as yet no known targets of CupA chaperone function, outside of CopA characterized here. Other functional roles for CupA are possible, particularly so given that the metallochaperone for the Cu_A subunit of a bacterial cytochrome c oxidase is itself a membrane-anchored cupredoxin-fold protein that binds a single Cu(I) ion^30,31. However, CupA is not performing this role in S. pneumoniae since it lacks cytochrome oxidase and an electron transport chain⁴⁵.

We propose that the primary role of CupA in S. pneumoniae is to chelate Cu(I) as soon as it enters the cytoplasm, near the plasma membrane, and via two-dimensional diffusion in the membrane, interacts with the effluxer and delivers Cu(I) directly to the core of CopA for Cu(I) efflux. The significant negative charge associated with the inner plasma membrane may aid in this process by holding the positively charged Cu(I) cation near the membrane for subsequent binding by CupA. Any Cu(I) that becomes cytoplasmic is then sensed by CopY, which binds Cu(I) and induces upregulation of CupA and CopA in an effort to reduce intracellular Cu content via efflux. Such strict control of bioavailable Cu(I) in the cytoplasm might be dictated by the unique physiology of S. pneumoniae relative to those bacteria previously studied. Spn is an aerotolerant anaerobe that generates millimolar levels of H₂O₂ used to kill other bacteria in the community⁴⁵. As such, Spn may go to great lengths to resist the potential collateral damage of endogenous H₂O₂⁴⁶. These studies identify potential new targets for the development of antibiotics to combat emerging multidrug resistant strains of S. pneumoniae and related pathogenic streptococci⁴⁷.

ONLINE METHODS

Bacterial strains and growth conditions

Streptococcus pneumoniae serotype 2 strain D39 and its derivatives were used in this study⁴⁸. Strains containing antibiotic markers were constructed by transforming linear DNA amplicons synthesized by overlapping fusion PCR into competent pneumococcal cells⁴⁹. Strains containing markerless copY, cupA or copA and respective FLAG-tagged alleles in native gene loci (Supplementary Table 1) were generated using the P_c-[kan^R-rpsL⁺] (Janus cassette) allele replacement method⁴⁹. ΔcopY and ΔcopA alleles in IU3566 (D39 ΔcopY) and IU5975 (D39 ΔcopA) strains were constructed by deletion of the gene sequences except for the 60 bp at the 5’ and 3’ end. ΔcupA allele in IU5971 (D39 ΔcupA) was constructed by deletion of cupA gene sequence except for the 5’ 42 bp and 3’ 60 bp. All constructs were confirmed by DNA sequencing of the amplicon region used for transformation. Strains were grown on plates containing Trypticase Soy Agar II (Modified) (Becton-Dickinson; BD) and 5% (v/v) defibrinated sheep blood (TSAII BA), and incubated at 37 °C in an atmosphere of 5% CO₂. For antibiotic selections, TSAII BA plates were supplemented with 250 µg kanamycin per mL or 250 µg streptomycin per mL. For liquid cultures, strains were cultured statically in BD Brain-Heart Infusion (BHI) broth at 37 °C in an atmosphere of 5% CO₂. To obtain growth curves, overnight cultures were obtained from frozen stock inoculums into 3 mL of BHI broth in 17-mm-diameter polystyrene plastic tubes and serially diluted over five tubes. Overnight cultures still in log-phase growth were diluted to OD₆₂₀ of 0.002 in BHI with or without 0.2 or 0.5 mM CuSO₄. Growth was monitored by OD₆₂₀ using a Spectronic 20 Genesys spectrophotometer.

Cell fractionation and subcellular localization of CupA and CopA in S. pneumoniae D39

Biochemical fractionation of pneumococcal cells was performed as described⁵⁰ with strains IU6041 (cupA-(C)-FLAG) and IU6044 (copA-(C)-FLAG) in BHI supplemented with 0.3 mM CuSO₄.

