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.     

Effects of thermodynamic nonideality in kinetic studies

Experimental evidence is presented for concentration dependence of the pseudo-firstorder rate constant describing the rate of inversion of sucrose by 2 m HCl; and also of the increase in maximal velocity for the catalytic reduction of pyruvate by lactate dehydrogenase that results from addition of the inert macromolecular solutes bovine serum albumin, ovalbumin, and Dextran T70. These somewhat unusual and seemingly diverse observations are examined in terms of a theory formulated on the basis of two equilibrium reactions, the first describing complex formation between two reactants, and the second isomerization of that complex to an activated state prior to product formation. This formulation permits consideration of activity coefficient ratios relevant to the equilibria and the expression of these ratios as power series in total solution composition. Quantitative assessment of the experimental results is made possible in these terms by estimating the magnitudes of the constant coefficients of the virial expansions as excluded volumes. It is concluded that the result observed in the sucrose inversion study finds rational explanation in thermodynamic nonideality factors governing the overall equilibrium between the reactants and the activated complex of sucrose and hydronium ion. For the enzyme-catalyzed reaction the same general equation applies but particular attention is given to the simplified form that is relevant to high substrate concentrations, where, in the absence of inert compounds, the conventional maximal velocity is approached. In this region an increase in velocity observed upon addition of an inert macromolecular component may be considered explicitly in terms of excluded volume effects related to a shape change in the isomerization between enzyme-substrate complex and its activated state.     

Effects of thermodynamic nonideality on the kinetics of ester hydrolysis by alpha-chymotrypsin: a model system with preexistence of the isomerization equilibrium

The effects of a small inert solute, sucrose, on the kinetics of hydrolysis of N-acetyl-tryptophan ethyl ester by bovine alpha-chymotrypsin have been investigated. In studies at pH 7 and 20 degrees C the presence of 0.5 M sucrose in assay mixtures caused no discernible change in kinetic parameters, a result consistent with existence of the enzyme in a single conformational state under those conditions. However, at pH 3.5 and 50 degrees C, conditions under which the enzyme comprises an equilibrium mixture of compact and expanded isomeric states, inclusion of the inert solute led to a considerable decrease in Michaelis constant (0.84 to 0.61 mM) but no significant change in maximal velocity. These results were shown to be amenable to quantitative interpretation in terms of thermodynamic nonideality effects on catalysis by an enzyme undergoing reversible isomerization in the absence of substrate. For that analysis, which required experimental estimates of the equilibrium constant for preexisting isomerization of enzyme and the activity coefficient of substrate, the magnitude of the former (0.3) was obtained by difference spectroscopy: liquid-liquid partition studies with bromobenzene as organic phase were used to determine the effect of sucrose on the activity coefficient of N-acetyltryptophan ethyl ester. Such agreement between experimental kinetic findings and theoretical predictions based on considerations of excluded volume points to the possible use of the space-filling effects of small solutes for delineating the gross extent of conformational changes associated with reversible isomerization of proteins, and hence to the potential of thermodynamic nonideality as a probe for studying protein denaturation mechanisms as well as substrate-mediated changes associated with enzyme reaction mechanisms.     

Effect of sucrose on the dimerization of alpha-chymotrypsin. Allowance for thermodynamic nonideality arising from the presence of a small inert solute

The space-filling effects of sucrose on the dimerization of alpha-chymotrypsin have been investigated by sedimentation equilibrium studies on the enzyme in acetate-chloride buffer, pH 3.9, I 0.2. From the extent of enhancement of the apparent dimerization constant in the presence of 0.05-0.16 M sucrose, it is concluded that this effect of thermodynamic nonideality finds quantitative explanation in terms of excluded volume. However, the suggested approximation that the radius of an inert small solute would be sufficiently small to be neglected in the calculation of covolumes (D.J. Winzor and P.R. Wills, Biophys. Chem. 25 (1986) 243) has not withstood the more stringent test afforded by the present study of alpha-chymotrypsin dimerization. A value of 0.34 nm for the effective thermodynamic radius of sucrose was inferred from the covolume for self-interaction obtained by frontal gel chromatography on Sephadex G-10 under the conditions of the ultracentrifugal studies. Finally, results of sedimentation equilibrium experiments on alpha-chymotrypsin in the presence of 0.1 M glycerol were also shown to be consistent with interpretation in terms of the model of space-filling effects entailing complete exclusion of small solute from the hydrated protein domain.     

