Noncooperative cadmium(II) binding to human metallothionein 1a

The two-domain (βα) mammalian metallothionein binds seven divalent metals, however, the binding mechanism is not well characterized and recent reports require the presence of the partially metallated protein. In this paper, step-wise metallation of the metal-free, two-domain βα-rhMT and the isolated β-rhMT using Cd(II) is shown to proceed in a noncooperative manner by analysis of electrospray ionization mass spectrometric data. Under limiting amounts of Cd(II), all intermediate metallation states up to the fully metallated Cd₃-β-rhMT and Cd₇-βα-rhMT were observed. Addition of excess Cd(II), resulted in formation of the supermetallated (metallation in excess of normal levels) Cd₄-β- and Cd₈-βα-metallothionein species. These data establish that noncooperative cadmium metallation is a property of each isolated domain and the complete two-domain protein. Our data now also establish that supermetallation is a property that may provide information about the mechanism of metal transfer to other proteins.     

Metal exchange in metallothioneins: a novel structurally significant Cd(5) species in the alpha domain of human metallothionein 1a

Metallothioneins (MTs) are cysteine-rich, metal-binding proteins known to provide protection against cadmium toxicity in mammals. Metal exchange of Zn(2+) ions for Cd(2+) ions in metallothioneins is a critical process for which no mechanistic or structural information is currently available. The recombinant human alpha domain of metallothionein isoform 1a, which encompasses the metal-binding cysteines between Cys33 and Cys60 of the alpha domain of native human metallothionein 1a, was studied. Characteristically this fragment coordinates four Cd(2+) ions to the 11 cysteinyl sulfurs, and is shown to bind an additional Cd(2+) ion to form a novel Cd(5)alpha-MT species. This species is proposed here to represent an intermediate in the metal-exchange mechanism. The ESI mass spectrum shows the appearance of charge state peaks corresponding to a Cd(5)alpha species following addition of 5.0 molar equivalents of Cd(2+) to a solution of Cd(4)alpha-MT. Significantly, the structurally sensitive CD spectrum shows a sharp monophasic peak at 254 nm for the Cd(5)alpha species in contrast to the derivative-shaped spectrum of the Cd(4)alpha-MT species, with peak maxima at 260 nm (+) and 240 nm (-), indicating Cd-induced disruption of the exciton coupling between the original four Cd(2+) ions in the Cd(4)alpha species. The (113)Cd chemical shift of the fifth Cd(2+) is significantly shielded (approximately 400 p.p.m.) when compared with the data for the Cd(2+) ions in Cd(4)alpha-MT by both direct and indirect (113)Cd NMR spectroscopy. Three of the four original NMR peaks move significantly upon binding the fifth cadmium. Evidence from indirect (1)H-(113)Cd HSQC NMR spectra suggests that the coordination environment of the additional Cd(2+) is not tetrahedral to four thiolates, as is the case with the four Cd(2+) ions in the Cd(4)alpha-MT, but has two thiolate ligands as part of its ligand environment, with additional coordination to either water or anions in solution.     

Peptide folding, metal-binding mechanisms, and binding site structures in metallothioneins

This minireview specifically focuses on recent studies carried out on structural aspects of metal-free metallothionein (MT), the mechanism of metal binding for copper and arsenic, structural studies using x-ray absorption spectroscopy and molecular mechanics modeling, and speciation studies of a novel cadmium and arsenic binding algal MT. Molecular mechanics-molecular dynamics calculations of apo-MT show that significant secondary structural features are retained by the polypeptide backbone upon sequential removal of the metal ions, which is stabilized by a possible H-bonding network. In addition, the cysteinyl sulfurs were shown to rotate from within the domain core, where they are found in the metallated state, to the exterior surface of the domain, suggesting an explanation for the rapid metallation reactions that were measured. Mixing Cu6beta-MT with Cd4alpha-MT and Cu6alpha-MT with Cd3beta-MT resulted in redistribution of the metal ions to mixed metal species in each domain; however, the Cu+ ions preferentially coordinated to the beta domain in each case. Reaction of As3+ with the individual metal-free beta and alpha domains of MT resulted in three As3+ ions coordinating to each of the domains, respectively, in a proposed distorted trigonal pyramid structure. Kinetic analysis provides parameters that allow simulation of the binding of each of the As3+ ions. X-ray absorption spectroscopy provides detailed information about the coordination environment of the absorbing element. We have combined measurement of x-ray absorption near edge structure (XANES) and extended x-ray absorption fine structure (EXAFS) data with extensive molecular dynamics calculations to determine accurate metal-thiolate structures. Simulation of the XANES data provides a powerful technique for probing the coordination structures of metals in metalloproteins. The metal binding properties of an algal MT, Fucus vesiculosus, has been investigated by UV absorption and circular dichroism spectroscopy and electrospray ionization-mass spectrometry. The 16 cysteine residues of this algal MT were found to coordinate six Cd2+ ions in two domains with stoichiometries of a novel Cd3S7 cluster and a beta-like Cd3S9 cluster.     

