Reconsideration of sedimentation equilibrium distributions reflecting the effects of small inert cosolutes on the dimerization of alpha-chymotrypsin

A reported discrepancy between quantitative estimates of the extent of enhanced alpha-chymotrypsin dimerization in the presence of sucrose is traced to different consequences of using an incorrect value of the buoyant molecular weight in the analysis of sedimentation equilibrium distributions. Support is thereby provided for the earlier contention that the effect of sucrose, as well as of glucose and raffinose, on dimerization may be rationalized quantitatively in terms of molecular crowding by an inert cosolute.     

Allowance for thermodynamic nonideality in the characterization of protein interactions by spectral techniques

Theory is developed for the characterization of protein interactions by spectral techniques, where the constraints of constant temperature and pressure demand that thermodynamic activity be defined on the molal concentration scale. The customary practice of defining the equilibrium constant (K) on a molar basis is accommodated by developing expressions to convert those experimental values (K_molar) to their thermodynamically more rigorous counterparts (K_molal). Such procedures are illustrated by reanalysis of published results for the effects of molecular crowding agents on the isomerisation of α-chymotrypsin and reversible complex formation between catalase and superoxide dismutase. Although those reanalyses have led to only minor refinements of the quantitative interpretation, it is clearly preferable to adopt thermodynamic rigor throughout future spectral studies by employing the molal concentration scale from the outset.     

Analysis of sedimentation equilibrium distributions reflecting nonideal macromolecular associations

A rigorous statistical-mechanical approach is adopted to derive general quantitative expressions that allow for the effects of thermodynamic nonideality in equilibrium measurements reflecting interaction between dissimilar macromolecular reactants. An analytical procedure based on these expressions is then formulated for obtaining global estimates of equilibrium constants and the corresponding reference thermodynamic activities of the free reactants in each of several sedimentation equilibrium experiments. The method is demonstrated by application to results from an ultracentrifugal study of an electrostatic interaction between ovalbumin and cytochrome c (Winzor, D. J., M. P. Jacobsen, and P. R. Wills. 1998. Biochemistry. 37:2226-2233). It is demonstrated that reliable estimates of relevant thermodynamic parameters are extracted from the data through statistical analysis by means of a simple nonlinear fitting procedure.     

Allowance for effects of electrostatic repulsion on protein dimerization

A simple procedure for assessing the extent of electrostatic effects on protein dimerization is described and illustrated by application to published results on the ionic strength dependence of the dimerization constant for alpha-chymotrypsin at pH 4 (Aune, K.C., Goldsmith, L.C. and Timasheff, S.N. (1971) Biochemistry 10, 1617-1622). From the analysis it is concluded that the inverse dependence of alpha-chymotrypsin dimerization upon ionic strength is predominantly a general electrostatic effect, rather than a consequence of repulsion between two specific charged residues on the adjacent monomers comprising dimer.     

Characterization of weak protein dimerization by direct analysis of sedimentation equilibrium distributions: the INVEQ approach

Closer scrutiny has been accorded a recently reported procedure for characterizing weak protein dimerization by sedimentation equilibrium (INVEQ) in which the equilibrium distribution is analyzed as a dependence of radial distance on solute concentration rather than of solute concentration on radial distance. By demonstrating theoretically that the fundamental parameter derived from the analysis is simply the difference between the dimerization constant and the osmotic second virial coefficient for monomer-monomer interaction, this investigation refutes the original claim that independent estimates of these two parameters can be obtained by nonlinear curve fitting of the sedimentation equilibrium distribution. This criticism also applies to conventional analyses of sedimentation distributions by the commonly employed Beckman Origin and NONLIN software. Numerically simulated distributions are then analyzed to demonstrate limitations of the procedure and also to indicate a means of improving the reliability of the returned estimate of the dimerization constant. These features are illustrated by applying the original and revised analytical procedures to a sedimentation equilibrium distribution for alpha-chymotrypsin (pH 4.0, I 0.05 M).     

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.     

