Simplified Equilibrium Model for Exploring the Combined Influences of Concentration, Aggregate Shape, Excluded Volume, and Surface Adsorption upon Aggregation Propensity and Distribution of Globular Macromolecules.

A mesoscopic model for the equilibrium self-association of a globular macromolecule that may form oligomers of various shapes and unlimited sizes is presented. Allowance is made within this model for the effects of variation in the free energy of subunit contact within an oligomer of specified size and different shapes, the free energy of adsorption of an oligomer of specified size and shape to a planar surface, and the free energy of nonspecific excluded volume interaction between an oligomer of specified size and shape and an inert species occupying a specified fraction of total volume. The model is analytically soluble and permits rapid calculation and analysis of the effects of variation in each of the three free energy parameters upon the concentration dependence of the weight-average stoichiometry of the oligomer, the fraction of total macromolecule that is adsorbed, and the fraction of differently shaped oligomers that are adsorbed and in free solution.

Influence of Nonspecific Interactions on Protein Associations: Implications for Biochemistry In Vivo.

The cellular interior is composed of a variety of microenvironments defined by distinct local compositions and composition-dependent intermolecular interactions. We review the various types of nonspecific interactions between proteins and between proteins and other macromolecules and supramolecular structures that influence the state of association and functional properties of a given protein existing within a particular microenvironment at a particular point in time. The present state of knowledge is summarized, and suggestions for fruitful directions of research are offered.

Water Loss in Aging Erythrocytes Provides a Clue to a General Mechanism of Cellular Senescence.

Experimental evidence for age-dependent loss of intracellular water content as a widespread concomitant of cellular senescence is reviewed. Quantitative models are presented, indicating that an age-dependent increase in macromolecular crowding resulting from water loss may be responsible for three observed phenomena: a general age-dependent loss of intracellular protein solubility, a delayed and rapid appearance of high molecular weight aggregates, and an age-dependent transfer of intracellular protein from dilute to concentrated or condensed phases.

Implications of excluded volume for chemical inhibition of protein fibrillation.

Two quantitative models for the effect of high total macromolecular volume occupancy ('macromolecular crowding') upon the chemical inhibition of protein fibrillation are presented. The first assumes that fibrillation is reversible, and the second assumes that fibrillation is irreversible. Both models predict that small molecule inhibitors will be less effective in crowded media than in dilute media, whereas macromolecular inhibitors are likely to retain their efficiency in crowded media. It is suggested that the coupling of one or more small-molecule inhibitors to an "inert" macromolecular support will increase inhibition efficiency in crowded media.

Simple Calculation of Phase Diagrams for Liquid-Liquid Phase Separation in Solutions of Two Macromolecular Solute Species.

A simple method is described for the calculation of two- and three-dimensional phase diagrams describing stability and coexistence curves or surfaces separating one- and two-phase regions in composition/temperature space of a solution containing solute species 1 and 2. The calculation requires a quantitative description of the intermolecular potentials of mean force acting between like (1-1 and 2-2) and unlike (1-2) species. Example calculations are carried out for solutions of species interacting via spherically symmetric square-well potentials as first-order models for protein-protein interaction. When the interaction between species 1 and 2 is more repulsive than those acting between like species, the two-phase region is characterized by an equilibrium between a phase enriched in 1 and depleted in 2 and a phase enriched in 2 and depleted in 1. When the interaction between species 1 and 2 is more attractive than those acting between like species, the two-phase region is characterized by an equilibrium between a phase enriched in both species and a phase depleted in both species. The latter example provides a first-order description of coacervate formation without postulating specific interactions between the two solute species.

The Cumulative Effect of Surface Adsorption and Excluded Volume in 2D and 3D on Protein Fibrillation.

A refined mesoscopic model for the cumulative effect of repulsive excluded volume protein-protein interaction and attractive protein-surface interaction upon the properties of a trace protein capable of fiber formation is presented. The model predicts that very small changes in the magnitude of bulk volume occupancy or the strength of protein-surface attraction may result in very large changes in the extent of trace protein fibrillation and the distribution of trace protein between bulk and adsorbed phases.

Comparison of composition-gradient sedimentation equilibrium and composition-gradient static light scattering as techniques for quantitative characterization of biomolecular interactions: A case study.

The equilibrium hetero-association of NADH oxidase and peroxiredoxin was characterized by means of independently conducted measurements of composition-gradient sedimentation equilibrium and composition-gradient static light scattering. Results obtained from both experiments were quantitatively accounted for by a model according to which a dimer of NADH oxidase forms a 1:1 equilibrium complex with a decamer of peroxiredoxin under the conditions of these experiments. The best-fit equilibrium constants for heteroassociation of the two proteins obtained from the two measurements were found to be identical to well within the uncertainty of estimate of each of the two methods. The relative virtues of each of the methods are discussed.