Noncooperative metalation of metallothionein 1a and its isolated domains with zinc

Mammalian metallothioneins (MTs) are a family of small cysteine-rich proteins capable of binding 7 Zn(2+) or Cd(2+) ions into two distinct domains: an N-terminal β-domain that binds 3 Zn(2+) or Cd(2+) and a C-terminal α-domain that binds 4 Zn(2+) or Cd(2+). MT has been implicated in a number of physiological functions, including metal ion homeostasis, toxic metal detoxification, and as a protective agent against oxidative stress. Conventionally, MT has been understood to coordinate metal ions in a cooperative fashion. Under this mechanism of metalation, the only species of biological relevance would be the metal-free (apo-) form of the protein and the fully metalated (holo-) form of the protein. However, an increasing body of evidence suggests that metalation occurs in a noncooperative manner. If this latter mechanism is correct, then partially metalated forms of the protein will be stable and able to take part in cellular chemistry. We report in this paper conclusive evidence that shows that biologically essential zinc binds to MT in a noncooperative manner. In addition, we report for the first time the stability of a Zn(5)-MT species. The implications of these findings are discussed in terms of the mechanism of metalation.     

A spectroscopic study of rat liver and Scylla serrata crab metallothioneins

The absorption, circular dichroism (CD) and magnetic circular dichroism (MCD) spectra of native rat liver and crab (Scylla serrata) Cd,Zn-metallothionein have been measured and the data are compared. The MCD data indicate that there are close similarities in the geometries of the cadmium-binding sites in both of these proteins; however, the CD spectra are quite different for the rat liver and crab proteins. The CD spectrum for the crab metallothionein is unlike any previously reported for a cadmium-containing metallothionein. This suggests that the CD spectrum is sensitive to the different bridging pattern used in the binding sites in the crab compared with the rat-liver metallothionein. Cadmium binding to the metal-free metallothionein is demonstrated for both proteins and it is shown that there are only minor structural differences between the native and remetallated proteins. The structural changes that occur near to the cadmium-binding sites during cadmium loading to the native proteins have been followed using absorption and CD spectroscopy. Marked changes are observed in the CD spectrum which can be associated with a two-phase reaction: initially Zn2+ is displaced by the Cd2+, then at higher concentrations of Cd2+ the tetrahedral geometry of the Cd2+-binding sites is lost as more Cd2+ is bound using the same thiolate groups. While this latter reaction results in considerable change to the CD spectrum, only minor changes are observed in the absorption spectrum. A significant red shift is observed in the S leads to Cd charge transfer transition region of the MCD spectrum (230-270 nm) following both cadmium loading of native rat liver, Cd,Zn-metallothionein and the metallation of metal-free metallothionein with cadmium. There are two contributions to this effect in Cd,Zn-metallothionein: (i) there is a S leads to Zn band underlying the S leads to Cd band; and (ii) the occupation of zinc sites by cadmium changes the energy of the S leads to Cd transition.     

Interaction of platinum with metallothionein-like ligands in the rat kidney after administration of cis-dichlorodiammine platinum II