Effects of thermodynamic nonideality on protein interactions. Equivalence of interpretations based on excluded volume and preferential solvation

Published results on the stabilization of proteins by sucrose (J.C. Lee and S.N. Timasheff, J. Biol. Chem. 256 (1981) 7193) have been reexamined and interpreted in terms of thermodynamic nonideality. The composition dependence of activity coefficients may be accounted for on a statistical-mechanical basis using the concept of excluded volume. An expression is derived in which the effect of sucrose on determination of the partial specific volume of a protein, previously interpreted in terms of preferential protein solvation, is also seen to be attributable to excluded volume. Gel chromatographic studies of the reversible unfolding of alpha-chymotrypsin are presented which demonstrate temperature- and sucrose-mediated changes in the effective volume of the enzyme. These measurements support the quantitative interpretation of the stabilization in terms of thermodynamic nonideality arising from the difference between covolumes for sucrose and the two isomeric states of alpha-chymotrypsin. By establishing the equivalence of the two approaches that have been used to account for the effects of inert solutes on protein transitions, the present investigation eliminates the need for any distinction between such solutes on the basis of molecular size; and also enhances greatly the potential sensitivity of thermodynamic nonideality as a means of probing protein isomerizations, since greater displacement of the equilibrium position may be effected by small rather than by macromolecular solutes present at the same weight concentrations.     

Interactions of glycolytic enzymes with erythrocyte membranes

Partition equilibrium experiments have been used to characterize the interactions of erythrocyte ghosts with four glycolytic enzymes, namely aldolase, glyceraldehyde-3-phosphate dehydrogenase, phosphofructokinase and lactate dehydrogenase, in 5 mM sodium phosphate buffer (pH 7.4). For each of these tetrameric enzymes a single intrinsic association constant sufficed to describe its interaction with erythrocyte matrix sites, the membrane capacity for the first three enzymes coinciding with the band 3 protein content. For lactate dehydrogenase the erythrocyte membrane capacity was twice as great. The membrane interactions of aldolase and glyceraldehyde-3-phosphate dehydrogenase were mutually inhibitory, as were those involving either of these enzymes and lactate dehydrogenase. Although the binding of phosphofructokinase to erythrocyte membranes was inhibited by aldolase, there was a transient concentration range of aldolase for which its interaction with matrix sites was enhanced by the presence of phosphofructokinase. In the presence of a moderate concentration of bovine serum albumin (15 mg/ml) the binding of aldolase to erythrocyte ghosts was enhanced in accordance with the prediction of thermodynamic nonideality based on excluded volume. At higher concentrations of albumin, however, the measured association constant decreased due to very weak binding of the space-filling protein to either the enzyme or the erythrocyte membrane. The implications of these findings are discussed in relation to the likely subcellular distribution of glycolytic enzymes in the red blood cell.     

Elimination of self-association as the source of the thermodynamic nonideality in aqueous proline solutions

The effect of high concentrations of proline on the diffusion coefficient of water has been examined to assess the extent to which the resulting thermodynamic nonideality could be explained on the statistical-mechanical basis of excluded volume. In fact, such a space-filling role not only accounts for the proline concentration-dependence of the diffusion coefficient of water but it also accounts for the nonideality of proline in freezing point depression and isopiestic measurements. These findings refute the conclusion (Schobert, B. and Tschesche, H. (1978) Biochim. Biophys. Acta 541, 270–277) that the stabilization of enzyme structure by high concentrations of proline stems from self-association of the imino acid via intermolecular hydrogen bonding; and thereby support the concept that the protective effect of proline on enzyme stability must reside mainly in its action as an inert, space-filling solute.     

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.     

Quantitative considerations of the consequences of an interplay between ligand binding and reversible adsorption of a macromolecular solute

Explicit expressions are derived which determine the equilibrium composition of mixtures comprising a multivalent, insoluble matrix, a multivalent, macromolecular solute (acceptor) and a univalent ligand. With three-reactant mixtures of this type a range of combinations of interactions is possible wherein the ligand interacts with either the acceptor or the matrix, in either event perturbing the acceptor-matrix equilibria. Theory encompassing this range of possibilities is written in terms of a single site-binding constant for each type of interaction to account, in general terms, for both multiple binding and crosslinking effects. These explicit thermodynamic relationships are discussed, with the use of reported findings on several biological systems, in two frameworks. First, it is established that the theory is applicable to the quantitative interpretation of affinity chromatography experiments designed to elucidate the thermodynamic interaction parameters governing the various types of interacting system. Second, it is emphasized that the relationships are also relevant to metabolite-induced changes in the subcellular distribution of macromolecular species.     

