• Abstract
• Table of Contents
• Figures
• Literature Cited

Abstract

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Living organisms grow, differentiate, reproduce, and respond to their environment via specific and integrated interactions between biomolecules. The investigation of molecular interactions therefore constitutes a major area of biochemical study, occupying a ubiquitous and central position between molecular physiology on the one hand and structural chemistry on the other. While specificity resides in the details of structural recognition, the dynamic interplay between biomolecules is orchestrated precisely by the thermodynamics of the biomolecular equilibria involved. A common set of physicochemical principles applies to all such phenomena, irrespective of whether the interaction of interest involves an enzyme and its substrate or inhibitor, a hormone or growth factor and its receptor, an antibody and its antigen, or, indeed, the binding of effector molecules that modulate these interactions. The binding affinity, binding specificity, number of binding sites per molecule, as well as the enthalpic and entropic contributions to the binding energy are common parameters that assist an understanding of the biochemical outcome. This unit aims to provide an overview of the design and interpretation of binding experiments.

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• Rectangular Hyperbolic Binding Responses
• Quantitative Characterization of a Hyperbolic Response
• Illustrative Analysis of Experimental Results
• Binding Responses Deviating from Rectangular Hyperbolic Form
• Complications Arising from Nonspecific Binding
• Concluding Remarks
• Literature Cited
• Figures

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  Figure a0.5A.1 Illustrative dependences of the binding function ( r ) upon free ligand concentration ( C S ) for various types of acceptor‐ligand interaction. Rectangular hyperbolic dependence (—) for an acceptor with two equivalent and independent sites ( K AS = K 1 = K 2 = K 3 = K 4 = 105 M?1 ). Binding curve (‐ ‐ ‐) for an acceptor with two independent but nonequivalent sites ( K 1 = K 4 = 106 M?1 ; K 2 = K 3 = 104 M?1 ). Sigmoidal binding curve (‐ ‐ ‐) for an acceptor with two equivalent but dependent sites ( K 1 = K 2 = 104 M?1 ; K 3 = K 4 = 106 M?1 ). See Equations ‐ for equilibrium constant nomenclature.

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  Figure a0.5A.2 Illustrative characterization of an acceptor‐ligand interaction for a system with limited ligand solubility. (A ) Estimation of the number of binding sites by titration of 3 μM acceptor with ligand under stoichiometric conditions: p = 2 on the grounds that 6 μM ligand is required to titrate 3 μM acceptor. (B ) Binding data obtained (for example) by equilibrium dialysis over the limited range of ligand solubility (<10 μM), together with the best‐fit rectangular hyperbolic relationship (Equation ) for a system with p = 2 (see A).

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• ?	Figure a0.5A.3 Use of various linear transforms (Equations ‐ ) of the rectangular hyperbolic binding equation to characterize an acceptor‐ligand interaction with p = 2 and K AS = 105 M?1 . (A ) Scatchard plot; (B ) Hames plot; (C ) double‐reciprocal plot.

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• ?	Figure a0.5A.4 Schematic representation of the strategy for the quantitative characterization of a binding response. Taken from Winzor and Sawyer ().

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  Figure a0.5A.5 Results obtained by equilibrium dialysis (filled circles) and sedimentation velocity (open circles) for the interaction of methyl orange (S) with bovine serum albumin (A). (A ) Semilogarithmic representation of the results, together with the double‐reciprocal transform of the equilibrium dialysis data (inset). (B ) Untransformed dependence of the binding function upon free ligand concentration, together with the best‐fit description by nonlinear regression analysis according to Equation . Equilibrium dialysis data are taken from Klotz et al. (), and sedimentation velocity data from Steinberg and Schachman ().

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  Figure a0.5A.6 Characterization of the interaction between NADH and rabbit muscle lactate dehydrogenase (pH 7.4; ionic strength, I , 0.15) by nonlinear regression analysis of the untransformed gel chromatographic binding data in terms of Equation : the upper pattern shows random scatter in the residuals plot. The inset displays the same data in semilogarithmic format. Data taken in part from Ward and Winzor ().

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  Figure a0.5A.7 Evaluation of the stoichiometry of an acceptor‐ligand interaction by stoichiometric titration. Curves have been constructed on the basis of a single acceptor site with a binding constant ( K AS ) of 106 M?1 and total acceptor concentrations ( C A ) of 10?4 M (curve a), 10?5 M (curve b), and 10?6 M (curve c).

