Free energy coupling within macromolecules. The chemical work of ligand binding at the individual sites in co-operative systems

Individual-site binding curves such as those obtainable from techniques of DNase footprinting or nuclear magnetic resonance spectroscopy can be used to monitor structurally localized events within biopolymers. This paper discusses thermodynamic aspects of individual-site ligand binding for co-operative systems where the binding of ligand at a local site is coupled to binding of the same ligand species at other sites within the macromolecule. Individual-site binding isotherms have the following properties. (1) They provide a direct indication of the role played by the particular site in the overall binding reaction. (2) They can be used to determine the energetic contribution of loading the site regardless of the complexity of the system. (3) They can be used to resolve microscopic equilibrium constants and co-operativity constants in cases where the classical isotherm is incapable of such resolution. The microscopic constants bear a complex relation to the chemical work of loading each individual site. For a system with two interacting sites we derive analytical relationships between the individual-site loading energies and the microscopic constants. These relationships prescribe, for any values of the microscopic constants, how the co-operative energy is partitioned between events at the two sites. At fixed ligand activity the binding free energy can be estimated directly from an individual-site isotherm. This quantity, which is also a composite of the microscopic constants, provides a useful measure of site--site interaction. Several examples and applications are discussed for these properties of individual-site binding reactions.     

Proton-linked contributions to site-specific interactions of lambda cI repressor and OR

The effects of proton activity on the site-specific interactions of cI repressors with operator sites OR were studied by using DNase I footprint titration. Individual-site binding isotherms were obtained for the binding of repressor to each site of wild-type OR and of mutant operators in which binding to some sites is eliminated. The Gibbs energies for binding and for cooperativity (in every operator configuration) were determined at each pH (range 5-8). The proton-linked effects clearly account for a significant fraction of the difference in affinities for the three operator sites. The most dramatic effects on the repressor-operator binding interactions are at acid pH, and therefore do not involve the basic groups in the repressor N-terminal arm known to contact the DNA. Also, the proton-linked effects are different at the three operator sites as indicated by significantly different derivative relationships, partial derivative of ln k versus partial derivative of ln aH = net proton absorption (delta nu bar(H)). These results implicate ionizable repressor groups which may not contact the DNA and conformational differences between the three repressor-operator site complexes as being important components to the mechanism of site specificity. The extensive data base generated by these studies was also used to reevaluate the traditional models used to describe cooperativity in this system. The results confirm the lack of significant cooperative interaction between OR1 and OR3 at all conditions. However, the data for some experimental conditions are clearly inconsistent with the (selection) rule, that cooperative interaction between OR2 and OR3 is eliminated by ligation at OR1.     

Cooperative protein-DNA interactions: effects of KCl on lambda cI binding to OR.

The effects of monovalent salt activity on the site-specific and cooperative interactions of cI repressor with its three operator sites OR were studied by using quantitative DNase I footprint titration methods. Individual-site binding isotherms were obtained for binding repressor dimers to each site of wild-type OR and to mutant operator templates in which binding to one or two sites has been eliminated. The standard Gibbs energies for intrinsic binding, delta G1, delta G2, and delta G3, and cooperative interactions, delta G12 and delta G23, were determined at each condition (range 50-200 mM KCl). It is found that the dimer affinity for each of the three sites increases as [KCl] decreases, a striking result given that the monomer-dimer equilibrium shifts toward monomer formation under identical solution conditions [Koblan, K. S., & Ackers, G. K. (1991) Biochemistry (preceding paper in this issue)]. The magnitudes of ion-linked effects are found to differ at the three operator sites, while the intrinsic interaction binding free energies for sites OR1 and OR3 change in parallel over the entire range of [KCl]. The KCl dependencies at OR1 and OR3 represent the average release of 3.7 +/- 0.6 and 3.8 +/- 0.6 apparent ions, respectively. By contrast, the KCl dependency of OR2 binding corresponds to the displacement of 5.2 +/- 0.7 apparent ions. The ability of cI repressor to discriminate between the three operator sites thus appears linked to ion binding/release reactions.     

The ionization of clusters. II. Pairwise isotropic interactions and individual site binding data

Evaluation of the parameters describing the binding of protons to clusters of interacting sites requires some reasonable assumptions and procedures because it is impossible to observe an unperturbed site in its interacting environment. When the unperturbed sites are not identical, individual site binding data allow for the evaluation of the differences (or ratios) between the unperturbed (or intrinsic) binding constants but not their actual values (or the interaction energies). In this paper we extend our previous treatment of the ionization of clusters in order to generalize pairwise isotropic interactions and take into account the present availability of individual site binding data.     

