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.     

Further evidence for the reliance of catalysis by rabbit muscle pyruvate kinase upon isomerization of the ternary complex between enzyme and products

Isothermal calorimetry has been used to examine the effect of thermodynamic non-ideality on the kinetics of catalysis by rabbit muscle pyruvate kinase as the result of molecular crowding by inert cosolutes. The investigation, designed to detect substrate-mediated isomerization of pyruvate kinase, has revealed a 15% enhancement of maximal velocity by supplementation of reaction mixtures with 0.1 M proline, glycine or sorbitol. This effect of thermodynamic non-ideality implicates the existence of a substrate-induced conformational change that is governed by a minor volume decrease and a very small isomerization constant; and hence, substantiates earlier inferences that the rate-determining step in pyruvate kinase kinetics is isomerization of the ternary enzyme product complex rather than the release of products.     

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.     

Thermodynamic nonideality as a probe of allosteric mechanisms: preexistence of the isomerization equilibrium for rabbit muscle pyruvate kinase

Sedimentation velocity studies in the presence and absence of an inert space-filling solute, sucrose, have been used to establish preexistence of the isomerization equilibrium responsible for the allosteric behavior of rabbit muscle pyruvate kinase. Whereas the inclusion of phenylalanine (5 mM) with enzyme gives rise to a decrease of 0.3 S in the sedimentation coefficient of pyruvate kinase, the corresponding effect of phosphoenolpyruvate is to increase the sedimentation coefficient by 0.03 S. Consideration of these findings to signify the existence of an isomeric equilibrium between compact and expanded forms of the enzyme is substantiated by the finding that inclusion of sucrose (0.1 M) also brings about the change in sedimentation coefficient effected by phosphoenolpyruvate. By demonstrating that rabbit muscle pyruvate kinase undergoes isomerization in the absence of substrate, this study removes any necessity to consider the existence of an isomerization equilibrium that is substrate-induced; and thereby provides experimental support for adoption of the Monod model of allostery to interpret enzyme kinetic data for pyruvate kinase [R. W. Oberfelder, B. G. Barisas, and J. C. Lee (1984) Biochemistry 23, 3822-3826].     

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.     

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.     

Cyanide binding to cytochrome c peroxidase (H52L)

Cyanide binding to a cytochrome c peroxidase (CcP) variant in which the distal histidine has been replaced by a leucine residue, CcP(H52L), has been investigated as a function of pH using spectroscopic, equilibrium, and kinetic methods. Between pH 4 and 8, the apparent equilibrium dissociation constant for the CcP(H52L)/cyanide complex varies by a factor of 60, from 135 microM at pH 4.7 to 2.2 microM at pH 8.0. The binding kinetics are biphasic, involving bimolecular association of the two reactants, followed by an isomerization of the enzyme/cyanide complex. The association rate constant could be determined up to pH 8.9 using pH-jump techniques. The association rate constant increases by almost 4 orders of magnitude over the pH range investigated, from 1.8 x 10(2) M(-1) s(-1) at pH 4 to 9.2 x 10(5) M(-1) s(-1) at pH 8.6. In contrast to wild-type CcP, where the binding of HCN is the dominant binding pathway, CcP(H52L) preferentially binds the cyanide anion. Above pH 8, cyanide binding to CcP(H52L) is faster than cyanide binding to wild-type CcP. Cyanide dissociates 4 times slower from the mutant protein although the pH dependence of the dissociation rate constant is essentially identical for CcP(H52L) and CcP. Isomerization of the CcP(H52L)/cyanide complex is observed between pH 4 and 8 and stabilizes the complex. The isomerization rate constant has a similar magnitude and pH dependence as the cyanide dissociation rate constant, and the two reactions are coupled at low cyanide concentrations. This isomerization has no counterpart in the wild-type CcP/cyanide complex.     

