An evaluation of ways of using equilibrium dialysis to quantify the binding of ligand to macromolecule

Quantitative Microdialysis: Experimental Protocol and Software for Small Molecule Protein Affinity Determination and for Exclusion of Compounds with Poor Physicochemical Properties

Quantitative microdialysis is a traditional biophysical affinity determination technique. In the development of the detailed experimental protocol presented, we used commercially available equipment, rapid equilibrium dialysis (RED) devices (ThermoFisher Scientific), which means that it is open to most laboratories. The target protein and test compound are incubated in a chamber partitioned to allow only small molecules to transition to a larger reservoir chamber, then reversed-phase high performance liquid chromatography (RP-HPLC) or liquid chromatography–mass spectrometry (LC–MS) is used to determine the abundance of compound in each chamber. A higher compound concentration measured in the chamber that contains the target protein indicates binding. As a novel, and differentiating contribution, we present a protocol for mathematical analysis of experimental data. We provide the equations and the software to yield dissociation constants for the test compound-target protein complex up to 0.5 mM K_D, and we quantitatively discuss the limitations of affinities in relation to measured compound concentrations.

Evaluation of the binding properties of drugs to albumin from DSC thermograms

There is a demand in rapid and robust methods to determine the affinity of drugs to receptors, enzymes, and transport proteins. Differential scanning calorimetry (DSC) is a common method to prove the existence of ligand-protein binding from the shift of denaturation peak, but it is rarely used to obtain the binding constant values. The work is aimed to prove that the DSC experiments can be a source of reliable values of the binding constants and information on the stoichiometry of drug-albumin binding. DSC thermograms of bovine serum albumin denaturation in the presence of several drugs with different affinity and stoichiometry of binding to albumin: naproxen, warfarin, ibuprofen, and isoniazid were recorded. The dependences of the denaturation peak maximum temperature and area on the molar drug/protein ratio, which varied from 0 to 100, were considered. With the help of numerical modeling of the DSC curves, these dependences were predicted using the binding parameters determined in independent experiments and a simple two-state model of denaturation. The DSC data at relatively small concentrations of ligands are in good agreement with the calculation results. The deviations from the model predictions at high ligand concentrations in the cases of naproxen and ibuprofen indicate that albumin is able to bind several additional molecules of these drugs with its low-affinity sites. The fit was improved by using a sequential binding model with two binding constants K₁ = 1.0 × 10⁷ and K₂ = 1.0 × 10⁴ for naproxen and a cooperative binding model for ibuprofen. The stoichiometry of drug-albumin complexes fully saturated with drug ligand was calculated from the dependence of the denaturation temperature on the drug concentration. In the case of isoniazid, DSC thermograms indicated very weak binding to albumin.

Sebacic acid binding to human plasma albumin

Sebacic (decanedioic) acid is a dicarboxylic acid proposed recently as an alternative energy substrate in total parenteral nutrition. In this paper, binding of sebacic acid to defatted human plasma albumin, also in the presence of decanoic acid, was studied by means of equilibrium dialysis. In addition, the binding of sebacic acid in human serum was investigated. Binding to defatted albumin was analysed by a model with two independent classes of sites with different affinity constants. The fitting procedure took into account some of the measurement errors that are likely to affect the equilibrium dialysis technique. We found for sebacic acid one binding site with affinity constant 3.69 x 10(4) M-1 and four to five sites with affinity constant 7.14 x 10(2) M-1. Association constants for decanoic acid are 3-4-fold larger than those of sebacic acid. Data of binding of sebacic acid in human serum suggested that only three to five of the low affinity sites are available for binding. When disodium sebacate is administered i.v. for total parenteral nutrition, a substantial fraction of sebacic anions is likely to be bound in serum.