Protein surface-distribution and protein-protein interactions in the binding of peripheral proteins to charged lipid membranes.

The binding of native cytochrome c to negatively charged lipid dispersions of dioleoyl phosphatidylglycerol has been studied over a wide range of ionic strengths. Not only is the strength of protein binding found to decrease rapidly with increasing ionic strength, but also the binding curves reach an apparent saturation level that decreases rapidly with increasing ionic strength. Analysis of the binding isotherms with a general statistical thermodynamic model that takes into account not only the free energy of the electrostatic double layer, but also the free energy of the surface distribution of the protein, demonstrates that the apparent saturation effects could arise from a competition between the out-of-plane binding reaction and the lateral in-plane interactions between proteins at the surface. It is found that association with nonlocalized sites results in binding isotherms that display the apparent saturation effect to a much more pronounced extent than does the Langmuir adsorption isotherm for binding to localized sites. With the model for nonlocalized sites, the binding isotherms of native cytochrome c can be described adequately by taking into account only the entropy of the surface distribution of the protein, without appreciable enthalpic interactions between the bound proteins. The binding of cytochrome c to dioleoyl phosphatidylglycerol dispersions at a temperature at which the bound protein is denatured on the lipid surface, but is nondenatured when free in solution, has also been studied. The binding curves for the surface-denatured protein differ from those for the native protein in that the apparent saturation at high ionic strength is less pronounced. This indicates the tendency of the denatured protein to aggregate on the lipid surface, and can be described by the binding isotherms for nonlocalized sites only if attractive interactions between the surface-bound proteins are included in addition to the distributional entropic terms. Additionally, it is found that the binding capacity for the native protein is increased at low ionic strength to a value that is greater than that for complete surface coverage, and that corresponds more closely to neutralization of the effective charge (determined from the ionic strength dependence), rather than of the total net charge, on the protein. Electron spin resonance experiments with spin-labeled lipids indicate that this different mode of binding arises from a penetration or disturbance of the bilayer surface by the protein that may alleviate the effects of in-plane interactions under conditions of strong binding.     

Linkage between cooperative oxygenation and subunit assembly of cobaltous human hemoglobin.

The thermodynamic linkage between cooperative oxygenation and dimer-tetramer subunit assembly has been determined for cobaltous human hemoglobin in which iron(II) protoporphyrin IX is replaced by cobalt(II) protoporphyrin IX. The equilibrium parameters of the linkage system were determined by global nonlinear least-squares regression of oxygenation isotherms measured over a range of hemoglobin concentrations together with the deoxygenated dimer-tetramer assembly free energy determined independently from forward and reverse reaction rates. The total cooperative free energy of tetrameric cobalt hemoglobin (over all four binding steps) is found to be 1.84 (+/- 0.13) kcal, compared with the native ferrous hemoglobin value of 6.30 (+/- 0.14) kcal. Detailed investigation of stepwise cooperativity effects shows the following: (1) The largest change occurs at the first ligation step and is determined on model-independent grounds by knowledge of the intermediate subunit assembly free energies. (2) Cooperativity in the shape of the tetrameric isotherm occurs mainly during the middle two steps and is concomitant with the release of quaternary constraints. (3) Although evaluation of the pure tetrameric isotherm portrays identical binding affinity between the last two steps, this apparent noncooperativity is the result of a "hidden" oxygen affinity enhancement at the last step of 0.48 (+/- 0.12) kcal. This quaternary enhancement energy is revealed by the difference in subunit assembly free energies of the triply and fully ligated species and is manifested visually by the oxygenation isotherms at high versus low hemoglobin concentration. (4) Cobaltous hemoglobin dimers exhibit apparent anticooperativity of 0.49 (+/- 0.16) kcal (presumed to arise from heterogeneity of subunit affinities).(ABSTRACT TRUNCATED AT 250 WORDS)     

Energetics of protein–DNA interactions: An exact calculation for binding of ligands to a lattice of overlapping sites