A Hilly path through the thermodynamics and statistical mechanics of protein solutions

The opus of Don Winzor in the fields of physical and analytical biochemistry is a major component of that certain antipodean approach to this broad area of research that blossomed in the second half of the twentieth century. The need to formulate problems in terms of thermodynamic nonideality posed the challenge of describing a clear route from molecular interactions to the parameters that biochemists routinely measure. Mapping out this route required delving into the statistical mechanics of solutions of macromolecules, and at every turn mathematically complex, rigorous, general results that had previously been derived previously, often by Terrell Hill, came to the fore. Central to this work were the definition of the “thermodynamic activity”, the pivotal position of the polynomial expansion of the osmotic pressure in terms of molar concentration and the relationship of virial coefficients to details of the forces between limited-size groups of interacting molecules. All of this was richly exploited in the task of taking account of excluded volume and electrostatic interactions, especially in the use of sedimentation equilibrium to determine values of constants for molecular association reactions. Such an approach has proved relevant to the study of molecular interactions generally, even those between the main macromolecular solute and components of the solvent, by using techniques such as exclusion and affinity chromatography as well as light scattering.     

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 self-association induced by macromolecular crowding: a quantitative analysis by magnetic relaxation dispersion

In the presence of high concentrations of inert macromolecules, the self-association of proteins is strongly enhanced through an entropic, excluded-volume effect variously called macromolecular crowding or depletion attraction. Despite the predicted large magnitude of this universal effect and its far-reaching biological implications, few experimental studies of macromolecular crowding have been reported. Here, we introduce a powerful new technique, fast field-cycling magnetic relaxation dispersion, for investigating crowding effects on protein self-association equilibria. By recording the solvent proton spin relaxation rate over a wide range of magnetic field strengths, we determine the populations of coexisting monomers and decamers of bovine pancreatic trypsin inhibitor in the presence of dextran up to a macromolecular volume fraction of 27%. Already at a dextran volume fraction of 14%, we find a 30-fold increase of the decamer population and 510(5)-fold increase of the association constant. The analysis of these results, in terms of a statistical-mechanical model that incorporates polymer flexibility as well as the excluded volume of the protein, shows that the dramatic enhancement of bovine pancreatic trypsin inhibitor self-association can be quantitatively rationalized in terms of hard repulsive interactions.     

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.     

Crowding Activates ClpB and Enhances Its Association with DnaK for Efficient Protein Aggregate Reactivation

Reactivation of intracellular protein aggregates after a severe stress is mandatory for cell survival. In bacteria, this activity depends on the collaboration between the DnaK system and ClpB, which in vivo occurs in a highly crowded environment. The reactivation reaction includes two steps: extraction of unfolded monomers from the aggregate and their subsequent refolding into the native conformation. Both steps might be compromised by excluded volume conditions that would favor aggregation of unstable protein folding intermediates. Here, we have investigated whether ClpB and the DnaK system are able to compensate this unproductive effect and efficiently reactivate aggregates of three different substrate proteins under crowding conditions. To this aim, we have compared the association equilibrium, biochemical properties, stability, and chaperone activity of the disaggregase ClpB in the absence and presence of an inert macromolecular crowding agent. Our data show that crowding i), increases three to four orders of magnitude the association constant of the functional hexamer; ii), shifts the conformational equilibrium of the protein monomer toward a compact state; iii), stimulates its ATPase activity; and iv), favors association of the chaperone with substrate proteins and with aggregate-bound DnaK. These effects strongly enhance protein aggregate reactivation by the DnaK-ClpB network, highlighting the importance of volume exclusion in complex processes in which several proteins have to work in a sequential manner.     

Kinetic parameters of enzymatic reactions in states of maximal activity; an evolutionary approach

A theoretical investigation is presented which allows the calculation of states of maximal reaction rates for single enzymes and for unbranched enzymatic chains. As an extension to previous papers (Heinrich & Holzhütter, 1985, Biomed. biochim. Acta 44, 959-969; Heinrich et al., 1987, Bull. math. Biol. 49, 539-595) a detailed enzymatic mechanism was taken into consideration. Conclusions are drawn for the optimal values of the microscopic rate constants as well as of the maximal activities and Michaelis constants. Ten solutions are found which depend on the equilibrium constant as well as on the concentrations of substrates and products. It is shown that for high equilibrium constants one of the solutions applies to a very large range of the concentrations of the outer reactants. This solution is characterized by maximal values of the rate constants of all forward reactions and by non-maximal values of the rate constants of all backward reactions. In contrast to previous assumptions (Albery & Knowles, 1976b, Biochemistry 15, 5631-5640; Burbaum et al., 1989, Biochemistry 28, 9293-9305) states of maximal reaction rate are not always characterized by the highest possible values of the second-order rate constants which are related to the diffusion of the substrate and the product to the active site of the enzyme. Predictions are made concerning the ratios of maximal activities in optimal states as well as for the adaptation of the Michaelis constants to the concentrations of the outer reactants. Using metabolic control analysis it is shown that the solutions obtained for single enzymes may also be applied in multi-enzyme systems.     

