Principles and practice of determining metal–protein affinities

Metal–protein interactions have played many critical roles in biology since life first evolved. Around one third of all proteins and nearly half of all enzymes require a metal cofactor for their functions [1,2], but non-essential metals can be toxic and even the essential metals, if not handled properly, can be detrimental [3]. Evaluation and understanding of the acquisition of metals by competing protein sites, in healthy or diseased cells, is a major focus in the fascinating field of Metallomics. The thermodynamic affinity of a metal–protein interaction, expressed by the metal dissociation constant, K_D, is a key parameter for such evaluation and understanding in a biological context. Innovative new research has quantified the thermodynamic availability of common transition metals inside a cell [4,5], making it possible to predict in vivo metal occupancy of proteins using their in vitro affinity data as input [6]. However, the accuracy of these calculations relies on the accurate quantification of such affinity data from in vitro experiments which is not a trivial matter and requires a combination of meticulous sample preparation, judicious experimental design, careful execution of experiments with appropriate controls, and adequate analysis and processing of the experimental data. Mishandling of these processes may lead to large errors in the determined affinity values, as exemplified by the highly dispersed metal affinity data reported in the literature for many proteins including, notoriously, Cu(I)-binding proteins, amyloid β peptides and zinc figure peptides whose reported affinities are scattered by 2–4 (or even >10 in certain cases) orders of magnitude [7–9]. This review outlines the fundamental principles and practical considerations which are key to accurate evaluation of metal–protein affinities, including the conditions under which direct titration or ligand competition approaches can be reliably employed (some other general aspects on determining metal affinities are covered elsewhere [10–12]). Furthermore, we assess a suite of spectroscopic ligand probes which can be used readily and conveniently to quantify a diverse range of biologically significant metal-binding interactions.

The ^aK_D(P) term, defined by equation 6b, may be regarded as a measure of the sum of the concentrations of all protein-unbound metal-containing species, $[M]aq+∑⁡[M(Lad)]$⁠, at 50% metal occupancy of the protein P. Many ^aK_D(P) values, defined this way, have been determined by direct metal titration but have been reported simply as (conditional) K_D(P): This is highly problematic and has led to erroneous K_D(P) values being propagated in the literature. It can be seen from equation 6b that the condition for ^aK_D(P) ∼ K_D(P) is $∑⁡KA[Lad]≪1$⁠. However, this condition is often not met, even for a weak-binding buffer with small K_A since its concentration is relatively high. For example, although Tris buffer has a relatively modest affinity for Cu²⁺ (K_D ∼ 0.6 mM at pH 7 [18]) a direct titration of Cu²⁺ into protein in the presence of 50 mM Tris at pH 7 will underestimate the conditional protein affinity by almost 2 orders of magnitude (i.e. the term K_A[L_ad] ∼ 83) if the buffer is not accounted for.

The impacts of adventitious ligands (buffers, reductants, salts, etc.) may be ruled out as negligible if systematic control titrations using the same [P] but with varying [L_ad] are indistinguishable [19] (i.e. $∑⁡KA[Lad]≪1$⁠), or may be accounted for if the term $∑⁡KA[Lad]$ can be estimated (in such cases the experiment may be broadly classified as a ligand competition between L_ad and [P]) [20–22]. However, in many direct metal titrations the impacts of L_ad are neither negligible nor accounted for (K_A and $∑⁡[Lad]$ may be unknown, for example) and the resulting ^aK_D(P) value may hardly be a true ‘constant’ and may underestimate the conditional metal–protein affinity by many orders of magnitude [7,9,11,23].

Although it can be difficult to determine reliably a (pH-conditional) K_D(P) for transition metal-binding to a protein by direct metal titration due to the two challenges discussed above, it is possible, when K_D(P) ≥ 0.05 [P]_tot, for simple metal ligands and some small peptides with careful control of the experimental conditions. For examples, the Cu(II) K_D (= 0.38 µM for the fully deprotonated ligand) of a Monovalent Copper Ligand, MCL-1, was readily determined by direct Cu²⁺ titration of MCL-1 at 50 µM in a pH 5.0 buffer, which increased the complex dissociation (due to the protonation of MCL-1, pK_a ∼ 7.1) and suppressed Cu²⁺ hydrolysis at high µM concentrations [24]. The weak Ni(II) affinities of several zinc finger peptides (K_D ∼ 3 µM) were determined readily by direct metal titration, but the corresponding Co(II) affinities at K_D ∼ 3 nM are too tight to be determined reliably by direct metal titration of the peptides at 10 s of µM [23]. In one of our best efforts to determine the Cu(II) affinity of a sensitive fluorescent peptide probe (DP1, see section ‘Dansylated peptides (DP1–4)’) by direct Cu²⁺ titration, we tackled the two challenges discussed above by: (i) employing the lowest detectable DP1 concentration (0.2 µM) to ensure a detectable dissociation of the target Cu^II–DP1 complex; and (ii) conducting the experiments in a carefully controlled pH buffer of low Cu(II) affinity (Mops, pH 7.4) at a limiting concentration of only 0.5 mM without addition of any salts to ensure $∑⁡KA[Lad]≪1$⁠. In this case, the apparent affinity estimated by direct metal titration (with the experimental data fitted to equation 5) was ^aK_D(P) = 10^−8.0 M which agreed with the conditional K_D(P) = 10^−8.1M determined by competition with the standard ligand glycine [19]. However, our same efforts to determine the Cu(II) affinity of a similar fluorescent peptide, Aβ16-WWA, allowed estimation of only a limiting ^aK_D(P) < 10^−9.1 M by direct metal titration but this value was still significantly larger (weaker in affinity) than the conditional K_D(P) = 10^−9.8M that we determined by ligand competition using two independent affinity standards [25]. Apparently, this sub-nanomolar (nM) affinity was too tight to be accessible by direct metal titration, even with the lowest possible experimental peptide concentration of just 0.2 µM. Thus, only for a limited number of cases where a metal–protein interaction is relatively weak and can be sensitively detected (i.e. enabling the experiment to be conducted at [P] ∼ K_D(P)), may a direct metal titration provide an accurate estimation of K_D(P) under the condition of $∑⁡KA[Lad]≪1$⁠.

Notoriously, the Cu(II) affinities of Aβ peptides were underestimated by 2–3 orders of magnitude in early years by direct metal titration but consolidated in later years by ligand competition [7,25,26]. Likewise, the Co(II) affinities of many zinc figure peptides were determined by direct metal titration with the convenience and advantage of the spectroscopic properties offered by this open d-shell metal, but the reported data are highly scattered and have also been underestimated, typically by 2–3 orders of magnitude, when compared with those data acquired via more stringent methods such as ligand competition or potentiometry [9,23]. These examples illustrate how use of the direct metal titration method to determine K_D(P) values can be challenging and problematic, particularly for tight metal–protein interactions. Even where measurable dissociation is observed, estimates of K_D(P) may be affected by contributions from adventitious ligands (including buffers, salts and reductants, see section ‘Adventitious metal ligands and the apparent dissociation constant’ discussed above). It is possible to evaluate such potential contributions, for example, by testing if the [buffer] and [salt] may be modified considerably without significant impact on the determined K_D(P) (i.e. if $∑⁡KA[Lad]≪1$⁠) [19]. However, unless contributions from all potential adventitious ligands can be ruled out, affinities should be confirmed by competition which is discussed next.