Exact equal ions are developed for analyzing the binding of ligands to a linear lattice of overlapping sites in which occupied–unoccupied as well as occupied–occupied interactions are included for the analysis of the binding isotherms. We demonstrate that positive cooperativity on the binding of ligands to multiple sites may derive from either occupied–unoccupied or occupied–occupied interactions. When the binding of proteins to linear polynucleotides and DNA has exhibited positive cooperativity protein–protein (occupied–occupied), interactions have heretofore been invoked as the sole energetic source in determining the cooperative effect. Models and equations developed previously for the analysis of these binding isotherms have included only the protein–protein interactions (usually characterized with the symbol ω). The exact equations of this paper are capable of analyzing binding data in a manner to evaluate the relative importance of both occupied–unoccupied and occupied–occupied interactions Relations derived here are employed to analyze some existing data, and the resulting parameter values are compared to those developed with equations employing only the protein–protein (occupied–occupied) interactions. The resulting parameter values are qualitatively different. Values of the binding constants differ by about three orders of magnitude. When only protein–protein interactions are taken into account, the resulting free energy of interaction is negative, indicating attractive forces between bound protein molecules; when both occupied–unoccupied and occupied–occupied interactions are applied, the resulting free energies of interaction are positive, indicating destabilizing forces acting primarily on the polynucleotide lattice. © 1995 John Wiley & Sons, Inc.     

Ligand-dependent aggregation and cooperativity: a critique

Ligand-dependent site-site (or subunit-subunit) interactions provide the basis for explaining cooperativity in chemical reactions. Even in the simplest possible nonaggregating system, interpretation of the interactions in terms of structural details requires an explicit assumption (or model) for the binding of the ligand to the sites when there are no interactions. This paper develops in detail the processes by which aggregation will yield ligand-dependent cooperativity. Two conceptually distinct free energy differences may contribute to cooperativity in an aggregation reaction. One is the free energy difference in ligand binding between the monomer and the aggregate. The other is derived from ligand-dependent interactions between the sites of the aggregate. In this analysis an explicit distinction is made between the experimentally accessible constants and those derived from assumed models. Experimental measurements of an aggregation cycle in which all of the species in equilibrium are defined do not allow for an evaluation of the energies of interaction without some model (or assumption). In the analysis presented, an explicit assumption is employed relating the constant for binding of the ligand to the isolated monomer and the constant for the binding of the ligand to aggregate under conditions where there are no ligand-dependent interactions.     

Continuum electrostatic analysis of preferred solvation sites around proteins in solution

To understand water-protein interactions in solution, the electrostatic field is calculated by solving the Poisson-Boltzmann equation, and the free energy surface of water is mapped by translating and rotating an explicit water molecule around the protein. The calculation is applied to T4 lysozyme with data available on the conservation of solvent binding sites in 18 crystallographically independent molecules. The free energy maps around the ordered water sites provide information on the relationship between water positions in crystal structure and in solution. Results show that almost all conserved sites and the majority of nonconserved sites are within 1.3 A of local free energy minima. This finding is in sharp contrast to the behavior of randomly placed water molecules in the boundary layer, which, on the average, must travel more than 3 A to the nearest free energy minimum. Thus, the solvation sites are at least partially determined by protein-water interactions rather than by crystal packing alone. The characteristic water residence times, obtained from the free energies at the local minima, are in good agreement with nuclear magnetic resonance experiments. Only about half of the potential sites show up as ordered water in the 1.7 A resolution X-ray structure. Crystal packing interactions can stabilize weak or mobile potential sites (in fact, some ordered water positions are not close to free energy minima) or can prevent water from occupying certain sites. Apart from a few buried water molecules that are strong binders, the free energies are not very different for conserved and nonconserved sites. We show that conservation of a water site between two crystals occurs if the positions of protein atoms, primarily contributing to the free energy at the local minimum, do not substantially change from one structure to the other. This requirement can be correlated with the nature of the side chain contacting the water molecule in the site.     

Interactions of two amphiphilic penicillins with myoglobin in aqueous buffered solutions: a thermodynamic and spectroscopy study

