Evaluation of dissociation constants from competition binding experiments based on the relative binding ratio

Methods probing protein–DNA associations include direct binding titrations and competition binding experiments. For the latter, we present here a simple procedure allowing the quantitative evaluation of dissociation constants. We show that the ratio between the fraction of a DNA probe bound to protein in the absence of competitor and that in the presence of competitor is, at large competitor concentrations, a linear function of the competitor concentration, and we derive equations allowing the dissociation constant for the protein–competitor complex to be evaluated from the slope. We show further that a self-competition experiment, where the DNA probe and competitor are chemically the same species, can be used as a complement to a direct titration to determine the fraction of protein that is correctly folded for specific DNA binding. Thus, such a combination of direct and self-competition titration can be used as a check of the conformational purity of DNA binding proteins.     

Rate constants and equilibrium constants for binding of actin to the 1:1 gelsolin-actin complex.

The rate constant and equilibrium constant of association of an actin monomer with 1:1 gelsolin-actin complex isolated from chicken were measured by using fluorescently labeled actin. According to fluorescence stopped-flow experiments, the rate constant of formation of the 1:2 gelsolin-actin complex from 1:1 gelsolin-actin complex and actin was found to be about 2 x 10(7) M-1 s-1 under conditions where gelsolin binds Ca2+. The rate of dissociation of one actin molecule from the 1:2 gelsolin-actin complex was determined by exchange of actin for fluorescently labeled actin. The rate constant of dissociation was about 0.02 s-1. Thus, the equilibrium constant for association of actin with 1:1 gelsolin-actin complex can be calculated to be in the range of 10(9) M-1. The rate of dissociation of actin from 1:2 gelsolin-actin complex was independent of the Ca2+ concentration. Ca2+ affects only the rate of association of actin with 1:1 gelsolin-actin complex.     

Determination of relative rate constants for in vitro RNA processing reactions by internal competition

Studies of RNA recognition and catalysis typically involve measurement of rate constants for reactions of individual RNA sequence variants by fitting changes in substrate or product concentration to exponential or linear functions. A complementary approach is determination of relative rate constants by internal competition, which involves quantifying the time-dependent changes in substrate or product ratios in reactions containing multiple substrates. Here, we review approaches for determining relative rate constants by analysis of both substrate and product ratios and illustrate their application using the in vitro processing of precursor transfer RNA (tRNA) by ribonuclease P as a model system. The presence of inactive substrate populations is a common complicating factor in analysis of reactions involving RNA substrates, and approaches for quantitative correction of observed rate constants for these effects are illustrated. These results, together with recent applications in the literature, indicate that internal competition offers an alternate method for analyzing RNA processing kinetics using standard molecular biology methods that directly quantifies substrate specificity and may be extended to a range of applications.     

Evaluation of equilibrium constants for the binding of N-acetyl-L-tryptophan to monomeric and dimeric forms of alpha-chymotrypsin

The binding of N-acetyl-tryptophan to the monomeric and dimeric forms of alpha-chymotrypsin in I = 0.2 acetate-chloride buffer, pH 3.86, has been studied quantitatively. Equilibrium sedimentation studies in the absence of inhibitor yielded a dimerization constant of 3.5 L/g. This value was confirmed by frontal gel chromatography of the enzyme on Bio-Gel P-30, which was also used to establish that N-acetyl-L-tryptophan binds preferentially to monomeric enzyme. From kinetic studies of competitive inhibition with N-acetyl-L-tryptophan ethyl ester as substrate, an equilibrium constant of 1300 M-1 was determined for the binding of N-acetyl-L-tryptophan to monomeric alpha-chymotrypsin. An intrinsic binding constant of 250 M-1 for the corresponding interaction with dimeric enzyme was calculated on the basis of these results and binding data obtained with concentrated (18.5 g/L) alpha-chymotrypsin. The present results refute earlier claims for exclusive binding of competitive inhibitors to monomer and also those for equivalence of inhibitor binding to monomeric and dimeric forms of alpha-chymotrypsin.     

A method for the preparation of steroid-protein antigens for the use in immunoassay of steroids

A general method for the preparation of steroid-protein conjugates coupled through carbon 6 of Δ⁴ steroids was demonstrated using 6β Br-testosterone acetate and 6β Br-progesterone covalently bound to sulfhydryl-group-enriched bovine serum albumin. The antigenicity of the conjugates and the specificity of the antibodies were evaluated. With anti-progesterone the assay accuracy was determined to be 10.3%, the intra-assay precision was 8.7% and the inter-assay precision was 12.6%. The material was used to assay the progesterone content of normal human male and female serum as well as the changes in this hormone following corpora lutea induction in constant-estrus androgenized female rats.     

