Sedimentation equilibrium in macromolecular solutions of arbitrary concentration. II. Two protein components

Relations describing sedimentation equilibrium in solutions containing two macromolecular solute components are derived for the following cases: (1) two nonassociating proteins at arbitrary concentration, (2) one dilute self-associating protein in the presence of a second inert protein at arbitrary concentration, and (3) two proteins at arbitrary concentration that can associate to form a single heterocomplex of arbitrary composition. As in earlier work (R. C. Chatelier and A. P. Minton (1987) Biopolymers, 26, 507–524), the relations are obtained by using scaled particle theory to calculate the thermodynamic activity of each species present at a given radial distance in the centrifuge. The results of numerical simulations of sedimentation equilibrium are presented as the dependence of apparent molecular weights, or apparent weight-average molecular weights, upon solution composition. Semiempirical methods are presented, by means of which the weight-average molecular weights of self- and heteroassociating proteins in highly nonideal solutions may be estimated from experimental data. It is found that the semiempirical methods yield reasonably accurate estimates of the true weight-average molecular weight over a broad range of experimental conditions, providing that the partial specific volumes of two components in a heteroassociating system do not differ by more than about 0.05 mL/g.     

Sedimentation equilibrium in a solution containing an arbitrary number of solute species at arbitrary concentrations: theory and application to concentrated solutions of ribonuclease

Simple expressions are derived describing the equilibrium concentration gradient of each species in a solution containing an arbitrary number of solute species at arbitrary concentration, as a function of the concentration of all species. Quantitative relationships between the species gradients and experimentally observable signal gradients are presented. The expressions are model-free and take into account both attractive and repulsive interactions between all species. In order to analyze data obtained from strongly nonideal solutions, a statistical thermodynamic model for repulsive solute-solute interactions is required. The relations obtained are utilized to analyze the dependence of the equilibrium gradient of ribonuclease A in phosphate-buffered saline, pH 7.4, upon total protein concentration. Experimental results are interpreted in the context of a model for weak self-association leading to the formation of significant amounts of oligomers at total protein concentrations exceeding 25 g/l.     

Sedimentation equilibrium in macromolecular solutions of arbitrary concentration. I. Self-associating proteins

Relations describing sedimentation equilibrium in solutions of self-associating macromolecules at arbitrary concentration are presented. These relations are obtained by using scaled-particle theory to calculate the thermodynamic activity of each species present at a given radial distance. The results are expected to be valid for solutions of globular proteins under conditions such that interactions between individual solute molecules may be approximated by a hard-particle potential. Sedimentation equilibria in solutions containing either a nonassociating solute or a solute that self-associates according to several different schemes are simulated using the derived relations. The results of these simulations are presented in terms of the dependence of apparent weight-average molecular weight upon solute concentration. Simple empirical relations are presented for estimating the true weight-average molecular weight from the apparent weight-average molecular weight, without reference to any particular self-association scheme. The weight-average molecular weight estimated in this fashion is within a few percent of the true weight-average molecular weight at all experimentally realizable solute concentrations ( < 400 g/L).     

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 effect of ionic strength, temperature, and pressure on the interaction potential of dense protein solutions: from nonlinear pressure response to protein crystallization

Understanding the intermolecular interaction potential, V(r), of proteins under the influence of temperature, pressure, and salt concentration is essential for understanding protein aggregation, crystallization, and protein phase behavior in general. Here, we report small-angle x-ray scattering studies on dense lysozyme solutions of high ionic strength as a function of temperature and pressure. We show that the interaction potential changes in a nonlinear fashion over a wide range of temperatures, salt, and protein concentrations. Neither temperature nor protein and salt concentration lead to marked changes in the pressure dependence of V(r), indicating that changes of the water structure dominate the pressure dependence of the intermolecular forces. Furthermore, by analysis of the temperature, pressure, and ionic strength dependence of the normalized second virial coefficient, b2, we show that the interaction can be fine-tuned by pressure, which can be used to optimize b2 values for controlled protein crystallization.     

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.     

Myelin basic protein interaction with zinc and phosphate: fluorescence studies on the water-soluble form of the protein.

The interaction of myelin basic protein (MBP) with zinc and phosphate ions has been studied by using the emission properties of the single tryptophan residue of the protein (Trp-115). The studies have been carried out by means of both static and time-resolved fluorescence techniques. The addition of either zinc to MBP in the presence of phosphate or phosphate to MBP in the presence of zinc resulted in an increase of fluorescence intensity and a blue shift of the emission maximum wavelength. Furthermore, a concomitant increase in the scattering was also detected. Anisotropy decay experiments demonstrated that these effects are due to the formation of MBP molecules into large aggregates. A possible physiological role for such interaction is discussed.     

Kinetic analysis of the pre-equilibrium steps in the self-assembly of RecA protein from Escherichia coli

Total intensity light scattering is employed to investigate the self-assembly kinetics of RecA protein. Reaction conditions are employed where the kinetics of self-assembly are slow enough to yield reliable scattered intensity measurements over the range of scattering angles from 40 to 130 degrees as a function of time. From these measurements the time-dependent behavior of the weight average molecular weight, Mr, and radius of gyration, RG, of the associating protein species as a function of [MgCl2], [NaCl], [RecA], and pH was determined. The temperature dependence of RecA self-assembly was also investigated and allowed an evaluation of the activation thermodynamic parameters of association. Results reveal RecA self-assembly is bi-phasic under all conditions examined. The first phase, referred to as "filamentation" is second-order in [RecA] and occurs via a quasi linear condensation scheme with an Arrhenius activation energy of 88.6 kcal/mol. Filamentation assembly involves the uptake of one proton, one MgCl2, the release of five to six NaCls, and is driven by the release of approximately 70 water molecules. The evaluated activation parameters of the first kinetic phase are consistent with the proposition that linear self-assembly of RecA protein into ordered filaments is entropically driven. The second kinetic phase, referred to as "bundling" is greater than second-order in both [RecA] and [MgCl2], is considerably slower that filamentation assembly, and is apparently initiated by 2nd order collisions of linear filaments.     

