An equilibrium binding study of the interaction of fructose 6-phosphate and fructose 1,6-bisphosphate with rabbit muscle phosphofructokinase.

Equilibrium binding studies of the interaction of rabbit muscle phosphofructokinase with fructose 6-phosphate and fructose 1,6-bisphosphate have been carried out at 5 degrees in the presence of 1-10 mM potassium phosphate (pH 7.0 and 8.0), 5 mM citrate (pH 7.0), or 0.22 mm adenylyl imidodiphosphate (pH 7.0 and 8.0). The binding isotherms for both fructose 6-phosphate and fructose 1,6-bisphosphate exhibit negative cooperativity at pH 7.0 and 8.0 in the presence of 1-10 mM potassium phosphate at protein concentrations where the enzyme exists as a mixture of dimers and tetramers (pH 7.0) or as tetramers (pH 8.0) and at pH 7.0 in the presence of 5 mM citrate where the enzyme exists primarily as dimers. The enzyme binds 1 mol of either fructose phosphate/mol of enzyme monomer (molecular weight 80,000). When enzyme aggregation states smaller than the tetramer are present, the saturation of the enzyme with either ligand is paralleled by polymerization of the enzyme to tetramer, by an increase in enzymatic activity and by a quenching of the protein fluorescence. At protein concentrations where aggregates higher than the tetramer predominate, the fructose 1,6-bisphosphate binding isotherms are hyperbolic. These results can be quantitatively analyzed in terms of a model in which the dimer is associated with extreme negative cooperativity in binding the ligands, the tetramer is associated with less negative cooperativity, and aggregates larger than the tetramer are associated with little or no cooperativity in the binding process. Phosphate is a competitive inhibitor of the fructose phosphate sites at both pH 7.0 and 8.0, while citrate inhibits binding in a complex, noncompetitive manner. In the presence of the ATP analog adenylyl imidodiphosphate, the enzyme-fructose 6-phosphate binding isotherm is sigmoidal at pH 7.0, but hyperbolic at pH 8.0. The characteristic sigmoidal initial velocity-fructose 6-phosphate isotherms for phosphofructokinase at pH 7.0, therefore, are due to an heterotropic interaction between ATP and fructose 6-phosphate binding sites which alters the homotropic interactions between fructose 6-phosphate binding sites. Thus the homotropic interactions between fructose 6-phosphate binding sites can give rise to positive, negative, or no cooperativity depending upon the pH, the aggregation state of the protein, and the metabolic effectors present. The available data suggest the regulation of phosphofructokinase involves a complex interplay between protein polymerization and homotropic and heterotropic interactions between ligand binding sites.     

The binding of a ligand to an acceptor undergoing indefinite self-association

Explicit expressions are derived which describe the binding of a univalent ligand to equivalent and independent sites on each state of an acceptor undergoing indefinite self-association that is governed by an isodesmic equilibrium constant KI. From considerations of systems in which the same site-binding constant kA applies to all acceptor-ligand interactions, the general forms of binding curves and Scatchard plots are deduced for situations in which binding sites are either created or lost at each monomer-monomer interface. Greater generality is then introduced into the model by allowing ligand interactions with polymeric acceptor states to be governed by a site-binding constant kp that differs in magnitude from that for monomeric acceptor kA. Finally, experimental results with the glutamate dehydrogenase-GTP and lysozyme-saccharide systems are used to illustrate ways in which the present quantitative expressions may be applied to the characterization of inteactions between a ligand and an indefinitely self-associating acceptor.     

Analysis of Competition Binding Assays: Assessment of the Range of Validity of a Commonly Invoked Assumption

