A quest for greater thermodynamic rigour in the quantitative characterization of protein self-association by direct assessment of sedimentation equilibrium distributions

This thesis involves the examination and description of the effects of thermodynamic non-ideality arising from the space-filling properties of solute species present in the system. Both developmental and applied aspects of nonideality are investigated.Expressions are derived in Chapter 1 for the effects of thermodynamic non-ideality arising from the use of high concentrations of small substrate in enzyme kinetic studies. Their application to experimental results for the hydrolysis of sucrose by yeast invertase (pH 4.9, 37°C) signifies that the progressive decrease in initial velocity at high sucrose concentrations is consistent with the occurence of isomeric expansion during the transition of enzyme-substrate complex to its activated state. Ultracentrifuge studies on the yeast enzyme preparation are then used to establish the physical acceptability of the volume change required to account for the kinetic effects in these terms: the postulated expansion of 1.3 litre/mol would represent a mere 0.16% increase in hydrated volume (or a corresponding increase in extent of asymmetry). In addition, although originally interpreted to signify an effect of sucrose on water concentration, published results for the invertase-sucrose system all find rational explanation in terms of the present analysis based on effects of thermodynamic non-ideality in enzyme kinetic studies.In Chapter 2 the space-filling effects of sucrose on the dimerization of α-chymotrypsin have been investigated by sedimentation equilibrium studies of 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 non-ideality finds quantitative explanation in terms of excluded volume. Results of sedimentation equilibrium experiments on α-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. However, the suggested approximation that the radius of small solute would be sufficiently small to be neglected in the calculation of covolumes [Winzor D.J. and Wills P.R., (1986) Biophys. Chem. 25, 243-251 DOI:10.1016/0301-4622(86)80016-3] has not withstood the more stringent test afforded by the present study of α-chymotrypsin dimerization: an effective thermodynamic radius for sucrose of 0.34 nm was employed in those calculations, a value inferred from the covolume for self-interaction (αM,M) obtained by frontal gel chromatography on Sephadex G-10 under the conditions of the ultracentrifugal studies. Finally, the utility of liquid-liquid partitioning as an alternative means of assessing activity coefficients of small solutes (αS,M) has been demonstrated.Second virial coefficients and hence covolumes for self-interaction of five proteins, viz., ribonuclease, ovalbumin, bovine serum albumin, catalase and α-crystallin, have been determined in Chapter 3 by analysing the concentration dependence of the partition coefficient obtained from frontal chromatographic studies on either Fractogel TSK HW55 or porous glass beads. The resulting estimates of the effective radii essentially duplicate their Stokes counterparts and thereby provide further justification for assuming the approximate identity of the thermodynamic and hydrodynamic radii of hydrated globular proteins. Gel chromatographic evaluation of second virial coefficients for protein-Dextran systems has led to elimination of the sphere-sphere model as a valid thermodynamic description of the space-filling effects in protein-polymer mixtures, since it does not predict the observed independence of covolume, expressed per g. of polymer, upon size of the polymer. This requirement is met by the sphere-rod model [Edmond, E. and Ogston, A.G. (1969) Biochem. J. 109, 569-576] and also by the sphere-flexible segment model [Hermans, J. (1982) J. Chem. Phys. 77, 2193-2203 DOI:10.1063/1.444026]. Furthermore, similar studies of the effect of solute radius on covolume for interaction with Dextran T70 attest to the adequacy of either model for predicting the thermodynamic non-ideality arising from the inclusion of Dextrans in protein solutions, and also provide the relevant calibration of the model.A combination of ultrafiltration with either equilibrium dialysis or frontal gel chromatography has been used to evaluate the effects of thermodynamic non-ideality in mixtures of bovine serum albumin and charged ligands in Chapter 4. Studies with methyl orange, chlorpromazine and chromate as ligand all demonstrated inadequacy of the Donnan effect for description of the difference between the concentrations of free ligand in a mixture and the protein-free phase with which it is in dialysis equilibrium. On the basis of a quantitative relationship derived for the situation in which Donnan and thermodynamic non-ideality effects both operate, values of the second virial coefficient for albumin and ligand have been determined. For albumin and either methyl orange or chlorpromazine the magnitude of this second virial coefficient has been rationalized on the statistical mechanical basis of excluded volume. For the albumin-chromate system, however, the thermodynamic non-ideality was manifested as a negative deviation from Raoult's Law, in keeping with the classical behaviour of electrolyte ions. From the viewpoint of the characterization of ligand binding, a unique feature of the ultrafiltration-gel chromatography and ultrafiltration-equilibrium dialysis methods is their ability to define not only the binding function but also the activity coefficient of ligand for a given acceptor-ligand mixture. Consequently, irrespective of whether the ligand is charged or uncharged, the intrinsic binding constant that is determined is the thermodynamic parameter instead of the apparent value that is obtained from methods based on assumed thermodynamic non-ideality.The thesis concludes with the application of thermodynamic non-ideality as a probe of specific protein interactions. In section A of Chapter 5, results of a sedimentation equilibrium study of the inhibitory effect of calcium ion on the dimerization of α-chymotrypsin (pH 3.9, I 0.2) are used to establish that the phenomenon does not reflect increased electrostatic repulsion between Ca2+-saturated enzyme molecules, but rather the displacement of the monomer-dimer equilibrium by the specific, weak interaction of metal ion with a single site on a monomeric enzyme.Thermodynamic non-ideality arising from the space-filling effects of added sucrose or glycerol has been employed in section B to confirm that the reversible unfolding of ribonuclease effected by acid and temperature should be considered in equilibrium terms. Whereas high concentrations of these two solutes have no effect on the pH-profile for the acid expansion of bovine serum albumin, the inclusion of sucrose (0.5 M) in ribonuclease solutions elicits displacement of the spectrally determined pH-profile for the unfolding in the acidic direction, a finding that is consistent with the action of sucrose as an inert space-filling solute on an isomerization equilibrium between native and acid-expanded states of the enzyme. The ratio of apparent isomerization constants, at any given pH, in the presence and absence of sucrose was therefore interpreted on the statistical mechanical basis of excluded volume to determine the change in enzyme volume required for the displacement to reflect thermodynamic non-ideality. Since the extent of the volume increase (5%) that is calculated by this means matches the value from viscosity measurements, the effect of sucrose on the unfolding of ribonuclease is entirely attributable to thermodynamic non-ideality arising from the space-filling property of this small solute. On the other hand, quantitative reappraisal of published results on the effects of glycerol on the thermal denaturation of ribonuclease at pH 2.8 [Gekko, K. and Timasheff, S.N. (1981) Biochemistry 20, 4677-4686 DOI:10.1021/bi00519a024] 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. Although the effects of glycerol on melting curves for ribonuclease are not interpretable solely on the basis of excluded volume, this deficiency of the quantitative analysis does not detract from the observation that glycerol exerted a net excluded volume effect, and hence the conclusion that the unfolding transition is an equilibrium phenomenon. These findings suffice to illustrate the utility of thermodynamic non-ideality as a probe for ascertaining the validity of considering an interconversion between native and unfolded states in terms of an equilibrium mechanism, which has been an inherent but untested assumption in most studies of protein denaturation.

