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 molecular crowding by saccharides on alpha-chymotrypsin dimerization

Given the importance of protein complexes as therapeutic targets, it is necessary to understand the physical chemistry of these interactions under the crowded conditions that exist in cells. We have used sedimentation equilibrium to quantify the enhancement of the reversible homodimerization of alpha-chymotrypsin by high concentrations of the osmolytes glucose, sucrose, and raffinose. In an attempt to rationalize the osmolyte-mediated stabilization of the alpha-chymotrypsin homodimer, we have used models based on binding interactions (transfer-free energy analysis) and steric interactions (excluded volume theory) to predict the stabilization. Although transfer-free energy analysis predicts reasonably well the relatively small stabilization observed for complex formation between cytochrome c and cytochrome c peroxidase, as well as that between bobtail quail lysozyme and a monoclonal Fab fragment, it underestimates the sugar-mediated stabilization of the alpha-chymotrypsin dimer. Although predictions based on excluded volume theory overestimate the stabilization, it would seem that a major determinant in the observed stabilization of the alpha-chymotrypsin homodimer is the thermodynamic nonideality arising from molecular crowding by the three small sugars.     

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.     

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.     

Substrate as a source of thermodynamic nonideality in enzyme kinetic studies: invertase-catalyzed hydrolysis of sucrose

Expressions for the effects of thermodynamic nonideality arising from the use of high concentrations of small substrate in enzyme kinetic studies are derived. Their application to experimental results for the hydrolysis of sucrose by yeast invertase (pH 4.9, 37 degrees C) signifies that the progressive decrease in initial velocity at high sucrose concentration is consistent with the occurrence of isomeric expansion during the transition of an 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 liter/mol would represent a mere 0.16% increase in hydrated volume (or a corresponding increase in extent of asymmetry). Finally, although originally interpreted to signify an effect of sucrose on water concentration, published results for the invertase-sucrose system [J. M. Nelson and M. P. Schubert (1928) J. Amer. Chem. Soc. 50, 2188-2193] also find a rational explanation in terms of the present analysis based on effects of thermodynamic nonideality in enzyme kinetic studies.     

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 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.     

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.     

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.     

Ultracentrifugal studies of the effect of molecular crowding by trimethylamine N-oxide on the self-association of muscle glycogen phosphorylase b.

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.     

The mechanism of cryoprotection of proteins by solutes

We have tested the capacity of 28 different compounds to protect lactate dehydrogenase from damage during freeze-thawing. These solutes come from very dissimilar chemical classes including sugars, polyols, amino acids, methylamines, and lyotropic salts. All the compounds tested, except NaCl, protected the enzyme, to varying degrees, from inactivation. The only characteristic that these compounds have in common, as a group, is that they have all been shown to be preferentially excluded from contact with the surface of proteins in aqueous solution. It has been demonstrated previously (via thermodynamic arguments) that this interaction of solutes with proteins leads to the stabilization of proteins in nonfrozen, aqueous systems. Conversely, those solutes, e.g., urea and guanidine HCl, that bind to proteins destabilize proteins in solution, and we have found that they also enhanced the inactivation of lactate dehydrogenase during freeze-thawing. Based on the results of our freeze-thawing experiments and a review of the theory of protein stabilization in nonfrozen, aqueous solution we propose that the cryoprotection afforded to isolated proteins by solutes can be accounted for by the fact that these solutes are preferentially excluded from contact with the protein's surface.     

Solute excluded-volume effects on the stability of globular proteins: A statistical thermodynamic theory

A statistical thermodynamic theory is developed to investigate the effects of solute excluded volume on the stability of globular proteins. Proteins are modeled as two states in chemical equilibrium: the denatured state is modeled as a flexible chain of tangent hard spheres (pearl-necklace chain) while the native state is modeled as a single hard sphere. Study of model proteins bovine pancreatic trypsin inhibitor and lysozyme in a McMillan-Mayer model solution of hard spheres indicates that the excluded volume of solutes has three distinct types of effects on protein stability: (1) small-size solutes strongly denature proteins, (2) medium-size solutes stabilize proteins at low solute concentrations and destabilize them at high concentrations, and (3) large-size solutes stabilize native-state proteins across the whole liquid region. The study also finds that increasing the chain length of hard-chain polymer solutes has an effect on protein stability that is similar to increasing the diameter of spherical solutes. This work qualitatively explains why stabilizers tend to be large size molecules such as sugars, polymers, polynols, nonionic, and anionic surfactants while denaturants tend to be small size molecules such as alcohols, glycols, amides, formamides, ureas, and guanidium salts. Quantitative comparison between theoretical predictions and experimental results for folding free energy changes shows that the excluded-volume effect is at least as important as the binding and/or electrostatic effects on solute-assisted protein-denaturation processes. Our theory may also be able to explain the effect of excluded volume on the Φ condensation of DNA. © 1996 John Wiley & Sons, Inc.     

