Cooperativity of ligand binding as a function of monomer-dimer equilibrium parameters and acceptor concentration

A general monomer-dimer equilibrium system involving ligand interactions ispresented. Cooperativity features of specific limited models are analyzed by selecting the appropriate family of equilibrium constants from this general scheme. Each system is then characterized in terms of Hill coefficient dependency on alterations in values of equilibrium constants and total acceptor concentration. This method permits comparison of predicted cooperativity trends between systems. Contrasting reports concerning cooperativity dependencies for certain defined equilibrium systems are compared and the discrepancies resolved. Characteristics of cooperativity binding patterns are shown to include symmetry about dimerization association constant values, both positive and negative cooperativity for a single set of parameters, and significant changes in cooperativity features with relatively small changes in equilibrium parameters.     

Cooperative binding to the Ca2+-specific sites of troponin C in regulated actin and actomyosin

The Ca2+-binding component of troponin (TnC) and its proteolytic fragments containing Ca2+-binding sites I-III (TH1) or sites III and IV (TR2C) have been labeled with the fluorescent probes dansylaziridine (DANZ) at methionine 25 or 5-(iodoacetamidoethyl)amino-naphthalene-1-sulfonic acid (AEDANS) at cysteine-98. These probes report binding of Ca2+ to the low and high affinity sites, respectively. Fluorescence changes as a function of [Ca2+] were measured for the free peptides, their complexes with troponin I + troponin T, and these complexes bound to actin-tropomyosin in the presence of Mg2+ and ATP with and without myosin. An apparent Hill coefficient of 1.0-1.1 has been obtained for the Ca2+-induced fluorescence changes in TnC, its fragments, and their ternary complexes regardless of the label used. When a ternary complex containing appropriately labeled TnC or its fragment is bound to the actin-tropomyosin complex, the Hill coefficient for the titration of the low affinity sites increases to 1.5-1.6 and further increases to greater than 2 in the presence of myosin. To interpret the apparent Hill coefficients, we used a model containing two binding sites and a single reporter of the conformational change. Hill coefficients between 1.0 and 1.2 can be obtained for the fluorescence change without true cooperativity in metal binding, depending on the mechanism of the fluorescence change; i.e. the contribution of the singly or doubly occupied species to the fluorescence change. A Hill coefficient between 1.2 and 2, however, always indicates cooperativity in binding independently of the mechanism. Thus, our finding that fluorescence titrations of Ca2+ binding to TnCDANZ bound to actin-tropomyosin exhibit a Hill coefficient of 1.5 in the absence of myosin and 2.4 in its presence indicates the existence of true positive cooperativity in metal binding to sites I and II. No cooperativity was observed for AEDANS-labeled complexes that reflect Ca2+-binding to the high affinity sites. Plots of the Ca2+ dependence of myosin ATPase activity activated by actin-tropomyosin in the presence of any of the troponin complexes used had apparent Hill coefficients of approximately 4. The higher value suggests cooperative interactions in the activation of ATPase beyond those involved in Ca2+-binding to the Ca2+-specific sites.     

Interaction of muscle glycogen phosphorylase B with methotrexate, folic and folinic acids

The interaction of rabbit skeletal muscle glycogen phosphorylase b with methotrexate, folic and folinic acids has been studied. Microscopic dissociation constant for the glycogen phosphorylase b--methotrexate complex determined by analytical ultracentrifugation is 0.43 mM. A subunit of glycogen phosphorylase b is shown to have two sites for methotrexate binding. AMP and FMN diminish the affinity of glycogen phosphorylase b to methotrexate, whereas glycogen does not influence the methotrexate binding to the enzyme. Methotrexate, folic and folinic acids are found to be inhibitors of the muscle glycogen phosphorylase b. The inhibition is reversible and characterized by positive kinetic cooperativity (the Hill coefficient exceeds one unity). The value of the pterin concentration causing two-fold diminishing of the enzymatic reaction rate increased in the order: folic acid (0.65 mM), methotrexate (1.01 mM), folinic acid (3.7 mM). The antagonism between methotrexate, folic and folinic acids, on the one hand, and AMP and FMN, on the other, is revealed for their combined action.     

(Na+, K+)-activated adenosinetriphosphatase of axonal membranes, cooperativity and control. Steady-state analysis.