Allowance for effects of thermodynamic nonideality in sedimentation equilibrium distributions reflecting protein dimerization

Allowance for thermodynamic nonideality and Donnan effects in binding studies

The suitability of sedimentation equilibrium for characterizing the self-association of muscle glycogen phosphorylase b has been reappraised. Whereas sedimentation equilibrium distributions for phosphorylase b in 40 mM Hepes buffer (pH 6.8) supplemented with 1 mM AMP signify a lack of chemical equilibrium attainment, those in buffer supplemented additionally with potassium sulfate conform with the requirements of a dimerizing system in chemical as well as sedimentation equilibrium. Because the rate of attainment of chemical equilibrium under the former conditions is sufficiently slow to allow resolution of the dimeric and tetrameric enzyme species by sedimentation velocity, this procedure has been used to examine the effects of thermodynamic nonideality arising from molecular crowding by trimethylamine N-oxide on the self-association behaviour of phosphorylase b. In those terms the marginally enhanced extent of phosphorylase b self-association observed in the presence of high concentrations of the cosolute is taken to imply that the effects of thermodynamic nonideality on the dimer-tetramer equilibrium are being countered by those displacing the T<==>R isomerization equilibrium for dimer towards the smaller, nonassociating T state. Because the R state is the enzymically active form, an inhibitory effect is the predicted consequence of molecular crowding by high concentrations of unrelated solutes. Thermodynamic nonideality thus provides an alternative explanation for the inhibitory effects of high concentrations of glycerol, sucrose and ethylene glycol on phosphorylase b activity, phenomena that have been attributed to extremely weak interaction of these cryoprotectants with the T state of the enzyme.

