Determination of equilibrium constants and maximum binding capacities in complexIn vitro systems: I. The mammillary system

It is shown that in a system containingn types of mutually noninteracting binding sites, the association constants are then roots of annth order polynomial while the maximum binding capacities can be evaluated by solving a set ofn simultaneous linear equations. Thenth order polynomial and the system ofn linear equations are defined in terms of 2n intermediate coefficients, the coefficients being themselves evaluated by substituting 2n sets of appropriate experimental data into an auxiliary system of 2n linear equations. The existence and uniqueness of the solutions are established.     

The effect of ligand heterogeneity on the Scatchard plot. Particular relevance to lipoprotein binding analysis

Computer simulations of equilibrium binding studies of a mixture of two labeled ligands binding competitively to a single class of identical and independent sites (receptors) were performed to investigate how ligand heterogeneity affects the observed data in such studies. The simulated data are presented in Scatchard plots. Ligand heterogeneity was generally found to be indistinguishable from the case of a homogeneous ligand when usual experimental conditions applied (that is, Scatchard plots of the data were straight lines). Some factors that increased the probability of recognizing heterogeneity in the system were identified, however. These are 1) a large difference between the dissociation constants of the two ligands, 2) a high concentration of receptors relative to the dissociation constant of the higher-affinity ligand, 3) a high concentration of the lower-affinity ligand relative to that of the higher-affinity ligand, 4) a high specific activity of the lower-affinity ligand relative to that of the higher-affinity ligand, and 5) lack of experimental error. When ligand heterogeneity (under certain conditions) did cause curvilinearity in the Scatchard plot, the curve formed was always concave-downwards. Thus, ligand heterogeneity may occasionally mimic positive cooperativity, but never mimics negative cooperativity or multiple classes of binding sites. Implications of these findings for equilibrium binding studies involving lipoproteins (which are generally isolated as heterogeneous mixtures of particles) are discussed in detail. These findings are also relevant to equilibrium binding studies using ligands which are mixtures of stereoisomers or which contain chemical or radiochemical impurities.     

Some general aspects regarding the interpretation of binding data by means of a Scatchard plot

The question is quantitatively examined which general information can be obtained from experimental data of ligand binding to macromolecules if represented by a Scatchard plot. In particular, the curvature as well as the intercepts and slopes at both coordinate axes are analyzed assuming rather general conditions including cooperative behavior (with applications to some simplified cases of interest in practice). The results should provide a basis for attempts to elucidate the binding mechanism of a system encountered in experimental work.     

A manganese catalyzed covalent binding of estradiol - 17 beta to cytosol proteins of rabbit uterus.

Studies of the temperature sensitivity of estradiol receptor binding in rabbit uterine cytosol have revealed the existence of an enzyme which catalyzes the covalent binding of estradiol to cytosol proteins. A fraction, prepared by chromatography on Biogel P-200 and incubated at 37 degrees C in the presence of Mn++, exhibited a time-dependent, temperature-sensitive, oxidative binding of estradiol not seen in the crude cytosol preparation. Although the activity of this enzyme was shown to be independent of estradiol binding by the high affinity estrogen receptor, its presence may complicate studies of estrogen receptor action which involve the use of elevated temperatures.     

Determination of protein association constants by electrophoresis

An electrophoresis cell with scanning UV-absorption optics is presented. It allows the measurement of moving reaction boundaries of dilute protein solutions with a high-resolution. The protein profiles in the boundaries can be extrapolated to infinite time after an appropriate transformation of space and time coordinates and then evaluated with respect to association constants. This is demonstrated for the dimer-tetramer equilibrium of haemoglobin.     

Use of the direct linear plot to estimate binding constants for protein-ligand interactions.

The direct linear plot (Eisenthal and Cornish-Bowden[1974] Biochem. J. $\text{139}$, 715–720) for the determination of enzyme kinetic constants has been assessed as a means of describing specific steroid-protein interactions. In the rat uterine cytoplasmic estrogen receptor system, determination of the equilibrium dissociation constant (K_D) and of the total number of ligand-binding sites (B_max) has been made, and the results are in good agreement with those obtained by Scatchard and Lineweaver-Burk plot analyses. The usefulness of the direct linear plot lies in the speed and simplicity with which it can be constructed and interpreted.     

On the analysis of linear binding effects associated with curved Scatchard plots.

First the question is examined as to which binding data, especially if given as Scatchard plots, can be described in terms of a basic model mechanism. This referes to a linear lattice of equivalent binding sites (as for example located on a linear biopolymer) which can exert cooperative interaction between nearest neighbors. It is shown that the effect of overlapping of potential site (so-called "multiple-contact"binding), as may occur with larger ligands, will largely be compensated by a higher degree of cooperativity. Therefore, in practice such properties can scarcely be separated by means of oridnary binding experiments. A pronounced inflection point in the Scatchard plot turns out to be clearly indicating a more complex mechanism involving at least two rather antagonistic cooperative interactions which may, however, occur even between equivalent binding sites. Finally some consequences of different classes of bindings sites are considered. In particular a simple approach is introduced by which the binding to mutually exclusive classes of sites may be described. Such a model is of interest for multiple-mode binding of ionic ligands to oppositely charged polymers.     

