Thermodynamic Nonideality Research Articles

A potential role for isothermal calorimetry in studies of the effects of thermodynamic non-ideality in enzyme-catalyzed reactions.

Attention is drawn to the feasibility of using isothermal calorimetry for the characterization of enzyme reactions under conditions bearing greater relevance to the crowded biological environment, where kinetic parameters are likely to differ significantly from those obtained by classical enzyme kinetic studies in dilute solution. An outline of the application of isothermal calorimetry to the determination of enzyme kinetic parameters is followed by considerations of the nature and consequences of crowding effects in enzyme catalysis. Some of those effects of thermodynamic non-ideality are then illustrated by means of experimental results from calorimetric studies of the effect of molecular crowding on the kinetics of catalysis by rabbit muscle pyruvate kinase. This review concludes with a discussion of the potential of isothermal calorimetry for the experimental determination of kinetic parameters for enzymes either in biological environments or at least in media that should provide reasonable approximations of the crowded conditions encountered in vivo.

Simulation-Aided Optimization of Volatile Organic Compounds Recovery Using Condensation

A systematic simulation-based alternate approach for the recovery and recycle of volatile organic compounds (VOCs) from gaseous streams via condensation is introduced. This approach utilizes the application of the process simulation, and process integration techniques to achieve the optimum process condensation network. The optimal network is developed without pre-defining a structure for VOC condensation and with screening all the potential external cooling utility. This approach shows that the cost of cooling utilities can substantially be reduced through self-integration of the gaseous streams, and usage of the condensed liquid streams for cooling. The temperature path is used to facilitate the development of the optimal condensation network. In addition, linear programming is used to optimize the recycle of the recovered organics to process units (sinks) to reduce the process cost of fresh solvents. Using process simulators guarantees the thermodynamic non-ideality (phase equilibria) and the technical feasibility of the generated solutions. A case study is used to illustrate the effectiveness of the proposed methodology.

Effects of inert volume-excluding macromolecules on protein fiber formation. II. Kinetic models for nucleated fiber growth

A sequential model for nucleated protein fiber formation is proposed that is similar in broad outline to models proposed previously (Thermodynamics of the Polymerization of Protein, Academic Press, New York, (1975); Biophys. J. 50 (1986) 583) but generalized to allow for thermodynamic nonideality resulting from a high degree of volume occupancy by inert macromolecular cosolutes (macromolecular crowding). The effect of volume occupancy on the rate of fiber formation is studied in the transition-state rate-limited regime through systematic variation of rate-limiting step (prenuclear oligomer formation, nucleus formation or fiber growth), shape of prenuclear oligomer, size of nucleus, extent of reversibility, nature of inert cosolute (hard globular particle or random coil polymer) and size of inert cosolute relative to that of fiber-forming protein. It is found that crowding can accelerate the rate of fiber formation by as much as several orders of magnitude. The extent of acceleration for a given degree of volume occupancy depends upon several factors, the most conspicuous of which is the stoichiometry of the nucleus. In contrast, the rate of redistribution of fiber length, which occurs on a much slower time scale than polymer formation, is found to be insensitive to the extent of crowding.

Preferential interactions in aqueous solutions of urea and KCl

A quantitative characterization of the thermodynamic effects due to interactions of salt ions and urea in aqueous solution is needed for rigorous analyses of the effects of changing urea concentration on biopolymer processes in solutions that also contain salt. Therefore, we investigate preferential interactions in aqueous solutions containing KCl and urea by using vapor pressure osmometry (VPO) to measure osmolality as a function of the molality of urea (component 3) over the range 0.09⩽ m 3⩽1.65 m at two fixed molalities of KCl (component 2) ( m 2=0.212 and 0.427 m). With this experimental input and corresponding VPO measurements on solutions that contain only urea or KCl, we evaluate approximately the chemical potential derivative μ 23=( ∂μ KCl/ ∂m urea) T, P, m KCl =( ∂μ urea/ ∂m KCl) T, P, m urea = μ 32 and hence the preferential interaction coefficients Γμ 3 and Γμ 1,μ 3. These results show that for water–KCl–urea solutions neither of these coefficients is determined primarily by contributions from thermodynamic nonideality to μ 23. In aqueous solutions containing a biopolymer and a small solute, the contribution of ideal mixing entropy to μ 23 is negligible in comparison with the experimental uncertainty, whereas in KCl–urea solutions the contribution due to ideal mixing entropy accounts for at least half of the magnitude of μ 23. For comparison, we analyze literature data for NaCl–urea interactions and find again that nonideality makes a smaller contribution to μ 23 than does ideal mixing entropy. In contrast, for aqueous solutions of urea and the protein bovine serum albumin, the experimentally determined contribution of nonideality to μ 23 exceeds the contribution of ideal mixing by a factor of ∼2×10 2.