After the administration of the anticancer drug cis-dichlorodiammine platinum II (cisplatin) to male rats, the Pt in the soluble fraction of the kidney is isolated, by gel filtration, in association with a high molecular weight component and a low molecular weight fraction. At 24 h, Pt is also recovered in a metallothionein-like fraction which elutes from Sephadex G-50 with a lower apparent molecular weight than endogenous (Cu, Zn)-thionein or Cd-thionein isolated from the kidneys of Cd2+-treated rats. None of these low molecular weight metal-binding fractions binds to Octyl Sepharose CL-4B. On DE-52 ion exchange chromatography, Cd-thionein is resolved into two isometallothioneins whereas the low molecular weight Pt-binding fraction is only partially purified and contains at least six components which elute at higher gradient concentrations than metallothionein. Pretreatment with Cd2+ which stimulates the synthesis of renal and hepatic metallothionein has no effect on the uptake and subcellular distribution of Pt in the liver and kidneys. Cisplatin treatment reduces the concentration of Cu and Zn in the renal metallothionein and other soluble protein fractions in the kidney. When administered to Cd2+-pretreated rats, cisplatin promotes the loss of Zn from the soluble protein fractions but causes the redistribution of Cd from the metallothionein to the high molecular weight fraction and fails to inhibit the Cd2+-induced accumulation of Cu in the kidneys and the binding of Cu to the soluble protein fractions. It is suggested that metallothionein probably does not have a significant role in the renal metabolism of Pt following the administration of cisplatin to rats.     

Chemical modifications of metallothionein. Preparation and characterization of polymers.

Reaction of rat liver metallothionein-II with two bifunctional cross-linking reagents, glutaraldehyde and dimethyl suberimidate, produces high yields of polymeric species. It is argued that cross-linking is trapping preformed aggregates of the protein, which therefore represent a stabilized quaternary structure of metallothionein. The two polymeric species differ in a number of respects. With dimethyl suberimidate, the polymer retains all metal-binding sites of the monomer, and has an unaltered isoelectric point. Reaction with glutaraldehyde causes loss of one or two Cd2+/Zn2+-binding sites and elevates the pI. Both species are nearly spherical aggregates, in contrast with the highly asymmetrical metallothionein. Both polymers are linked through lysine residues, and the thiol groups remain reduced. The biological significance of these aggregates is discussed.     

Cu+ distribution in metallothionein fragments

The differential distribution of Cu+ between separate alpha and beta domains of metallothionein (the isolated peptide fragments) and the rate of transfer of Cu+ between the two domains using copper-thiolate specific emission spectroscopy are reported. Kinetic data show the rate of transfer of Cu+ from the Cu6alpha to the Cd3beta domain is 2 x 10(-1) s(-1) while the transfer from Cu6beta to the Cd4alpha domain is much slower at 8 x 10(-3) s(-1), indicating the greater binding affinity of Cu+ for the MT beta domain. We report that the emission intensity of Cu6beta is 0.45 the emission intensity of Cu6alpha-MT. Lambda(max) is shown to be a probe of the environment of the Cu+. A series of copper-containing domain intermediates to the formation of the filled Cu6S9-beta and Cu6S11-alpha-clusters are identified. A mechanism is proposed for the formation of Cu12(betaalpha)-MT that involves metal exchange reactions of Cu+ ions from the alpha to the beta domain with initial formation of a Cu4beta-cluster.     

Order of metal binding in metallothionein

Purified isoforms of rat liver apometallothionein were reconstituted in vitro with Cd and Zn ions to study the order of binding of the 7 metal sites in the two separate metal clusters, one containing four metal ions (cluster A) and the other containing three (cluster B). Reconstitution with 7 Cd ions resulted in a metalloprotein similar to induced Cd,Zn-metallothionein by the criteria of electrophoretic mobility, insensitivity to proteolysis by subtilisin, and the pH-dependent release of Cd. Proteolytic digestion of metallothionein reconstituted with suboptimal quantities of Cd followed by separation of Cd-containing polypeptide fragments by electrophoresis and chromatography revealed metal ion binding initially occurs in the 4-metal center, cluster A. Upon saturation of the 4 sites in cluster A, binding occurs in the 3-metal center, cluster B. Samples reconstituted with 1 to 4 Cd ions per protein molecule, followed by digestion with subtilisin, yielded increasing amounts of a proteolytically stable polypeptide fragment identical with the alpha fragment domain that is known to encompass the 4-metal center. Samples renatured with 5 to 7 Cd ions per metallothionein molecule showed decreasing quantities of alpha fragment and increasing amounts of native-like metallothionein. Similar results were obtained in reconstitution studies with Zn ions. Samples reconstituted with 7 Cd eq followed by incubation with EDTA revealed that cluster B Cd ions were removed initially. The binding process in each domain is cooperative. Reconstitution of apometallothionein with 2 Cd ions followed by proteolysis yields a 50% recovery of saturated Cd4 alpha cluster. Likewise, when Cd5-renatured metallothionein was digested with subtilisin, 30% of the molecules were identified as Cd7 metallothionein with the remainder as Cd4 alpha fragment.     