Abstract

A common assumption invoked in the analysis of competition binding assays is that the fractional saturation of sites with the unlabeled ligand is given by 1 - (the concentration of bound labeled ligand in the presence of unlabeled ligand)/(the concentration of bound labeled ligand in the absence of unlabeled ligand). This assumption is critically evaluated in the context of several binding models: (a) binding of univalent ligands to multiple classes of equivalent and independent sites, with and without nonspecific binding; (b) cooperative binding of univalent ligands; and (c) binding of multivalent ligands to a single class of univalent acceptors. We show that the conventional assumption is only valid when the labeled ligand is mainly in the free form, occupies a small fraction of the total sites and binds univalently to all sites in an equivalent and independent manner, and when the unlabeled ligand forms l : l complexes with the acceptor sites. When these conditions are satisfied, the conventional assumption is valid even if the unlabeled ligand binds to nonequivalent sites or exhibits cooperativity. Finally, we apply the theory derived for case (a) above to the binding of fluoresceinated epidermal growth factor to A431 cells and demonstrate that the analysis of data obtained from both conventional and competition assays provides information which is difficult, if not impossible, to obtain from either assay alone.     

An equilibrium study of the cooperative binding of adenosine cyclic 3',5'-monophosphate and guanosine cyclic 3',5'-monophosphate to the adenosine cyclic 3',5'-monophosphate receptor protein from Escherichia coli

The binding of adenosine cyclic 3',5'-monophosphate (cAMP) and guanosine cyclic 3',5'-monophosphate (cGMP) to the adenosine cyclic 3',5'-monophosphate receptor protein (CRP) from Escherichia coli was investigated by equilibrium dialysis at pH 8.0 and 20 degrees C at different ionic strengths (0.05--0.60 M). Both cAMP and cGMP bind to CRP with a negative cooperativity that is progressively changed to positive as the ionic strength is increased. The binding data were analyzed with an interactive model for two identical sites and site/site interactions with the interaction free energy--RT ln alpha, and the intrinsic binding constant K and cooperativity parameter alpha were computed. Double-label experiments showed that cGMP is strictly competitive with cAMP, and its binding parameters K and alpha are not very different from that for cAMP. Since two binding sites exist for each of the cyclic nucleotides in dimeric CRP and no change in the quaternary structure of the protein is observed on binding the ligands, it is proposed that the cooperativity originates in ligand/ligand interactions. When bound to double-stranded deoxyribonucleic acid (dsDNA), CRP binds cAMP more efficiently, and the cooperativity is positive even in conditions of low ionic strength where it is negative for the free protein. By contrast, cGMP binding properties remained unperturbed in dsDNA-bound CRP. Neither the intrinsic binding constant K nor the cooperativity parameter alpha was found to be very sensitive to changes of pH between 6.0 and 8.0 at 0.2 M ionic strength and 20 degrees C. For these conditions, the intrinsic free energy and entropy of binding of cAMP are delta H degree = -1.7 kcal . mol-1 and delta S degree = 15.6 eu, respectively.     

Effects of heterogeneity and cooperativity on the forms of binding curves for multivalent ligands

An exploratory investigation is made of the binding behavior that is likely to be encountered with multivalent ligands under circumstances where a single intrinsic binding constant does not suffice to describe all acceptor-ligand interactions. Numerical simulations of theoretical binding behavior have established that current criteria for recognizing heterogeneity and cooperativity of acceptor sites on the basis of the deviation of the binding curve from rectangular hyperbolic form for univalent ligands also apply to the interpretation of the corresponding binding curves for multivalent ligands. However, for systems in which the source of the departure from equivalence and independence of binding sites resides in the ligand, these criteria are reversed. On the basis of these observations a case is then made for attributing results of an experimental binding study of the interaction between pyruvate kinase and muscle myofibrils to positive cooperativity of enzyme sites rather than to heterogeneity or negative cooperativity of the myofibrillar sites.     

Measures of cooperativity in the binding of ligands to proteins and their relation to non-additivity in protein-protein interactions

The analogy between cooperativity in the binding of ligands to proteins and non-additivity in protein-protein interactions is demonstrated and discussed in terms of the Wong and the Hill coefficients. A measure of non-additivity, the interaction constant, is rigorously derived for four thermodynamic cycles, involving the binding of small molecules to proteins and protein association. It is the reciprocal of the 'defect factor' of Laskowski et al. in Proteinase inhibitors: medical and biological aspects (ed. N. Katunuma et al.), pp. 55-68 (1983), and its logarithm is the Wong measure of cooperativity. These three measures are thus here given a common theoretical basis. The Hill coefficient for an asymmetric dimer that binds two different ligands which do not compete for the same site, at 50% saturation of each site, is derived. It is shown to be a function of the interaction constant and of the fraction of protein to which ligand is bound at both sites. These relations for protein-ligand interactions are then discussed in the context of non-additivity in protein-protein interactions.     

