Effects of thermodynamic nonideality in kinetic studies

A method for quantifying how the activity of an enzyme is affected by the net charge of its nearest crowded neighbor

The electrostatic effects of protein crowding have not been systematically explored. Rather, protein crowding is generally studied with co‐solvents or crowders that are electrostatically neutral, with no methods to measure how the net charge (Z) of a crowder affects protein function. For example, can the activity of an enzyme be affected electrostatically by the net charge of its neighbor in crowded milieu? This paper reports a method for crowding proteins of different net charge to an enzyme via semi‐random chemical crosslinking. As a proof of concept, RNase A was crowded (at distances ≤ the Debye length) via crosslinking to different heme proteins with Z = +8.50 ± 0.04, Z = +6.39 ± 0.12, or Z = −10.30 ± 1.32. Crosslinking did not disrupt the structure of proteins, according to amide H/D exchange, and did not inhibit RNase A activity. For RNase A, we found that the electrostatic environment of each crowded neighbor had significant effects on rates of RNA hydrolysis. Crowding with cationic cytochrome c led to increases in activity, while crowding with anionic “supercharged” cytochrome c or myoglobin diminished activity. Surprisingly, electrostatic crowding effects were amplified at high ionic strength (I = 0.201 M) and attenuated at low ionic strength (I = 0.011 M). This salt dependence might be caused by a unique set of electric double layers at the dimer interspace (maximum distance of 8 Å, which cannot accommodate four layers). This new method of crowding via crosslinking can be used to search for electrostatic effects in protein crowding.

Foreword to 'Quantitative and analytical relations in biochemistry'-a special issue in honour of Donald J. Winzor's 80th birthday

The purpose of this special issue is to honour Professor Donald J. Winzor's long career as a researcher and scientific mentor, and to celebrate the milestone of his 80th birthday. Throughout his career, Don has been renowned for his development of clever approximations to difficult quantitative relations governing a range of biophysical measurements. The theme of this special issue, 'Quantitative and analytical relations in biochemistry', was chosen to reflect this aspect of Don's scientific approach.

Skeletal muscle sarcoplasmic reticulum glycogen status influences Ca2+ uptake supported by endogenously synthesized ATP

The purpose of this investigation was to determine whether there is a link between sarcoplasmic reticulum (SR) glycogen status and SR Ca2+ handling. In this investigation, skeletal muscle SR was purified from female Sprague-Dawley rats (200-250 g). Glycogen was extracted from the SR purified from one hindlimb, whereas the SR purified from the contralateral limb served as control. Before removal of the tissue, the animals were anesthetized with an intraperitoneal injection of ketamine (80 mg/kg) and xylazine (10 mg/kg). Both alpha-amylase treatment (AM) and removal of EDTA from the homogenization and storage buffers reduced the amount of glycogen associated with the SR (P < 0.05). AM treatment reduced the glycogen phosphorylase content of SR (P < 0.05). In contrast, creatine kinase (CK) and pyruvate kinase (PK) contents were increased after both glycogen extraction protocols (P < 0.05). Under exogenous ATP conditions, both AM and EDTA-free (EF) treatments resulted in an increase in Ca2+-stimulated ATPase activity when normalized to sarco(endo)plasmic reticulum calcium-ATPase (SERCA) content (P < 0.05). CK and PK-supported SR Ca2+ uptake was decreased (P < 0.05) in the AM group when normalized to SERCA and CK or SERCA and PK content, respectively. AM was more effective than the EF for extracting glycogen associated with purified SR. Glycogen extraction alters the yield of purified SR proteins and must be taken into account when investigating SR calcium handling. Removal of glycogen from purified SR causes a change in Ca2+-handling properties as measured by ATPase and uptake activities.

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.

Thermodynamic non-ideality as an alternative source of the effect of sucrose on the thrombin-catalyzed hydrolysis of peptide p-nitroanilide substrates

The inhibitory effect of sucrose on the kinetics of thrombin-catalyzed hydrolysis of the chromogenic substrate S-2238 (D-phenylalanyl-pipecolyl-arginoyl-p-nitroanilide) is re-examined as a possible consequence of thermodynamic non-ideality-an inhibition originally attributed to the increased viscosity of reaction mixtures. However, those published results may also be rationalized in terms of the suppression of a substrate-induced isomerization of thrombin to a slightly more expanded (or more asymmetric) transition state prior to the irreversible kinetic steps that lead to substrate hydrolysis. This reinterpretation of the kinetic results solely in terms of molecular crowding does not signify the lack of an effect of viscosity on any reaction step(s) subject to diffusion control. Instead, it highlights the need for development of analytical procedures that can accommodate the concomitant operation of thermodynamic non-ideality and viscosity effects.