Study of the relationship between estimates of enzyme kinetic parameters

Previous indications of an intrinsic relationship between estimates of Km and Vmax calculated from the Michaelis-Menten equation have been explored further. A mathematically linear relationship could be established for the estimates of the two parameters. The relationship--the trend line--holds whether or not the experimental error is linked to the rate of reaction, the substrate concentration or both, provided that the distribution of errors is symmetrical. The practical implication is that enzyme variants with low values of Km and Vmax may not be distinguishable from those with high values of Km and Vmax.

Binding of NAD+ by cholera toxin

1. The Km for NAD+ of cholera toxin working as an NAD+ glycohydrolase is 4 mM, and this is increased to about 50 mM in the presence of low-Mr ADP-ribose acceptors. Only molecules having both the adenine and nicotinamide moieties of NAD+ with minor alterations in the nicotinamide ring can be competitive inhibitors of this reaction. 2. This high Km for NAD+ is also reflected in the dissociation constant, Kd, which was determined by a variety of methods. 3. Results from equilibrium dialysis were subject to high error, but showed one binding site and a Kd of about 3 mM. 4. The A1 peptide of the toxin is digested by trypsin, and this digestion is completely prevented by concentrations of NAD+ above 50 mM. Measurement (by densitometric scanning of polyacrylamide-gel electrophoretograms) of the rate of tryptic digestion at different concentrations of NAD+ allowed a more accurate determination of Kd = 4.0 +/- 0.4 mM. Some analogues of NAD+ that are competitive inhibitors of the glycohydrolase reaction also prevented digestion.

Immunochemistry of scorpion alpha-toxins: purification and characterization of two functionally independent IgG populations raised against toxin II of Androctonus australis Hector

We report the isolation and characterization of two IgG populations specific to two synthetic peptides corresponding to two antigenic sites of toxin II of the North African scorpion Androctonus australis Hector. Firstly, thanks to the use of: (1) antigenic homology studies between toxin II of A. australis Hector and toxin III of Buthus occitanus tunetanus, (2) chemical modification of toxin II of A. australis Hector, and (3) prediction of the localization of the four major antigenic sites of scorpion alpha-toxins by the method developed by Hopp and Woods [Proc. natn. Acad. Sci. U.S.A. 78, 3824-3828 (1981)], we have established that the region around the disulfide bridge between cysteines 12 and 63 as well as the stretch of residues 50-59 probably each enclosed an antigenic site. Secondly, the synthetic replicates of these regions linked to Sepharose allowed us to isolate, by immunoaffinity chromatography, two IgG populations from the whole anti-toxin II of A. australis Hector IgGs. Finally, each of these two IgG populations was shown to be specific to one antigenic site as evidenced by the multideterminant effect on the slopes of binding curves developed by Berzofsky et al. [Biochemistry 15, 2113-2121 (1976)]. Furthermore, these two IgG populations were found to be functionally independent and this could be related to the fact that the two regions carrying the two antigenic sites are not close to each other in space and that there is neither steric hindrance nor cooperative effects between them. The association constant of these site-specific IgG populations was calculated and found to be equal to 1.18-5.14 X 10(9) l/mole for IgG anti-site 1 and 1.16-5.62 X 10(9) l/mole for IgG anti-site 2 respectively by Sips [J. chem. Phys. 16, 490-495 (1948)], Scatchard [Am. N.Y. Acad. Sci. 51, 660-772 (1949)] and Steward and Petty [Immunology 23, 881-887 (1972)] representations. The index of heterogeneity of 0.9 for anti-P1 and anti-P2 indicates the purification of essentially homogeneous affinity IgG populations.

Ultrafiltration vs equilibrium dialysis for determination of free fraction

The analytical basis of membrane separation in determining plasma free drug concentrations is developed from consideration of the generalised ideal mass action and conservation laws applied to thermodynamic states of differing component volumes. The intuitively surprising theoretical independence of free drug concentration with changing fractional volume of protein predicts the equivalence of final free drug concentration after uniform pre-dilution with that after equilibrium dialysis against the same volume of buffer. Similarly, the ultrafiltrate free concentration of drugs in ideal plasma binding equilibrium is theoretically constant, regardless of the extent of reduction in fractional volume of binding protein during filtration. The pitfalls in calculating free and bound fraction and concentration from equilibrium dialysis are reviewed and expressions presented to correct the major artefacts. The dilution behaviour of drugs is predicted from the normalised mass action model. Practical aspects of validating ultrafiltration free drug levels using equilibrium dialysis are outlined.