Allowance for the effect of protein charge in the characterization of nonideal solute self-association by sedimentation equilibrium

This thesis commences with two Chapters concerned with methodological aspects of the study of ligand binding to macromolecular acceptors. First, a slightly modified but theoretically analogous version of the rate-of-dialysis method for investigating ligand binding [Colowick, S.P. and Womack, F.C. (1969) J. Biol. Chem. 244, 774-777] has been developed in order to examine more closely the principle of the procedure. It is shown that the method is described by the theory that pertains to measurement of diffusion coefficients by the diaphragm cell method. Secondly, a recycling gel partition technique has been developed for acceptor-ligand systems that exhibit isosbestic points, its use being illustrated with a study of the binding of methyl orange to bovine serum albumin. A combination of binding studies and sedimentation velocity experiments is then used to dispel the concept [Klotz, I.M. and Urquhart, J.M. (1949) J. Phys. Colloid Chem. 53, 100-114 DOI: 10.1021/j150466a008 ] that the binding curve for this system shows a dependence upon the albumin concentration used for its measurement.In Chapter 3 a technique for the measurement of the net charge of a protein is reported which depends upon assessment of the Donnan effect by a combination of equilibrium dialysis and ultrafiltration in conjunction with conductivity measurements. Studies with ovalbumin, bovine serum albumin and lysozyme are used to illustrate the method, a decided advantage of which is the absence of assumptions about the extent of specific ion binding.Advantage is then taken, in Chapter 4, of this procedure for valence estimation to examine the concept of charge conservation in two macromolecular interactions. First, concomitant measurement of the binding function and the net charge for a series of bovine serum albumin-methyl orange mixtures (pH 7.4, I = 0.05 M) showed that the magnitude of the negative charge on the albumin increased linearly with the number of molecules of methyl orange bound to the protein, the observed slope (0.96 ± 0.08) being in excellent agreement with that predicted on the basis of charge conservation for attachment of this univalent, negatively charged ligand. Secondly, in a study of the self-associating enzyme α-chymotrypsin at pH 3.9, I = 0.11 M, the net charge (expressed per base-mole) was shown to be invariant (+10) in solutions in which the mole fraction of monomeric enzyme varied between 0.47 and 0.88, the extent of the range having been established by means of sedimentation equilibrium studies of this monomer-dimer system.Chapter 5 considers the effects of thermodynamic nonideality on the quantitative characterization of the interaction between a small ligand and a macromolecular acceptor by two types of experimental procedure. The first involves determination of the concentration of ligand in dialysis equilibrium with acceptor-ligand mixture; and the second, direct measurement of the concentration of unbound ligand in the reaction mixture. Explicit expressions are formulated for the appropriate binding functions, with allowances made for composition-dependent nonideality effects assessed on the statistical mechanical basis of covolumes; and then applied to experimental studies on the binding of L-tryptophan and of methyl orange to bovine serum albumin. By showing that the theoretically predicted dependence of the binding functions on acceptor concentration is likely to be insignificant experimentally, this study provides reassurance that the consequences of thermodynamic nonideality in the multiple binding of ligands to a single macromolecular state of a protein are likely to be second-order effects.This thesis concludes with consideration of the possibility that thermodynamic nonideality arising from inclusion of an inert macromolecular solute may provide the means for detecting isomeric equilibria. Gel chromatographic results obtained in the presence and absence of Dextran T70 and T10 show that the acid-expansion of bovine serum albumin should not be considered in terms of a pH-dependent isomerization equilibrium between native and acid-expanded states, a conclusion confirmed by examining the effect of rotor speed on the sedimentation coefficient of albumin at pH 3.2. Theoretical considerations of the aspartate transcarbamoylase system have indicated that differential gel chromatographic studies in the presence and absence of Dextran T70 have the potential to prove the existence of the isomerization equilibrium (ligand-induced or pre-existing) responsible for the allosteric behaviour of this enzyme. It would appear that nonideality may provide the means of distinction, for some systems at least, between the Monod-Wyman-Changeux and Koshland-Nemethy-Filmer models of allostery, which hitherto have been conceptually different but thermodynamically indistinguishable.