The estimation of affinity constants for the binding of model peptides to DNA by equilibrium dialysis.

The binding of lysine model peptides of the type Lys-X-Lys, Lys-X-X-Lys and Lys-X-X-X-Lys (X = different aliphatic and aromatic amino acids) has been studied by equilibrium dialysis. It was shown that the strong electrostatic binding forces generated by protonated amino groups of lysine can be distinguished from the weak forces stemming from neutral and aromatic spacer amino acids. The overall binding strength of the lysine model peptides is modified by these weak binding forces and the apparent binding constants are influenced more by the hydrophobic character of the spacer amino acid side chains than by the chainlength of the spacers.     

Linearization of two ligand-one binding site scatchard plot and the "IC50" competitive inhibition plot: application to the simplified graphical determination of equilibrium constants

A simple procedure for linearizing the curved, two ligand-one binding site Scatchard plot resulting from the presence of a constant concentration of competitive inhibitor is proposed; the same procedure may also be applied to the analysis of data derived from the "IC50" competitive inhibition experimental design. Furthermore, a useful generalization of the Cheng-Prusoff correction is presented.     

Rate constants and equilibrium constants for binding of the gelsolin-actin complex to the barbed ends of actin filaments in the presence and absence of calcium

The equilibrium constant for binding of the gelsolin-actin complex to the barbed ends of actin filaments was measured by the depolymerizing effect of the gelsolin-actin complex on actin filaments. When the gelsolin-actin complex blocks monomer consumption at the lengthening barbed ends of treadmilling actin filaments, monomers continue to be produced at the shortening pointed ends until a new steady state is reached in which monomer production at the pointed ends is balanced by monomer consumption at the uncapped barbed ends. By using this effect the equilibrium constant for binding was determined to be about 1.5 X 10(10) M-1 in excess EGTA over total calcium (experimental conditions: 1 mM MgCl2, 100 mM KCl, pH 7.5, 37 degrees C). In the presence of Ca2+ the equilibrium constant was found to be in the range of or above 10(11) M-1. The rate constant of binding of the gelsolin-actin complex to the barbed ends was measured by inhibition of elongation of actin filaments. Nucleation of new filaments by the gelsolin-actin complex towards the pointed ends was prevented by keeping the monomer concentration below the critical monomer concentration of the pointed ends where the barbed ends of treadmilling actin filaments elongate and the pointed ends shorten. The gelsolin-actin complex was found to bind fourfold faster to the barbed ends in the presence of Ca2+ (10 X 10(6) M-1 s-1) than in excess EGTA (2.5 X 10(6) M-1 s-1). Dissociation of the gelsolin-actin complex from the barbed ends can be calculated to be rather slow. In excess EGTA the rate constant of dissociation is about 1.7 X 10(-4) s-1. In the presence of Ca2+ this dissociation rate constant is in the range of or below 10(-4) s-1.     

Substrate binding to chloramphenicol acetyltransferase: evidence for negative cooperativity from equilibrium and kinetic constants for binary and ternary complexes

Chloramphenicol acetyltransferase (CAT) catalyzes the acetyl-CoA-dependent acetylation of chloramphenicol by a ternary complex mechanism with a rapid equilibrium and essentially random order of addition of substrates. Such a kinetic mechanism for a two-substrate reaction provides an opportunity to compare the affinity of enzyme for each substrate in the binary complexes (1/Kd) with corresponding values (1/Km) for affinities in the ternary complex where any effect of the other substrate should be manifest. The pursuit of such information for CAT involved the use of four independent methods to determine the dissociation constant (Kd) for chloramphenicol in the binary complex, techniques which included stopped-flow measurements of on and off rates, and a novel fluorometric titration method. The binary complex dissociation constant (Kd) for acetyl-CoA was measured by fluorescence enhancement and steady-state kinetic analysis. The ternary complex dissociation constant (Km) for each substrate (in the presence of the other) was determined by kinetic and fluorometric methods, using CoA or ethyl-CoA to form nonproductive ternary complexes. The results demonstrate an unequivocal decrease in affinity of CAT for each of its substrates on progression from the binary to the ternary complex, a phenomenon most economically described as negative cooperativity. The binary complex dissociation constants (Kd) for chloramphenicol and acetyl-CoA are 4 microM and 30 microM whereas the corresponding dissociation constants in the ternary complex (Km) are 12 microM and 90 microM, respectively.(ABSTRACT TRUNCATED AT 250 WORDS)     

A gel electrophoresis method for determining the relative binding constants of biologically active, intercalating fluorescent stains.

