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

Macromolecular Crowding and DNA: Bridging the Gap between In Vitro and In Vivo

The cellular environment is highly crowded, with up to 40% of the volume fraction of the cell occupied by various macromolecules. Most laboratory experiments take place in dilute buffer solutions; by adding various synthetic or organic macromolecules, researchers have begun to bridge the gap between in vitro and in vivo measurements. This is a review of the reported effects of macromolecular crowding on the compaction and extension of DNA, the effect of macromolecular crowding on DNA kinetics, and protein-DNA interactions. Theoretical models related to macromolecular crowding and DNA are briefly reviewed. Gaps in the literature, including the use of biologically relevant crowders, simultaneous use of multi-sized crowders, empirical connections between macromolecular crowding and liquid-liquid phase separation of nucleic materials are discussed.

Use of molecular crowding for the detection of protein self-association by size-exclusion chromatography

The feasibility of employing molecular crowding cosolutes to facilitate the detection of protein self-association by zonal size exclusion chromatography is investigated. Theoretical considerations have established that although the cosolute-induced displacement of a self-association equilibrium towards the oligomeric state invariably occurs in the mobile phase of the column, that displacement is only manifested as a decreased protein elution volume for cosolutes sufficiently small to partition between the mobile and stationary phases. Indeed, the use of a crowding agent sufficiently large to be confined to the mobile phase gives rise to an increased elution volume that could be misconstrued as evidence of cosolute-induced protein dissociation. Those theoretical considerations are reinforced by experimental studies of α-chymotrypsin (a reversibly dimerizing enzyme) on Superdex 200. The use of cosolutes such as sucrose and small polyethylene glycol fractions such as PEG-2000 is therefore recommended for the detection of protein self-association by molecular crowding effects in size exclusion chromatography.

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.

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.

Molecular crowding and solvation: direct and indirect impact on protein reactions

The typical environment for biomolecules in vivo is highly crowded. Under such conditions chemical activities, rather than simply concentrations, govern the behavior of the molecules. In this chapter we discuss the underlying solvation principles that give rise to the chemical activities. We focus on simple experimentally accessible examples, macromolecular crowding, protein folding, and ligand binding under crowded conditions. We discuss effects of high concentrations of both macromolecules and small molecules in terms of the Kirkwood-Buff theory, which couples solution structure to thermodynamics.

Effects of osmolytes on hexokinase kinetics combined with macromolecular crowding

We investigated the effect of compatible and non-compatible osmolytes in combination with macromolecular crowding on the kinetics of yeast hexokinase. This was motivated by the fact that almost all studies concerning the osmolyte effects on enzyme activity have been performed in diluted buffer systems, which are far from the physiological conditions within cells, where the cytosol contains several hundred mg protein ml(-1). Four organic (glycerol, betaine, TMAO and urea) and one inorganic (NaCl) osmolyte were tested. It was concluded that the effect of compatible osmolytes (glycerol, betaine and TMAO) on V(max) and K(M) was practically equivalent in pure buffer and in 200-250 mg BSA ml(-1) supporting the view that these small organic osmolytes do minimal perturbance on enzyme function in physiological solutions. The effect of urea on enzyme kinetics was not independent of protein concentration, since the presence of 250 mg BSA ml(-1) partly compensated the perturbing effect of urea. Even though the organic osmolytes glycerol, betaine and TMAO are generally considered compatible with enzyme function, especially glycerol did have a significant effect on hexokinase kinetics, decreasing both k(cat), K(M) and k(cat)/K(M). The osmolytes decreased k(cat)/K(M) in the order: NaCl>Urea>TMAO/glycerol>betaine. For the organic osmolytes this order correlates with the degree of exclusion from protein-water interfaces. Thus, the stronger the exclusion the weaker the perturbing effects on k(cat)/K(M).

Protein phase diagrams II: nonideal behavior of biochemical reactions in the presence of osmolytes

In the age of biochemical systems biology, proteomics, and high throughput methods, the thermodynamic quantification of cytoplasmatic reaction networks comes into reach of the current generation of scientists. What is needed to efficiently extract the relevant information from the raw data is a robust tool for evaluating the number and stoichiometry of all observed reactions while providing a good estimate of the thermodynamic parameters that determine the molecular behavior. The recently developed phase-diagram method, strictly speaking a graphical representation of linkage or Maxwell Relations, offers such capabilities. Here, we extend the phase diagram method to nonideal conditions. For the sake of simplicity, we choose as an example a reaction system involving the protein RNase A, its inhibitor CMP, the osmolyte urea, and water. We investigate this system as a function of the concentrations of inhibitor and osmolyte at different temperatures ranging from 280 K to 340 K. The most interesting finding is that the protein-inhibitor binding equilibrium depends strongly on the urea concentration--by orders-of-magnitude more than expected from urea-protein interaction alone. Moreover, the m-value of ligand binding is strongly concentration-dependent, which is highly unusual. It is concluded that the interaction between small molecules like urea and CMP can significantly contribute to cytoplasmic nonideality. Such a finding is highly significant because of its impact on renal tissue where high concentrations of cosolutes occur regularly.