Usually, it is imperative to choose a competing ligand whose metal-binding properties are well-characterised since errors in the ligand affinity will be transmitted to the protein affinity. However, if the affinity of a ligand standard is unknown or controversial, a control experiment with a well-characterised competing ligand should be conducted in tandem under identical conditions as a calibration of both probe affinity and probe response. For example, the spectroscopic properties and formation constant β₂ of chromophoric probe Zn^II(Par)₂ are highly pH-dependent with somewhat inconsistent literature values [27]. When it was used to determine the affinities of several Zn(II)-binding protein domains according to equation 7b, the classic metal ligand Egta, which is spectroscopically silent but has a well-characterised ‘absolute’ Zn(II) affinity (i.e. $KD(Egta)abs$⁠) that may be converted to conditional affinities for specific pH with known pK_a values [11], was used as an affinity calibrator [28,29]. Thus, neither the probe response nor the formation constant of Zn^II(Par)₂ had to be known accurately, since they both became relative values with the two similar tandem competitions for Zn(II) between probe ligand Par and protein P or control ligand Egta with a relationship $KD(P)=KD(Egta)Kex(Egta)/Kex(P)$ where K_ex is the respective exchange constant of equation 7b.

A general principle for ligand competition experiments is to enable detection of a competitive metal-binding response that differs significantly (ideally within 20–80%) from the non-competitive response in at least some of the data set (e.g. in Figure 1B the most sensitive point of the titration is at [M]_tot = [P]_tot). To this end, different strategies may be applied to experimental design and optimisation, depending on the nature of the detection probe and the availability of a suitable competing partner. In the next three sections, we consider the design of the most common type of ligand competition experiments where the metal, M, is the limiting reagent: In such cases, the binding of M to one of the two competing partners (P or L) must be sensitively detected and M must be measurably partitioned between P and L (defined as 20–80% distribution of M_tot between the two partners) to prevent small errors in detection of MP (or ML_x where x = 1 or 2) being transmitted to large errors in derived K_D values. Firstly, the optimally matched competing partners may be selected based on the relative K_D(P), K_D(L) and β₂ (discussed in section ‘Optimal conditions for both metal partitioning and metal occupancy’). Secondly, for the poorly matched competing partners, measurable metal partitioning may be achieved by optimising the relative concentrations of the two (discussed in section ‘Adjusting the application window of ligand probes by variation of [L]tot/[P]tot’) but potential impacts on detection sensitivity must be carefully assessed (discussed in section ‘Consequences of [P]tot/[L]tot variation and probe tolerance to low metal occupancy’). Then, we note that there is a special case where the protein (acting as the probe ligand) is limiting, i.e. [P]_tot≪ [M]_tot < [L]_tot, and the 20–80% metal partitioning rule does not apply but instead, a 20–80% probe occupancy rule supports reliable equilibrium measurements (discussed in section ‘Alternative experimental design where protein is the limiting reagent’). Finally, we consider the case of inter-metal competition with a strategy to avoid potential adventitious attacks of metal ions in excess (discussed in section ‘Inter-metal competition experiments’).

Consider a titration of metal, M, into an equimolar mixture of a protein, P, and competing ligand, L, assuming that both bind one equivalent of M competitively with high affinities, leaving negligible free M_aq in solution before both ligands are saturated (i.e. the situation described by equation 7a). Metal-binding responses detected by the probe (either P or L) can be simulated for different $logKex=log(KD(P)/KD(L))$ and are shown in Figure 1B (here P is assumed to act as the detection probe). The binding isotherm for $logKex=0$ symbolises equal affinities and is a diagonal straight line, indicating that the added metal ions are distributed evenly between the two competing partners. If $logKex<0$⁠, the probe P binds M with tighter affinity and the binding isotherms bend up but if $logKex>0$⁠, the competing ligand L binds M with tighter affinity and the isotherms bend down, indicating an unequal distribution of metal ions between the two competitors. A sensitive application window of the probe for $KD(P)/KD(L)$ may be approximately set to a probe response within the 20–80% range of the control response (in the absence of a competing partner) at the metal titration point of $[M]tot/[P]tot=1$⁠, since the metal-binding isotherms are well-resolved within this range but converge rapidly outside this range towards one of the two non-competing metal-loading curves: Either that of the probe (the two oblique straight lines) or that of its non-probe partner (the two horizontal straight lines) (Figure 1B; black traces). This window covers a range of $1/16≤KD(P)/KD(L)≤16/1$ according to equation 8a: Thus, the ideal application window of a metal probe P for reliable determination of K_D of itself or its competing partner is approximately $logKD(L)=logKD(P)±1.2$ under the condition of [P]_tot = [L]_tot = [M]_tot, and this optimal window remains unchanged when the concentration of each component changes proportionally. This scenario is described by case 3 of Table 1.

Similar considerations for the competition involving a 1 : 2 ML₂ complex under the condition of [M]_tot = [P]_tot = ½ [L]_tot leads to an equivalent ‘optimal’ case 9 in Table 1 where log K_ex = 4.7 (i.e. $KD(P)=104.7(β2)−1$⁠) for [M]_tot = 10 µM or, more generally, $KD(P)=(2[M]totβ2)−1$⁠. This latter relationship between K_D(P) and $(β2)−1$ may be taken as an approximate comparison of the relative affinities between MP and ML₂ complexes and it is noted that such comparison is [M]_tot-dependent. For example, the $β2$ values of four Cu(I) chromophoric probes Cu^IL₂ (L = Fs, Fz, Bca, Bcs; see Figure 4) have been determined to be 10^13.7, 10^15.1, 10^17.2 and 10^19.8M⁻², respectively [8,33] and they are expected to have an ‘optimal’ application for protein targets with K_D(P) = 10^−9.5, 10^−10.9, 10^−13.0 and 10^−15.6M, respectively, when [Cu(I)]_tot = 30 µM. However, in practice, their optimal targeting K_D(P) values are about one order of magnitude tighter in affinity (see Figure 5) since these probe ligands are most reliably employed in excess (i.e. under condition [L]_tot > 2 [M]_tot) to supress potential 1 : 1 complexes (see the arrows pointing to revised conditions of case 9 in Table 1). It is noted that K_D and$(β2)−1$⁠, the metal affinities for 1 : 1 (ML) and 1 : 2 (ML₂) complexes, have sometimes been compared directly but such comparison is incorrect and misleading, since these two constants, K_D and$(β2)−1$⁠, have different units (M vs M²) and are neither equivalent nor directly comparable [11].