The effect of multicomponent diffusion on NAPL dissolution from spherical ternary mixtures

This paper investigates the dissolution characteristics of ternary nonaqueous phase liquid (NAPL) mixtures with the goal of comparing the relative contributions of multicomponent (intra-NAPL) diffusion, film transfer and thermodynamic nonideality. These contributions are compared at the pore scale and intermediate scale (several centimeters downstream from the source). Trichloroethene (TCE), tetrachloroethene (PCE) and 1,1,1-trichloroethane (TCA) were selected to model a reasonably ideal mixture; TCE, PCE and octanol were selected as a relevant nonideal mixture. A multicomponent diffusion-based dissolution model incorporating hydrodynamic theory was formulated to estimate intra-NAPL concentration gradients and associated aqueous interfacial concentrations for ideally shaped (spherical) NAPL blobs. Pore scale dissolution times for this model were compared to those generated using the conventional well-mixed NAPL dissolution model, applying the same film transfer boundary condition in both cases. Activity coefficients (spatially and temporally variable for the diffusion model, temporally variable for the well-mixed model) were estimated using UNIFAC. NAPL interfacial concentration histories generated using the pore scale models were used as input in a three-dimensional groundwater transport model (MT3DMS) to compare downstream concentration distributions. For the relatively large NAPL bodies simulated ( r=0.6 cm), intra-NAPL diffusion effects were found to be significant at the pore scale and were strongly impacted by the mixture's thermodynamic ideality. At the intermediate scale, and for the conditions tested, modest differences in the simulations suggested that intra-NAPL diffusion effects would be negligible compared to those associated with mixture composition uncertainty, dissolution rate processes related to NAPL-induced permeability effects and hydrodynamic issues associated with flow field heterogeneity.

Allowance for thermodynamic non-ideality in the characterization of protein self-association by frontal exclusion chromatography: hemoglobin revisited

This investigation re-examines theoretical aspects of the allowance for effects of thermodynamic non-ideality on the characterization of protein self-association by frontal exclusion chromatography, and thereby provides methods of analysis with greater thermodynamic rigor than those used previously. Their application is illustrated by reappraisal of published exclusion chromatography data for hemoglobin on the controlled-pore-glass matrix CPG-120. The equilibrium constant of 100/M that is obtained for dimerization of the α 2β 2 species by this means is also deduced from re-examination of published studies of concentrated hemoglobin solutions by osmotic pressure and sedimentation equilibrium methods.

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.

Some Aspects of Rubberlike Elasticity Useful in Teaching Basic Concepts in Physical Chemistry

There are several advantages to including polymer topics in both undergraduate and graduate physical chemistry courses. The first is to illustrate similarities and differences between systems with which the student is already familiar (such as ideal gases and metals) and more complex materials (in the present case polymeric materials having elastomeric properties). Another advantage is to provide particular examples illustrating the validity of very general results, such as the Carnot cycle analysis being independent of the working substance. It is possible to use aspects of rubberlike elasticity to illustrate a number of general molecular and thermodynamic concepts, making them more meaningful to the student. The items chosen here for this purpose are: (i) random flights of polymer chains and excluded volume effects, (ii) molecular origins of the elasticities of some types of materials, (iii) equations of state, (iv) thermodynamic non-ideality, (v) temperature changes during deformations and retractions, (vi) Carnot cycles and mechanochemistry, (vii) energy storage and hysteresis, and (viii) gel collapse.

Calorimetric demonstration of the potential of molecular crowding to emulate the effect of an allosteric activator on pyruvate kinase kinetics.

A method based on isothermal calorimetry is described for the direct kinetic assay of pyruvate kinase. In agreement with earlier findings based on the standard coupled assay system for this enzyme in the presence of a fixed ADP concentration, the essentially rectangular hyperbolic dependence of initial velocity upon phosphoenolpyruvate concentration is rendered sigmoidal by the allosteric inhibitor phenylalanine. This effect of phenylalanine can be countered by including a high concentration of a space-filling osmolyte such as proline in the reaction mixtures. This investigation thus affords a dramatic example that illustrates the need to consider potential consequences of thermodynamic nonideality on the kinetics of enzyme reactions in crowded molecular environments such as the cell cytoplasm.