Analysis of protein self-association under conditions of the thermodynamic non-ideality

Analysis of protein-protein interactions in highly concentrated solutions requires a consideration of the non-ideality in such solutions which is expressed by the virial coefficients. Different equations are presented to estimate effects of the thermodynamic non-ideality on the macromolecular interaction of self-associating proteins in sedimentation equilibrium experiments. Usually the influence of thermodynamic non-ideal behavior are described by concentration power series. The convergence of such power series is limited at high solute concentration. When expressing the thermodynamic non-ideality by an activity power series this disadvantage can be minimized. The developed centrifuge equations are the basis for a global analysis to estimate equilibrium constants and the corresponding thermodynamic activities of the reactants. Based on fit analysis of synthetic concentration profiles it was established that marked deviations from the expected association constants are observed for proteins with strong association forces between solute molecules. Considerable differences were also observed in weakly interacting systems. This was due to the excluded volume of the protein which is similar in magnitude to the binding constant. For interactions with moderate affinities values extremely close to the true binding values were obtained, as confirmed by experimental results with concanavalin A.     

Role of isomerization of initial complexes in the binding of inhibitors to dihydrofolate reductase

Stopped-flow measurements of protein fluorescence quenching when methotrexate (MTX) binds to dihydrofolate reductase (isoenzyme II) of Streptococcus faecium (SFDHFR II) analyze as the sum of two differentials: a rapid binding phase and a second phase for which the observed rate constant is independent of methotrexate concentration. Analysis of variation of the ratio of the amplitude of the fast and slow phases with methotrexate concentration indicates that the second phase is an isomerization of the initial binary complex. At pH 7.3, the equilibrium constant for this isomerization is 21.9, and the forward and reverse rate constants are 0.57 and 0.026 s-1, respectively. Similar results were obtained for binding of 3-deazamethotrexate to SFDHFR II, but the forward rate constant is greater (2.9 s-1 at pH 7.3). The equilibrium constants for these isomerizations are pH independent, but the rate constants decrease as the pH is raised, probably due to deprotonation of one or more groups on the enzyme. Analysis of progress curves obtained by the development of inhibition when SFDHFR II is added last to reaction mixtures containing dihydrofolate, NADPH, and MTX gives an association constant for initial reactions of 4.3 X 10(7) M-1. Since a preliminary estimate of the association constant for the binding reaction is 7.6 X 10(5) M-1, this suggests an isomerization of the ternary complex(es) with an equilibrium constant of about 56. In addition, analysis of the progress of development of inhibition indicates a further very slow isomerization with equilibrium constant 419 and forward rate constant 2.6 min-1.(ABSTRACT TRUNCATED AT 250 WORDS)     

Crowding Activates ClpB and Enhances Its Association with DnaK for Efficient Protein Aggregate Reactivation

Reactivation of intracellular protein aggregates after a severe stress is mandatory for cell survival. In bacteria, this activity depends on the collaboration between the DnaK system and ClpB, which in vivo occurs in a highly crowded environment. The reactivation reaction includes two steps: extraction of unfolded monomers from the aggregate and their subsequent refolding into the native conformation. Both steps might be compromised by excluded volume conditions that would favor aggregation of unstable protein folding intermediates. Here, we have investigated whether ClpB and the DnaK system are able to compensate this unproductive effect and efficiently reactivate aggregates of three different substrate proteins under crowding conditions. To this aim, we have compared the association equilibrium, biochemical properties, stability, and chaperone activity of the disaggregase ClpB in the absence and presence of an inert macromolecular crowding agent. Our data show that crowding i), increases three to four orders of magnitude the association constant of the functional hexamer; ii), shifts the conformational equilibrium of the protein monomer toward a compact state; iii), stimulates its ATPase activity; and iv), favors association of the chaperone with substrate proteins and with aggregate-bound DnaK. These effects strongly enhance protein aggregate reactivation by the DnaK-ClpB network, highlighting the importance of volume exclusion in complex processes in which several proteins have to work in a sequential manner.