The application windows discussed in the above section may be extended by lifting the restriction of [P]_tot = [L]_tot for ML or [P]_tot = ½ [L]_tot for ML₂ to compensate for the difference in their relative affinities and thereby to maintain effective metal partitioning according to equation 8a or 8b. Table 1 describes a variety of experimental setups in which the condition $[L]tot/[P]tot$ may be optimised for different $logKex$ to achieve an optimal metal distribution between P and L (i.e. $[MP]/[M]tot=0.5$⁠). For example, consider a ligand L, with a 10-fold weaker affinity than the probe P (i.e. log K_ex = –1 in equation 7a). Under the condition of $[L]tot/[P]tot=1$⁠, the probe detects a response that is 76% of the non-competitive control at [M]_tot = [P]_tot (the red trace in Figure 1B). However, upon increasing $[L]tot/[P]tot$ from 1 to 5.5, the probe response is shifted to its most sensitive position at 50% (Figure 1C). Indeed, even for a ligand L with a 100-fold weaker affinity (logK_ex = –2), the corresponding unreliable probe response of 91% at $[L]tot/[P]tot=1$ is shifted progressively to more reliable values of 79% and 50% of the non-competitive control when the $[L]tot/[P]tot$ ratio is increased to 5.5 and 50.5, respectively (Figure 1B–D, the green traces). Clearly, an increase in relative concentration of the competing ligand promotes MP complex dissociation. For competitions involving a 1 : 2 ML₂ complex (equation 7b), calculations of metal partitioning via equation 8b also enable the design of a range of optimal experimental conditions that target different K_D(P), shown in cases 5–10 of Table 1.

Notably, the extension of the probe detection window to tighter or weaker affinity ranges comes at the expense of low metal occupancy on the weaker affinity partner, P or L, that must be present in excess to maintain the optimal 20–80% metal partitioning between the two (see Table 1). The consequence on the probe detection sensitivity must be carefully assessed. For example, consider a case of equation 7a where P acts as the detection probe and L is a ‘silent’ competitor, where both M and P are present in limiting concentrations and L is in excess (e.g. cases 1 and 2 in Table 1). This results in a low (<20%) metal occupancy on the L component but, provided that the silent ligand L does not interfere with the probe response and has negligible impact on [MP] detection, a low metal occupancy of a non-probe competitor is generally tolerated. In contrast, when M and L are limiting and the probe ligand P must be present in excess, the metal occupancy of the probe will fall below 20% (as in case 4): This, depending on the nature of the detection probe, may compromise the detection sensitivity. These different cases are analysed in detail next with various practical examples.

If detection of metal-binding relies on a readout from the probe ligand itself, then it may be considered broadly to be a ‘turn-off’ probe. This type of probe detects its metal-loaded form indirectly, by reporting the relative concentrations of its metal-loaded and metal-free forms (i.e. probe response $∝$[MP]/[P]_tot). Consequently, if the probe must be present in excess with a low metal occupancy, its detection sensitivity is compromised. For this reason, a turn-off probe can generally only be applied to determine the metal affinity of a competitor with comparable or weaker affinity (i.e. a larger K_D value) but not to the one with stronger affinity, and its application window is restricted by the condition: $log KD(L)≥logKD(P)−1.2$⁠. For example, a metal-responsive variant of the Salmonella typhimurium formaldehyde sensor (FrmRE64H), which binds four Zn(II) ions per protein tetramer with varying affinities, competed for Zn(II) overwhelmingly against probe mag-fura-2 (Mf2; K_D(L) ∼ 20 nM at pH 7.0) for the tightest three sites at a level of <10% probe response (Figure 2A,B). This experiment, with only weak metal competition from the probe, allowed a quick estimation of a (weak) affinity limit for these three metal sites at the sub-nM level [34]. However, the excess concentration of Mf2 that would be required to impose an effective competition with FrmRE64H for Zn(II) (e.g. case 1 in Table 1) could not be employed while retaining the necessary detection sensitivity. Thus, a subsequent competitive experiment with a better-matched probe of higher affinity, quin-2 (K_D(L) = 3.7 pM at pH 7.0) was employed to provide a more reliable estimation of the average Zn(II) affinity of the three tight sites (K_D(P) = 23 pM at pH 7.0) (Figure 2C) [34]. Similarly, a variant of the high-affinity Cu(II)-binding protein CopC from Pseudomonas fluorescens (CopC-H85F) withheld one equivalent of Cu(II) completely from the turn-off fluorescent probe DP2 (K_D(L) = 790 pM at pH 7.4) but competed effectively with probe DP4 of femtomolar (fM) affinity (K_D(L) = 7.9 fM at pH 7.4), enabling a protein affinity of K_D(P) = 2.5 fM to be determined reliably (Figure 2D–F) [35]. Interestingly, the presence of a hexa-His tag (in CopC-H85F-6H) generated an additional, weaker Cu(II) site (⁠$KD(His−tag)=400pM$ at pH 7.4) that could be quantified reliably with probe DP2 of comparable affinity (Figure 2E) but had no detectable impact on quantification of the fM affinity site in CopC by the probe DP4 (Figure 2F; note the indistinguishable Cu(II) competitions between DP4 and CopC-H85F or CopC-H85F-6H) [35]. This example also indicates that a purification tag will interfere with the characterisation of native site(s) of comparable affinity but not with native site(s) of much tighter affinity.