A comparison of methods for estimating the kinetic parameters of two simple types of transport process

Sets of experimental data, with known characteristics and error structures, have been simulated for the Michaelis-Menten equation plus a second term, either for linear transport or for competitive inhibition. The Michaelis-Menten equation plus linear term was fitted by several methods and the accuracy and the precision of the parameter estimates from the several methods were compared. The model-fitting methods were: three for least-squares non-linear regression, computer versions of two graphical methods and of two non-parametric methods. The most precise and accurate method was that of D.W. Marquardt (J. Soc. Ind. Appl. Math. 11 (1963) 431--441). The Michaelis-Menten equation with competitive inhibition was also fitted by several methods, viz., two for least-squared non-linear regression, non-parametric method and four variants of the Preston-Schaeffer-Curran plot (Preston, R.L. et al. (1974) J. Gen. Physiol. 64, 443--467). The most precise and accurate of these was the non-linear regression method of W.W. Cleland (Adv. Enzymol. 29 (1967) 1--32). For both these models, the various graphical methods and non-parametric methods gave poor results and are not recommended.

Thermodynamics and membrane processes

This review represents a personal view of membrane thermodynamics. I do not intend to deal at all with the irreversible thermodynamics of membrane mass transfer processes. This aspect has been covered far more competently and completely by other people (Bittar, 1970; Paterson, 1970; Rottenberg, Caplan & Essig, 1970; Mitchell, 1970; Rothschildet al.1980; Oster, Perelson & Katchalsky, 1973; Kedem & Katchalsky, 1958; Schwartz, 1971). The recent review on osmosis by Hill (1979) is a particularly succinct appraisal of a facet of irreversible membrane thermodynamics. Arata & Nishimura (1980) have considered the coupling of electron transfer to vectorial processes in biological membranes.

Determination of affinity of monoclonal antibodies against human IgG

A method for determining the affinity and the concentration of mouse monoclonal antibodies against human IgG has been developed. The method comprises two steps. First, monoclonal antibodies are allowed to combine with radioiodinated human IgG. Secondly, mouse monoclonal IgG with and without complexed IgG is precipitated with rabbit IgG against mouse IgG. As the antigen is divalent complexes of varying composition are formed in this system leading to deviations from linearity in plots obtained in commonly employed analytical systems. The theoretical background of these systems has been studied by computer stimulation, and a concentration effect on the formation of immune complexes were demonstrated. The affinities (in terms of the association constants (of 6 monoclonal antibodies were estimated and found to be in the range from 2 X 10(6) M-1 to 5 X 10(8) M-1.

A modified equilibrium dialysis method for studying fatty acid binding to proteins

A modified equilibrium dialysis method is described which is suitable for investigating the binding of fatty acids in the form of aqueous micellar dispersions to proteins. The method uses a permeant chromophore which complexes reversibly with free fatty acid within the dialysis bag. The concentration outside the dialysis bag is determined spectrophotometrically. Binding of oleic acid to bovine serum albumin is given as an example. A simplified analysis of fatty acid binding is given and used to indicate the potential of the method.

A method to estimate binding constants at variable protein concentrations

The association constants of the binding of chlorpromazine and imipramine to serum albumin at low saturation of the protein were determined by a new experimental approach with the protein concentration rather than the ligand concentration being varied. This approach is suitable for estimating binding constants in systems with one class of binding sites. In addition, the method is proposed to complement conventional binding studies of systems with two classes of binding constant with higher accuracy.