Western blotting to quantitate cellular expression levels of CupA and CopA in various cupA or copA mutants

Whole cell lysates were prepared from the indicated strains using the FastPrep method on cell cultures grown overnight in BHI and then diluted to 0.0035 (cupA (C)-FLAG, WT, copA (C)-FLAG and copA (C49S)-(C)-FLAG) or 0.005 (all other mutant strains) in 30 mL BHI, and allowed to grow to an OD₆₂₀ of 0.04 (cupA (C)-FLAG, WT, copA (C)-FLAG and copA (C49S)-(C)-FLAG) or 0.06 (all other strains) or ≈3 doublings, at which time CuSO₄ was added to a final concentration of 0.2 mM. 2.5 h after addition of Cu, at an OD₆₂₀ of ≈0.25 for cupA-FLAG strains (≈2 doublings for Cu-sensitive mutant alleles and ≈3 doublings for WT and cupA (C)-FLAG) and at an OD₆₂₀ of ≈0.5 for copA-FLAG strains (≈2 doublings for Cu-sensitive mutant alleles and ≈3 doublings for WT, copA (C)-FLAG and copA (C49S)-(C)-FLAG), cells were centrifuged at 14,500 × g for 5 min at 4 °C. Supernatants were removed and pellets were placed on ice and suspended in 1.0 mL of cold 20 mM Tris pH 7.0 and 8 µL of protease inhibitor cocktail set III (Calbiochem) and transferred to chilled Lysing Matrix B tubes (MP Biomedicals). Matrix tubes were secured in a 24 × 2 mL-tube adapter in a FastPrep-24 instrument (MP Biomedicals) stored at 4 °C. Cells were disrupted by three consecutive runs of 40 sec each at a speed setting = 6.0 m/s. Lysed cell mixtures were placed on ice and centrifuged at 10,000 × g for 1 min at 4 °C. 100 µL of supernatant was transferred to a tube containing 100 µL of cold 2× Laemmli sample buffer (containing 5% (vol/vol) of freshly added β-mercaptoethanol), boiled for 5 min and placed on ice. Gel loading volumes were calculated to adjust for the slightly different cell culture densities. Visualization and relative quantitation of FLAG-tagged proteins were achieved with Western blotting with primary anti-FLAG polyclonal antibody (Sigma, F7425) and an IVIS imaging system⁴⁸.

Bioinformatics analysis

The sequences of CupA and B. subtilis CopZ and Synechocystis (sc) Atx1 were used as query in a pBLAST analysis against non-redundant protein sequence database of all bacterial genomes. Criteria for designation as a CupA, CopZ and scAtx1 are shown in Supplementary Fig. 3.

ICP-MS analysis

1.5 mL aliquots of S. pneumoniae strains were centrifuged and washed once with BHI containing 1 mM nitrilotriacetic acid (Aldrich), then twice with PBS that had been treated overnight with Chelex-100 (Biorad) according to the manufacturer’s protocol. The cell pellets were dried overnight, 400 µL of 2.5% v/v nitric acid (Ultrapure, Sigma- Aldrich) containing 0.1% v/v Triton-X 100 was added to solubilize the cell pellets, and were lysed for 10 min at 95 °C with shaking at 500 rpm followed by vigorous vortexing for 20 s. 200 µL of the lysed cell solution (equivalent to 0.75 mL total cell culture) was added to 2.8 mL of 2.5% v/v nitric acid for ICP-MS analysis. Analyses were performed using a Perkin Elmer ELAN DRCII ICP-MS essentially as described earlier²⁰. Germanium at 50 ppb was added as an internal standard using an EzyFit glass mixing chamber. Metal concentration per mg protein were determined in the following way. ICP-MS gave [metal] in µg/L * 0.003 L sample equals total µg metal in 0.75 mL of cell culture. The µg metal * 1000 * 2 gave the ng metal in the original 1.5 mL of culture. Protein samples were resuspended in 100 µL buffer and concentrations were determined in mg/mL using a Bradford assay (Biorad). Total protein in 1.5 mL was calculated multiplying by 0.1 to correct for the resuspension volume. The final copper concentration as expressed by ng metal/mg protein determined by dividing those two values (ng/1.5 mL)/(mg/1.5 mL) = ng/mg protein.