If detection of metal-binding to a probe ligand relies on a readout from its metal complex, that is independent of the probe ligand itself, it may be considered broadly to be a ‘turn-on’ probe. A turn-on probe detects its metal-loaded form directly with no restriction on the concentration of its metal-free form. Therefore, a low metal occupancy is generally well-tolerated and does not affect the detection sensitivity. For this reason, a turn-on probe is more flexible and versatile in its application than a turn-off probe. This is demonstrated nicely by the applications of the above-mentioned four Cu(I) probes Cu^IL₂ (L = Fs, Fz, Bca, Bcs) for quantification of the Cu(I)-binding properties of various protein targets. These probes are chromophoric ML₂-type Cu(I) complexes with characteristic absorbance in the visible spectral range. They display different detection sensitivity but the probe ligands themselves have little absorbance above 450 nm (Figure 3A,E,I), and thus they may be classified as turn-on Cu(I) probes. The difference in their formation constants mean that their optimal targeting affinities are different (see section ‘Optimal conditions for both metal partitioning and metal occupancy’ discussed above), but by varying the silent probe ligand concentrations, their effective application windows may be significantly extended to cover a wide spectrum of affinities under different experimental conditions as suggested for the various cases in Tables 1 and 2. For example, the weakest probe Cu^I(Fs)₂ has a predicted ‘best-matched’ targeting affinity of K_D(P) ∼ 10^−9.5M at [M]_tot = 30 µM (section ‘Optimal conditions for both metal partitioning and metal occupancy’) and was proved to be an ideal probe for quantification of the Cu(I)-binding stoichiometry, under a non-competitive condition (close to case 8 in Table 1), of a bacterial copper-binding protein CopK, but with an increase in probe ligand Fs concentration (close to case 7 in Table 1), the same probe determined a reliable K_D(P) = 10^−11.2M at pH 7.0 for CopK (see Figure 3B,C and Table 2) [33]. This K_D(P) value was confirmed independently by the better-matched probe Cu^I(Fz)₂ (whose ‘optimal’ targeting affinity was predicted to be K_D(P) = 10^−10.9M at [M]_tot = 30 µM; with experimental conditions close to case 8 (Figure 3D; Table 2). Even the probe Cu^I(Bca)₂, which has a much tighter predicted ‘optimal’ targeting affinity (K_D(P) ∼ 10^−13.0M), was employed to determine the CopK affinity under an extreme condition, close to case 10, with a large excess of CopK (100–400 µM) but limiting Bca (45 µM) [36]. However, the estimated K_D(P) = 10^−10.7 M was modestly larger (weaker in affinity) than the K_D(P) = 10^−11.2 M determined with the Cu^I(Fs)₂ or Cu^I(Fz)₂ probes. The difference may have arisen from two sources: (i) apo-CopK exists in a monomer-dimer equilibrium (K_D ∼ 0–50 µM) and was present mainly as an apo-dimer at high concentrations (>100 µM) required with the Cu^I(Bca)₂ assay but dissociated to an apo-monomer at lower concentrations (<70 µM) required with the Cu^I(Fs)₂ or Cu^I(Fz)₂ assays. However, Cu(I)-binding dissociated apo-CopK dimer into Cu^I-CopK monomer at all concentrations and thus the Cu(I)-binding equilibria at high and low CopK concentrations were different; (ii) for any assay involving two competing ligands with large differences in concentrations and thus in metal occupancies, the experimental errors, although less sensitive to the concentration of the component with lower metal occupancy (CopK in this case), become much more sensitive to the concentration of the component with higher metal occupancy (the ligand Bca in this case): A small error in Bca concentration may transmit larger error to the derivation of K_D(P). For this second reason, experimental conditions that may lead to very low metal occupancy on a competing partner, such as cases 5 and 10 in Table 1, should be avoided where possible by choosing a ‘better-matched’ competing partner for a given protein target (see section ‘Optimal conditions for both metal partitioning and metal occupancy’).

The Cu^I(Bcs)₂ probe has a predicted optimal sub-fM targeting affinity and is far too strong to allow a meaningful evaluation of the Cu(I) affinity of CopK that is weaker by over four orders of magnitude. However, Cu^I(Bcs)₂ was an ideal probe for human glutaredoxin protein (hGrx1) and determined a Cu(I) K_D(P) = 10^−15.6M at pH 7.0 with conditions close to the revised case 9 in Table 1 (see Figure 3H and Table 2) [37]. This value matched K_D(P) = 10^−15.5M determined with the weaker probe Cu^I(Bca)₂ in the presence of a large excess of probe ligand Bca, at conditions between case 6 and case 7 in Table 1 (see Figure 3G and Table 2) [37]. The Cu^I(Bca)₂ probe is too weak to allow a quantitative evaluation of the attomolar (aM) Cu(I) affinities of yeast Cu(I)-carrying protein Atox1 or the linked N-terminal metal-binding domains 5 and 6 of human Wilson disease protein, WLN5–6, even in the presence of a large excess of Bca ligand, a condition similar to case 5 in Table 1. However, this does mean that Cu^I(Bca)₂ is an excellent probe to quantify the Cu(I) stoichiometries of both Atx1 and WLN5–6 (see Figure 3J) [8]. Notably, the determined Cu(I) stoichiometries for Atx1 (n = 1) and WLN5–6 (n = 2) remained unchanged with free [Cu⁺] varying between pCu⁺ = 12–16 (see the entry j in Table 2), suggesting that there were no other competing Cu(I) sites within this affinity window (this is in contrast to the case of hGrx1 in Figure 3F). The aM affinities of both proteins were confirmed consistently with the Cu^I(Bcs)₂ probe using two separate assay conditions close to cases 5 and 6 in Table 1 (see Figure 3K,L and Table 2) [8]. It is also noted that, in the presence of 5 mM Bcs ligand, a condition beyond case 5 of Table 1, the Cu^I(Bcs)₂ probe was used to quantify the extreme zeptomolar (zM) Cu(I) affinities of two high-affinity Cu(I)-binding methanobactin peptides from Methylosinus trichosporium OB3b [38]. It is concluded from these demonstrated examples that: (i) the application windows of the ML₂-type turn-on probes may be extended from their predicted optimal targeting affinity considerably, as suggested from the modelling cases 5–10 of Table 1; (ii) the experiments modelled in Table 1 may be executed via different experimental procedures (by variation of [M]_tot, [P]_tot or [L]_tot) but with consistent outcomes.

One illustrative example of this type of experimental design is the determination of the Cu(II) affinity of labile sites in the multicopper oxidase, CueO, using Bis-Tris pH buffer as the competing ligand [20]. The phenol oxidation activity of the enzyme relies on Cu(II) occupation of the labile sites [39] and was used as a sensitive turn-on probe to quantify the Cu(II)-binding to these sites. However, their average Cu(II) affinity (K_D∼ 5 nM) was over 1000 times stronger than that of Bis-Tris at pH 7 (K_D ∼ 7 µM) and required a large excess (mM level) of Bis-Tris to impose an effective competition [20]. By supplementing 50 mM Bis-Tris with different concentrations of [Cu(II)]_tot (10–500 µM), a series of Cu²⁺-buffers with different but stable and well defined [Cu_aq²⁺] (ranging from 1 to 30 nM) were produced. This enabled the fractional metalation of the labile sites to be varied according to equation 10 and the CueO enzyme (present at only 0.1 µM) was found to exhibit a 50% maximal activity at [Cu_aq²⁺] ∼ 5.5 nM, thus an average Cu(II) affinity of these labile sites was determined [20].

Other similar examples where protein was used as the limiting reagent in the presence of excess ligand-buffered metal include the quantification of Zn(II)-binding to variant forms of the enzyme carbonic anhydrase by competition with dipicolinic acid (DPA) [40], quantification of Zn(II)-binding to the metalloregulator ZntR by competition with TPEN [41] and quantification of Cu(I)-binding to the fluorescent probe CS1 by competition with thiourea (where CS1 acts as ‘P’) [42]. In each case the concentration of metal-bound protein was sensitively detected, with a metal occupancy covering the range between 20% and 80% at numerous points in the titration, enabling reliable measurements of the competition equilibrium K_ex and thus K_D(P).

