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.

Surfaces as frameworks for intracellular organization.

A large fraction of soluble protein within the interior of living cells may reversibly associate with structural elements, including proteinaceous fibers and phospholipid membranes. In this opinion, we present theoretical and experimental evidence that many of these associations are due to nonspecific attraction between the protein and the surface of the fiber or membrane, and that such associations may lead to substantial changes in the association state of the adsorbed proteins, the biological function of the adsorbed proteins, and the distribution of these proteins between the many microenvironments existing within the cell.

The effect of Ficoll 70 on thermally-induced and chemically-induced conformational transitions of an RTX protein is quantitatively accounted for by a unified excluded volume model.

A unified excluded volume model based upon the effective hard particle approximation is developed and used to quantitatively model previously published experimental measurements of the effect of adding high concentrations of an "inert" polymer, Ficoll 70, on conformational transitions of the toxin protein RCL that are induced by addition of calcium at constant temperature or by increasing temperature in the absence and presence of high calcium concentrations. The best-fit of this model, which accounts quantitatively for all of the published data to within experimental precision, yields an estimate of the volume of solution excluded to Ficoll by each of four identified conformational states of RCL: H - the most compact conformation adopted in the limits of high calcium concentration and low temperature, H* - the conformation adopted in the limits of high calcium concentration and high temperature, A - the conformation adopted in the limits of low (or no) calcium at low temperature, and A* - the conformation adopted in the limits of low calcium and high temperature. Ficoll exclusion volumes increase in the order H < H* < A < A*. These results are discussed in the context of the physiological functions of the RTX proteins, which are involved in the secretion process and the calcium-induced folding of bacterial virulence factors.

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.

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.

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.

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.

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.

An equilibrium model for the combined effect of macromolecular crowding and surface adsorption on the formation of linear protein fibrils.

The formation of linear protein fibrils has previously been shown to be enhanced by volume exclusion or crowding in the presence of a high concentration of chemically inert protein or polymer, and by adsorption to membrane surfaces. An equilibrium mesoscopic model for the combined effect of both crowding and adsorption upon the fibrillation of a dilute tracer protein is presented. The model exhibits behavior that differs qualitatively from that observed in the presence of crowding or adsorption alone. The model predicts that in a crowded solution, at critical values of the volume fraction of crowder or intrinsic energy of the tracer-wall interaction, the tracer protein will undergo an extremely cooperative transition-approaching a step function-from existence as a slightly self-associated species in solution to existence as a highly self-associated and completely adsorbed species. Criteria for a valid experimental test of these predictions are presented.

Thermal Stabilization of Proteins by Mono- and Oligosaccharides: Measurement and Analysis in the Context of an Excluded Volume Model.

The reversible thermal denaturation of apo α-lactalbumin and lysozyme was monitored via measurement of changes in absorbance and ellipticity in the presence of varying concentrations of seven mono- and oligosaccharides: glucose, galactose, fructose, sucrose, trehalose, raffinose, and stachyose. The temperature dependence of the unfolding curves was quantitatively accounted for by a two-state model, according to which the free energy of unfolding is increased by an amount that is independent of temperature and depends linearly upon the concentration of added saccharide. The increment of added unfolding free energy per mole of added saccharide was found to depend approximately linearly upon the extent of oligomerization of the saccharide. The relative strength of stabilization of different saccharide oligomers could be accounted for by a simplified statistical-thermodynamic model attributing the stabilization effect to volume exclusion deriving from steric repulsion between protein and saccharide molecules.

Dynamic interaction of the Escherichia coli cell division ZipA and FtsZ proteins evidenced in nanodiscs.

The full-length ZipA protein from Escherichia coli, one of the essential components of the division proto-ring that provides membrane tethering to the septation FtsZ protein, has been incorporated in single copy into nanodiscs formed by a membrane scaffold protein encircling an E. coli phospholipid mixture. This is an acellular system that reproduces the assembly of part of the cell division components. ZipA contained in nanodiscs (Nd-ZipA) retains the ability to interact with FtsZ oligomers and with FtsZ polymers. Interactions with FtsZ occur at similar strengths as those involved in the binding of the soluble form of ZipA, lacking the transmembrane region, suggesting that the transmembrane region of ZipA has little influence on the formation of the ZipA·FtsZ complex. Peptides containing partial sequences of the C terminus of FtsZ compete with FtsZ polymers for binding to Nd-ZipA. The affinity of Nd-ZipA for the FtsZ polymer formed with GTP or GMPCPP (a slowly hydrolyzable analog of GTP) is moderate (micromolar range) and of similar magnitude as for FtsZ-GDP oligomers. Polymerization does not stabilize the binding of FtsZ to ZipA. This supports the role of ZipA as a passive anchoring device for the proto-ring with little implication, if any, in the regulation of its assembly. Furthermore, it indicates that the tethering of FtsZ to the membrane shows sufficient plasticity to allow for its release from noncentral regions of the cytoplasmic membrane and its subsequent relocation to midcell when demanded by the assembly of a division ring.