The effect of non-binding molecules on the gelation of HbS

The influence of an inert globular macromolecule upon the solubility of sickle cell hemoglobin has been determined as a function of the degree of oxygenation. The thermodynamic theory required to treat this and related problems is derived partition function. The treatment includes non-ideal solution behaviour as measured by osmotic pressure of highly concentrated macromolecular. solutions. Application of the theoretical equations demonstrates how the solubility of hemoglobin is influenced by the presence of the binding ligand (oxygen) and the inert macromolecule, bovine serum albumin (BSA). Good agreement is obtained between experimentally determined and theoretically calculated solubilities using 1) oxygen binding curves to solution and gel phases, 2) activity coefficients from osmotic pressure data, 3) one solubility under the condition where oxygen and BSA are absent, and 4) the value of the water content of the gel phase. Examination of the theoretical equations suggests that inert molecules of intermediate size, that are partially excluded from crystalline or gel phases, have the potential of generally increasing the solubility when non-ideal solution effects are small.     

Effects of molecular crowding on the interaction between DNA and the Escherichia coli regulatory protein TyrR

Fluorescence quenching has been used to measure quantitatively the effects of sucrose and triethylene glycol on the interaction between the Escherichia coli regulatory protein TyrR and a 30-basepair oligonucleotide containing the strong TyrR box of the TyrR operon. It was observed that the apparent binding constant increased in the presence of co-solutes, the dependence of the logarithm of the apparent binding constant on molar concentration being indistinguishable and essentially linear for both co-solutes. This activation of the TyrR-oligonucleotide interaction is attributed to thermodynamic nonideality arising from molecular crowding, an interpretation which is supported by the reasonable agreement observed between the experimental extent of reaction enhancement and that predicted on the statistical-mechanical basis of excluded volume.     

Space-filling effects of inert solutes as probes for the detection and study of substrate-mediated conformational changes by enzyme kinetics: theoretical considerations

From expressions derived for the space-filling effects of small inert solutes on kinetic parameters for univalent enzymes undergoing isomerizations that are substrate-induced and pre-existing, it is concluded that experimental observation of an enhanced maximal velocity in the presence of inert solute can only reflect the existence of the former type of conformational change; and that the isomerization must be governed by a relatively small equilibrium constant. Similar conclusions apply to multivalent enzymes exhibiting Michaelis-Menten kinetics. Extension of the theory to provide quantitative expressions for multivalent enzymes has made possible the numerical simulation of thermodynamic non-ideality effects on systems conforming with the Monod and Koshland models of allostery. In that regard the simulated Scatchard plots for the two models differ sufficiently in form to suggest that detailed examination of the space-filling effects of small solutes on the kinetics of an allosteric enzyme may, under favourable circumstances, allow identification of the appropriate allosteric mechanism. Finally, these considerations of thermodynamic non-ideality in relation to the kinetics of allosteric enzymes have revealed formal similarities between the consequences of space-filling by inert solutes and the specific effects of allosteric activators or inhibitors. Attention is drawn to the possible implications of this observation in relation to the functioning of allosteric enzymes in vivo, where catalytic performance may be modified by factors no more specific than the ability of unrelated solutes to occupy space in the highly concentrated cellular environment.     

The use of analytical sedimentation velocity to extract thermodynamic linkage

For 25 years, the Gibbs Conference on Biothermodynamics has focused on the use of thermodynamics to extract information about the mechanism and regulation of biological processes. This includes the determination of equilibrium constants for macromolecular interactions by high precision physical measurements. These approaches further reveal thermodynamic linkages to ligand binding events. Analytical ultracentrifugation has been a fundamental technique in the determination of macromolecular reaction stoichiometry and energetics for 85 years. This approach is highly amenable to the extraction of thermodynamic couplings to small molecule binding in the overall reaction pathway. In the 1980s this approach was extended to the use of sedimentation velocity techniques, primarily by the analysis of tubulin-drug interactions by Na and Timasheff. This transport method necessarily incorporates the complexity of both hydrodynamic and thermodynamic nonideality. The advent of modern computational methods in the last 20 years has subsequently made the analysis of sedimentation velocity data for interacting systems more robust and rigorous. Here we review three examples where sedimentation velocity has been useful at extracting thermodynamic information about reaction stoichiometry and energetics. Approaches to extract linkage to small molecule binding and the influence of hydrodynamic nonideality are emphasized. These methods are shown to also apply to the collection of fluorescence data with the new Aviv FDS.     