It is possible to correlate the relative binding tightness of a variety of biologically active, intercalating fluorescent stains through the use of a simple gel electrophoresis method. By prebinding the stains to a homologous series of oligodeoxyribonucleotides and subjecting them to electrophoresis, a size determination of the smallest oligomer to which they remain bound may be obtained from that oligomer's fluorescence using short-wavelength ultraviolet irradiation. This method may prove to be quite practical for the preclinical testing of certain drug derivatives used in cancer chemotherapy. An estimate of the relative effectiveness of new derivatives, as compared to previously tested drugs, might be obtained from this type of analysis.     

Competitive blocking of epithelial sodium channels by organic cations: The relationship between macroscopic and microscopic inhibition constants

Fluctuation analysis of Na current passing the apical membrane in the skin of Rana ridibunda was used to study the kinetics of Na-channel blocking by several organic cations present in the outer solution together with 60 mM Na. The ratios of the apparent off-rate and on-rate constants (the microscopic inhibition constants) thus obtained for triamterene, triaminopyrimidine (TAP), 5,6-diCl-amiloride, 5H-amiloride and amiloride itself are found to be in the mean about sevenfold smaller than the corresponding inhibition constants obtained from macroscopic dose-response curves. The apparent discrepancy is explicable by competition of the organic blocker with the channel block by Na ions (the self-inhibition effect). The type of interaction between extrinsic blockage and self-inhibition may be purely competitive or mixed. However, in case of mixed inhibition the competitive component must dominate the noncompetitive component by at least seven to one.     

Determination of equilibrium constants for a sequential model of dioxygen binding by hemoglobin-inositol hexaphosphate complexes: the structural pathway from deoxy- to oxy-hemoglobin

The affinity of human hemoglobin (Hb4) for dioxygen was determined in 0.050 M bistris, 0.005 M inositol hexaphosphate (IHP) at pH 7.0 and 20.0 degrees C. Binding of dioxygen by Hb4 was determined by detailed spectroscopic analysis of the absorption spectrum in the region from 460 to 620 nm. The absorption spectrum of samples at intermediate values of fractional saturation (F) could not be resolved into components of Hb4 and (HbO2)4 without generating a residual spectrum, the amplitude of which was greatest at F from 0.4 to 0.5 and least at values of F of 0 and 1. An equation of state for dioxygen binding by the Hb4-IHP complex was formulated and tested by its ability to predict (i) the equilibrium binding curve and (ii) the variation in amplitude of the residual spectrum with F. The equilibrium binding data was fitted to the following equation of state: (Formula: see text) where K1 is the equilibrium constant for binding of dioxygen to an alpha chain of the Hb4-IHP complex, K2 is the constant for the second alpha chain, K3 is the equilibrium constant for the large-scale conformational change, K4 is the equilibrium constant for binding of oxygen by both beta chains, and (L) is the ligand concentration. The best-fitting values were as follows: K1, 0.03497 mm Hg-1; K2, 0.01368 mm Hg-1; K3, 2.44; K4, 0.0008867 mm Hg-2. The residual spectra were attributed to differential loading of dioxygen by the alpha and beta chains. Equations of state for F of each chain are presented, and the amplitude of the residual spectra was shown to be accurately predicted by the differences in F of each chain when subjected to the constraint that the best-fitting values of K1-K4 be used in predicting saturation of each chain with dioxygen.     

The determination of equilibrium constants for heterogeneous macromolecular interactions

A method has been developed to determine the association constant for a heterogeneous association of the type A + B in equilibrium AB. This method requires knowledge of the two initial concentrations and of the resulting weight-average molecular weight for each data point. Computer simulations using Gaussian-distributed error on the measured parameters show that the researcher can readily determine whether the particular concentration range chosen is appropriate for the strength of binding and therefore how reliable the calculated constant might be. It is also shown that errors in measuring molecular weight have, in general, a more profound effect than do errors in concentration.     

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.     

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.