The interactions and complexation process of the amphiphilic penicillins sodium cloxacillin and sodium dicloxacillin with horse myoglobin in aqueous buffered solutions of pH 4.5 and 7.4 have been examined by equilibrium dialysis, zeta-potential, isothermal titration calorimetry (ITC) and UV-Vis absorbance techniques. A more opened structure of the protein molecules is detected as a consequence of the reduction of pH from 7.4 to 4.5. Binding isotherms and derived Hill coefficients reflect a cooperative binding behavior. Gibbs energies of binding per mole of drug were obtained from equilibrium dialysis data and compared with those derived from the zeta potential taking into account cooperativity. DeltaGads degrees values so obtained are large and negative at low concentrations where binding to the "high-energy" sites occurs and decreases with the drug concentration. The enthalpies of binding have been obtained from ITC and are small and exothermic so that the Gibbs energies of binding are dominated by large increases in entropy consistent with hydrophobic interactions. Other thermodynamic quantities of the binding mechanism, that is, entropy, DeltaSITCi, Gibbs energy, DeltaGITCi, the binding constant, KITCi, and the number of binding sites, ni, were also obtained, confirming the above results. From ITC data and following a theoretical model, the number of bound and free penicillin molecules was calculated, being higher at pH 4.5 than at pH 7.4. The binding of penicillin causes a conformational transition on protein structure as a consequence of the resulting intramolecular repulsion between the penicillin molecules bound to the protein. Thermodynamic quantites (the Gibbs energy of the transition in water, DeltaGw degrees , and in a hydrophobic environment, DeltaGhc degrees) of the denaturation process were calculated, indicating that at pH 4.5 some of the histidine residues are protonated, becoming accessible to solvent and giving rise to a more opened protein structure.     

The interaction mechanism between lipopeptide (daptomycin) and polyamidoamine (PAMAM) dendrimers

The interaction mechanism of lipopeptide antibiotic daptomycin and polyamidoamine (PAMAM) dendrimers was studied using fluorescence spectroscopy. The fluorescence changes observed are associated with daptomycin–dendrimer interactions. The binding isotherms were constructed by plotting the fluorescence difference at 460 nm from kynurenine (Kyn‐13) of daptomycin in the presence and absence of dendrimer. A one‐site and two‐site binding model were quantitatively generated to estimate binding capacity and affinity constants from the isotherms. The shape of the binding isotherm and the dependence of the estimated capacity constants on dendrimer sizes and solvent pH values provide meaningful insight into the mechanism of interactions. A one‐site binding model adequately describes the binding isotherm obtained under a variety of experimental conditions with dendrimers of various sizes in the optimal binding pH region 3.5 to 4.5. Comparing the pH‐dependent binding capacity with the ionization profiles of daptomycin and dendrimer, the ionized aspartic acid residue (Asp‐9) of daptomycin primarily interact with PAMAM cationic surface amine. Copyright © 2015 European Peptide Society and John Wiley & Sons, Ltd.     

Binding of n-mers to one-dimensional lattices with longer than close-contact interactions

A general formalism is derived for the evaluation of binding isotherms of n-mers (ligands) to one-dimensional polymers in the presence of ligand-ligand interactions which extend over several binding sites with distance-dependent interaction energies (multi-parameter model). This is an extension of the usual n-mer binding theory developed by several investigators in which ligand-ligand interaction occurs only when two ligands are in close contact (one-parameter model). The difference in binding isotherms between a one-parameter model and a multi-parameter model is studied numerically using the present formalism.     

Site-specific enthalpic regulation of DNA transcription at bacteriophage lambda OR.

Binding of cI repressor to DNA fragments containing the three specific binding sites of the right operator (OR) of bacteriophage lambda was studied in vitro over the temperature range 5-37 degrees C by quantitative footprint titration. The individual-site isotherms, obtained for binding repressor dimers to each site of wild-type OR and to appropriate mutant operator templates, were analyzed for the Gibbs energies of intrinsic binding and pairwise cooperative interactions. It is found that dimer affinity for each of the three sites varies inversely with temperature, i.e., the binding reactions are enthalpy driven, unlike many protein-DNA reactions. By contrast, the magnitude of the pairwise cooperativity terms describing interaction between adjacently site-bound repressor dimers is quite small. This result in combination with the recent finding that repressor monomer-dimer assembly is highly enthalpy driven (with delta H degrees = -16 kcal mol-1) [Koblan, K. S., & Ackers, G. K. (1991) Biochemistry 30, 7817-7821] indicates that the associative contacts between site-bound repressors that mediate cooperativity are unlikely to be the same as those responsible for dimerization. The intrinsic binding enthalpies for all three sites are negative (exothermic) and nearly temperature-invariant, indicating no heat capacity changes on the scale of those inferred in other protein-DNA systems. However, the three operator sites are affected differentially by temperature: the intrinsic binding free energies for sites OR1 and OR3 change in parallel over the entire range, delta H0OR1 = -23.3 +/- 4.0 kcal mol-1 and delta H0OR3 = -22.7 +/- 1.2 kcal mol-1.(ABSTRACT TRUNCATED AT 250 WORDS)     