1. The ATP sites. Homotropic interactions between ATP sites have been studied in a very large range of Na+ and K+ concentrations. The ( Na+, K+)-activated ATPase displays Michaelis-Menten kinetics for ATP under standard concentration conditions of Na+ (100 mM) and K+ (10 mM). The steady-state kinetics behavior changes at very low concentrations of K+ where negative cooperativity is observed. The existence of a high affinity and a low affinity site for ATP was clearly demonstrated from the study of the ATP stimulated hydrolysis of p-nitrophenylphosphate in the presence of Na+ and K+. The ratio of apparent affinities of high and low affinity sites for ATP is 86 at pH 7.5. 2. The Na+ sites. The binding of Na+ to its specific stimulatory sites (internal sites) is characterized by positive cooperativity with a Hill coefficient n(H(Na+))=2.0. Homotropic interactions between Na+ sites are unaffected by variations of the K+ concentration. 3. The K+ sites. (a) Binding of K+ to the (external) stimulatory site of the ATPase has been analyzed by following the (Na+, K+)-ATPase activity as well as the p-nitrophenylphosphatase activity in the presence of Na+ and K+ (with or without ATP). Binding is characterized by a Hill coefficient of 1.0 and a K(0.5(K+))=0.1 to 0.8 mM. The absence of positive or negative cooperativity persists between 5 mM and 100 mM Na+. (b) The analysis of the p-nitrophenylphosphatase or of the 2, 4 dinitrophenylphosphatase activity in the presence of K+ alone indicates the existence of low affinity sites for K+ with positive homotropic interactions. The characteristics of stimulation in that case are, K(0.5)=5 mM, n(H)=1.9. The properties of this family of site(s) are the following: firstly, saturation of the low affinity site(s) by K+ prevents ATP binding to its high affinity internal site. Secondly, saturation of the low affinity sites for K+ prevents binding of Na+ to its internal sites. Thirdly, this family of sites disappears in the presence of ATP, p-nitrophenylphosphate or of both substrates, when Na+ binds to its internal sites. Na+ binding to its specific stimulatory sites provokes the formation of the high affinity type of site for K+. 4. Mg2+ stimulation of the (Na+, K+)-ATPase is characterized by a Hill coefficient n(H(Mg2+))=1.0 and a K(0.5(Mg2+))=1 mM stimulation is essentially a V effect. Heterotropic effects between binding of Mg2+ and substrate to their respective sites are small. Heterotropic interactions between the Ms2+, Na+ and K+ sites are also small. 5. The fluidity of membrane lipids also controls the (Na+, K+)-ATPase activity. Phase transitions or separations in the membrane hardly affect recognition properties of substrates, Na+, K+ and Mg2+ for their respective sites on both sides of the membrane. Only the rate of the catalytic transformation is affected.     

Negative cooperativity associated with binding of multivalent carbohydrates to lectins. Thermodynamic analysis of the "multivalency effect".

Our previous study demonstrated that isothermal titration microcalorimetry (ITC) could be used to determine the thermodynamics of binding of a series of synthetic multivalent carbohydrates to the Man/Glc-specific lectins concanavalin A (ConA) and Dioclea grandiflora lectin (DGL) [Dam, T. K., Roy, R., Das, S. K., Oscarson, S. and Brewer, C. F. (2000) J. Biol. Chem. 275, 14223-14230]. The higher affinities of the multivalent carbohydrates for the two lectins were shown to be due to their greater positive entropy of binding contributions relative to monovalent analogues. In the present study, ITC data from our previous report for binding of di-, tri-, and tetravalent carbohydrate analogues possessing terminal 3,6-di-O-(alpha-D-mannopyranosyl)-alpha-D-mannopyranoside residues to ConA and DGL were subjected to Hill plot analysis. Hill plots of the binding of monovalent methyl 3,6-di-O-(alpha-D-mannopyranosyl)-alpha-D-mannopyranoside to ConA and DGL are linear with slopes near 1.0, demonstrating a lack of binding cooperativity and allosteric transitions in the proteins. However, Hill plots for the binding of the di-, tri-, and tetravalent trimannoside analogues to both lectins are curvilinear with decreasing tangent slopes below 1.0, indicating increasing negative cooperativity upon binding of the analogues to the lectins. The curvilinear Hill plots are consistent with decreasing affinity and functional valencies of the multivalent analogues upon sequential binding of lectin molecules to the carbohydrate epitopes of the analogues. The following paper [Dam, T. K., Roy, R., Pagé, D., and Brewer, C. F. (2002) Biochemistry 41, 1359-1363] provides direct evidence of the decreasing affinity constants of multivalent carbohydrates upon sequential binding of lectin molecules.     

