Chemical Reaction Equilibrium Analysis: Theory and Algorithms. with their natural ligands share several properties. Specificity Biological receptors generally bind tightly to a single natural ligand. (This specificity need not be absolute. For example, a number of natural toxins, such as -bungarotoxin, carry out their mischief by binding to the acetylcholine receptor.) Ligand specificity can be readily assessed through a competitive-binding assay. Here, the amount of ligand bound to a receptor is usually measured in the presence of other putative ligands. If the receptor is indeed specific for the original ligand, the amount of ligand bound is not affected by the presence of the other ligands. For example, the addition of a 1000-fold molar excess of serum albumin does not decrease the amount of diphtheria toxin bound to its cell-surface receptor. Affinity Molecules interact noncovalently with other molecules. For example, proteins tend to stick to glass, due in part to polar Rabbit Polyclonal to CLNS1A surfaces interacting with one another. The surface of a cell is also quite polar, due largely to the extensive amount of carbohydrate that extends from membrane proteins and membrane lipids. Consequently, all proteins have some affinity for cell surfaces. ReceptorCligand interactions are distinguished from other noncovalent interactions between molecules by their high affinity. Saturation A receptor has a limited number of binding sites, and is therefore saturated at high ligand concentrations. A plot of the concentration of bound ligand versus that of total ligand is usually curvilinear when all the binding sites are occupied, there is no further increase in binding with increasing ligand concentration (Fig. 1). Open in a separate window Physique 1 Common saturation curve for a receptorCligand conversation. The curve was generated from an conversation with = 0.10, 1.1, 2.5, 3.9, 4.3, 6.7, 10, 15, 23, 40, 90, 990. The insert shows that the binding observed at row concentrations of ligand (< for [LR], free or for [L], and =?ln?= + versus gives a line with a slope of ?now plotted versus (Fig. 2B), and the double-reciprocal plot, AZ1 which is usually analogous to the LineweaverCBurk plot (Fig. 2C). These three plots are often used to calculate parameters in receptorCligand interactions. All three, however, are algebraic manipulations AZ1 of the same equation and hence contain the same information. Open in a separate window Physique 2 Linear transformations of binding data for the receptorCligand conversation portrayed in Physique 1. (A) Scatchard plot; (B) EadieCHofstee plot; (C) double-reciprocal plot AZ1 (= 0.10 not shown); and (D) Hill plot (= 1). Linear regression analysis of a linear transformation such as a Scatchard plot weighs data points improperly and can therefore lead to gross errors. The graphs should therefore be used only to obtain initial estimates of the parameters. These estimates can then be used to arrive by iteration at more accurate values for the parameters. Although these plots should not be used to derive the values of the parameters, each is an effective vehicle for displaying binding data and for examining the quality of such data. Nonlinear Scatchard Plols The Scatchard plot for the binding of [125I]insulin to cultured human lymphocytes is usually curvilinear, rather than linear (Fig. 3) (9). Three situations lead to such nonlinear Scatchard plots (10C12). The binding sites for the ligand may be heterogeneous; the ligand might be binding to one site with a dissociation constant of =?=?ln?versus gives a line with a slope of is the Hill constant (16). Given an accurate estimate of the value of can AZ1 he estimated from a Hill plot, which arises from the Hill equation. versus log [and = 1, the receptor has a single binding site and, of course, exhibits no cooperativity in its binding of ligand. Nonintegral values of are AZ1 consistent with cooperativity. Numerical Analysis of Hyperbolic Plots Various computer programs are available for fitting binding data to a hypothetical model (17C20). The general strategy in using these programs is usually to fit the data to.