Effects of thermodynamic nonideality in ligand binding studies

Effects of thermodynamic nonideality are considered in relation to the quantitative characterization of the interaction between a small ligand. S, and a macromolecular acceptor. A, by two types of experimental procedure. The first involves determination of the concentration of ligand in dialysis equilibrium with the acceptor/ligand mixture, and the second, measurement of the concentration of unbound ligand in the reaction mixture by ultrafiltration or the rate of dialysis method. For each situation explicit expressions are formulated for the appropriate binding function with allowance for composition-dependent nonideality effects expressed in terms of molar volume, charge-charge interaction and covolume contributions. The magnitudes of these effects are explored with the aid of experimental studies on the binding of tryptophan and of methyl orange to bovine serum albumin. It is concluded for experiments conducted utilizing either equilibrium dialysis or frontal gel chromatography that, provided a correction is made for any Donnan redistribution of ligand, theoretically predicted acceptor-concentration dependence is likely to be negligible and that use of the conventional binding equation written for an ideal system is appropriate to the analysis of the results. Use of ultrafiltration or the rate of dialysis method requires examination of the assumption that the activity coefficient ratio y(A)y(s)/y(AS) for the reaction mixture approximates unity; but again reassurance is provided that nonideality manifested as a dependence of the binding function on acceptor concentration is unlikely to be significant.     

Experimental tests of charge conservation in macromolecular interactions

A combination of equilibrium dialysis and ultrafiltration has been used to demonstrate the conservation of charge in the interaction between bovine serum albumin and methyl orange in Tris-HCl buffer, pH 7.4, I = 0.05 M; and also in the dimerization of alpha-chymotrypsin in acetate/chloride buffer, pH 3.9, I = 0.11 M, containing various concentrations of indole (0-10 mM) in order to displace the equilibrium position towards monomer. In the former study the magnitude of the negative charge on the albumin was shown to increase linearly with the number of molecules of methyl orange bound to the protein, the observed slope (0.96 +/- 0.08) of this relationship being in excellent agreement with that predicted on the basis of charge conservation for attachment of the univalent, negatively charged methyl orange ligand. In the study of alpha-chymotrypsin, the net charge (expressed per monomeric enzyme unit) was +10 in solutions in which the mole fraction of monomer varied between 0.47 and 0.88, the extent of this range having been established by means of constituent association equilibrium constants obtained from sedimentation equilibrium studies.     

The Donnan Equilibrium: A Theoretical Study of the Effects of Interionic Forces

We investigate the conditions under which nonideality in solution influences the Donnan equilibrium. Of the various parameters that characterize this equilibrium, the osmotic pressure established across the Donnan membrane is found to be particularly sensitive to intermolecular interactions between the diffusible and nondiffusible ionic species. Under physiologically appropriate conditions, we find that it is almost never valid to use Debye-Hückel theory to calculate ionic activities: it is important to take proper account of ion size. When the diffusible species is a 1-1 electrolyte, this can be done using the mean spherical approximation (MSA) for a mixture of ions of different diameters. For 2-2, or higher-valent, electrolytes one should also include the effects of the second ionic virial coefficient, which the MSA omits.     

Nonequivalence of second virial coefficients from sedimentation equilibrium and static light scattering studies of protein solutions

Experimental data for ovalbumin and lysozyme are presented to highlight the nonequivalence of second virial coefficients obtained for proteins by sedimentation equilibrium and light scattering. Theoretical considerations confirm that the quantity deduced from sedimentation equilibrium distributions is B(22), the osmotic second virial coefficient describing thermodynamic nonideality arising solely from protein self-interaction. On the other hand, the virial coefficient determined by light scattering is shown to reflect the combined contributions of protein-protein and protein-buffer interactions to thermodynamic nonideality of the protein solution. Misidentification of the light scattering parameter as B(22) accounts for published reports of negative osmotic second virial coefficients as indicators of conditions conducive to protein crystal growth. Finally, textbook assertions about the equivalence of second virial coefficients obtained by sedimentation equilibrium and light scattering reflect the restriction of consideration to single-solute systems. Although sedimentation equilibrium distributions for buffered protein solutions are, indeed, amenable to interpretation in such terms, the same situation does not apply to light scattering measurements because buffer constituents cannot be regarded as part of the solvent: instead they must be treated as non-scattering cosolutes.     