Energetics and conformational changes upon complexation of a phenothiazine drug with human serum albumin

The interactions and complexation process of the amphiphilic phenothiazine fluphenazine hydrochloride with human serum albumin in aqueous buffered solutions of pH 3.0 and 7.4 have been examined by zeta-potential, isothermal titration calorimetry (ITC), UV-vis spectroscopy, and dynamic light scattering (DLS) techniques with the aim of analyzing the effect of hydrophobic and electrostatic forces on the complexation process and the alteration of protein conformation upon binding. Thus, the energetics and stoichiometry of the binding process were derived from ITC data. The enthalpies of binding obtained are small and exothermic, so the Gibbs energies of binding are dominated by large increases in entropy, consistent with hydrophobic interactions at a acidic pH. However, at physiological pH, binding to the first class of binding sites is dominated by an enthalpic contribution due to the existence of electrostatic interactions and probably some hydrogen bonding. Binding isotherms were obtained from microcalorimetric data by using a theoretical model based on the Langmuir isotherm. zeta-Potential data showed a reversal in the sign of the protein charge at pH 7.4, as a consequence of the binding of the drug to the protein. Gibbs energies of drug binding per mole of drug were also derived from zeta-potential data. On the other hand, binding of the phenothiazine that causes a conformational transition on the protein structure was followed as a function of drug concentration using UV-vis spectroscopy, and the data were analyzed to obtain the Gibbs energy of the transition in water (deltaG(degree)w) and in a hydrophobic environment (deltaG(degree)hc). Finally, the population distribution of the different species in solution and the size of the complexes were analyzed through dynamic light scattering. The existence of an aggregation process of drug/protein complexes, as a consequence of the expanded structure of the protein induced by the drug and subsequent further binding, is in agreement with ITC data. In addition, detection of drug aggregates at concentrations below the drug critical micelle concentration was also detected by this technique.     

What determines the van der Waals coefficient beta in the LIE (linear interaction energy) method to estimate binding free energies using molecular dynamics simulations?

Recently a semiempirical method has been proposed by Aqvist et al. to calculate absolute and relative binding free energies. In this method, the absolute binding free energy of a ligand is estimated as deltaGbind = alpha + beta, where Vel(bound) and Vvdw(bound) are the electrostatic and van der Waals interaction energies between the ligand and the solvated protein from an molecular dynamics (MD) trajectory with ligand bound to protein and Vel(free) and Vel(free) and Vvdw(free) are the electrostatic and van der Waals interaction energies between the ligand and the water from an MD trajectory with the ligand in water. A set of values, alpha = 0.5 and beta = 0.16, was found to give results in good agreement with experimental data. Later, however, different optimal values of beta were found in studies of compounds binding to P450cam and avidin. The present work investigates how the optimal value of beta depends on the nature of binding sites for different protein-ligand interactions. By examining seven ligands interacting with five proteins, we have discovered a linear correlation between the value of beta and the weighted non-polar desolvation ratio (WNDR), with a correlation coefficient of 0.96. We have also examined the ability of this correlation to predict optimal values of beta for different ligands binding to a single protein. We studied twelve neutral compounds bound to avidin. In this case, the WNDR approach gave a better estimate of the absolute binding free energies than results obtained using the fixed value of beta found for biotin-avidin. In terms of reproducing the relative binding free energy to biotin, the fixed-beta value gave better results for compounds similar to biotin, but for compounds less similar to biotin, the WNDR approach led to better relative binding free energies.     

Mutagenic dissection of hemoglobin cooperativity: effects of amino acid alteration on subunit assembly of oxy and deoxy tetramers.

Free energies of oxygen-linked subunit assembly and cooperative interaction have been determined for 34 molecular species of human hemoglobin, which differ by amino acid alterations as a result of mutation or chemical modification at specific sites. These studies required the development of extensions to our earlier methodology. In combination with previous results they comprise a data base of 60 hemoglobin species, characterized under the same conditions. The data base was analyzed in terms of the five following issues. (1) Range and sensitivity to site modifications. Deoxy tetramers showed greater average energetic response to structural modifications than the oxy species, but the ranges are similar for the two ligation forms. (2) Structural localization of cooperative free energy. Difference free energies of dimer-tetramer assembly (oxy minus deoxy) yielded delta Gc for each hemoglobin, i.e., the free energy used for modulation of oxygen affinity over all four binding steps. A structure-energy map constructed from these results shows that the alpha 1 beta 2 interface is a unique structural location of the noncovalent bonding interactions that are energetically coupled to cooperativity. (3) Relationship of cooperativity to intrinsic binding. Oxygen binding energetics for dissociated dimers of mutants strongly indicates that cooperativity and intrinsic binding are completely decoupled by tetramer to dimer dissociation. (4) Additivity, site-site coupling and adventitious perturbations. All these are exhibited by individual-site modifications of this study. Large nonadditivity may be correlated with global (quaternary) structure change. (5) Residue position vs. chemical nature. Functional response is solely dictated by structural location for a subset of the sites, but varies with side-chain type at other sites. The current data base provides a unique framework for further analyses and modeling of fundamental issues in the structural chemistry of proteins and allosteric mechanisms.     