Analysis of thermodynamic non-ideality in terms of protein solvation

An improved procedure is described for the characterization of solute self-association by sedimentation equilibrium. Whereas previous statistical-mechanical approaches to allowance for the effects of thermodynamic nonideality have entailed tedious iteration because of their specification of activity coefficients in terms of the equilibrium concentrations of all species, such reliance upon knowledge of the solution composition is avoided by the adaptation of an alternative statistical-mechanical formulation [T. L. Hill and Y. D. Chen (1973) Biopolymers, Vol. 12, pp. 1285–1312] in which thermodynamic nonideality is expressed in terms of total solute concentration. The development of an analysis in terms of a relationship with total solute concentration as the experimental variable allows this attribute of the Adams-Fujita approach to be retained without sacrifice of statistical-mechanical rigor. Its use is illustrated by application to Rayleigh interferometric records of sedimentation equilibrium distributions reflecting α-chymotrypsin dimerization and lysozyme self-association. © 1996 John Wiley & Sons, Inc.

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

Effects of thermodynamic nonideality in kinetic studies

Procedures are developed for the characterization of thermodynamically ideal complex formation between dissimilar macromolecular reactants by direct analysis of sedimentation equilibrium distributions. Studies of an electrostatic interaction between ovalbumin and cytochrome c are used to illustrate the application of analyses pertaining to (i) the situation in which separate sedimentation equilibrium distributions for the two macromolecular constituents are available, (ii) that in which the experimental record reflects the distribution of only one constituent, and (iii) the situation in which a composite distribution for both constituents is the sole experimental record. An association constant of 63 000 (+/- 2000) M-1 is obtained for the 1:1 interaction between ovalbumin and cytochrome c under the conditions examined (pH 6.3, I 0.03). Because of their inherent simplicity, these direct analytical procedures offer potential for accommodating the effects of thermodynamic nonideality in dissimilar reactant systems.

Effects of thermodynamic nonideality in protein crystal growth

General quantitative expressions are developed to take rigorous statistical-mechanical account of the effects of thermodynamic nonideality in sedimentation equilibrium distributions reflecting interaction between dissimilar macromolecular reactants. These quantitative expressions form the basis of an analysis which yields global estimates of the equilibrium constant(s) and the corresponding reference thermodynamic activities of free reactants in several experiments. Simulated data for 1:1 complex formation between dissimilar reactants are used to illustrate the procedure, which is currently unable to take advantage of the third virial coefficient terms to nonideality because of the lack of expressions for the excluded-volume contribution of three-body clusters of dissimilar species. In the absence of experimental studies where chemical interaction is sufficiently weak to warrant the use of concentrations commensurate with significant thermodynamic nonideality effects, published data on lysozyme self-association have been analysed to demonstrate the experimental application of the global analysis.

This review of the characterization of protein interactions by sedimentation equilibrium emphasizes procedures that entail direct determination of the thermodynamic activity of the smallest species contributing to the concentration distribution for that constituent. This approach, which has been regarded as an Australasian oddity for over two decades, is first illustrated by evaluating the association constant for α-chymotrypsin dimerization by the original omega analysis and subsequent refinements thereof. Notable in that regard is the introduction of the psi function, which has evolved from its omega counterpart. Application of the corresponding approach to sedimentation distributions for mixtures of ovalbumin and cytochrome c is presented to illustrate the potential of the psi function for characterizing interactions between dissimilar macromolecular reactants. Also discussed is the means by which these direct analyses of sedimentation equilibrium distributions afford realistic allowance for effects of thermodynamic nonideality on the statistical-mechanical basis of excluded volume.

Effects of thermodynamic nonideality in ligand binding studies