Ligand-induced DNA condensation: choosing the model

We test and compare different models for ligand-induced DNA condensation. Using 14C-labeled spermidine3+, we measure the binding to condensed DNA at micromolar to molar polyamine concentrations. DNA aggregates at a critical polyamine concentration. Spermidine3+ binding becomes highly cooperative at the onset of aggregation. At higher concentrations, spermidine3+ binding to condensed DNA reaches a plateau with the degree of binding equal to 0.7 (NH(4+)/PO3-). Condensed DNA exists in a wide range of spermidine concentrations with the roughly constant degree of ligand binding. At greater concentrations, the degree of binding increases again. Further spermidine penetration between the double helices causes DNA resolubilization. We show that a simple two-state model without ligand-ligand interactions qualitatively predicts the reentrant aggregation-resolubilization behavior and the dependence on the ligand, Na+, and DNA concentrations. However, such models are inconsistent with the cooperative ligand binding to condensed DNA. Including the contact or long-range ligand-ligand interactions improves the coincidence with the experiments, if binding to condensed DNA is slightly more cooperative than to the starting DNA. For example, in the contact interaction model it is equivalent to an additional McGhee-von Hippel cooperativity parameter of approximately 2. Possible physical mechanisms for the observed cooperativity of ligand binding are discussed.     

Sequence distribution and intercooperativity detection for two ligands simultaneously binding to DNA

A method for detecting and quantifying the cooperativity in the simultaneous binding of two ligands, A and B, to DNA (intercooperativity; omega(AB)) is proposed. This involves the determination of an apparent affinity constant K(app) for one of the ligands (A) in the limit of its null saturation (nu(Alpha) --> 0), in the presence of the second one (B). A definition for this constant is given and an expression is derived corresponding to a simple model of competitive binding to an unbranched three-state homogeneous polar lattice with nearest-neighbor interactions (Markov chain). The ratio between the apparent and intrinsic affinity constants of one ligand in the maximum saturation limit of the other one becomes omega(2)(AB), and thus can be graphically obtained from K(app)(A) vs nu(B) plots. All the frequencies that define the sequence distribution of ligands can be easily calculated by introducing some generalized statistical weights for the free lattice monomer in a standard sequence generating function procedure. A model of fluorescence quenching emission is obtained from such frequencies under the hypothesis of a short-range electron transfer mechanism of the deactivation; it confirms, as suggested by the binding model, an outstanding influence of the intercooperativity on the distribution.     

Linked-function origins of cooperativity in a symmetrical dimer

The thermodynamic origins of substrate binding cooperativity in a dimeric enzyme that can bind one substrate (A) and one allosteric ligand (X) to each of two identical subunits are discussed. It is assumed that maximal activity is not subject to allosteric modification and that the substrates and allosteric ligands achieve binding equilibrium in the steady state. Each uniquely ligated form is assumed to be capable of exhibiting unique binding properties, and only the principles of thermodynamic linkage are used to constrain the system further. The explicit relationship between the Hill coefficient, the concentration of X, and the magnitudes of the relevant coupling free energies and dissociation constants is derived. In the absence of X only the homotropic coupling between substrate sites contributes to a nonhyperbolic substrate saturation profile. An allosteric ligand, X, can alter the cooperativity in two distinct ways, one mechanism being manifested when X is saturating and the only only when X is present at saturating concentrations. By evaluating the concentration of substrate required to produce half-maximal velocity as a function of [X], as well as the Hill coefficients when X is absent and fully saturating, the dissociation and coupling constants most important for understanding the mechanisms of allosteric action in an enzyme of this type can be determined.     

Thermodynamic model of cooperativity in a dimeric protein: unique and independent parameters formulation.