Interaction of lysozyme with dyes. II. Binding of bromophenol blue

The binding of lysozyme with bromophenol blue (BPB) at various dye concentrations and pH was carried out at 25 degrees C by equilibrium dialysis, ultraviolet (UV) difference and circular dichroism (CD) spectral techniques. Binding isotherms at pH 5.0 show non-cooperative binding at low dye concentrations, which change over to cooperative binding at higher concentrations indicating biphasic nature. However, binding isotherms at pH 7.0 and 9.0 show cooperative binding only, at all concentrations of the dye. The number of available binding sites decreases with the increase of pH. Gibbs free energy change, calculated on the basis of Wyman's binding potential concept, decreases with the increase of pH. Binding isotherms at pH 5.0 obtained at a lower temperature of 8 degrees C, also indicate the biphasic nature similar to those observed at 25 degrees C, but with a slight decreased strength of binding. The UV difference spectra of the complex do not show any distinct peaks in the 285 to 297 nm region eliminating any possible interaction of BPB with tryptophan and tyrosine residues of the lysozyme molecule. The CD spectra of lysozyme-BPB complex show a decrease in ellipticities with reference to native lysozyme in the near UV and far UV regions. This indicates that the lysozyme-BPB complex has a lower helical content probably due to the conformational changes induced into the native enzyme. The appearance of new positive peaks at 315 nm in the near UV region and at 592 nm in the visible region of the CD spectra may be due to the induced asymmetry into the BPB molecule as a result of its binding to a cationic residue (probably a lysine residue) of lysozyme.(ABSTRACT TRUNCATED AT 250 WORDS)     

Thermodynamic linked-function analysis of Mg(2+)-activated yeast pyruvate kinase.

Yeast pyruvate kinase (YPK) is regulated by intermediates of the glycolytic pathway [e.g., phosphoenolpyruvate (PEP), fructose 1,6-bisphosphate (FBP), and citrate] and by the ATP charge of the cell. Recent kinetic and thermodynamic data with Mn(2+)-activated YPK show that Mn(2+) mediates the allosteric communication between the substrate, PEP, and the allosteric effector, FBP [Mesecar, A., and Nowak, T. (1997) Biochemistry 36, 6792, 6803]. These results indicate that divalent cations modulate multiligand interactions, and hence cooperativity with YPK. The nature of multiligand interactions on YPK was investigated in the presence of the physiological divalent activator Mg(2+). The binding interactions of PEP, Mg(2+), and FBP were monitored by fluorescence spectroscopy. The binding data were subject to thermodynamic linked-function analysis to determine the magnitudes of the multiligand interactions governing the allosteric activation of YPK. The two ligand coupling free energies between PEP and Mg(2+), PEP and FBP, and FBP and Mg(2+) are 0.88, -0.38, and -0.75 kcal/mol, respectively. The two-ligand coupling free energies between PEP and Mn(2+) and FBP and Mn(2+) are more negative than those with Mg(2+) as the cation. This indicates that the interactions between the divalent cation and PEP with YPK are different for Mg(2+) and Mn(2+) and that the interaction is not simply electrostatic in nature, as originally hypothesized. The magnitude of the heterotropic interaction between the metal and FBP is similar with Mg(2+) and Mn(2+). The simultaneous binding of Mg(2+), PEP, and FBP to YPK is favored by 3.21 kcal/mol compared to independent binding. This complex is destabilized by 3.30 kcal/mol relative to the analogous YPK-Mn(2+)-PEP-FDP complex. Interpretation of K(d) values when cooperative binding occurs must be done with care as these are not simple thermodynamic constants. These data demonstrate that the divalent metal, which activates phosphoryl transfer in YPK, plays a key role in modulating the various multiligand interactions that define the overall allosteric properties of the enzyme.