Quantitative assessment of the relative contributions of steric repulsion and chemical interactions to macromolecular crowding.

The term "macromolecular crowding" denotes the combined effects of high volume fractions of nominally unrelated macromolecules upon the equilibrium and transport properties of all macrosolutes, dilute as well as concentrated, in the crowded medium. We present a formal partitioning of the total crowding effect into contributions from steric exclusion (excluded volume) and weak, nonspecific attractive interactions between a concentrated "crowding agent" and reactant and product species present at trace concentration. A numerical example of the combined effect of both steric and chemical interactions between crowder and tracer upon the reversible dimerization of tracer is presented, based upon reasonable estimates of the magnitude of both repulsive and attractive interactions between tracer and crowder species.

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.

An equilibrium model for the Mg(2+)-linked self-assembly of FtsZ in the presence of GTP or a GTP analogue.

The concerted formation of a narrow distribution of oligomeric FtsZ species in the presence of GTP or a GTP analogue under close to physiological conditions (neutral pH and 0.5 M K(+)) has been characterized recently by various biophysical methods [Monterroso, B., et al. (2012) Biochemistry 51, 4541-4550]. An equilibrium model may semiquantitatively account for the results of this study; in the model, FtsZ self-associates in a noncooperative fashion to form linear fibrils, that upon increasing to a certain size exhibit an increasing tendency to form closed cyclic fibrils, as previously suggested [González, J. M., et al. (2005) Proc. Natl. Acad. Sci. U.S.A. 102, 1895-1900]. The closed cyclic fibrils are formed when the natural curvature and flexibility of a linear oligomer bring the ends of a linear fiber sufficiently close to overcome the entropic barrier to loop closure. The size distribution of cyclic oligomers is thus a reflection of the tendency toward curvature of linear fibrils of FtsZ under the conditions used in these experiments.

Mg(2+)-linked self-assembly of FtsZ in the presence of GTP or a GTP analogue involves the concerted formation of a narrow size distribution of oligomeric species.

The assembly of the bacterial cell division FtsZ protein in the presence of constantly replenished GTP was studied as a function of Mg(2+) concentration (at neutral pH and 0.5 M potassium) under steady-state conditions by sedimentation velocity, concentration-gradient light scattering, fluorescence correlation spectroscopy, and dynamic light scattering. Sedimentation velocity measurements confirmed previous results indicating cooperative appearance of a narrow size distribution of finite oligomers with increasing protein concentration. The concentration dependence of light scattering and diffusion coefficients independently verified the cooperative appearance of a narrow distribution of high molecular weight oligomers, and in addition provided a measurement of the average size of these species, which corresponds to 100 ± 20 FtsZ protomers at millimolar Mg(2+) concentration. Parallel experiments on solutions containing guanosine-5'-[(α,ß)-methyleno]triphosphate, sodium salt (GMPCPP), a slowly hydrolyzable analogue of GTP, in place of GTP, likewise indicated the concerted formation of a narrow size distribution of fibrillar oligomers with a larger average mass (corresponding to 160 ± 20 FtsZ monomers). The closely similar behavior of FtsZ in the presence of both GTP and GMPCPP suggests that the observations reflect equilibrium rather than nonequilibrium steady-state properties of both solutions and exhibit parallel manifestations of a common association scheme.

Capillary viscometer for fully automated measurement of the concentration and shear dependence of the viscosity of macromolecular solutions.

The construction and operation of a novel viscometer/rheometer are described. The instrument is designed to measure the viscosity of a macromolecular solution while automatically varying both solute concentration and shear rate. Viscosity is calculated directly from Poiseuille's law, given the measured difference in pressure between two ends of a capillary tube through which the solution is flowing at a known rate. The instrument requires as little as 0.75 mL of a solution to provide a full profile of viscosity as a function of concentration and shear rate, and it can measure viscosities as high as 500 cP and as low as 1 cP, at shear rates between 10 and 2 × 10(3) s(-1). The results of control experiments are presented to document the accuracy and precision of measurement at both low and high concentration of synthetic polymers and proteins.