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.

Analysis of thermodynamic non-ideality in terms of protein solvation

The effects of thermodynamic non-ideality on the forms of sedimentation equilibrium distributions for several isoelectric proteins have been analysed on the statistical–mechanical basis of excluded volume to obtain an estimate of the extent of protein solvation. Values of the effective solvation parameter δ are reported for ellipsoidal as well as spherical models of the proteins, taken to be rigid, impenetrable macromolecular structures. The dependence of the effective solvated radius upon protein molecular mass exhibits reasonable agreement with the relationship calculated for a model in which the unsolvated protein molecule is surrounded by a 0.52-nm solvation shell. Although the observation that this shell thickness corresponds to a double layer of water molecules may be of questionable relevance to mechanistic interpretation of protein hydration, it augurs well for the assignment of magnitudes to the second virial coefficients of putative complexes in the quantitative characterization of protein–protein interactions under conditions where effects of thermodynamic non-ideality cannot justifiably be neglected.

Interpretation of the reversible inhibition of adenosine deaminase by small cosolutes in terms of molecular crowding.

Published results on the inhibitory effects of small cosolutes on adenosine deamination by adenosine deaminase [Kurz, L. C., Weitkamp, E., and Frieden, C. (1987) Biochemistry 26, 3027-3032; Dzingeleski, G., and Wolfenden, R. (1993) Biochemistry 32, 9143-9147] have been reexamined. Results for sucrose, dioxane, methanol, and ethanol are shown to be qualitatively consistent with thermodynamic interpretation in terms of molecular crowding effects arising from the occurrence of a minor increase in enzyme volume and/or asymmetry during the kinetic reaction--a conformational transition that could be either preexisting or ligand induced. Direct evidence for the existence of the putative isomeric transition is provided by active enzyme gel chromatography on Sephadex G-100, which demonstrates a negative dependence of enzyme elution volume upon substrate concentration and is therefore consistent with substrate-mediated conformational changes that favor a larger (or more asymmetric) isomeric state of the enzyme. There are thus experimental grounds for adopting the present description of the inhibitory effects of unrelated cosolutes on the kinetics of adenosine deamination by adenosine deaminase in terms of thermodynamic nonideality.

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 α-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).

Interpreting the effects of small uncharged solutes on protein-folding equilibria.

Proteins are designed to function in environments crowded by cosolutes, but most studies of protein equilibria are conducted in dilute solution. While there is no doubt that crowding changes protein equilibria, interpretations of the changes remain controversial. This review combines experimental observations on the effect of small uncharged cosolutes (mostly sugars) on protein stability with a discussion of the thermodynamics of cosolute-induced nonideality and critical assessments of the most commonly applied interpretations. Despite the controversy surrounding the most appropriate manner for interpreting these effects of thermodynamic nonideality arising from the presence of small cosolutes, experimental advantage may still be taken of the ability of the cosolute effect to promote not only protein stabilization but also protein self-association and complex formation between dissimilar reactants. This phenomenon clearly has potential ramifications in the cell, where the crowded environment could well induce the same effects.

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.

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.

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.

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

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

Effects of thermodynamic nonideality in protein crystal growth

The driving force for crystallization is the difference in chemical potential between the protein in supersaturated solution and at its solubility. This chemical potential difference depends in a complicated manner on protein concentration and solution conditions (temperature, ionic strength and pH). Consequently, driving forces estimated from the nominal ideal solution supersaturation may be in error. In this work, the chemical potential of protein in solution is estimated from a virial expansion in protein concentration. The thermodynamic driving force for the crystallization of hen egg white lysozyme is calculated as a function of temperature, salt concentration, and protein concentration. In all cases examined here, the driving force for crystallization is lower than that for the corresponding ideal solution and the deviation from ideal solution behavior increases with the protein solubility.

Analytical Centrifugation: Equilibrium Approach

The specific interaction of biological molecules with one another is fundamental to the biochemistry of all living things. Equilibrium sedimentation is a classic method of biochemistry that provides first-principle thermodynamic information about the molar mass, association energy, association stoichiometry, and thermodynamic nonideality of molecules in solution. It is one of the most rigorous, powerful, and readily adapted methods for characterizing solution interactions.