Construction of overexpression plasmids and protein purification

The pHis-parallel plasmid was used to subclone sCupA (residues 29–123 of the 123-residue CupA) and the CopA^MBD (residues 1–99 of CopA). These constructs, following TEV protease cleavage, yield a non-native Gly-Ala-Met N-terminal sequence for sCupA (denoted residues 26–28 in the structure) and a single non-native N-terminal Gly in the case of CopA^MBD(denoted Gly0). E. coli BL21 (DE3) competent cells were transformed with the resultant plasmids. For unlabeled proteins, overnight cultures were inoculated into LB containing 100 µg/mL ampicillin. For the ¹⁵N/¹³C labeled proteins, overnight cultures were inoculated into M9 minimal media (pH 7.4) containing 100 µg/mL ampicillin, supplemented with ¹⁵NH₄Cl (1 g/L) (Cambridge Isotope Laboratories) and [¹³C₆]-D-glucose (2.5 g/L) (Cambridge Isotope Laboratories). For both media, the cells were grown at 37 °C to OD₆₀₀ = 0.6 with isopropyl β-d-thiogalactopyranoside (IPTG) added to a final concentration of 0.4 mM and cultures continued at 16 °C for 20 h. The cells were harvested by centrifugation and kept at –80 °C. All buffers in the purification were placed under argon using a Schlenk line immediately before use. For lysis, cells were resuspended in buffer R (25 mM Tris, pH 8.0, 200 mM NaCl, 5 mM TCEP). The resuspended cells were lysed by a sonic dismembranator (Fisher). The recombinant proteins were purified using HisTrap FF columns (GE Healthcare) using a gradient of imidazole from 10 mM to 300 mM in buffer R. The appropriate fractions were pooled and subjected to TEV protease cleavage at for 16 °C for 36 h. The proteins were further purified using HisTrap FF columns (GE Healthcare) and Superdex 75 16/60 column (GE Healthcare). The purity of the proteins was estimated to be >95 % as judged by SDS-PAGE. Protein concentration was determined by A₂₈₀ with an extinction coefficient of 4595 M⁻¹cm⁻¹. The number of reduced thiols was 1.9 for sCupA and 1.7 for CopA^MBD (2.0 expected). Mutants of sCupA and CopA^MBD were generated using a standard site-directed mutagenesis strategy (Stratagene), and mutant proteins purified as described above.

Cu(I) Binding Affinity Measurements

Bathocuproine disulfonate (BCS) and bicinchoninic acid (BCA) were used for Cu(I) binding affinity determination of sCupA and CopA^MBD by direct Cu(I) titration into a mixture of chelator and apoprotien essentially as described previously or titration of apoprotein into a chelator-copper complex³⁴. Apoproteins were buffer exchanged into degassed buffer B (25 mM HEPES, pH 7.0, 200 mM NaCl) in an anaerobic chamber. The Cu(I) stock was prepared by taking the supernatant following anaerobic dissolution of solid CuCl into fully degassed buffer B (25 mM HEPES, pH 7.0, 200 mM NaCl). The concentration of Cu(I) stock was determined by atomic absorption spectroscopy (Perkin Elmer AAS-400) with a typical stock concentration of ≈10 mM. For direct Cu(I) titrations, the final solution to be titrated contained 20 or 30 µM sCupA or CopA^MBD and 30 or 40 µM BCA (BCS) in Buffer B. Each 120 µL aliquot of titration solution was mixed with increasing Cu(I) titrant. For apoprotein titrations, a concentrated stock solution of the apo-sCupA was titrated into a solution containing 27–40 µM Cu(I) and 80–162 µM BCS or 25–35 µM Cu(I) and 170–285 µM BCA. Under these conditions all the Cu(I) is bound as a Cu:BCS₂ or Cu:BCA₂ chelate, respectively, prior to addition of apo-CupA.

In both experiments, the optical spectra of BCA or BCS were recorded from 200 nm to 900 nm. Corrected spectra were obtained by subtracting apo-sCupA (or CopA^MBD) spectrum from each Cu(I)-addition spectrum and then corrected for dilution. A₄₈₃ was used to determine the concentration of Cu^I:BCS₂ complex with an extinction coefficient of 13500 M⁻¹cm⁻¹. A₅₆₂ was used to determine the concentration of Cu^I:BCA₂ complex with an extinction coefficient of 7700 M⁻¹cm⁻¹. All the data were fitted to the appropriate competition model using Dynafit⁵¹.