Macromolecular crowding: effects on actin polymerisation

Dextran has been found to enhance the polymerisation of actin. This enhancement increases exponentially with increasing mass concentrations of dextran, in a manner that is consistent with excluded volume theory. Mathematical prediction of experimental results is difficult due to the fact that all participating species, namely F-actin, G-actin and dextran are best represented by differently shaped hard particles. Modelling dextran as a sphere of radius defined by an effective thermodynamic radius (Reff), we have predicted our experimental results to an acceptable degree, given the relative crudity of the model. The results imply that the highly crowded cellular environment may help to stabilise the filamentous actin network in vivo.

Measurement of thermodynamic nonideality arising from volume-exclusion interactions between proteins and polymers

The effective thermodynamic radii of 23 ribosomal proteins from the 50 S subunit have been determined by gel chromatography on Sephadex G-50, thereby supporting the contention that most of the proteins of the 50 S ribosomal unit exhibit reasonably globular structures. To investigate further the usefulness of modelling proteins as spheres, the second virial coefficient describing excluded volume interactions of some ribosomal proteins with two inert polymers, polyethylene glycol (PEG) and dextran, has been determined by gel chromatography and/or sedimentation equilibrium techniques. Protein-polymer excluded volumes obtained with PEG 20000 and Dextran T70 as the space-filling solute are shown to conform reasonably well with a quantitative expression describing interaction between an impenetrable sphere and an ideal Brownian path (K.M. Jansons and C.G. Phillips, J. Colloid Interface Sci., 137 (1990) 75).

Thermodynamic nonideality of enzyme solutions supplemented with inert solutes: yeast hexokinase revisited

Published experimental results on the activating effect of polyethylene glycol on the interaction of yeast hexokinase with glucose (R.P. Rand, N.L. Fuller, P. Butko, G. Francis and P. Nicholls, Biochemistry, 32 (1993) 5925) are reinterpreted in statistical-mechanical terms of excluded volume. Of particular interest is the ability of this standard treatment of thermodynamic nonideality to accommodate the observed non-exponential dependence of the activation upon osmotic pressure of the polyethylene glycol solution--a dependence which is not predicted by analyses based on the concept of osmotic stress that was invoked originally to account for the results.

Effects of dextran on the self-association of human spectrin

The self-association of human spectrin is enhanced in the presence of dextran. The equilibrium constant for association of two heterodimers to form a tetramer is increased by an order of magnitude in the presence of 20% dextran. The rate constant for association is also enhanced, while the rate constant for dissociation is almost independent of dextran concentration. The degree of enhancement of association is dependent only on the mass concentration of dextran; for a given mass concentration of dextran the effect is independent of dextran molecular weight. These effects are believed to be due to excluded volume phenomena, and a model is presented that realistically accounts for the effects. These results imply that the association of spectrin within the erythrocyte will be enhanced by the presence of hemoglobin.

Effects of thermodynamic nonideality in kinetic studies: evidence of an expanded intermediate complex in the inactivation of thrombin by antithrombin III

The technique of competitive chromogenic substrate hydrolysis is used to examine the inhibitory effects of sucrose and glycerol on the inactivation of thrombin by antithrombin III. This inhibition is attributed to the existence of a slight increase in volume/asymmetry associated with formation of the thrombin-antithrombin complex that subsequently undergoes covalent modification in an irreversible inactivation step. Partial reversal of the equilibrium step is thus considered to result from the effects of molecular crowding in the highly concentrated environment that is generated by the inclusion of these small insert solutes.

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.

Allowance for thermodynamic nonideality and Donnan effects in binding studies. Activity coefficients of charged ligands in the presence of albumin

A combination of ultrafiltration with either equilibrium dialysis or frontal gel chromatography has been used to evaluate the effects of thermodynamic nonideality in mixtures of bovine serum albumin and charged ligands. 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 nonideality 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 nonideality 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 ideality.

Thermodynamic nonideality in macromolecular solutions. Evaluation of parameters for the prediction of covolume effects

Second virial coefficients and hence covolumes for self-interaction of five proteins, viz. ribonuclease, ovalbumin, bovine serum albumin, catalase and alpha-crystallin, have been determined by analyzing 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 unit mass of polymer, upon size of the polymer. This requirement is met by the sphere/rod model [Edmond, E. & Ogston, A. G. (1968) Biochem. J. 109, 569-576] and also by the sphere/flexible-segment model [Hermans, J. (1982) J. Chem. Phys. 77, 2193-2203]. 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 nonideality arising from the inclusion of dextrans in protein solutions, and also provide the relevant calibration of the model.