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).     

Protein stabilization by osmolytes from hyperthermophiles: effect of mannosylglycerate on the thermal unfolding of recombinant nuclease a from Staphylococcus aureus studied by picosecond time-resolved fluorescence and calorimetry

2-O-alpha-Mannosylglycerate, a negatively charged osmolyte widely distributed among (hyper)thermophilic microorganisms, is known to provide notable protection to proteins against thermal denaturation. To study the mechanism responsible for protein stabilization, pico-second time-resolved fluorescence spectroscopy was used to characterize the thermal unfolding of a model protein, Staphylococcus aureus recombinant nuclease A (SNase), in the presence or absence of mannosylglycerate. The fluorescence decay times are signatures of the protein state, and the pre-exponential coefficients are used to evaluate the molar fractions of the folded and unfolded states. Hence, direct determination of equilibrium constants of unfolding from molar fractions was carried out. Van't Hoff plots of the equilibrium constants provided reliable thermodynamic data for SNase unfolding. Differential scanning calorimetry was used to validate this thermodynamic analysis. The presence of 0.5 m potassium mannosylglycerate caused an increase of 7 degrees C in the SNase melting temperature and a 2-fold increase in the unfolding heat capacity. Despite the considerable degree of stabilization rendered by this solute, the nature and population of protein states along unfolding were not altered in the presence of mannosylglycerate, denoting that the unfolding pathway of SNase was unaffected. The stabilization of SNase by mannosylglycerate arises from decreased unfolding entropy up to 65 degrees C and from an enthalpy increase above this temperature. In molecular terms, stabilization is interpreted as resulting from destabilization of the denatured state caused by preferential exclusion of the solute from the protein hydration shell upon unfolding, and stabilization of the native state by specific interactions. The physiological significance of charged solutes in hyperthermophiles is discussed.     

Correlation between the stability of alpha-chymotrypsin at high temperatures and "salting in" of a strong solution]

A correlation was found between the thermal stability of alpha-chymotrypsin and the coefficient Ks of the Sechenov equation as a quantitative measure of the "salting-in" or "salting-out" capacity of solutes. At high temperatures, an increase in the concentration of "salting-in" agents (KSNC, GuHCl, urea, formamide) resulted in thermal stabilization of alpha-chymotrypsin. The maximal (about 100-fold) stabilizing effect in concentrated solutions of salting-in agents was comparable with those induced by covalent modification with hydrophilic reagents or immobilization. Conversely, an increase in the concentration of "salting-out" agents stabilized the enzyme only marginally at high temperatures. An additivity of solutes' action on the thermal stability of the protein has been demonstrated. The observed correlation was explained in terms of the solutes' action on the reversible conformational transition of the enzyme native form into a much more stable form existing at high temperatures.     

Protein stability in mixed solvents: a balance of contact interaction and excluded volume

Changes in excluded volume and contact interaction with the surface of a protein have been suggested as mechanisms for the changes in stability induced by cosolvents. The aim of the present paper is to present an analysis that combines both effects in a quantitative manner. The result is that both processes are present in both stabilizing and destabilizing interactions and neither can be ignored. Excluded volume was estimated using accessible surface area calculations of the kind introduced by Lee and Richards. The change in excluded volume on unfolding, deltaX, is quite large. For example, deltaX for ribonuclease is 6.7 L in urea and approximately 16 L in sucrose. The latter number is greater than the molar volume of the protein. Direct interaction with the protein is represented as the solvent exchange mechanism, which differs from ordinary association theory because of the weakness of the interaction and the high concentrations of cosolvents. The balance between the two effects and their contribution to overall stability are most simply presented as bar diagrams as in Fig. 3. Our finding for five proteins is that excluded volume contributes to the stabilization of the native structure and that contact interaction contributes to destabilization. This is true for five proteins and four cosolvents including both denaturants and osmolytes. Whether a substance stabilizes a protein or destabilizes it depends on the relative size of these two contributions. The constant for the cosolvent contact with the protein is remarkably uniform for four of the proteins, indicating a similarity of groups exposed during unfolding. One protein, staphylococcus nuclease, is anomalous in almost all respects. In general, the strength of the interaction with guanidinium is about twice that of urea, which is about twice that of trimethylamine-N-oxide and sucrose. Arguments are presented for the use of volume fractions in equilibrium equations and the ignoring of activity coefficients of the cosolvent. It is shown in the Appendix that both the excluded volume and the direct interaction can be extracted in a unified way from the McMillan-Mayer formula for the second virial coefficient.     

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.