Crystallization and crystal structure determination

Apo protein (sCupA or CopA^MBD) was first buffer exchanged to fully degassed buffer A (25 mM Tris, pH 8.0, 200 mM NaCl) in an anaerobic glove box. A ≈10 mM Cu(I) stock solution was prepared by taking the supernatant from dissolution of solid CuCl into fully degassed buffer B (25 mM HEPES, pH 7.0, 200 mM NaCl) with the concentration of Cu determined by atomic absorption spectroscopy. Cu(I) loaded proteins were prepared by mixing apo protein with a freshly prepared Cu(I) stock in the glove box at a 1:2 protein:Cu molar ratio. Cu(I)-sCupA was crystallized by hanging drop vapor diffusion at 20 °C against a well buffer of 30 % (w/v) PEG 3350, 0.1 M sodium citrate tribasic dihydrate pH 5.0 and Big CHAP Deoxy. The cryosolvent was prepared using 35 % (w/v) polyethylene glycerol 3350 in the well solution. Cu(I)-CopA^MBD was crystallized by hanging drop vapor diffusion at 20 °C against a well buffer of 28 % (w/v) polyethylene glycerol monomethyl ether 2000, 0.1 M Bis-Tris pH 6.5. The cryosolvent was prepared by using 35 % (w/v) polyethylene glycerol monomethyl ether 2000 in the well solution. For CopA^MBD, diffraction data for the native data set were collected at −160 °C on an R-AXIS IV+ detector at Indiana University, Bloomington. The space group of the crystal was P2₁2₁2₁ with one monomer in the asymmetric unit. All data were processed with HKL2000 and diffraction data for the initial phase determination collected on ALS 4.2.2 (Advanced Light Source, Lawrence Berkeley National Laboratory). Initial phases for the structure of CopA^MBD were determined by single-wavelength anomalous dispersion (SAD) techniques from a dataset collected on beamline 4.2.2 at the Advanced Light Source with Cu(I) providing an anomalous signal for phasing. The structure of CopA^MBD was solved and auto-built with PHENIX⁵². Two Cu(I) atoms were found in the structure. Iterative rounds of model building and refinement were carried out in Coot⁵³ and PHENIX⁵², respectively. Ramachandran statistics were 98% of the residues in the allowed region, 2% generously allowed, and 0% disallowed. For sCupA, diffraction data were collected at Indiana University, Bloomington, as described above. The space group of the crystal was P2₁2₁2 with one monomer in the asymmetric unit. Following processing with HKL2000, initial phases were calculated using a truncated model of CopA^MBD as a molecular replacement search model in PHENIX⁵² with the structure refined as described above for CopA^MBD. Ramachandran statistics for sCupA were 100% of the residues in the allowed region with 0% in the generously allowed and disallowed regions. All structure related figures were prepared using PyMOL (Delano Scientific).

NMR methods

Typical NMR sample solution conditions were 300–600 µM ¹⁵N, ¹³C-labeled sCupA or CopA^MBD, pH 6.0, 50 mM sodium phosphate, 50 mM NaCl, 0.02% (w/v) NaN₃ and 10% (v/v) ²H₂O, 25 °C. All NMR samples were prepared in an anaerobic glove box. Apo state samples (sCupA and CopA^MBD) were prepared with 5 mM TCEP. Cu₁ sCupA samples contained 0.9 mol equiv of Cu(I) and Cu₂ sCupA samples contained 1.9 mol equiv of Cu(I). Cu₁ CopA^MBD samples contained 0.8 mol equiv of Cu(I) and Cu₂ CopA^MBD samples contain 1.8 mol equiv of Cu(I). NMR spectra were acquired with a Varian DDR 800 MHz spectrometer equipped with a cryogenic probe at the Indiana University METACyt Biomolecular NMR laboratory. The NMR spectra were processed using NMRPipe⁵⁴ and analyzed using Sparky (T. D. Goddard and D. G. Kneller, SPARKY 3, University of California, San Francisco). Chemical shifts are referenced relative to internal 2,2-dimethyl-2-silapentene-5-sulfonic acid (DSS).

Sequential backbone resonance assignments of all six states (apo, Cu₁ and Cu₂ states of sCupA and CopA^MBD) were obtained using ¹H-¹⁵N heteronuclear single quantum coherence (HSQC), HADAMAC-2⁵⁵, and triple resonance CBCA(CO)NH, CBCANH, HNCO and Best-HNCA⁵⁶ spectra. The automatic backbone assignment server PINE was employed to aid in obtaining assignments. Methionine ¹³CH₃ resonance assignments of Cu₂ sCupA were obtained from a ¹H, ¹³C HSQC experiment using HCCH-TOCSY, HCCH-COSY and ¹³C-edited NOESY-HSQC experiments. The NOESY experiments were conducted using standard pulse sequences from the Varian Biopack with τ_m=100 ms. 1024×200×70 data points were acquired for the ¹³C -edited NOESY-HSQC experiment.