A model of the cooperative interaction of ligand binding to a dimeric protein is presented based upon the unique and independent parameters (UIP) thermodynamic formulation (Gutheil and McKenna, Biophys. Chem. 45 (1992) 171-179). The analysis is developed from an initial model which includes coupled conformational and ligand binding equilibria. This completely general model is then restricted to focus on conformationally mediated cooperative interactions between the ligands and the expressions for the apparent ligand binding constant and the apparent ligand-ligand interaction constant are derived. The conditions under which there is no cooperative interaction between the ligands are found as roots to a polynomial equation. Consideration of the distribution of species among the various conformational states in this general model leads to a set of inequalities which can be represented as a two dimensional plot of boundaries. By superimposing a contour plot of the value of the apparent ligand-ligand interaction constant over the plot of boundaries a complete graphical representation of this system is achieved similar to a phase diagram. It is found that the parameter space homologous to Koshland-Nemethy-Filmer type of model is most consistent with both positive and negative cooperativity in this model. The maximal amount of positive and negative cooperativity are found to be simple functions of Kc, the equilibrium constant associated with the change of a subunit and ligand from the unligated to ligated conformation. It is shown that under certain limiting conditions the apparent allosteric interaction between ligands is equal to the conformational interaction between subunits. The methods presented are generally applicable to the theoretical analysis of thermodynamic interactions in complex systems.     

A simple model for proteins with interacting domains. Applications to scanning calorimetry data

A simple thermodynamic model is formulated for the purpose of interpreting scanning calorimetry data on proteins that have interacting domains. Interactions are quantified by inclusion of an interface free energy, delta GAB, in the thermodynamics of unfolding for multidomain proteins. The assumption is made that delta GAB goes to zero with the unfolding of either domain involved in pairwise interaction, so the interaction term appears to stabilize only the domain with the lower TM. Application of the model to calorimetric data leads to an estimate of -25,000 cal/mol for interactions between the regulatory and catalytic subunits of native aspartate transcarbamoylase and to a value of 0 for delta GAB between the transmembrane and cytoplasmic domains of band 3 of the human erythrocyte membrane. Estimates of changes in delta GAB are also obtained for mutant forms of yeast phosphoglycerate kinase that have been altered in the hinge region between amino-terminal and carboxy-terminal domains. The model is also applied to ligand binding to proteins having domains that communicate through pairwise interaction. It is shown that whenever the delta GAB term is ligand-dependent, then attachment of the ligand to the binding domain will be partially controlled by the other (regulatory) domain. This situation can sometimes be recognized and quantified when calorimetric scans are carried out at varying ligand concentrations. According to the model, the binding of MgATP to the carboxy-terminal domain of phosphoglycerate kinase is strongly stabilized (ca. 20% of the unitary free energy of binding) by participation of the amino-terminal domain, which acts to increase the binding constant 25-fold.(ABSTRACT TRUNCATED AT 250 WORDS)     

DNA bis-intercalation: Theoretical calculation of binding curves

A statistical mechanical calculation of the binding properties of DNA bis-intercalators is presented, based on the sequence-generating function method of Lifson. The effects of binding by intercalation of one or both chromophores of a bifunctional intercalating agent are examined. The secular equation for a general model that includes the effects of neighbor (nearest and non-nearest) exclusion and/or cooperativity in the binding of both singly and doubly intercalated ligands is derived. Numerical results for binding curves are presented for a more restricted model in which each type of bound ligand rigorously excludes its nearest neighbor and the total number of sites covered by a doubly intercalated ligand is variable. At low values of free ligand concentration bis-intercalation dominates the binding process, while at high value of free ligand concentration, intercalation of only one chromophore per ligand becomes significant due to the unavailability of contiguous free sites required for bis-intercalation. Also, depending on the binding parameters, the free energy of the system can be lowered by a loss of doubly intercalated ligands in favor of singly intercalated ones. Corresponding to this transition in binding mode, the average number of sites occupied by a bound ligand decreases from that characteristic of bis-intercalation to that characteristic of mono-intercalation as free ligand concentration increases. An analysis of Scatchard plots describing bis-intercalation is presented.     