Bismuth binding studies to the human metallothionein using electrospray mass spectrometry

Bismuth compounds are currently used to treat gastric ailments and to prevent the toxic side effects of cancer treatments. The affinity of bismuth for binding to sulfur compounds has been reported and one such target biomolecule is the cysteine-rich metalloprotein metallothionein. Renal mammalian metallothionein has been shown to be induced by Bi salts, with the Bi³⁺ binding to the renal MT. However, the exact metal-to-metallothionein stoichiometric ratios for the 2-domain βα mammalian protein and the individual β and α domain fragments remain unknown. We now report that the maximum metal-to-MT stoichiometries for the individual domain fragments and the entire 2-domain protein are Bi₃-S₉-βhMT, Bi₄-S₁₁-αhMT, and Bi₇-S₂₀-βαhMT, respectively. Electrospray mass spectrometry data also unambiguously show the existence of partially metalated Bi-containing MT species during the titration of apo-MT with Bi³⁺, which demonstrates that Bi-metalation to MT occurs in a noncooperative manner.     

Copper speciation in the alpha and beta domains of recombinant human metallothionein by electrospray ionization mass spectrometry.

ESI-MS data are reported for Cu(I) binding to the metal-free and cadmium-alpha and beta domains of recombinant human metallothionein. These data provide information on the stoichiometric ratios of copper and cadmium that bind to the 11 thiolate sulfurs in the alpha fragment and the nine thiolate sulfurs in the beta fragment. The data show the effects of the existing three-dimensional structure on the formation of different Cu(I)-thiolate clusters. Charge-state spectra are reported for a range of Cu(I) binding at low and neutral pH to the isolated alpha and beta domains. There is an uneven distribution of charge states that show that changes in the three-dimensional structure take place as a function of Cu(I) loading. Metallation of the alpha domain at low pH takes place in a series of steps with the Cu7 species dominating until at higher levels of Cu(I) the clusters become unstable resulting in increased concentrations of the metal-free being detected. We interpret this behavior as being the result of the expansion of the Cu-S domain structure to accommodate digonal co-ordination for the increased Cu(I) loading. This larger structure is unstable in the mass spectrometer and demetallation takes place. Metallation of the beta domain at low pH proceeds in steps that involve initial formation of a Cu5S9 cluster, followed by the Cu6S9 at higher concentrations of Cu(I). The charge state spectra indicate a significant change in exposure of protonatable amino acids between Cu5S9 and Cu6S9 clusters, which indicates a change in peptide conformation when the Cu6S9 cluster forms. Metallation at neutral pH follows this same trend, namely, a much greater range of copper species is found during titrations of the Cd4S11-alpha fragment compared with the number of species that form when Cu(I) is added to Cd3S9-beta. The mass spectral data indicate that at neutral pH, the presence of the tetrahedral geometry of the Cd(II) facilitates formation of mixed trigonal and digonal geometries for the incoming Cu(I) so that the most prominent species in the beta fragment is Cd1Cu5S9 which transforms into Cu7S9 at higher concentrations of Cu(I), and finally to Cu9S9 at saturation, all species involving a number of Cu(I) in digonal geometries. The observation that the metallation patterns of the alpha and beta clusters follow different pathways at both low and neutral pH's, suggests that the structures in the two domains are quite different, in agreement with previous proposals     

Spectroscopic studies on cadmium (II)- and cobalt(II)-substituted metallothionein from the crab Cancer pagurus. Evidence for one additional low-affinity metal-binding site