This approach was pioneered very recently by an example that determined the Zn(II) affinity of a Co(II)-carrying protein CobW that helps to deliver and insert an essential Co(II) ion into vitamin B₁₂ [6]. This protein, upon binding nucleotide (GTP) and Mg(II), assembles a metal site that can bind either Co(II) or Zn(II) with high affinity [6]. The Co(II)-bound form exhibits characteristic S^– → Co(II) ligand to metal charge transfer (LMCT) absorbance in the near UV region, providing a convenient direct probe for the affinity determination by classic ligand competition (K_D(Co) = 10^−10.5M at pH 7.0). The affinity for the spectroscopically silent Zn(II) (K_D(Zn) = 10^−12.7M at pH 7.0) was determined subsequently by reverse Zn²⁺ titration into the pre-formed Co^II-CobW-Mg^IIGTP complex in the presence of various concentrations of excess Co²⁺ ions that were fully protected by ligand nitrilotriacetic acid (NTA; K_D(Co-NTA) = 10^−7.6M and K_D(Zn-NTA) = 10^−7.9M at pH 7.0) [6]. Here, the NTA affinities for both metals were weaker than the corresponding protein affinities by three (or more) orders of magnitude, ensuring little competition (with the protein) from NTA for either metal. On the other hand, the NTA affinities for both metals are high enough to provide adequate protection for all protein-unbound metal ions.

Notably, the NTA affinities for Co(II) and Zn(II) are very close, demonstrating the strong offsetting effect of the NTA chelation on equation 9a. The Zn(II) affinity for a protein determined by the reverse titration method depends heavily on the initially determined Co(II) affinity for the same protein site and therefore, a primary source of discrepancy in Zn(II) affinity determinations is more likely due to an unreliable reference Co(II) affinity and less likely to the technique of the reverse titration itself. Nevertheless, the competition based on equations 12(a-e) will ensure an elimination of the method error due to adventitious bindings. In addition, in this example the protein affinities for both metals, although differing by about two orders of magnitude, are still within the manageable range to allow optimisation of the experimental conditions to establish an effective competition for a reliable determination (see discussion in section ‘Design and optimisation of ligand or inter-metal competition experiments’) [6]. This example may provide a useful guide for a systematic re-evaluation of Zn(II) affinities to various zinc finger peptides via the reverse titration and NTA may be an excellent protecting ligand for many applications. But, of course, the reference affinities of the probe metals, Co(II) and Ni(II), to the proteins or peptides must be determined reliably first (see section ‘Illustrative examples of metal affinity determination by direct metal titration’ and refs. [9,23]).

Any biophysical or biochemical response or process capable of quantifying the concentration of any single species of equations 3, 7a or 7b at equilibrium may be employed for K_D(P) determination [11,43]. Common readouts for detection and analysis may be catalogued into three broad classes: (i) direct analysis of protein metal occupancy via equilibrium separation, followed by direct metal quantification; (ii) analysis of the reaction enthalpy generated from metal-binding to the target protein via isothermal titration calorimetry (ITC); and (iii) direct detection and analysis of one or more species in the metal-binding equilibrium via spectroscopic methods.

This method reported the first attempt in quantification of metal-binding in a protein [44]. It requires separation of protein components from the equilibrated metal-containing buffer without perturbing the established metal-binding equilibria, followed by direct metal analysis of the separated fractions. Depending on the metal affinity of the protein target, the metal availability (i.e. p[M] = −log [M]) of the metal buffer may need to be adjusted by various metal-buffer ligands such as Tris, Bis-Tris, glycine, histidine, or even Egta and Edta, etc., to ensure a fractional metal occupation on protein within the 0.2–0.8 range for a sensitive and reliable analysis (see section ‘Design and optimisation of ligand or inter-metal competition experiments’). The separation may be accomplished by a protein-impermeable membrane such as a diaflow filtration unit or a dialysis chamber [40,45], by protein sedimentation via ultracentrifugation [46] or by chromatographic separation via a column elution [47,48]. The metal analysis is nowadays undertaken routinely by robust approaches such as atomic absorption spectroscopy (AAS) and inductively coupled plasma mass spectrometry (ICP-MS). These methods offer an advantage that almost any metal ion can be analysed. However, with the exception of chromatography, these methods generally require very extensive equilibrium time (hours to days) and may not work for small proteins or peptides; while the chromatographic separation may cause some disturbance to the established binding equilibria, especially for those proteins with labile metal-binding kinetics and thus may not be suitable for quantitative analysis in such cases.

This method is normally conducted under the condition [P]_tot∼ [M]_tot for weak binding or [P]_tot ≤ [M]_tot < [L]_tot for tight binding and so the principle and equations 10, 11a, 11b discussed in the above section ‘Alternative experimental design where protein is the limiting reagent’ apply. For dialysis separation, the metal content of the protein, [MP], at equilibrium is the difference between the metal concentrations of the two separated fractions and so the metal occupancy on the protein, [MP]/[P]_tot, may be obtained if the [P]_tot of the protein-containing fraction is determined. For diaflow filtration or ultracentrifugation separation, the [MP] at equilibrium is the difference between the metal concentrations of the protein solution before the filtration (or centrifugation) and the protein-free solution after the separation. The protein concentration before the separation is taken as [P]_tot for the metal occupancy calculation. Notably, the total protein concentration in the filtration or centrifugation process changes constantly during the course of the separation but this does not change the initial metal-binding equilibria established before the separation, provided that (i) both metal-free and metal-containing protein species contain the same protein stoichiometry (this indeed is the case for equations 3, 7a and 7b); (ii) all non-protein components can pass the membrane freely or cannot be sedimented while all protein components are impermeable to the membrane or sedimented completely off the top solution to be taken for the metal analysis.