Interaction of protein with a self-associating ligand. Deviation from a hyperbolic binding curve and the appearance of apparent co-operativity in the Scatchard plot

We derived a general formula to analyze a binding system in which a ligand self-associates, in terms of experimentally determinable quantities, i.e. r, the average number of bound ligands per protein molecule, and Lft, the total free ligand concentration, which are expressed as a ligand monomer unit. The limiting behaviors of the Scatchard plot (r/Lft vs r plot), that is, the intercepts on the r-axis and the r/Lft-axis, and the limiting slopes, are generally given. Three models that may be encountered are considered in detail. Numerical examples are also presented to illustrate how the self-association of a ligand affects the binding curves. The ligand self-association alone can cause deviation of the profile of the binding curve (r vs Lft plot) from a hyperbola, resulting in a nonlinear Scatchard plot. Therefore, analysis of the binding data without consideration of ligand self-association may lead to erroneous conclusions as to the numbers and classes of binding sites, co-operativity among the sites and binding parameter values.     

Evidence for involvement of tyrosine in estradiol binding by rat uterus estrogen receptor

The possibility of tyrosine involvement in steroid binding by rat uterus estrogen receptor (rER) was investigated. Chemical modification of rER with reagents such as tetranitromethane (TNM) and N-acetylimidazole (NAcI) inhibited estradiol binding. Steroid binding was inhibited to a greater extent at pH 8 than at pH 6, indicating the participation of tyrosine (TNM has increasing affinity for cysteine ove tyrosine at pH 6). Inhibition patterns remained similar for incubations at 0-4 degrees C or 37 degrees C. NAcI inhibited rER steroid binding at 37 degrees C, but not at 0-4 degrees C. Hydroxylamine incubated in the presence of rER and NAcI appeared to reverse this inhibition. Thus, these findings indicate that the phenyl ring and possibly the phenolic hydroxyl of tyrosine are involved in steroid binding of the receptor.     

Determination of first order rate constants by natural logarithm of the slope plot exemplified by analysis of Aspergillus niger in batch culture

Finding rate constants from experimental data is often difficult because of offset and noise. A computer program was developed to average experimental data points, reducing the effect of noise, and to produce a log_e of slope plot – a plot of the natural logarithm of the slope of a curve – eliminating the effect of any offset. If y-values depend exponentially on x-values the log_e of slope plot is rectilinear and the slope is equal to the first order rate constant. Therefore the log_e of slope plot provides easy identification of exponential sections of any experimental or calculated data, corresponding rate constants, and small changes in the rate constant as exemplified by analysis of titrant added to a batch culture of Aspergillus niger. The log_e of slope plot was easily applicable and superior to conventional methods of analysis of exponential decreasing or increasing data.     

Mutational analysis of the energetics of the GrpE.DnaK binding interface: equilibrium association constants by sedimentation velocity analytical ultracentrifugation

DnaK, the prokaryotic Hsp70 molecular chaperone, requires the nucleotide exchange factor and heat shock protein GrpE to release ADP. GrpE and DnaK are tightly associated molecules with an extensive protein-protein interface, and in the absence of ADP, the dissociation constant for GrpE and DnaK is in the low nanomolar range. GrpE reduces the affinity of DnaK for ADP, and the reciprocal linkage is also true: ADP reduces the affinity of DnaK for GrpE. The energetic contributions of GrpE side-chains to GrpE-DnaK binding were probed by alanine-scanning mutagenesis. Sedimentation velocity (SV) analytical ultracentrifugation (AUC) was used to measure the equilibrium constants (Keq) for GrpE binding to the ATPase domain of DnaK in the presence of ADP. ADP-bound DnaK is the natural target of GrpE, and the addition of ADP (final concentration of 5 microM) to the preformed GrpE-DnaK(ATPase) complexes allowed the equilibrium association constants to be brought into an experimentally accessible range. Under these experimental conditions, the substitution of one single GrpE amino acid residue, arginine 183 with alanine, resulted in a GrpE-DnaK(ATPase) complex that was weakly associated (Keq =9.4 x 10(4) M). This residue has been previously shown to be part of a thermodynamic linkage between two structural domains of GrpE: the thermosensing long helices and the C-terminal beta-domains. Several other GrpE side-chains were found to have a significant change in the free energy of binding (DeltaDeltaG approximately 1.5 to 1.7 kcal mol(-1)), compared to wild-type GrpE.DnaK(ATPase) in the same experimental conditions. Overall, the strong interactions between GrpE and DnaK appear to be dominated by electrostatics, not unlike barnase and barstar, another well-characterized protein-protein interaction. GrpE, an inherent thermosensor, exhibits non-Arrhenius behavior with respect to its nucleotide exchange function at bacterial heat shock temperatures, and mutation of several solvent-exposed side-chains located along the thermosensing indicated that these residues are indeed important for GrpE-DnaK interactions.     

The nuclear binding of estradiol stimulates ribonucleoprotein transport in the rat uterus

An inverse relationship exists in the rat uterus between the endogenous estradiol concentration and the rate of accumulation within the nuclei of ribonucleoproteins (RNP) that bind estradiol. Exposure of the uterine nuclei to physiological concentrations of estradiol, either in vivo or in vitro, results in the hormone binding to the nuclear RNP and the transport of the RNP-estradiol complex from the nuclei. Evidences suggest that the RNP-estradiol complex, thus released upon in vivo exposure of the nuclei to estradiol, associates with the ribosomes forming polysomes. The polysome profiles show that the hormone-binding activity is mainly associated with the rapidly sedimenting polysomal fractions.