Effects of clustered epitopes in multivalent ligand-receptor interactions

Many biological ligands are composed of clustered binding epitopes. However, the effects of clustered epitopes on the affinity of ligand-receptor interactions in many cases are not well understood. Clustered carbohydrate epitopes are present in naturally occurring multivalent carbohydrates and glycoproteins, which are receptors on the surface of cells. Recent studies have provided evidence that the enhanced affinities of lectins, which are carbohydrate binding proteins, for multivalent carbohydrates and glycoproteins are due to internal diffusion of lectin molecules from epitope to epitope in these multivalent ligands before dissociation. Indeed, binding of lectins to mucins, which are large linear glycoproteins, appears to be similar to the internal diffusion mechanism(s) of protein ligands binding to DNA, which have been termed the "bind and slide" or "bind and hop" mechanisms. The observed increasing negative cooperativity and gradient of decreasing microaffinity constants of a lectin binding to multivalent carbohydrates and glycoproteins result in an initial fraction of lectin molecules that bind with very high affinity and dynamic motion. These findings have important implications for the mechanisms of binding of lectins to mucins, and for other ligand-biopolymer interactions and clustered ligand-receptor systems in general.     

Oxygen binding by alpha(Fe2+)2beta(Ni2+)2 hemoglobin crystals

Oxygen binding by hemoglobin fixed in the T state either by crystallization or by encapsulation in silica gels is apparently noncooperative. However, cooperativity might be masked by different oxygen affinities of alpha and beta subunits. Metal hybrid hemoglobins, where the noniron metal does not bind oxygen, provide the opportunity to determine the oxygen affinities of alpha and beta hemes separately. Previous studies have characterized the oxygen binding by alpha(Ni2+)2beta(Fe2+)2 crystals. Here, we have determined the three-dimensional (3D) structure and oxygen binding of alpha(Fe2+)2beta(Ni2+)2 crystals grown from polyethylene glycol solutions. Polarized absorption spectra were recorded at different oxygen pressures with light polarized parallel either to the b or c crystal axis by single crystal microspectrophotometry. The oxygen pressures at 50% saturation (p50s) are 95 +/- 3 and 87 +/- 4 Torr along the b and c crystal axes, respectively, and the corresponding Hill coefficients are 0.96 +/- 0.06 and 0.90 +/- 0.03. Analysis of the binding curves, taking into account the different projections of the alpha hemes along the optical directions, indicates that the oxygen affinity of alpha1 hemes is 1.3-fold lower than alpha2 hemes. Inspection of the 3D structure suggests that this inequivalence may arise from packing interactions of the Hb tetramer within the monoclinic crystal lattice. A similar inequivalence was found for the beta subunits of alpha(Ni2+)2beta(Fe2+)2 crystals. The average oxygen affinity of the alpha subunits (p50 = 91 Torr) is about 1.2-fold higher than the beta subunits (p50 = 110 Torr). In the absence of cooperativity, this heterogeneity yields an oxygen binding curve of Hb A with a Hill coefficient of 0.999. Since the binding curves of Hb A crystals exhibit a Hill coefficient very close to unity, these findings indicate that oxygen binding by T-state hemoglobin is noncooperative, in keeping with the Monod, Wyman, and Changeux model.     

Attractant regulation of the aspartate receptor-kinase complex: limited cooperative interactions between receptors and effects of the receptor modification state

The manner by which the bacterial chemotaxis system responds to a wide range of attractant concentrations remains incompletely understood. In principle, positive cooperativity between chemotaxis receptors could explain the ability of bacteria to respond to extremely low attractant concentrations. By utilizing an in vitro receptor-coupled kinase assay, the attractant-dependent response curve has been measured for the Salmonella typhimurium aspartate chemoreceptor. The attractant chosen, alpha-methyl aspartate, was originally used to quantitate high receptor sensitivity at low attractant concentrations by Segall, Block, and Berg [(1986) Proc. Natl. Acad. Sci. U.S.A. 83, 8987-8991]. The attractant response curve exhibits limited positive cooperativity, yielding a Hill coefficient of 1.7-2.4, and this Hill coefficient is relatively independent of both the receptor modification state and the mole ratio of CheA to receptor. These results disfavor models in which there are strong cooperative interactions between large numbers of receptor dimers in an extensive receptor array. Instead, the results are consistent with cooperative interactions between a small number of coupled receptor dimers. Because the in vitro receptor-coupled kinase assay utilizes higher than native receptor densities arising from overexpression, the observed positive cooperativity may overestimate that present in native receptor populations. Such positive cooperativity between dimers is fully compatible with the negative cooperativity previously observed between the two symmetric ligand binding sites within a single dimer. The attractant affinity of the aspartate receptor is found to depend on the modification state of its covalent adaptation sites. Increasing the the level of modification decreases the apparent attractant affinity at least 10-fold in the in vitro receptor-coupled kinase assay. This observation helps explain the ability of the chemotaxis pathway to respond to a broad range of attractant concentrations in vivo.     