The ITC method quantifies the reaction enthalpy (ΔH^o) of metal-binding to a protein and thus offers an obvious advantage that the method may be applicable to any metal-binding event and can derive a set of thermodynamic parameters including reaction enthalpy (ΔH^o), entropy (ΔS^o) and binding affinity (K_D). However, this also means that the method lacks specificity: All coupled reactions (such as dilution, buffer or specific ligand competition and proton displacement) or unwanted side reactions (such as metal hydrolysis and redox) could make substantial contributions to the experimental enthalpy ΔH_ITC which could be very different from the targeting ΔH^o specific to equation 3 that is required for an accurate derivation of K_D(P). Consequently, great care must be taken in experimental design and execution to avoid unwanted side reactions and to ensure effective binding competition (see section ‘Design and optimisation of ligand or inter-metal competition experiments’) with consideration and deduction of all coupled reactions in the data processing. All these aspects have been reviewed in great detail by Grossoehme, et al [49,50]. In short, the fundamental principles and strategies in handling metal-binding (equation 3) and ligand competition (equations 7a and 7b) discussed above in sections ‘Determination of metal-protein affinities via direct metal titration’ to ‘Design and optimisation of ligand or inter-metal competition experiments’ as well as the controls required in section ‘Key controls’ discussed later all apply equally to the ITC analysis. In reality, ITC may not detect equation 3 purely and thus the direct experimental values, K_ITC and ΔH_ITC, can only be taken as the condition-dependent apparent values which must be converted to pH-dependent conditional values, K_D(P) and ΔH^o in most cases (see equations 6b, 8a, 8b). In addition, ITC may have difficulty in handling slow kinetic processes. Lack of these considerations and corrections are the major sources of discrepancy in metal-binding ITC and have led to reports of many widely dispersed apparent ^aK_D values in the literature, as highlighted in ref [51]. A recent study of the reduction thermodynamics of blue copper proteins provides an excellent example on how to undertake ITC analysis correctly [22].

This method is so far the most commonly used technique in metal–protein affinity determination. It offers an obvious advantage of being able to detect and quantify at least one species in the competition equilibrium directly without disturbing the established equilibrium based on a characteristic spectroscopic readout of that species in the system. The spectroscopic readout may include signal derived from UV–visible absorbance, fluorescence, circular dichroism, electron paramagnetic resonance (EPR) or nuclear magnetic resonance (NMR) [11,43]. The readout from a single species is usually enough for quantification of the binding equilibrium such as equations 3, 7a or 7b but it is sometimes possible, and may increase robustness, to detect multiple species in equilibrium simultaneously [52]. In the next section, we review in detail the application of some commonly used spectroscopic probes in metal–protein affinity determination.

Spectroscopic probes based on solution absorbance and fluorescence are most widely used. In some cases, metal-binding may elicit a response from the protein itself: Some common examples include LMCT or metal d–d transitions originating from the metal–protein interaction [9,53,54]; and changes in native protein fluorescence, due to fluorescence quenching by paramagnetic metal ions, fluorescence enhancement by direct metal-fluorophore interaction, or protein conformational change as a result of metal-binding [41,55,56]. In such cases the protein itself or its metal complex may act as the detection probe and any metal ligand with matching or weaker affinity, provided that it does not interfere with the probe signalling, may be employed as a metal competitor. A large number of classic metal chelators with well-characterised affinities, such as Egta and Edta, are readily available for this purpose [11,15]. However, where the metal–protein interaction itself cannot be detected directly, a competing ligand that can report the metal-binding event (such as a spectroscopic probe) is a convenient tool. While many spectroscopic metal probes have been reported [11,12,57–59], only a handful are both robustly characterised with well-documented metal-binding affinities and readily available either commercially or via simple laboratory synthesis procedures. These factors are key to enabling their widespread practical applications. Selected examples of such probes for common transition metal ions (including Mn(II), Fe(II), Co(II), Ni(II), Cu(I), Cu(II) and Zn(II)) are given below. Their structures are shown in Figure 4 and their key properties are summarised in Tables 3 and 4.

The fluorescent probe fura-2 (Figure 4) forms 1 : 1 complexes with numerous divalent transition metal ions. Paramagnetic Mn(II) and Co(II) strongly quench the fluorescence signal [61,62] while diamagnetic Zn(II) blue-shifts the fluorescence excitation spectrum [61] and the binding affinities have been determined for each of these metal ions (Table 3). Fura-2 has proven particularly useful in the determination of Co(II)-binding affinities, including Co(II)-sensing transcription factors from Escherichia coli [63], Synechocystis [64], and S. typhimurium [34] and the Co(II) chelatase, CbiK, for the anaerobic vitamin B₁₂ pathway in S. typhimurium [5]. Spectroscopic responses for Fe(II) [61] and Ni(II) [62] have also been reported and a robust characterisation of their binding affinities could further extend the applications of fura-2.

Mag-fura-2 (Mf2, Figure 4) forms 1 : 1 metal complexes with characterised affinities for a variety of different ions (Table 3), making it a convenient and versatile probe. Metal-binding can be followed by changes in either absorbance or fluorescence spectra [65–67]. The apo-probe displays an absorbance maxima at ∼366 nm which blue-shifts to ∼325 nm upon binding numerous metal ions (including Mn(II), Fe(II), Co(II), Ni(II), Zn(II); see Figure 2A and Table 3) and the change in absorbance at either wavelength can be quantitatively correlated to the concentration of the metal-bound probe: extinction coefficients, ε, for the apo- and metal-bound probe are of the order of ∼10⁴M^–1 cm^–1 at the respective maxima [5,66] and the precise differences in ε at each wavelength, i.e. the Δε values associated with metal-binding, can be quantified by a control titrations of Mf2 with the metal of interest under bespoke experimental conditions (i.e. pH, [salt]; see section ‘Non-competitive controls, medium pH and buffers’). Alternatively, changes in fluorescence spectra upon metal-binding may be monitored: metal-binding typically leads to a decrease in Mf2 fluorescence (at ∼500 nm) when the excitation wavelength is set to ∼370 nm [67]. Mf2 has been widely used to quantify K_D values in the µM to nM range including various metal affinities (Mn(II), Co(II), Ni(II), Zn(II), Cd(II)) of the manganese transport regulator, MntR, from Bacillus subtilis [67]; affinity of the E. coli transcriptional regulator, RcnR, for one of its cognate metals, Ni(II) [63]; and affinities of S. typhimurium CbiK for non-cognate metals (Mn(II), Fe(II), Ni(II), Zn(II)) [5]. Mf2 has also been applied to define the stoichiometries of metalloproteins with tighter affinities, such as the human proteins calprotectin [68] and S100A12 [69] with sub-nM affinities for Zn(II).

Quin-2 (Figure 4) forms a 1 : 1 complex with Zn(II) ions at pH 7.0 and binding can be monitored via the UV-difference spectra [70], however, the signal change in the UV region (at λ ∼ 265 nm, see Table 3) is susceptible to interference from competing proteins (via absorbance of aromatic amino acids) and from cofactors (e.g. nucleotides) which are sometimes present in competition experiments. Interfering factors should be taken into consideration in the experimental design and analysis, with appropriate controls carried out. The tight affinity of quin-2 has proven useful for quantifying binding affinities of native Zn(II) proteins where Mf2 is too weak to impose an effective competition, such as the Zn(II)-sensors ZntR and Zur from S. typhimurium [34] and AdcR from S. pneumoniae [71].