Evaluation of nonideality from gel chromatographic partition coefficients. A technique with greater versatility than equilibrium dialysis

Frontal gel chromatography has been used to measure partition coefficients which enable a quantitative evaluation of the thermodynamic nonideality of small solutes generated by the presence of high concentrations of macromolecular solutes. Equivalence of results obtained by the present method and by equilibrium dialysis is demonstrated in a comparison of results for dextran sulfate-NaCl and dextran-sorbitol systems. Interaction coefficients obtained for dextran-sorbitol and protein-polyethylene glycol 4000 systems yields results which are in reasonable agreement with those predicted on the statistical-mechanical basis of excluded volume. Because of its greater versatility in regard to the range of systems that may be studied, the frontal gel chromatographic procedure is likely to be of particular value for the quantitative characterization of thermodynamic nonideality arising from excluded volume effects in concentrated mixtures of macromolecular solutes.     

Negative second virial coefficients as predictors of protein crystal growth: evidence from sedimentation equilibrium studies that refutes the designation of those light scattering parameters as osmotic virial coefficients

The effects of ammonium sulphate concentration on the osmotic second virial coefficient (BAA/MA) for equine serum albumin (pH 5.6, 20 degrees C) have been examined by sedimentation equilibrium. After an initial steep decrease with increasing ammonium sulphate concentration, BAA/MA assumes an essentially concentration-independent magnitude of 8-9 ml/g. Such behaviour conforms with the statistical-mechanical prediction that a sufficient increase in ionic strength should effectively eliminate the contributions of charge interactions to BAA/MA but have no effect on the covolume contribution (8.4 ml/g for serum albumin). A similar situation is shown to apply to published sedimentation equilibrium data for lysozyme (pH 4.5). Although termed osmotic second virial coefficients and designated as such (B22), the negative values obtained in published light scattering studies of both systems have been described incorrectly because of the concomitant inclusion of the protein-salt contribution to thermodynamic nonideality of the protein. Those negative values are still valid predictors of conditions conducive to crystal growth inasmuch as they do reflect situations in which there is net attraction between protein molecules. However, the source of attraction responsible for the negative virial coefficient stems from the protein-salt rather than the protein-protein contribution, which is necessarily positive.     

Interaction of phenolsulphonphthalein dyes with rabbit plasma and rabbit serum albumin.

Interaction of various substituted phenolsulphonphthalein dyes to rabbit plasma and rabbit serum albumin has been studied by ultrafiltration, equilibrium dialysis and spectrophotometry. The results obtained by ultrafiltration and equilibrium dialysis showed that the degree of binding of these dyes to protein increases in the following order: Phenol red less than bromophenol blue less than bromocresol green less than bromothymol blue. Analysis of binding results revealed that five molecules of bromothymol blue bound very strongly to a molecule of rabbit albumin, whereas only two and three molecules of bromophenol blue and bromocresol green strongly interact with the protein, respectively. It is suggested that strong binding of these substances to protein may be related to the hydrophobicity of these compounds. Finally, an attempt has been made to evaluate the possibility, whether the spectral changes occurred during interaction of dyes to albumin can be utilized for the determination of binding of these ligands to proteins.     

Graphical analysis of binding data reflecting competition between two ligands for the same acceptor sites

A theoretical expression is derived for the analysis of results from competitive binding studies in which two multivalent ligands compete for acceptor sites, and a linear transform is suggested for simple graphical representation and assessment of experimental results. The protocol is illustrated by application to competitive binding data, obtained by ultrafiltration, on the interactions of bovine serum albumin with two structurally similar organic anions, methyl orange and methyl red. In a second experimental study the present approach is then used to establish that lactate dehydrogenase and aldolase compete for the same myofibrillar sites of bovine cardiac muscle. Finally, numerically simulated behavior of systems with additional binding sites for either ligand is used to emphasize that the criterion for classical (complete) competition is agreement between an experimentally determined equilibrium constant for ligand binding and the apparent value deduced from competitive binding studies. Nevertheless, the present analysis of competitive binding data should still offer considerable scope for screening quantitatively the cross-reactivities of drug and antigen analogs for their respective specific protein-acceptor sites.     

Binding of radioiodinated human beta-endorphin to serum proteins from rats and humans, determined by several methods

Binding of immunoreactive radioiodinated human beta-endorphin (125I-beta-EP) to rat serum was demonstrated by gel filtration of 125I-beta-EP in pooled rat serum on Sephadex G-200. Two radioactive peaks associated with proteins eluted from the column. The first peak eluted at the void volume containing lipoproteins, alpha 2- and beta 2-macroglobulins, and the second peak at the fraction of albumin. Binding of 125I-beta-EP to albumin was directly proved by gel filtration of 125I-beta-EP in buffer containing 4% human serum albumin on Sephadex G-200. Equilibrium dialysis was not applicable to investigating the interaction of 125I-beta-EP with serum proteins, because of the intense nonspecific adsorption to the semipermeable membrane and the degradation of the peptide during dialysis. Therefore, in order to quantitatively evaluate the binding of 125I-beta-EP in sera from rats and humans, we utilized four other methods (ultrafiltration, charcoal adsorption, polyethylene glycol precipitation and equilibrium gel filtration). These methods corresponded well with each other and indicated 35-44% binding of 125I-beta-EP in rat serum. Binding of 125I-beta-EP in normal human serum was 36%, determined by ultrafiltration. Serum protein binding of 125I-beta-EP was concentration independent over the concentration range studied (1-1000 nM).     