The relationship between effector binding and inhibition of activity in D-3-phosphoglycerate dehydrogenase

The binding of L-serine to phosphoglycerate dehydrogenase from Escherichia coli displays elements of both positive and negative cooperativity. At pH 7.5, approximately 2 mol of serine are bound per mole of tetrameric enzyme. A substantial degree of positive cooperativity is seen for the binding of the second ligand, but the binding of the third and fourth ligand display substantial negative cooperativity. The data indicate a state of approximately 50% inhibition when only one serine is bound and approximately 80-90% inhibition when two serines are bound. This is consistent with the tethered domain hypothesis that has been presented previously. Comparison of the data derived directly from binding stoichiometry to the binding constants determined from the best fit to the Adair equation, produce a close agreement, and reinforce the general validity of the derived binding constants. The data also support the conclusion that the positive cooperativity between the binding to the first and second site involves binding sites at opposite interfaces over 110 A apart. Thus, an order of binding can be envisioned where the binding of the first ligand initiates a conformational transition that allows the second ligand to bind with much higher affinity at the opposite interface. This is followed by the third ligand, which binds with lesser affinity to one of the two already occupied interfaces, and in so doing, completes a global conformational transition that produces maximum inhibition of activity and an even lower affinity for the fourth ligand, excluding it completely. Thus, maximal inhibition is accomplished with less than maximal occupancy of effector sites through a mechanism that displays strong elements of both positive and negative cooperativity.     

The concentration dependence of active K+ transport in the turkey erythrocyte. Hill analysis and evidence for positive cooperativity between ion binding sites

A mathematical model is presented which describes the theoretical relationship between ligand concentration and physiological response for systems in which the response is dependent upon simultaneous occupancy of two receptor ligand-binding sites. The treatment considers both the possibility of intrinsic differences between the binding sites with regard to ligand affinity, as well as the possibility of mutually induced changes in affinity resulting from allosteric interactions. Unlike the Monod-Wyman-Changeux formulation for allosteric enzymes, the general model put forward here makes double occupancy an absolute requirement for enzymatic function. It is shown that such a model leads to the prediction of a curvilinear Hill plot from which one can obtain an explicit estimate of the degree of allosteric interaction between the two ligand binding sites as well as the Gibbs standard free energy change for the overall binding reaction. It is then shown that, in the specific instance of Na, K-ATPase-mediated K+ transport by the turkey erythrocyte, the configuration of the Hill curve describing the rate of ouabain-sensitive K+ transport as a function of external K+ concentration conforms closely to that predicted by the model described above. The results are of particular interest because they indicate a strongly cooperative interaction between the two K+ binding sites on the transport protein such that occupancy of one site results in an enhancement of the affinity of the other site for K+ by a minimum of 15- to 20-fold. Finally, we consider in detail a model of the Monod-Wyman- Changeux type in which, by contrast, both singly and doubly occupied forms of the enzyme are assumed to be catalytically active, and which we analogously extend to allow for the possibility of asymmetry between the two ligand binding sites. Although it is shown that the two models can not be differentiated from each other in the present experimental system, they yield virtually identical estimates for the degree of positive cooperativity between the two K+ binding sites.     

Analysis of individual-site binding data.

Individual-site isotherms add experimental data which may allow for a more detailed definition of the parameters in a system with interacting binding sites. Individual-site isotherms accomplish the following: (A) In general, they define little more than the total or combined isotherm except to reveal the existence of different sites. (B) Under the limiting conditions of symmetrical interactions in two site systems they define: (1) the ratio of the unperturbed or intrinsic binding constants rather than their actual values, (2) the unperturbed shape of the total isotherm, that is, the shape of the total isotherm if there were no ligand dependent interactions between the sites, and (3) the perturbation of the shape of the total isotherm derived from interactions between the sites. (C) They do not define the nature of the interactions; that is, they do not resolve the free energies of the interactions between the sites. (D) When some assumptions about the nature of the interactions are made they may aid in defining some free energies of interaction between the sites.     