On the role of enzyme cooperativity in metabolic oscillations: analysis of the Hill coefficient in a model for glycolytic periodicities.

The role of enzyme cooperativity in the mechanism of metabolic oscillations is analyzed in a concerted allosteric model for the phosphofructokinase reaction. This model of a dimer enzyme activated by the reaction product accounts quantitatively for glycolytic periodicities observed in yeast and muscle. The Hill coefficient characteristic of enzyme-substrate interactions is determined in the model, both at the steady state and in the course of sustained oscillations. Positive cooperativity is a prerequisite for periodic behavior. A necessary condition for oscillation in a dimer K system is a Hill coefficient larger than 1.6 at the unstable stationary state. The analysis suggests that positive as well as negative effectors of phosphofructokinase inhibit glycolytic oscillations by inducing a decrease in enzyme cooperativity. The results are discussed with respect to glycolytic and other metabolic periodicities.     

Binding Cooperativity Matters: A GM1-Like Ganglioside-Cholera Toxin B Subunit Binding Study Using a Nanocube-Based Lipid Bilayer Array

Protein-glycan recognition is often mediated by multivalent binding. These multivalent bindings can be further complicated by cooperative interactions between glycans and individual glycan binding subunits. Here we have demonstrated a nanocube-based lipid bilayer array capable of quantitatively elucidating binding dissociation constants, maximum binding capacity, and binding cooperativity in a high-throughput format. Taking cholera toxin B subunit (CTB) as a model cooperativity system, we studied both GM₁ and GM₁-like gangliosides binding to CTB. We confirmed the previously observed CTB-GM₁ positive cooperativity. Surprisingly, we demonstrated fucosyl-GM₁ has approximately 7 times higher CTB binding capacity than GM₁. In order to explain this phenomenon, we hypothesized that the reduced binding cooperativity of fucosyl-GM₁ caused the increased binding capacity. This was unintuitive, as GM₁ exhibited higher binding avidity (16 times lower dissociation constant). We confirmed the hypothesis using a theoretical stepwise binding model of CTB. Moreover, by taking a mixture of fucosyl-GM₁ and GM₂, we observed the mild binding avidity fucosyl-GM₁ activated GM₂ receptors enhancing the binding capacity of the lipid bilayer surface. This was unexpected as GM₂ receptors have negligible binding avidity in pure GM₂ bilayers. These unexpected discoveries demonstrate the importance of binding cooperativity in multivalent binding mechanisms. Thus, quantitative analysis of multivalent protein-glycan interactions in heterogeneous glycan systems is of critical importance. Our user-friendly, robust, and high-throughput nanocube-based lipid bilayer array offers an attractive method for dissecting these complex mechanisms.     

Cofactor binding to Escherichia coli D-3-phosphoglycerate dehydrogenase induces multiple conformations which alter effector binding

The inhibition of Escherichia coli d-3-phosphoglycerate dehydrogenase by l-serine is positively cooperative with a Hill coefficient of approximately 2, whereas the binding of the inhibitor, l-serine, to the apoenzyme displays positive cooperativity in the binding of the first two serine molecules and negative cooperativity in the binding of the last two serine molecules. An earlier report demonstrated that the presence of phosphate appeared to lessen the degree of both the positive and negative cooperativity, but the cause of this effect was unknown. This study demonstrates that the presence of intrinsically bound NADH was responsible to a substantial degree for this effect. In addition, this study also provides evidence for negative cooperativity in NADH binding and for at least two NADH-induced conformational forms of the enzyme that bind the inhibitor in the physiological range. Successive binding of NADH to the enzyme resulted in an increase in the affinity for the first inhibitor ligand bound and a lessening of both the positive and negative cooperativity of inhibitor binding as compared with that seen in the absence of NADH. This effect was specific for NADH and was not observed in the presence of NAD+ or the substrate alpha-ketoglutarate. Conversely, the binding of l-serine did not have a significant effect on the stoichiometry of NADH binding, consistent with it being a V-type allosteric system. Thus, cofactor-related conditions were found in equilibrium binding experiments that significantly altered the cooperativity of inhibitor binding. Since the result of inhibitor binding is a reduction in the catalytic activity, the binding of inhibitor to these NADH-induced conformers must also induce additional conformations that lead to differential inhibition of catalytic activity.     