Cooperative elution of oligoadenylic acid in polyU immobilized chromatography.

Characterization of polyU immobilized chromatography was performed in order to use this technique as an analytical device. A method of analysis of the elution profile related to thermodynamic parameters was also developed. Sites of attachment of polyU to agarose gel activated by cyanogen bromide were studied using uridine diphosphate and adenine. Independent equilibrium dialysis of ApA for different states of polyU, in solution and immobilized in gel, were carried out. These results show that the immobilized polyU is attached to agarose only at the 5′-terminal phosphate groups and behaves as it does in solution. Column chromatography of ApA with the immobilized polyU was performed at several temperatures and concentrations. To analyze the elution profile, the theory of cooperative binding of oligonucleotides to polynucleotides was extended to the frame-work of plate theory. A computer simulation for the elution profiles was performed using thermodynamic parameters obtained by equilibrium dialysis. This simulation duplicated the experimental results. This fact shows that the peculiar leading form of elution profile is due to the cooperative binding. The thermodynamic parameters of the polyU–ApA system were obtained from the “peak trajectory.”     

Assessment of the validity of the Adams and Fujita approximation for the higher oligomers of human spectrin

Analysing the self-association behaviour of human erythrocyte spectrin is complicated by a large degree of nonideality. Adams and Fujita [1] proposed that, as a first order approximation, the logarithm of the activity coefficient of the protomer of a self-associating system can be considered to be linearly dependent on the total concentration of the protein, and that the same second virial coefficient could be considered to apply to all species. As a consequence of the Adams and Fujita approximation, the apparent equilibrium constant is equal to the thermodynamic equilibrium constant. The equilibrium concentrations at 30°C of each oligomer spectrin species up to the 14-mer were determined after electrophoresis at low temperature. An apparent equilibrium constant for forming tetramer (K_2,4) of (1.2 ± 0.1) × 10⁶ l/mol was obtained, a value of (9.4 ± 0.7) × 10⁴ l/mol was obtained for K_4,6 and for all reactions forming oligomers higher than the hexamer an average approximate value of (2.7 ± 0.4) × 10⁵ l/mol was obtained. The apparent equilibrium constants for the formation of all oligomer species of spectrin up to the tetrakaidecamer (14-mer) remain relatively independent of total spectrin concentration, and indicate that within the precision of the measurements a single virial coefficient is sufficient to account for the nonideality of spectrin self-association over the range 2–42 g/l, thus further justifying the use of the Adams and Fujita approximation for this protein over this concentration range.     

Stability, pKa and plasma protein binding of roscovitine

In the present investigation, the binding of roscovitine (100, 500 and 1500 ng/mL) to plasma proteins was studied at 25 and 37 degrees C by ultrafiltration and equilibrium dialysis methods. Drug stability in plasma was assessed during a 48 h at 4, 25 and 37 degrees C. The effect of thawing and freezing on drug stability was studied. The pKa of roscovitine was measured using capillary electrophoresis coupled with mass spectrometry. Roscovitine was quantified utilizing liquid chromatography and tandem mass spectrometry. Roscovitine is highly bound to plasma proteins (90%). Binding of roscovitine to human serum albumin was constant (about 90%) within concentration range studied while the binding to alpha1-acid glycoprotein decreased with increasing drug concentration indicating that albumin is more important in clinical settings. However, alpha1-acid glycoprotein might be important when plasma proteins change with disease. Protein binding was higher at 25 degrees C compared to 37 degrees C. The results obtained by equilibrium dialysis were in good agreement with those obtained by ultrafiltration. Roscovitine was stable at all temperatures studied during 48 h. Roscovitine has a pKa of 4.4 showing that the drug mainly acts like a weak mono-base. The results obtained in our studies are important prior to clinical trials and to perform pharmacokinetic studies.     