Cooperative ligand-lattice binding. Approximate Gaussian binding distribution

Nearest-neighbor cooperative binding of a ligand covering n sites and binding with equilibrium constant K and cooperativity factor omega to a large molecule with m binding sites (m much greater than n omega, n/omega) can be approximately described by a Gaussian distribution P(q-qmax), where q is the number of ligands bound and qmax the most probable value of q. The variance of the Gaussian is equal to the derivative dqmax/d ln(L), where L is the free ligand concentration. This variance, sigma 2, is a complicated function of qmax. However, in the limits of very large cooperativity, omega much greater than 1, very large anticooperativity, omega much less than 1, or noncooperativity, omega = 1, simpler expressions for sigma 2 can be given. For qmax = m/(n + 1), where the most probable number of bound ligands equals the number of free binding sites, sigma 2 has a particularly simple form: sigma 2 = 2m omega 1/2/(n + 1)3. The Gaussian and the infinite lattice approximations for the average number of ligands bound are good approximations only if sigma is much smaller than the number of binding sites. The variance may therefore provide an easy check on the validity of the infinite lattice approximation, which is commonly used to analyze experimental binding data.     

Quantitative measurements of the cooperativity in an EF-hand protein with sequential calcium binding.

Positive cooperativity, defined as an enhancement of the ligand affinity at one site as a consequence of binding the same type of ligand at another site, is a free energy coupling between binding sites. It can be present both in systems with sites having identical ligand affinities and in systems where the binding sites have different affinities. When the sites have widely different affinities such that they are filled with ligand in a sequential manner, it is often difficult to quantify or even detect the positive cooperativity, if it occurs. This study presents verification and quantitative measurements of the free energy coupling between the two calcium binding sites in a mutant form of calbindin D9k. Wild-type calbindin D9k binds two calcium ions with similar affinities and positive cooperativity--the free energy coupling, delta delta G, is around -8 kJ.mol-1 (Linse S, et al., 1991, Biochemistry 30: 154-162). The mutant, with the substitution Asn 56-->Ala, binds calcium in a sequential manner. In the present work we have taken advantage of the variations among different metal ions in terms of their preferences for the two binding sites in calbindin D9k. Combined studies of the binding of Ca2+, Cd2+, and La3+ have allowed us to conclude that in this mutant delta delta G < -6.4 kJ.mol-1, and that Cd2+ and La3+ also bind to this protein with positive cooperativity. The results justify the use of the (Ca2+)1 state of the Asn 56-->Ala mutant, as well as the (Cd2+)1 state of the wild type, as models for the half-saturated states along the two pathways of cooperative Ca2+ binding in calbindin D9k.     

Determining binding sites of polycyclic aromatic small molecule-based amyloid-beta peptide aggregation modulators using sequence-specific antibodies

Numerous aromatic small molecule modulators of amyloid-beta peptide (Aβ) monomer aggregation and neurotoxicity have been identified with the ultimate goal of Alzheimer’s disease (AD) treatment. Determining binding sites of these modulators on Aβ monomer is an important topic in the mechanistic understanding of AD pathology and drug development. However, Aβ monomer binding sites have been reported for only a very limited number of Aβ modulators. In this article, we present a convenient method for determining aggregation-modulating polycyclic aromatic small molecule ligand binding sites on Aβ monomer using immunostaining with a panel of Aβ sequence-specific antibodies. To validate our technique, we first examined one modulating aromatic ligand, Congo Red, with known binding sites, which yielded consistent results with previous findings. Then, using the same technique, binding sites on Aβ of four known Aβ monomer aggregation modulators, Erythrosin B, Eosin Y, Phloxine B, and Rose Bengal, were determined. The identified ligand binding sites were also confirmed by a separate fluorescence quenching-based assay using a panel of overlapping Aβ sub-fragments. The technique described here greatly increases researchers’ ability to determine the Aβ monomer binding site(s) of aggregation-modulating aromatic small molecule ligands and to screen for new ligands that bind specific regions on Aβ.     

Cooperativity: over the Hill

Cooperativity, the ability of ligand binding at one site on a macromolecule to influence ligand binding at a different site on the same macromolecule, is a fascinating biological property that is often poorly explained in textbooks. The Hill coefficient is commonly used in biophysical studies of cooperative systems although it is not a quantitative measure of cooperativity. The free energy of interaction between binding sites (ΔΔG) is a more stringent definition of cooperativity and provides a direct quantitative measure of how the binding of ligand at one site affects the ligand affinity of another site.