Kinetic cooperativity in the concerted model for allosteric enzymes.

The cooperativity of enzyme-substrate interactions is investigated in the concerted allosteric model of Monod, Wyman and Changeux. The general case of K-V systems is considered, in which the two protomer conformational states R and T postulated in the theory differ in catalytic and binding properties. An expression for the Hill coefficient nH defined with respect to the asymptotic velocity V infinity to is analyzed in conditions which exclude substrate inhibition. Kinetic cooperativity is always positive (nH greater than 1) in the case of a dimer enzyme, and in the case of an inactive T state. Slight kinetic negative cooperativity (nH less than 1) occurs under restrictive conditions for larger numbers of protomers when the substrate binds significantly to the less active state of the enzyme, but the phenomenon remains negligible for trimers and tetramers. These conclusions differ from those obtained [A. Goldbeter, J. Mol.Biol.90 (1974) 185] with the Hill coefficient based on the absolute maximum velocity, which may exceed the experimental value V infinity to in K-V systems. The results extend those of Paulus and DeRiel [J. Mol. Biol. 97 (1975) 667] and support the view that in most cases, negative cooperativity is not compatible with a mechanism based on a concerted and conservative allosteric transition. The Hill coefficients for binding and catalysis are compared in K-V systems.     

Thermodynamics of nucleotide binding to the chaperonin GroEL studied by isothermal titration calorimetry: evidence for noncooperative nucleotide binding.

We characterized the thermodynamics of binding reactions of nucleotides ADP and ATPgammaS (a nonhydrolyzable analog of ATP) to GroEL in a temperature range of 5 degrees C to 35 degrees C by isothermal titration calorimetry. Analysis with a noncooperative binding model has shown that the bindings of nucleotides are driven enthalpically with binding constants of 7x103 M-1 and 4x104 M-1 for ADP and ATPgammaS, respectively, at 26 degrees C and that the heat capacity change DeltaCp is about 100 cal/mol.K for both the nucleotides. The stoichiometries of binding were about 8 and 9 molecules for ADP and ATPgammaS, respectively, per GroEL tetradecamer at 5 degrees C, and both increased with temperature to reach about 14 (ADP) and 12 (ATPgammaS) for both nucleotides at 35 degrees C. The absence of initial increase of binding heat as well as Hill coefficient less than 1.2, which were obtained from the fitting to the model curve by assuming positive cooperativity, showed that there was virtually no positive cooperativity in the nucleotide bindings. Incorporating a difference in affinity for the nucleotide (ADP and ATPgammaS) between the two rings of GroEL into the noncooperative binding model improved the goodness of fitting and the difference in the affinity increased with decreasing temperature.     

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.     

Galectins bind to the multivalent glycoprotein asialofetuin with enhanced affinities and a gradient of decreasing binding constants

Our previous isothermal titration microcalorimetry (ITC) studies of the binding of synthetic multivalent carbohydrates to the Man/Glc-specific lectins concanavalin A (ConA) and Dioclea grandiflora lectin (DGL) showed negative binding cooperativity that was due to the carbohydrate ligands and not the proteins [Dam, T. K., et al. (2002) Biochemistry 41, 1351-1358]. The negative cooperativity was associated with the decreasing functional valence of the carbohydrates upon progressive binding of their epitopes. The present study also shows negative cooperativity in the ITC binding data of asialofetuin (ASF), a glycoprotein that possesses nine LacNAc epitopes, to galectin-1, -2, -3, -4, -5, and -7, and truncated, monomer versions of galectin-3 and -5, which are members of a family of animal lectins. Although the observed K(a) values for binding of ASF to the galectins and two truncated forms are only 50-80-fold greater than that of LacNAc, analysis of the data in terms of the relationship between the observed macroscopic free energy of binding and the decreasing microscopic free energies of binding of the epitopes shows that the first LacNAc epitope of ASF binds with approximately 6000-fold higher affinity than the last epitope. Thus, the microscopic binding constants of the galectins for the first epitope(s) of ASF are in the nanomolar range, with a gradient of decreasing binding constants of the remaining epitopes. The results indicate that the above galectins bind with fractional, high affinities to multivalent glycoproteins such as ASF, independent of the quaternary structures of the galectins. These findings have important implications for the binding of galectins to multivalent carbohydrate receptors.     