Quantitative characterization of the concentration-dependent interaction between molecules of Dextran 70 in aqueous solution: Measurement and analysis in the context of thermodynamic and compressible sphere models.

The static light scattering and sedimentation equilibrium of solutions of Dextran 70 were measured as functions of concentration up to 100 g/L in pH 7.4 phosphate-buffered saline at temperatures between 5 and 37 °C. The concentration dependence of scattering intensity and the apparent molar mass obtained from sedimentation equilibrium were found to be nearly independent of temperature over this range to within the uncertainty of measurement. Global analysis of the concentration dependence of both properties yielded a reliable estimate of the concentration-dependent thermodynamic activity coefficient, a quantitative measure of the free energy of self-interaction. The self-interaction between Dextran molecules is compared with that of a globular protein (BSA) and a highly crosslinked polymer of similar molar mass (Ficoll 70). The observed concentration dependence of the free energy of Dextran self-interaction may be quantitatively accounted for by a semi-empirical model in which the polymer molecule is represented by a compressible sphere.

Non-specific Interactions Between Macromolecular Solutes in Concentrated Solution: Physico-Chemical Manifestations and Biochemical Consequences.

A general thermodynamic formulation of the effect of hard and soft non-specific intermolecular interactions upon reaction equilibria is summarized. A highly simplified quantitative model for non-specific intermolecular interaction is introduced. This model is used to illustrate how the magnitudes of attractive and repulsive components of the overall intermolecular interaction, and the balance between them, influence the concentration-dependent properties of a highly concentrated solution of a single macromolecular solute. The properties calculated using the results of computer simulation and an approximate analytical model are found to agree qualitatively with the results of experimental measurements on protein solutions over a broad range of concentration.

Comparison of the thermal stabilization of proteins by oligosaccharides and monosaccharide mixtures: Measurement and analysis in the context of excluded volume theory.

The thermal stability of apo α-lactalbumin (α-LA) and lysozyme was measured in the presence of mixtures of glucose, fructose, and galactose. Mixtures of these monosaccharides in the appropriate stoichiometric ratio were found to have a greater stabilizing effect on each of the two proteins than equal weight/volume concentrations of di- tri- and tetrasaccharides with identical subunit composition (sucrose, trehalose, raffinose, and stachyose). The excluded volume model for the effect of a single saccharide on the stability of a protein previously proposed by Beg et al. [Biochemistry 54 (2015) 3594] was extended to treat the case of saccharide mixtures. The extended model predicts quantitatively the stabilizing effect of all monosaccharide mixtures on α-LA and lysozyme reported here, as well as previously published results obtained for ribonuclease A [Biophys. Chem. 138 (2008) 120] to within experimental uncertainty.

Toward an understanding of biochemical equilibria within living cells.

Four types of environmental effects that can affect macromolecular reactions in a living cell are defined: nonspecific intermolecular interactions, side reactions, partitioning between microenvironments, and surface interactions. Methods for investigating these interactions and their influence on target reactions in vitro are reviewed. Methods employed to characterize conformational and association equilibria in vivo are reviewed and difficulties in their interpretation cataloged. It is concluded that, in order to be amenable to unambiguous interpretation, in vivo studies must be complemented by in vitro studies carried out in well-characterized and controllable media designed to contain key elements of selected intracellular microenvironments.

Nucleotide and receptor density modulate binding of bacterial division FtsZ protein to ZipA containing lipid-coated microbeads.

ZipA protein from Escherichia coli is one of the essential components of the division proto-ring that provides membrane tethering to the septation FtsZ protein. A sedimentation assay was used to measure the equilibrium binding of FtsZ-GDP and FtsZ-GTP to ZipA immobilized at controlled densities on the surface of microbeads coated with a phospholipid mixture resembling the composition of E. coli membrane. We found that for both nucleotide-bound species, the amount of bound FtsZ exceeds the monolayer capacity of the ZipA immobilized beads at high concentrations of free FtsZ. In the case of FtsZ-GDP, equilibrium binding does not appear to be saturable, whereas in the case of FtsZ-GTP equilibrium binding appears to be saturable. The difference between the two modes of binding is attributed to the difference between the composition of oligomers of free FtsZ-GDP and free FtsZ-GTP formed in solution.

Explicit Incorporation of Hard and Soft Protein-Protein Interactions into Models for Crowding Effects in Protein Mixtures. 2. Effects of Varying Hard and Soft Interactions upon Prototypical Chemical Equilibria.