Direct allowance for the effects of thermodynamic nonideality in the quantitative characterization of protein self-association by osmometry

A procedure is described for the direct analysis of osmotic pressure data for reversibly dimerizing proteins that makes allowance for effects of thermodynamic nonideality on the statistical–mechanical basis of the potential-of-mean-force between molecules. Detailed consideration is also given to calculation of the magnitudes of the required virial coefficients. After illustration of the approach with analysis of simulated osmotic pressure data, the method is used to obtain dimerization constants from published osmotic pressure data for soybean proteinase inhibitor, hemoglobin and α-chymotrypsin.     

Rationalization of the effects of compatible solutes on protein stability in terms of thermodynamic nonideality.

Inhibition by compatible solutes such as proline and glycine betaine of the rate of coagulation, at 60 degrees C, of bovine serum albumin in 0.1 M acetate buffer, pH 5, is used as a model system to substantiate the concept that the production of high concentrations of osmolytes by plants and other organisms in response to stress (e.g., drought) results in stabilization of native enzyme structures via nonspecific excluded volume effects. The paradoxical situation whereby this effect of compatible solutes counters to some extent the protein-precipitating effect of poly(ethylene glycol) is also seemingly resolved.     

Interpretation of thermodynamic non-ideality in sedimentation equilibrium experiments on proteins

This investigation re-examines theoretical aspects of the allowance for effects of thermodynamic non-ideality on the sedimentation equilibrium distribution for a single macromolecular solute, and thereby resolves the question of the constraints that pertain to the definition of the activity coefficient term in the basic sedimentation equilibrium expression. Sedimentation equilibrium results for ovalbumin are then presented to illustrate a simple procedure for evaluating the net charge (valence) of a protein from the magnitude of the second virial coefficient in situations where the effective radius of the protein can be assigned. Finally, published sedimentation equilibrium results on lysozyme are reanalysed to demonstrate the feasibility of employing the dependence of the second virial coefficient upon ionic strength to evaluate both the valence and the effective radius of the non-interacting solute.     

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 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.     

Analysis of the thermodynamic non-ideality of proteins by sedimentation equilibrium experiments

This paper presents a modified method to determine experimentally the second virial coefficient of protein solutions by sedimentation equilibrium experiments. The improvement is based on the possibility of fitting simultaneously up to seven radial concentration distribution curves of solutions with different loading concentrations. The possibility of precise determination of the second virial coefficient allows estimation of the net charge and the excluded volume of a monomeric protein. Application of the method is demonstrated for lysozyme and ovalbumin. In 0.1 M sodium acetate buffer, pH 4.5, the second virial coefficient of hen egg white lysozyme amounts to 24 +/- 1 ml/g. Analysis based on spherical particle theory yield an excluded volume of 3.5 ml/g and a charge dependent value of 20.5 ml/g which is induced by a net charge number of 14.1 +/- 1. Under low salt conditions self-association processes on lysozyme are unfavorable due to electrostatic repulsion. To overcome these repulsive contributions, either a shift to neutral pH or addition of at least 2% NaCl is necessary. In this way the charge dependent contribution decreases below the value responsible for the excluded volume and allows crystallization of the protein. Similar effects can be observed with ovalbumin. The high virial coefficient observed at pH 8.5 is induced by the high net charge number of 27 +/- 1.     

Studies of solute self-association by sedimentation equilibrium: allowance for effects of thermodynamic non-ideality beyond the consequences of nearest-neighbor interactions

A sedimentation equilibrium study of alpha-chymotrypsin self-association in acetate-chloride buffer, pH 4.1 I 0.05, has been used to illustrate determination of a dimerization constant under conditions where thermodynamic non-ideality is manifested beyond the consequences of nearest-neighbor interactions. Because the expressions for the experimentally determinable interaction parameters comprise a mixture of equilibrium constant and excluded volume terms, the assignment of reasonable magnitudes to the relevant virial coefficients describing non-associative cluster formation is essential for the evaluation of a reliable estimate of the dimerization constant. Determination of these excluded volume parameters by numerical integration over the potential-of-mean-force is shown to be preferable to their calculation by approximate analytical solutions of the integral for this relatively small enzyme monomer with high net charge (+10) under conditions of low ionic strength (0.05 M).