Direct measurement of protein osmotic second virial cross coefficients by cross-interaction chromatography

The importance of weak protein interactions, such as protein self-association, is widely recognized in a variety of biological and technological processes. Although protein self-association has been studied extensively, much less attention has been devoted to weak protein cross-association, mainly due to the difficulties in measuring weak interactions between different proteins in solution. Here a framework is presented for quantifying the osmotic second virial cross coefficient directly using a modified form of self-interaction chromatography called cross-interaction chromatography. A theoretical relationship is developed between the virial cross coefficient and the chromatographic retention using statistical mechanics. Measurements of bovine serum albumin (BSA)/lysozyme cross-association using cross-interaction chromatography agree well with the few osmometry measurements available in the literature. Lysozyme/alpha-chymotrypsinogen interactions were also measured over a wide range of solution conditions, and some counterintuitive trends were observed that may provide new insight into the molecular origins of weak protein interactions. The virial cross coefficients presented in this work may also provide insight into separation processes that are influenced by protein cross-interactions, such as crystallization, precipitation, and ultrafiltration.     

Liver function and protein binding in camels

1. Dehydration of camels for 10 days resulted in reduction of liver functions, expressed in longer half life and reduced clearance of bromosulfophthalein (BSP), elevated AST (ALT levels were below the limit of detection of the method) and reduced serum albumin concentrations. 2. Binding of BSP to camel serum proteins by gel permeation chromatography and by equilibrium dialysis showed very strong binding. 3. Binding parameters of various drugs to camels serum by equilibrium dialysis showed close similarities both qualitatively and quantitatively to those of humans. 4. Albumin seems to be the major serum binding protein of BSP.     

Error analysis in equilibrium dialysis: evaluation of adsorption phenomena

Various sources of error in equilibrium dialysis may lead to inaccurate results of binding experiments: (i) the finite time of dialysis; (ii) the Donnan effects; (iii) the adsorption of ligand to the membrane; and (iv) release of contaminating material from dialysis casings. These errors were analyzed for a polynucleotide-oligopeptide model system with particular regard to adsorption phenomena and the underlying mechanisms. Adsorption data were treated according to Freundlich and Langmuir isotherms. The latter turned out to be more appropriate for the consideration of adsorption phenomena with respect to a minimum error propagation. Furthermore, it was shown that the degree of adsorption varies with ionic strength and temperature and could be interpreted in terms of polyelectrolyte theory. The kinetics of both adsorption and of the ligand distribution between the polymer and buffer compartments follow first order at the beginning of dialysis which is in line with a simple diffusion process. After 13-15 h data deviate from first order kinetics indicating an alteration in the transport mechanism. The effects of errors on binding parameters were determined and a detailed protocol for correction is presented allowing one to obtain binding data from equilibrium dialysis experiments with the required degree of accuracy. The fundamental principles and results for the system under investigation generally apply to all protein-ligand systems.     

Controlling protein transport in ultrafiltration using small charged ligands

Previous studies have demonstrated that protein transport during ultrafiltration can be strongly influenced by solution pH and ionic strength. The objective of this study was to examine the possibility of controlling protein transmission using a small, highly charged ligand that selectively binds to the protein of interest. Experiments were performed using bovine serum albumin and the dye Cibacron Blue. Protein sieving data were obtained with essentially neutral and negatively charged versions of a composite regenerated cellulose membrane to examine the effects of electrostatic interactions. The addition of only 1 g/L of Cibacron Blue to an 8 g/L BSA solution reduced the BSA sieving coefficient through the negatively-charged membrane by more than two orders of magnitude, with this effect being largely eliminated at high salt and with the neutral membrane. Protein sieving data were in good agreement with model calculations based on the partitioning of a charged sphere in a charged pore accounting for the change in net protein charge due to ligand binding and the increase in solution ionic strength due to the free ligand in solution.     

Measurement of thermodynamic nonideality arising from volume-exclusion interactions between proteins and polymers

The effective thermodynamic radii of 23 ribosomal proteins from the 50 S subunit have been determined by gel chromatography on Sephadex G-50, thereby supporting the contention that most of the proteins of the 50 S ribosomal unit exhibit reasonably globular structures. To investigate further the usefulness of modelling proteins as spheres, the second virial coefficient describing excluded volume interactions of some ribosomal proteins with two inert polymers, polyethylene glycol (PEG) and dextran, has been determined by gel chromatography and/or sedimentation equilibrium techniques. Protein-polymer excluded volumes obtained with PEG 20000 and Dextran T70 as the space-filling solute are shown to conform reasonably well with a quantitative expression describing interaction between an impenetrable sphere and an ideal Brownian path (K.M. Jansons and C.G. Phillips, J. Colloid Interface Sci., 137 (1990) 75).