Inhibition of muscle glycogen phosphorylase b by 5-methyltetrahydrofolic acid, 3'-chloro- and 3',6'-dichloromethotrexates

Inhibition of rabbit skeletal muscle glycogen phosphorylase b by 5-methyl-5,6,7,8-tetrahydrofolic acid, 3'-chloro- and 3',5'-dichloromethotrexates has been studied. The inhibition is reversible and characterized by positive kinetic cooperativity (Hill coefficient exceeds 1). The values of pterin concentration causing two-fold diminishing of the enzymatic reaction rate increased in the order: 3',5'-dichloromethotrexate, 3'-chloromethotrexate, 5-methyl-5,6,7,8-tetrahydrofolic acid (0.24, 0.40 and 1.87 mM, respectively). Comparison of "half-saturation" concentrations for the above compounds and for methotrexate and folinic acid shows that pterin affinity to glycogen phosphorylase b is affected by substituents both in pteridine and in p-aminobenzoic moieties of the pterin molecule. The antagonism between 5-methyl-5,6,7,8-tetrahydrofolic acid, 3'-chloro- and 3',5'-dichloromethotrexates, on the one hand, and AMP and FMN, on the other, is revealed for combined action of modifiers on glycogen phosphorylase b.     

Kinetic characterization of rabbit skeletal muscle phosphorylase ab hybrid

Phosphorylase ab was prepared in vitro by partial phosphorylation of rabbit skeletal muscle phosphorylase b and was isolated by DEAE-Sephacel chromatography. Its phosphorylated and non-phosphorylated subunits could not be distinguished by different affinity to substrates, activators or inhibitors, indicating their coordinated function. In the absence of nucleotide activators, the Km values for Pi and glucose-1-P were 28 mM and 18 mM, respectively. Activity in the presence of 16 mM glucose-1-P was doubled by 10(-4) M AMP or 10(-3) M IMP, mainly by lowering the Km for glucose-1-P. Half-maximum activation was exerted by 2 microM AMP or 0.1 mM IMP. Activation by these nucleotides showed no cooperativity. Glucose exerted competitive inhibition with respect to glucose-1-P, while for the inhibition by glucose-6-P an allosteric mechanism is suggested; the appropriate Ki values were 4.5 mM and 1.5 mM, respectively. The Hill coefficient for glucose-1-P binding was about 1.0, even in the presence of glucose (up to 10 mM), but 10 mM glucose-6-P lowered it to 0.47, indicating a negative heterotropic cooperativity. Effective regulation of the activity of phosphorylase ab by physiological concentrations of Pi, AMP, IMP and glucose-6-P suggests its metabolic control under in vivo condition.     

Cooperativity among calmodulin's drug binding sites

The binding of felodipine, a dihydropyridine Ca2+ antagonist, to calmodulin has been studied by equilibrium dialysis and fluorescence techniques. Analysis using the Hill equation gives a Hill coefficient of 2. A plot of bound [felodipine] vs. free [felodipine]2 gives a Bmax of 1.9 mol/mol and a K0.5 of 22 microM. Two calmodulin antagonists, prenylamine and R24571, which have previously been shown to potentiate the fluorescent enhancement observed when felodipine binds to calmodulin [Johnson, J. D. (1983) Biochem. Biophys. Res. Commun. 112, 787], produce a reduction in Hill coefficient to 0.7 and 1.0, respectively, and account for the observed potentiation of felodipine binding. Titrations of felodipine with calmodulin in the absence and presence of prenylamine and R24571 suggest that these drugs decrease the K0.5 of calmodulin for felodipine by 25-fold. Thus, potentiating drugs (prenylamine and R24571) bind to either of the two felodipine binding sites and, through an allosteric mechanism, result in felodipine binding to the remaining site with greatly enhanced affinity. Two types of potentiating drugs are observed. Prenylamine exhibits a Hill coefficient of 0.8 whereas felodipine, R24571, and diltiazem exhibit Hill coefficients of 2 in their potentiation of felodipine binding. Titrations of felodipine and calmodulin with Ca2+ exhibit cooperativity with a Hill coefficient of 4. Half-maximal binding occurs near pCa 6.0. In the presence of R24571, the calcium dependence of felodipine binding is biphasic, now exhibiting a much higher affinity (pCa 7.6) component. A model is presented to explain the relationship of these various allosterically regulated conformers of calmodulin and their interactions and activation with its target proteins.