The binding of diamagnetic Cd(II) and paramagnetic Co(II) ions to the metal-free form of crab, Cancer pagurus, metallothionein (MT) was studied by various spectroscopic techniques. Both reconstituted and native Cd(II)-MT containing 6 mol Cd(II)/mol protein display electronic absorption, circular dichroism (CD) and magnetic circular dichroism (MCD) spectra which were indistinguishable. The stoichiometric replacement of Cd(II) ions in native Cd(II)6-MT by paramagnetic Co(II) ions enabled the geometry of the metal-binding sites to be probed. The electronic absorption and MCD spectra of Co(II)6-MT revealed features characteristic of distorted tetrahedral tetrathiolate Co(II) coordination for all six metal-binding sites. The stepwise incorporation of Cd(II) and Co(II) ions into this protein was monitored by electronic absorption and CD, and by electronic absorption and EPR spectroscopy, respectively. The results indicate that the metal-thiolate cluster structure is generated when more than four metal ions are bound. Below this titration point separate tetrahedral tetrathiolate complexes exist. This suggests that the cluster formation occurs in a two-step process. Furthermore, the spectroscopic features in both Cd(II)- and Co(II)-metal derivatives above the full metal occupancy of six suggest the existence of one additional metal-binding site. The subsequent loss of one Cd(II) ion from crab Cancer Cd(II)7-MT in the gel filtration studies demonstrate the low metal-binding affinity of the latter site. While the spectroscopic properties indicate an exclusively tetrahedral type of metal-thiolate sulfur coordination for the binding of the first six metal ions, they suggest that the seventh metal ion is coordinated in a different fashion.     

Independence of the domains of metallothionein in metal binding

Mammalian metallothionein is a low molecular weight protein with two metal-binding domains. To determine if metal binding in one domain affects binding in the other, we prepared peptides corresponding to the regions that enfold the two metal-thiolate clusters. Metal reconstitution studies of these peptides revealed stoichiometries of metal binding similar to those observed within the intact molecule. Thus, the alpha domain coordinates 4 Cd(II), 6 Cu(I), or 6 Ag(I) ions regardless of whether the domain is part of the total protein or is studied as a separate peptide. Likewise, the beta domain binds 3 Cd(II), 6 Cu(I), or 6 Ag(I) ions in both the intact protein and as a separate peptide. If cluster B in intact metallothionein is preformed with Cu(I) or Ag(I), cluster A saturates with either 4 mol eq of Cd(II) or 6 mol eq of Ag(I). Similarly, preformation of the A cluster with Cd(II) does not affect the binding of 6 Cu(I) ions in the B cluster. Therefore, the metal-dependent folding of the protein to create one cluster occurs independent of constraints or influences from the other domain. Formation of the protein with a tetrahedrally coordinated metal in one cluster and a trigonally coordinated metal in the other center is possible.     

High yield expression and single step purification of human thionein/metallothionein

Human metallothionein (MT), isoform 2, was expressed in Escherichia coli as an intein (protein splicing element) fusion protein in the absence of added metals and purified by intein-mediated purification with an affinity chitin-binding tag (IMPACT system). This procedure constitutes a novel and simple strategy to prepare thionein (T), the metal-free form, or MT when reconstituting T with metals in vitro. The yield was 8 mg of T or 6 mg of pure Cd(7)- or Zn(7)-MT from a 1-L culture, significantly higher than yields from any other expression system. Purified recombinant protein is indistinguishable from the native protein on the basis of its metal-binding ability, titration of its sulfhydryls, and UV and CD spectra. The MALDI-TOF mass spectrum is consistent with that of T with a free N-terminus.     

The de novo design of a rubredoxin-like Fe site.

A redox center similar to that of rubredoxin was designed into the 56 amino acid immunoglobulin binding B1 domain of Streptococcals protein G. The redox center in rubredoxin contains an iron ion tetrahedrally coordinated by four cysteine residues, [Fe(S-Cys)4](-1),(-2). The design criteria for the target site included taking backbone movements into account, tetrahedral metal-binding, and maintaining the structure and stability of the wild-type protein. The optical absorption spectrum of the Co(II) complex of the metal-binding variant is characteristic of tetrahedral chelation by four cysteine residues. Circular dichroism and nuclear magnetic resonance measurements reveal that the metal-free and Cd(II)-bound forms of the variant are folded correctly and are stable. The Fe(III) complex of the metal-binding mutant reproduces the optical and the electron paramagnetic resonance spectra of oxidized rubredoxin. This demonstrates that the engineered protein chelates Fe(III) in a tetrahedral array, and the resulting center is similar to that of oxidized rubredoxin.     