A series of peptide probes, each conjugated to a fluorescent dansyl moiety (λ_ex∼ 330 nm; λ_em ∼ 550 nm; Table 3) via the side-chain amine of a lysine residue (Figure 4), respond to Cu(II)-binding through fluorescence quenching [19]. The four different peptide sequences in DP1 to DP4 bind Cu(II) with increasing affinities and together can be used to determine Cu(II) K_D from µM to fM range at biological pH (see Figure 5). Probe responses and affinities across a wider pH range (6.2–9.2) have also been characterised [19]. The peptides, which can be synthesised in house or purchased from commercial companies, have been used to determine Cu(II) affinities of the extracellular domains of the human amyloid precursor protein [72], native and mutated amyloid β peptide sequences [73], and several variants of the high-affinity Cu(II) chaperone, CopC, from P. fluorescens (see examples in Figure 2D–F) [35,74].

The chromophoric ligand 4-(2-pyridylazo)resourcinol (Par; Figure 4) is commonly used to probe zinc-binding, which produces a red-shift (and visible colour change) in the ligand absorbance. At neutral pH, the Zn^II(Par)₂ complex has an intense absorbance peak at ∼495 nm with an extinction coefficient around 60 times that of the ligand alone [28,75]; thus the concentration of the Zn^II(Par)₂ complex can be sensitively quantified from the absorbance change (with respect to the ligand only solution; see Table 4). A complicating factor is that Par forms both 1 : 1 and 1 : 2 complexes at pH 7.0, with equilibrium favouring the 1 : 1 complex in the presence of excess Zn(II) and the 1 : 2 complex in the presence of excess ligand [27,75]. For quantitative experiments, Zn(II) can be forced to coordinate exclusively via the 1 : 2 complex (>95% as given by the relationship [ML₂]/[ML] = K_A2[L], see ref. [11]; with K_A2 = 5.5 × 10⁵M⁻¹ for Par at pH 7.0, see refs. [75,76]) by maintaining a free (uncomplexed) Par concentration of >35 μM, in which case the spectroscopic and binding properties specific to the 1 : 2 complex (Table 4) can be used reliably: Such experimental setups have been used to quantify Zn(II)-binding to the Synechococcus metalloregulatory protein SmtB [53], the metal-binding domains of Zn(II)-transporting P_1B-type ATPases (HMA2 and HMA4) from Arabidopsis thaliana [28,77], and to Zn(II)-finger peptides [27]. Notably, both the spectroscopic and metal-binding properties of Par are highly pH-dependent with a combination of different charge species present at physiological pH [27], thus particular care should be taken with pH control. Par also responds to several other divalent metal ions (including Fe(II), Co(II) and Ni(II) which each display 1 : 2 stoichiometry for metal : ligand binding) [27,78,79] and has been used, for example, to quantify Ni(II) release from proteins [80,81], but reported affinities determined in 50% dioxane/water solution [76] may differ in aqueous buffers. Slow ligand-exchange observed for Fe(II) complexes makes Par unsuitable as an equilibrium probe for Fe(II) (see a selected example in Figure 6) [78].

The chromophoric ligand 4-(2′-thiazolylazo)-resorcinol (Tar) is structurally similar to Par (Figure 4) and the free ligand displays a characteristic absorbance at ∼470 nm (Figure 6A). Tar forms 1 : 2 complexes with a variety of divalent metal ions at physiological pH, typically accompanied by a red-shift in the absorbance spectrum [6,78,82]. Fe(II)-binding produces an additional unique absorbance peak at 720 nm which is not observed for either the metal-free ligand or upon Fe(III)-binding to the ligand (although Fe(III) also displays a tight affinity; see Table 4). The Fe^II(Tar)₂ complex undergoes relatively fast ligand exchange with many other Fe(II) binders (an example is shown in Figure 6C) and thus Tar has been used as an effective probe to quantify enzyme-mediated Fe(II) oxidation [78]. Affinities for Fe(II) [78] and Ni(II) [6] have been quantified under physiological conditions (Table 4): For both metals, Tar can be used to quantify binding interactions which are too tight to be determined by Mf2 (Figure 5). Like Par, metal-binding properties of Tar (including spectroscopic responses and affinities) are pH-dependent, due to heterogeneous protonation/deprotonation of the benzenediol hydroxyl groups over physiological pH ranges [78].

Ferrene S (Fs), ferrozine (Fz), bicinchoninic acid (Bca) and bathocuproine disulfonate (Bcs) comprise a complementary set of Cu(I)-binding probe ligands that have been robustly characterised and together can be used to determine Cu(I) affinities from nM to zeptomolar (zM) range [8,33,38]. Each forms a ML₂-type Cu(I) complex with visible absorbance at wavelengths where the corresponding free ligands are spectroscopically silent (Figure 3A,E,I). These ligands can also bind Cu(II) but with weaker affinities and consequently, the respective Cu(I)-probe complexes can be readily prepared in situ by reaction of Cu(II) salts with an excess of each ligand in the presence of a suitable reductant (e.g. NH₂OH or ascorbic acid with a combination of both optimal for Fs, see ref. [33]). Other than the weak affinity probe Cu^I(Fs)₂ which is modestly air-sensitive and must be handled under strict anaerobic conditions with excess reductant, the other three probes of higher affinities are more air-stable and may be handled routinely in N₂-purged buffers in the presence of reductant NH₂OH [8,33]. Due to the low pK_a values of coordinating atoms, metal-binding affinities for Fs, Fz and Bca are pH-independent at pH > 5 and Bcs (pK_a ∼ 5.7) is pH-independent at pH > 7 [8,33]. The set of probes have been used to determine a broad spectrum of Cu(I)-binding affinities from Methanobactins peptides with zM affinities (K_D< 10⁻²⁰M at pH 8.0) to the human amyloid β peptide sequence (K_D = 10^−10.4M at pH 7.4 for Aβ1–16) and the D2 domain of amyloid precursor-like protein from Caenorhabditis elegans (K_D = 10^−8.6M at pH 7.0) [25,38,83]. In fact, considering the case of the application of Cu^I(Bca)₂ to CopK [36], an application window spanning almost 10 orders of magnitude of affinities has been reached with Cu^I(Bca)₂ and Cu^I(Bcs)₂ alone. However, Cu^I(Fs)₂ and Cu^I(Fz)₂ are more suitable probes for protein targets with the Cu(I) affinities in the K_D(P) ≥ pM range such as for the Aβ peptides and related protein domains derived from the human amyloid precursor protein [25,84].