A simple model for solvation in mixed solvents. Applications to the stabilization and destabilization of macromolecular structures

The properties of a simple model for solvation in mixed solvents are explored in this paper. The model is based on the supposition that solvent replacement is a simple one-for-one substitution reaction at macromolecular sites which are independent of one another. This leads to a new form for the binding polynomial in which all terms are associated with ligand interchange rather than ligand addition. The principal solvent acts as one of the ligands. Thermodynamic analysis then shows that thermodynamic binding (i.e., selective interaction) depends on the properties of K'-1, whereas stoichiometric binding (site occupation) depends on K'. K' is a 'practical' interchange equilibrium constant given by (f3/f1)K, where K is the true equilibrium constant for the interchange of components 3 and 1 on the site and f3 and f4 denote their respective activity coefficients on the mole fraction scale. Values of K' less than unity lead to negative selective interaction. It is selective interaction and not occupation number which determines the thermodynamic effects of solvation. When K' greater than 100 on the mole fraction scale or K' greater than 2 on the molality scale (in water), the differences between stoichiometric binding and selective interaction become less than 1%. The theory of this paper is therefore necessary only for very weak binding constants. When K'-1 is small, large concentrations of the added solvent component are required to produce a thermodynamic effect. Under these circumstances the isotherms for the selective interaction and for the excess (or transfer) free energy are strongly dependent on the behavior of the activity coefficients of both solvent components. Two classes of behavior are described depending on whether the components display positive or negative deviations from Raoult's law. Examples which are discussed are aqueous solutions of urea and guanidinium chloride for positive deviations and of sucrose and glucose for negative deviations. Examination of the few studies which have been reported in the literature shows that most of the qualitative features of the stabilization of proteins by sugars and their destabilization by urea and guanidinium chloride are faithfully represented with the model. This includes maxima in the free energy of stabilization and destabilization, decreased and zero selective interaction at high concentrations, etc. These phenomena had no prior explanation. Deficiencies in the model as a representation of solvation in aqueous solution are discussed in the appendix.     

Thermodynamic nonideality as a probe of reversible protein unfolding effected by variations in pH and temperature: studies of ribonuclease

Thermodynamic nonideality arising from the space-filling effect of added sucrose is employed to confirm that the reversible unfolding of ribonuclease A effected by acid may be described as an equilibrium between native and unfolded states of the enzyme. However, the extent of the volume change is far too small for the larger isomer to be the fully expanded state, a result signifying that the acid-mediated unfolding of ribonuclease does not conform with the two-state equilibrium model of protein denaturation. Although the thermal denaturation of ribonuclease A is characterized by a larger increase in volume, quantitative reappraisal of published results on the effects of glycerol on this transition at pH 2.8 (Gekko, K., and Timasheff, S. N., 1981 Biochemistry 20, 4677-4686) leads to an estimated volume increase that is much smaller than that inferred from hydrodynamic studies--a disparity attributed to the dual actions of glycerol as a space-filling solute and as a ligand that binds preferentially to the thermally unfolded form of the enzyme. Even in this unfavorable circumstance the fact that glycerol exerts a net excluded volume effect at least confirms that the thermal unfolding of ribonuclease A is an equilibrium transition between two discrete states. The strengths and limitations of using thermodynamic nonideality as a probe of the two-state equilibrium model of protein denaturation are discussed in the light of these findings.     

Macromolecular crowding enhances the binding of superoxide dismutase to xanthine oxidase: implications for protein-protein interactions in intracellular environments

Physiological medium constitutes a crowded environment that serves as the field of action for protein-protein interaction in vivo. Measuring protein-protein interaction in crowded solutions can mimic this environment. Here we report the application of fluorescence spectroscopy and resonant mirror biosensor to investigate the interactions of bovine milk xanthine oxidase and bovine erythrocyte copper, zinc-superoxide dismutase in crowded solutions. Four nonspecific high molecular mass crowding agents, poly(ethylene glycol) 2000 and 20,000, Ficoll 70, and dextran 70, and one low molecular mass compound, glycerol, are used. Superoxide dismutase shows a strong and macromolecular crowding agent concentration-dependent binding affinity to xanthine oxidase. Addition of high concentrations of such high molecular mass crowding agents increases the binding constant remarkably and thus stabilizes superoxide dismutase activity, compared to those in the absence of crowding agents. In contrast, glycerol has little effect on the binding constant and decreases superoxide dismutase activity over the same concentration range. Such a pattern suggests that the enhancing effects of polymers and polysaccharides on the binding are due to macromolecular crowding. Taken together, these results indicate that macromolecular crowding enhances the binding of superoxide dismutase to xanthine oxidase and is favorable to the function of superoxide dismutase.