Induction and degradation of Zn-, Cu- and Cd-thionein in Chang liver cells

Human liver cells (Chang liver) were exposed to 5 micrograms Zn, 2.5 micrograms Cu or 1 microgram Cd/ml in cultured medium. These exogeneous heavy metals were accumulated by the cells and induced de novo synthesis of metallothionein after a 3-h incubation period. The production of Zn-, Cu- or Cd-thionein started in the cells with accumulation of 1 nmol Zn, 0.3 nmol Cu and 0.1 nmol Cd/mg cytosol protein and subsequently the amounts of metal-binding thioneins increased in agreement with the relative amount of metal accumulated in the cytosol over a 24-h period. When cells containing Zn- or Cu-thionein were placed in metal free medium, 70% or 25% of the zinc or copper bound to each original metallothionein was released after 3 h; bound metals decreased to 85% and 65% respectively after 24 h. The disappearance of metal from metallothionein correlated with increases of metal in the medium. On the other hand, 35S-counts incorporated into Zn- and Cu-thionein decreased only to 40% and 15% of the levels in the original metallothionein after 3 h; 35S-counts decreased to 65% and 45%, respectively, after 24 h, indicating that metals bound to metallothionein decreased more quickly than 35S-counts. These results suggest that metals were released from metallothionein and were excreted into the medium. However, 35S- and 109Cd-counts in Cd-thionein changed very little, if at all, in the cells even after a 24-h incubation period. Our data strongly suggest that Zn- and Cu-thionein are degraded in the cells, but that Cd-thionein remains longer than either Zn- or Cu-thionein. When cells containing Zn-thionein were incubated in metal-free medium, Zn-thionein was digested in the cells and peptide fragments ranging about 200-400 daltons were excreted from the cells.     

Arsenic transfer between metallothionein proteins at physiological pH

As³⁺ bound to the two-domain, recombinant human metallothionein (isoform 1a) is stable at pH 7 and translocates via protein-protein interactions to other metallothionein proteins. The data show As³⁺ transfer from the two-domain β-α-hMT to binding sites in the isolated apo-β-hMT and apo-α-hMT. Under conditions of equilibrium, apo- and partially-metallated species coexist indicating that noncooperative demetallation of the As₆-βα-hMT occurrs. As³⁺ transfer under conditions (pH 7) where the free As³⁺ ion is not stable, provides evidence that Cd²⁺ and Zn²⁺ transfer may also take place through protein-protein interactions and that partially metallated Cd-MT and Zn-MT would be stable.     

Cadmium induction of metallothionein synthesis in Mytilus galloprovincialis

1. The accumulation and subcellular distribution of cadmium and resulting induction of metallothionein has been studied in mussels, Mytilus galloprovincialis, exposed to 400 μg Cd 1⁻¹.2. Cadmium accumulated by mussels was primarily associated with metallothionein: a maximum four-fold increase in concentrations of the metal-binding protein (3 mg g⁻¹ to 12 mg g⁻¹) was observed after 30 days.3. Results for M. galloprovincialis confirm the importance of metallothionein in the detoxification of intracellular cadmium and indicate that induction rates are identical to those observed in the closely-related M. edulis.4. Intercomposition of data between these species may therefore be valid when employing metallothionein assays to determine sub-lethal response to cadmium contamination.     

Asymmetric distribution of cooperativity in the binding cascade of normal human hemoglobin. 2. Stepwise cooperative free energy

Stepwise cooperative free energies and intermediate Hill coefficients are used to assess the presence of noncooperative sequences in the database of binding free energies previously obtained for the eight partially ligated intermediates of human hemoglobin, encompassing a variety of hemesite analog substitutions. This analysis is prompted by the observed noncooperative binding of two ligands to hemoglobins that are partially substituted with Zn2+-heme, an analog of deoxy Fe2+-heme (Holt et al. (2005) Biochemistry 44, XXXXX). The results show that noncooperative binding sequences are observed in all hemesite analog studied to date. The noncooperative binding observed in (alpha2Znbeta2FeO2) and (alpha2FeO2beta2Zn) is therefore not a Zn-specific substitution artifact. One of several binding sequences from singly to triply ligated hemoglobin is also observed to occur with little or no positive cooperativity. These results demonstrate the variability possible among different ligation pathways in a highly cooperative multi-subunit system such as hemoglobin. As a direct consequence of this variability, differences among ligation pathways are not always detectable using cooperativity functions based on statistical distributions, such as the Hill coefficient n(H). The limitations of Hill coefficient analysis in evaluating cooperativity in intermediates of complex systems is contrasted with the utility of the stepwise binding parameters.