Summarised in Figure 5 are the estimated affinity ranges of protein K_D(P) for several bio-essential first-row transition metals that may be determined reliably by the spectroscopic probes described above. The estimations are based on typical experimental designs detailed in the figure legend. However, as discussed in section ‘Design and optimisation of ligand or inter-metal competition experiments’, these ranges may be extended significantly by optimising the relative concentrations of each individual component including metal, protein and/or the competing ligand, provided that the detection sensitivity is not compromised with such optimisation. The application of turn-off probes fura-2, Mf2, quin-2 and DP peptides, which detect changes in the readout of the metal-free ligand upon metal-binding (see Table 3), can be extended to weaker affinity ranges by employing an excess of protein target, but not to much tighter affinity ranges since an excess of these metal-free probe ligands would compromise their detection sensitivities (see section ‘Turn-off probes and their restricted application windows’). In contrast, the turn-on probes Cu^I(Fs)₂, Cu^I(Fz)₂, Cu^I(Bca)₂, Cu^I(Bcs)₂ and Fe^II(Tar)₂, which detect metal-complex formation directly without interference from the free ligands, can be more flexibly extended to either weaker or tighter affinity ranges without interfering with the measured readout (see examples in Figure 3). Probes including Zn^II(Par)₂, Ni^II(Tar)₂ and Cu^I(Bca)₂ (using λ ∼ 358 nm, see Table 4), which sensitively detect their metal-bound forms but with a residual signal from the free ligands, can be extended to somewhat tighter affinities but there is a limit to the concentration of free ligand that may be employed without excessive interference. An illustration of how a probe application range can be extended, using Cu^I(Bcs)₂ as an example, is shown in Figure 5.

Several well-characterised and commercially available probe ligands, while not obviously superior, can be employed as viable alternatives to those described above. For example, K_D values of the ML-type fluorescent indicators FluoZin-3 and Newport Green have been determined for multiple transition metal ions and are typically in the µM–nM range [85]; the absorbance probe Zincon forms ML complexes with Zn(II) and Cu(II) with affinities in µM and fM ranges, respectively [86]; and the ML₂-type probe ligand Zinquin, which detects Zn(II) binding via absorbance or fluorescence, is well-matched for determining Zn(II) affinities in the nM range [87].

There are also many recently developed metal probes which can be used for protein affinity determinations and, indeed, may offer advantages for some applications. These include: a variety of highly sensitive, turn-on, ML-type Cu(I) probes such as the CS and CTAP series whose weak fluorescence, corresponding to the ligands alone, is dramatically enhanced (tens to hundreds of fold) in response to Cu(I)-binding [12,58]; a water-soluble bis(thiosemicarbazone) ligand that forms a 1 : 1 complex with Zn(II) that absorbs intensively in the visible region and was used as a sensitive chromophoric Zn(II) probe to quantify Zn(II) binding in proteins with nM affinities [88]; and a quinoline-based fluorescent sensor with fM-range affinity for Zn(II) [89], which could be applied to studies of tight Zn(II)-protein interactions beyond the application ranges of Par and quin-2. These ML-type probes may offer an advantage in avoiding formation of stable ternary complexes in rare cases where this might be a problem for the ML₂-type probes such as a recently reported case in our study of Cu(I)-binding to a protein E2 domain of amyloid precursor protein [84]. However, these highly sensitive ML-type probes are not currently widely available.

Metal–protein binding stoichiometry is another important parameter for characterisation of metal–protein interactions and is also a key step in building a correct binding model for reliable affinity evaluation. In contrast with the discussion above, determination of metal–protein stoichiometry requires an experimental condition allowing (essentially) stoichiometric metal-binding to the targeting metal site(s). This is commonly determined by metal saturation of protein, followed by removal of excess metal, for example via co-migration of the metal–protein complex through a gel-filtration matrix, and then conducting separate metal and protein analyses [5,28,55]. However, some metal ions bound in proteins (such as Cu⁺), although possessing high affinities to many metal sites, are kinetically labile and may not survive the gel-filtration elution. In addition, some proteins may possess multiple metal sites (including non-native site(s)) with different affinities. Metal saturation of all these sites may induce protein denaturing and precipitation.

Direct characterisation in solution with spectroscopic probes proves to be an attractive and efficient alternative approach. The non-competitive metal-binding experiments presented in Figures 2 and 3 are examples. The experiment may be conducted either by titration of metal ions into a mixture containing a non-competitive weak affinity probe and a target protein of much stronger affinity (e.g. Figures 2B,E) or by titration of the target protein into a metal–probe complex which enables non-competitive metal-transfer from the probe to the targeting metal site(s) (e.g. Figure 3B,F,J). Of course, if the protein itself can act as a detection probe for metal-binding, the quantification may be undertaken by direct metal titration in the absence of other controlling ligands, as suggested by the case of K_D< 0.05 [P]_tot in Figure 1A (see practical examples in refs. [5,6,34,41,55,56]). However, a bonus of competition with a metal probe is that the metal availability for a non-competitive metal-transfer to a specific protein targeting site may be controlled to distinguish bona-fide functional metal-binding from adventitious non-functional binding. This is demonstrated for hGrx1 in Figure 3F: as the Bca/Cu ratio was increased, progressively limiting the available [Cu_aq⁺], hGrx1 was shown to bind multiple Cu(I) ions with K_D(P)< 10⁻¹³M but only one Cu(I) with K_D(P)< 10⁻¹⁴M (Table 2) [37].

This section outlines the key practical considerations and control experiments that are important for reliable K_D determinations. Table 5 provides a practical ‘checklist’ for avoiding the most common pitfalls.

Measurements of metal affinity require accurate quantification of the equilibrium concentrations of each reaction component (M, L and P), and this is especially important for the limiting component(s). Proteins must be pure, metal-free, fully reduced (if they contain air-sensitive cysteinyl thiol groups that act as metal ligands), accurately quantified, and free of non-native metal-coordinating tags (if their metal affinities are comparable to those of the targeting protein sites). This can be confirmed via a series of control experiments outlined in Table 5. Ligand and metal concentrations should be calibrated via spectroscopy and/or elemental analysis (Table 5). Reaction conditions must be strictly controlled to avoid metal contamination and to prevent oxidation of susceptible metal ions or ligands (see Table 5). Chelants and reductants can be used to remove contaminating metals and to maintain reducing conditions during protein purification but must not be present in the final assay solutions, unless it has been explicitly demonstrated that their presence has negligible impact on the metal-binding equilibria. For example, both DTT and TCEP are commonly used protectants for protein thiols but they are strong chelators for Cu(I) and cannot be present for most Cu(I) affinity determinations [8,90,91]. On the other hand, sodium dithionite is a very strong reductant (E_1/2 = −0.66 V vs SHE) [92] and can reduce cysteinyl disulfide in situ rapidly, but dithionite itself and its oxidation products are not Cu(I) ligands. Consequently, dithionite has been used as a convenient in situ reductant for protein disulfide for Cu(I) affinity determination with Cu^I(Bca)₂ and Cu^I(Bcs)₂ probes [93,94], but dithionite is a strong reductant for some metal ligands such as Fs and Fz and is not compatible with the applications of these ligands [33].