Thermodynamic nonideality in enzyme catalysis. Effect of albumin on the reduction of pyruvate by lactate dehydrogenase

The enhanced catalytic reduction of pyruvate by rabbit muscle lactate dehydrogenase that results from the addition of serum albumin [Nichol, L. W., Sculley, M. J., Ward, L. D. & Winzor, D. J. (1983) Arch. Biochem. Biophys. 222, 574-581] is shown to emanate solely from an increase in maximal velocity, there being no discernible effect of this inert space-filling macromolecular solute on the Michaelis constant for either pyruvate or NADH. As part of the search for a mechanistic explanation of this kinetic phenomenon, the space-filling effects of albumin have been used to eliminate the possibility that the increase in sedimentation coefficient of lactate dehydrogenase effected by inclusion of oxamate with enzyme-NADH complex reflects preferential binding of this pyruvate analog to a more compact isomeric state of the binary complex. The enzyme kinetic results are therefore considered in terms of a reaction scheme entailing gross conformational changes during the formation of ternary enzyme-NADH-pyruvate complex and its isomerization to an activated transition state. The experimentally observed insensitivity of the Michaelis constant for pyruvate to albumin concentration is in keeping with theoretical prediction, but incorporation of the measured extent of maximal velocity enhancement into the kinetic model leads to a predicted volume for the fully saturated transition-state complex that is far too small to be experimentally feasible. A more complex mechanistic model involving additional isomerizations of enzyme-substrate species is thus required to achieve quantitative description of the albumin effect solely in terms of thermodynamic nonideality.

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.

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.

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.

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 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.

Effect of thermodynamic nonideality on the subcellular distribution of enzymes: adsorption of aldolase to muscle myofibrils

An expression is derived whereby allowance may be made for the effects of thermodynamic nonideality on the biphasic interaction of a macromolecular solute with an immobilized reactant. This quantitative description, written in terms of activity coefficients expressed as virial coefficients on the basis of excluded volume, also takes into account the space-filling effect of an inert macromolecule present in the reaction mixture. Advantage is then taken of the theory to consider the effect of bovine serum albumin on the interaction of aldolase with bovine cardiac muscle myofibrils in I 0.158 imidazole-chloride buffer, pH 6.8. Partition equilibrium studies are used to establish that inclusion of a moderate concentration (14 mg/ml) of serum albumin in reaction mixtures leads to a 35-40% increase in the apparent binding constant written in terms of reactant molarities, and that the enhancement is attributable entirely to nonideality inasmuch as the same thermodynamic binding constant pertains. This investigation of thermodynamic nonideality arising from the space-filling effects of inert macromolecules on enzyme partition reinforces the possibility that some enzymes may be distributed between soluble and adsorbed states in the highly concentrated macromolecular environment of the cell cytoplasm.

Effect of thermodynamic nonideality in kinetic studies: evidence for reversible unfolding of urease during urea hydrolysis

A combination of enzyme kinetic studies and active enzyme gel chromatography on Sepharose CL-6B was used to explore conformational changes of the enzyme urease as it catalyzes the hydrolysis of urea in 0.7 M phosphate buffer, pH 7.0, at 20 degrees C. It is shown that elucidation of this system is only possible by studying the effects of inert space-filling macromolecules (ovalbumin and bovine serum albumin) on enzymatic behavior. The resulting increases in reaction velocity are interpreted in terms of composition-dependent activity coefficients assessed on a statistical mechanical basis of excluded volume. The results are first considered in terms of two extreme models; one involving a volume change on the isomerization of the enzyme-substrate complex to its activated state, and the other an isomeric expansion of the enzyme-substrate complex to an inactive form. Although both extreme models provide satisfactory descriptions of the kinetic results, they lead to unrealistic values for the radii of the various states of the enzyme-substrate complex. It is concluded, therefore, that the two isomeric transitions act conjointly, a result in conformity with the previously postulated conformational change associated with formation of the activated enzyme-substrate complex [L. W. Nichol, M. J. Sculley, L. D. Ward, and D. J. Winzor (1983) Arch. Biochem. Biophys. 222, 574-581], and also with the well-established action of the substrate, urea, as an unfolding agent of proteins.

A macromolecular shape function based on sedimentation velocity parameters

A volume-independent shape function, experimentally determinable from sedimentation velocity experiments, was formulated explicitly in terms of the axial ratio of a macromolecule considered as an ellipsoid of revolution. Use of this function offers a simple first approach to the elucidation of macromolecular geometry as illustrated by calculations for ovalbumin, bovine serum albumin, and myosin.