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  Figure a0.5A.8 Fluorescence polarization (anisotropy) study of the interaction between E. coli cAMP receptor protein and a 32‐bp DNA fragment of the lac promoter. (A ) Stoichiometric titration of the fluorescently labeled DNA fragment with receptor protein in the presence of 0.2 mM cAMP. (B ) Equilibrium titration in the presence of 0.5 μM cAMP. (C ) Secondary plot of the equilibrium titration data as a binding curve, together with the best fit description ( p = 1, K AS = 6.0 × 107 M?1 ). Data taken from Heyduk and Lee ().

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• ?	Figure a0.5A.9 Schematic representation of the competitive interactions of soluble ligand (S) and immobilized affinity sites (X) for acceptor (A) in quantitative affinity chromatography.

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  Figure a0.5A.10 Studies of the interaction between acceptor and immobilized affinity sites by the recycling partition variant of quantitative affinity chromatography. (A ) Schematic representation of the experimental system. (B ) Scatchard plot of results obtained for the interaction of antithrombin with heparin‐Sepharose (Hogg et al., ).

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  Figure a0.5A.11 Characterization of an acceptor‐ligand interaction by competitive binding assay. (A ) Scatchard plot of equilibrium responses for the interaction of the soluble domain of interleukin 6 receptor (A) with interleukin 6 immobilized on the sensor surface of a BIAcore instrument. (B ) Plot of results obtained with interleukin 6 as the competing ligand (S) in accordance with Equation , with q = 2. Data taken from Ward et al. ().

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  Figure a0.5A.12 Illustrative Scatchard plots for the interaction of ligand with two independent but nonequivalent acceptor sites. The higher‐affinity site has been ascribed a binding constant of 105 M?1 , whereas the other has been accorded values of 5 × 104 M?1 (curve a), 104 M?1 (curve b), and 103 M?1 (curve c). The broken line describes the interaction of ligand with the higher‐affinity binding site, whereas the dotted lines have a common abscissa intercept of 2 and slopes characteristic of the weaker interactions.

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• ?	Figure a0.5A.13 Analysis of binding data for the interaction of aldolase with rabbit muscle myofibrils. (A ) Conventional Scatchard plot. (B ) Multivalent Scatchard plot according to Equation with f = 4. Data taken from Table 1 of Kuter et al. ().

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• ?	Figure a0.5A.14 Schematic representation of binding curves and their Scatchard transforms reflecting (A ) positive cooperativity and (B ) negative cooperativity of acceptor sites for a univalent ligand.

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  Figure a0.5A.15 Conflicting criteria for cooperative binding of multivalent ligands. (A ) Schematic binding curve and its multivalent Scatchard counterpart reflecting either positive cooperativity of acceptor sites or negative cooperativity of ligand sites. (B ) Corresponding plots reflecting either negative cooperativity of acceptor sites or positive cooperativity of ligand sites.

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  Figure a0.5A.16 Allosteric activation and inhibition of E. coli aspartate transcarbamylase by effectors. Open circles, dependence of initial velocity v (expressed relative to maximal value v m ) upon aspartate concentration ( C S ) in the presence of saturating carbamyl phosphate; filled circles and filled squares, corresponding dependences with 0.5 mM CTP and 2 mM ATP, respectively, included in the reaction mixtures. Data taken from Gerhart ().

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• ?	Figure a0.5A.17 Concentration dependence of the binding curve for a self‐associating acceptor. Binding curves for oxygen uptake by the indicated total concentrations of human hemoglobin (0.7 to 106 μg/ml) at pH 7.4. Data taken from Mills et al. ().

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  Figure a0.5A.18 Perturbation of the monomer‐dimer equilibrium for α‐chymotrypsin (pH 3.9, I 0.11) by the preferential interaction of indole with monomeric enzyme. Plot of results from sedimentation equilibrium experiments according to Equation A.5A.48 for enzyme alone (open symbols) and in the presence of 1 mM (filled circles) and 2 mM (filled squares) ligand.

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  Figure a0.5A.19 Nonspecific ligand interactions in studies involving membrane receptors. (A ) Binding of [125 I]insulin to insulin receptors on Chinese hampster ovary cells (filled squares), and the corrected binding curve (open squares) after allowance for bound radioactivity in the presence of excess nonlabeled insulin (filled circles). Adapted from Winzor and Sawyer (). (B ) Uptake of metoprolol as the result of physical partition into hepatic microsomes. Data taken from Bogoyevitch et al. ().

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  Figure a0.5A.20 Effects of nonspecificity in the binding of ligands to a sequence of residues on a linear polymer chain. (A ) Scatchard plot of experimental results (Latt and Sober, ) for the interaction of an ε‐dinitrophenyl‐labeled hexameric lysine oligopeptide with poly(I + C). (B ) Schematic representation of thermodynamic and kinetic aspects of nonspecific interaction between a ligand and three‐residue sequences on a twelve‐residue linear polymer.

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