X-ray Absorption Spectroscopy (XAS)

sCupA and MBD were concentrated to 2 mM and 1.2 mM respectively in 25 mM Hepes (pH 7.0) and 200 mM NaCl or NaBr. 0.8 molar equivalent of CuCl or CuBr was added to both MBD and CupA anaerobically. 30 µL of each sample was syringed into polycarbonate XAS holders that were wrapped in kapton tape and frozen in liquid nitrogen. XAS data were collected at beamline 7–3 at the Stanford Synchrotron Radiation Laboratory (SSRL). Data were collected at 10 K using a liquid helium cryostat (Oxford Instruments). The ring conditions were 3GeV and 80–100mA. Beamline optics consisted of a Si(220) double-crystal monochromator and two rhodium-coated mirrors. X-ray fluorescence was collected using a 30-element Ge detector (Canberra). Scattering was minimized using Soller slits and placing a Z-1 filter between the sample chamber and the detector.

The Cu_1.8 sCupA sample was prepared by adding 1.8 molar equivalents of CuBr to 3 mM sCupA in 25 mM Hepes (pH 7.0) and 200 mM NaBr and concentrated to 3 mM under anaerobic conditions. 60 µL was syringed into a polycarbonate XAS holder wrapped in kapton tape and frozen in liquid nitrogen. The data were collected at beam line X3b at the National Synchrotron Light Source (NSLS), Brookhaven National Laboratories. The samples were loaded into an aluminum sample holder, which was cooled to ~50 K using a He displex cryostat. Data were collected under ring conditions of 2.8 GeV and 120–300 mA using a sagitally focusing Si(111) double-crystal monochromator. Harmonic rejection was accomplished with a Ni-coated focusing mirror. X-ray fluorescence was collected using a 30-element Ge detector (Canberra). Scattering was minimized by placing a Z-1 filter between the sample chamber and the detector. For all samples, XANES was collected from ± 200 eV relative to the metal edge. The X-ray energy for the Cu metal K_α-edge was internally calibrated to the first inflection point, 8980.3 eV. EXAFS was collected to 15 k above the edge energy (E_o).

XAS Data Reduction and Analysis

The XAS data shown (vide infra) are the average of 8 scans. XAS data was analyzed using SixPack⁵⁷. The SixPack fitting software builds on the ifeffit engine^58,59. Each data set was background-corrected and normalized. For EXAFS analysis each data set was converted to k-space using the relationship

$$k={[2m_e(E-E_o)/{\hslash }^2]}^{1/2}$$

where m_e is the mass of the electron, ℏ is Plank’s constant divided by 2π, and E_o is the threshold energy of the absorption edge. The threshold energy chosen for copper is 8990 eV⁶⁰. The best fits for the data sets were obtained using a Fourier-transform of the data was produced using data over the range k = 2–14 Å⁻¹ (Cu_0.8 sCupA and Cu_0.8 CopA^MBD) or k = 2–12.5 Å⁻¹ (Cu_1.8 sCupA) where the upper limit was determined by the signal:noise ratio. Scattering parameters were generated using FEFF 8⁵⁹. The first coordination sphere was determined by setting the number of scattering atoms in each shell to integer values and systematically varying the combination of N/O and S-donors (Supplementary Tables 5–7). To compare different models of the same data set, ifeffit utilizes three goodness of fit parameters: χ², reduced χ², and the R-factor. χ² is given by equation 1, where N_idp is the number of independent data points, N_ε² is the number of uncertainties to minimize, Re(f_i) is the real part of the EXAFS function, and Im(f_i) is the imaginary part of the EXAFS fitting function (eq. 1)

$${\chi }^2=\frac{N_{\mathit{\text{idp}}}}{N_{{\epsilon }^2}}{\displaystyle \sum _{i=1}^N\left\{{\left[\text{Re}(f_i)\right]}^2+{[\text{Im}(f_i)]}^2\right\}}$$ (1)

Reduced χ² = χ²/(N_ind − N_{var ys}) where N_varys is the number of refining parameters and represents the degrees of freedom in the fit. Additionally Ifeffit calculates the R-factor for the fit, which is given by equation 2, and is scaled to the magnitude of the data making it proportional to χ² (eq. 2)

$$R=\frac{{\displaystyle \sum _{i=1}^N\left\{{[\text{Re}(f_i)]}^2+{[\text{Im}(f_i)]}^2\right\}}}{{\displaystyle \sum _{i=1}^N\left\{{\left[\text{Re}(\tilde{x}{\mathit{\text{data}}}_i)\right]}^2+{[\text{Im}(\tilde{x}{\mathit{\text{data}}}_i)]}^2\right\}}}$$ (2)

In comparing different models, the R-factor and reduced χ² parameter were used to determine which model was the best fit for the data. The R-factor will always generally improve with an increasing number of adjustable parameters, while reduced χ² will go through a minimum and then increase, indicating that the model is over fitting the data.