Previously derived approximate analytical relations for the activity coefficient of each solute in a mixture of up to three spherical solutes in a highly nonideal solution interacting via square well potentials of mean force (Hoppe, T.; Minton, A. P. J Phys Chem B. 2016, 120, 11866-11872) were used to explore the effect of heterogeneity in volume occupancy and intermolecular interactions upon prototypical schemes representing solubility, partitioning, conformational isomerization, and self-association in crowded solutions. Results generally indicate that all of the equilibria explored are exquisitely sensitive to variations in both volume occupancy and intermolecular interaction and have important implications for the design and execution of more detailed simulations of complex media.

The pH Dependence of Saccharides' Influence on Thermal Denaturation of Two Model Proteins Supports an Excluded Volume Model for Stabilization Generalized to Allow for Intramolecular Electrostatic Interactions.

The reversible thermal denaturation of apo α-lactalbumin (α-LA) and lysozyme was measured in the absence and presence of multiple concentrations of each of seven saccharides (glucose, galactose, fructose, sucrose, trehalose, raffinose, and stachyose) at multiple pH values. It was observed that with increasing pH, the absolute stability of α-LA decreased, whereas the stabilizing effect per mole of all saccharides increased, and that the absolute stability of lysozyme increased, whereas the stabilizing effect per mole of all saccharides decreased. All of the data may be accounted for quantitatively by straightforward electrostatic generalization of a previously introduced coarse-grained model for stabilization of proteins by sugars.

Incorporation of Hard and Soft Protein-Protein Interactions into Models for Crowding Effects in Binary and Ternary Protein Mixtures. Comparison of Approximate Analytical Solutions with Numerical Simulation.

In order to better understand how nonspecific interactions between solutes can modulate specific biochemical reactions taking place in complex media, we introduce a simplified model aimed at elucidating general principles. In this model, solutions containing two or three species of interacting globular proteins are modeled as a fluid of spherical particles interacting through square well potentials that qualitatively capture both steric hard core repulsion and longer-ranged attraction or repulsion. The excess chemical potential, or free energy of solvation, of each particle species is calculated as a function of species concentrations, particle radii, and square well interaction range and depth. The results of analytical models incorporating two-body and three-body interactions are compared with the estimates of free energy obtained via Widom insertion into simulated equilibrium square-well fluids. The analytical models agree well with results of numeric simulations carried out for a variety of model parameters and fluid compositions up to a total particle volume fraction of ca. 0.2.

Macromolecular Crowding In Vitro, In Vivo, and In Between.

Biochemical processes take place in heterogeneous and highly volume-occupied or crowded environments that can considerably influence the reactivity and distribution of participating macromolecules. We summarize here the thermodynamic consequences of excluded-volume and long-range nonspecific intermolecular interactions for macromolecular reactions in volume-occupied media. In addition, we summarize and compare the information content of studies of crowding in vitro and in vivo. We emphasize the importance of characterizing the behavior not only of labeled tracer macromolecules but also the composition and behavior of unlabeled macromolecules in the immediate vicinity of the tracer. Finally, we propose strategies for extending quantitative analyses of crowding in simple model systems to increasingly complex media up to and including intact cells.

Modulation of Conformational Equilibria in the S-Adenosylmethionine (SAM) II Riboswitch by SAM, Mg(2+), and Trimethylamine N-Oxide.

The dependence of the conformation of the S-adenosylmethionine (SAM) II riboswitch on the concentration of added Mg(2+) ions and SAM, individually and in mixtures, was monitored by circular dichroism (CD) spectroscopy and by measurement of the diffusion coefficient. The results are analyzed in the context of two complementary quantitative models, both of which are consistent with a single underlying physical model. Magnesium binding sites in the open state have an affinity on average higher than the affinity of those in the compact state, but formation of the compact state is accompanied by an increase in the number of binding sites. Consequently, at low Mg(2+) concentrations, Mg(2+) binds preferentially to the open state, favoring its formation, but at high concentrations, Mg(2+) binds preferentially to the compact state. The affinity of the riboswitch for SAM increases drastically with an increased level of binding of Mg(2+) to the compact pseudoknot conformation. The effect of increasing concentrations of trimethylamine N-oxide (TMAO), a well-studied molecular crowding agent, on the conformation of the riboswitch and its affinity for SAM were also monitored by CD spectroscopy and measurement of diffusion. In the absence of added Mg(2+), high concentrations of TMAO were found to induce a conformational change compatible with the formation of the pseudoknot form but have only a small effect on the affinity of the RNA for SAM.