Effect of osmolytes on the interaction of flavin adenine dinucleotide with muscle glycogen phosphorylase b

The effect of three osmolytes, trimethylamine N-oxide (TMAO), betaine and proline, on the interaction of muscle glycogen phosphorylase b with allosteric inhibitor FAD has been examined. In the absence of osmolyte, the interaction is described by a single intrinsic dissociation constant (17.8 microM) for two equivalent and independent binding sites on the dimeric enzyme. However, the addition of osmolytes gives rise to sigmoidal dependencies of fractional enzyme-site saturation upon free inhibitor concentration. The source of this cooperativity has been shown by difference sedimentation velocity to be an osmolyte-mediated isomerization of phosphorylase b to a smaller dimeric state with decreased affinity for FAD. These results thus have substantiated a previous inference that the tendency for osmolyte-enhanced self-association of dimeric glycogen phosphorylase b in the presence of AMP was being countered by the corresponding effect of molecular crowding on an isomerization of dimer to a smaller, nonassociating state.

Influence of Osmolytes on Inactivation and Aggregation of Muscle Glycogen Phosphorylase b by Guanidine Hydrochloride. Stimulation of Protein Aggregation under Crowding Conditions

The effects of the osmolytes trimethylamine-N-oxide (TMAO), betaine, proline, and glycine on the kinetics of inactivation and aggregation of rabbit skeletal muscle glycogen phosphorylase b by guanidine hydrochloride (GuHCl) have been studied. It is shown that the osmolytes TMAO and betaine exhibit the highest protective efficacy against phosphorylase b inactivation. A test system for studying the effects of macromolecular crowding induced by osmolytes on aggregation of proteins is proposed. TMAO and glycine increase the rate of phosphorylase b aggregation induced by GuHCl.

Biochemical effects of molecular crowding

Cell cytoplasm contains high concentrations of high-molecular-weight components that occupy a substantial part of the volume of the medium (crowding conditions). The effect of crowding on biochemical processes proceeding in the cell (conformational transitions of biomacromolecules, assembling of macromolecular structures, protein folding, protein aggregation, etc.) is discussed in this review. The excluded volume concept, which allows the effects of crowding on biochemical reactions to be quantitatively described, is considered. Experimental data demonstrating the biochemical effects of crowding imitated by both low-molecular-weight and high-molecular-weight crowding agents are summarized.

The Kirkwood–Buff theory and the effect of cosolvents on biochemical reactions

Cosolvents added to aqueous solutions of biomolecules profoundly affect protein stability, as well as biochemical equilibria. Some cosolvents, such as urea and guanidine hydrochloride, denature proteins, whereas others, such as osmolytes and crowders, stabilize the native structures of proteins. The way cosolvents interact with biomolecules is crucial information required to understand the cosolvent effect at a molecular level. We present a statistical mechanical framework based upon Kirkwood-Buff theory, which enables one to extract this picture from experimental data. The combination of two experimental results, namely, the cosolvent-induced equilibrium shift and the partial molar volume change upon the reaction, supplimented by the structural change, is shown to yield the number of water and cosolvent molecules bound or released during a reaction. Previously, denaturation experiments (e.g., m-value analysis) were analyzed by empirical and stoichiometric solvent-binding models, while the effects of osmolytes and crowders were analyzed by the approximate molecular crowding approach for low cosolvent concentration. Here we synthesize these previous approaches in a rigorous statistical mechanical treatment, which is applicable at any cosolvent concentration. The usefulness and accuracy of previous approaches was also evaluated.

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.

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.

Modern applications of analytical ultracentrifugation

Analytical ultracentrifugation is a classical method of biochemistry and molecular biology. Because it is a primary technique, sedimentation can provide first-principle hydrodynamic and first-principle thermodynamic information for nearly any molecule, in a wide range of solvents and over a wide range of solute concentrations. For many questions, it is the technique of choice. This review stresses what information is available from analytical ultracentrifugation and how that information is being extracted and used in contemporary applications.

Osmotic stress, crowding, preferential hydration, and binding: A comparison of perspectives

There has been much confusion recently about the relative merits of different approaches, osmotic stress, preferential interaction, and crowding, to describe the indirect effect of solutes on macromolecular conformations and reactions. To strengthen all interpretations of measurements and to forestall further unnecessary conceptual or linguistic confusion, we show here how the different perspectives all can be reconciled. Our approach is through the Gibbs-Duhem relation, the universal constraint on the number of ways it is possible to change the temperature, pressure, and chemical potentials of the several components in any thermodynamically defined system. From this general Gibbs-Duhem equation, it is possible to see the equivalence of the different perspectives and even to show the precise identity of the more specialized equations that the different approaches use.

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.

Influence of excluded volume upon macromolecular structure and associations in 'crowded' media

Results of experimental studies published since the last major review of excluded volume effects in biopolymer solutions in 1993 add to our appreciation of the scope and magnitude of such effects. Recent theoretical studies have improved incrementally our ability to understand and model excluded volume effects in simple model systems.