Comparison of Methods for Characterizing Nonideal Solute Self-Association by Sedimentation Equilibrium

We have examined in detail analytical solutions of expressions for sedimentation equilibrium in the analytical ultracentrifuge to describe self-association under nonideal conditions. We find that those containing the radial dependence of total solute concentration that incorporate the Adams-Fujita assumption for composition-dependence of activity coefficients reveal potential shortcomings for characterizing such systems. Similar deficiencies are shown in the use of the NONLIN software incorporating the same assumption about the interrelationship between activity coefficients for monomer and polymer species. These difficulties can be overcome by iterative analyses incorporating expressions for the composition-dependence of activity coefficients predicted by excluded volume considerations. A recommendation is therefore made for the replacement of current software packages by programs that incorporate rigorous statistical-mechanical allowance for thermodynamic nonideality in sedimentation equilibrium distributions reflecting solute self-association.     

Molecular modeling of the multidomain structures of the proteoglycan binding region and the link protein of cartilage by neutron and synchrotron X-ray scattering

The interaction of proteoglycan monomers with hyaluronate in cartilage is mediated by a globular binding region at the N-terminus of the proteoglycan monomer; this interaction is stabilized by link protein. Sequences show that both the binding region (27% carbohydrate) and the link protein (6% carbohydrate) contain an immunoglobulin (Ig) fold domain and two proteoglycan tandem repeat (PTR) domains. Both proteins were investigated by neutron and synchrotron X-ray solution scattering, in which nonspecific aggregate formation was reduced by the use of citraconylation to modify surface lysine residues. The neutron and X-ray radius of gyration RG of native and citraconylated binding region is 5.1 nm, and the cross-sectional RG (RXS) is 1.9-2.0 nm. No neutron contrast dependence of the RG values was observed; however, a large contrast dependence was seen for the RXS values which is attributed to the high carbohydrate content of the binding region. The neutron RG for citraconylated link protein is 2.9 nm, its RXS is 0.8 nm, and these data are also independent of the neutron contrast. The scattering curves of binding region and link protein were modeled using small spheres. Both protein structures were defined initially by the representation of one domain by a crystal structure for a variable Ig fold and a fixed volume for the two PTR domains calculated from sequence data. The final models showed that the different dimensions and neutron contrast properties of binding region compared to link protein could be attributed to an extended glycosylated C-terminal peptide with extended carbohydrate structures in the binding region.(ABSTRACT TRUNCATED AT 250 WORDS)     

Static Light Scattering From Concentrated Protein Solutions II: Experimental Test of Theory for Protein Mixtures and Weakly Self-Associating Proteins

Using an experimental technique recently developed in this laboratory (Fernández C. and A. P. Minton. 2008. Anal. Biochem. 381:254-257), the Rayleigh light scattering of solutions of bovine serum albumin, hen egg white ovalbumin, hen egg white ovomucoid, and binary mixtures of these three proteins was measured as a function of concentration at concentrations up to 125 g/L. The measured concentration dependence of scattering of both pure proteins and binary mixtures is accounted for nearly quantitatively by an effective hard particle model (Minton A. P. 2007. Biophys. J. 93:1321-1328) in which each protein species is represented by an equivalent hard sphere, the size of which is determined by the nature of repulsive interactions between like molecules under a given set of experimental conditions. The light scattering of solutions of chymotrypsin A was measured as a function of concentration at concentrations up to 70 g/L at pH 4.1, 5.4, and 7.2. At each pH, the measured concentration dependence is accounted for quantitatively by an effective hard particle model, according to which monomeric protein may self-associate to form an equilibrium dimer and, depending upon pH, an equilibrium pentamer or hexamer.     

Quantitative characterization of weak self-association in concentrated solutions of immunoglobulin G via the measurement of sedimentation equilibrium and osmotic pressure

The sedimentation equilibrium of solutions of immunoglobulin G in saline buffer, over a concentration range up to 125 g/L, was measured and analyzed in the context of a model that takes into account the possibility of attractive intermolecular interaction leading to the reversible formation of oligomeric species and repulsive intermolecular interaction leading to nonideal solution behavior. Additionally, previously published data on the concentration dependence of the osmotic pressure of immunoglobulin G under similar conditions, over a concentration range up to 400 g/L, were analyzed in the context of a newly developed thermodynamic formalism describing the osmotic pressure of a solution containing multiple nondiffusible solute species at an arbitrary concentration. Both sets of data are quantitatively accounted for by a model in which IgG self-associates at very high concentration to form (predominantly) trimers under the conditions of these experiments.     

Effective hard particle model for the osmotic pressure of highly concentrated binary protein solutions

The experimentally measured concentration dependence of the osmotic pressure of an equimolar mixture of hen egg ovalbumin and bovine serum albumin at pH 7.0 and 25°C in the presence of 0.15 M NaCl is shown to be quantitatively accounted for by a model in which each protein species is represented by an effective hard sphere. The size of this sphere is determined by analysis of the concentration dependence of the osmotic pressure of the isolated protein.     

Backbone and side-chain contributions in protein denaturation by urea

Urea is a commonly used protein denaturant, and it is of great interest to determine its interaction with various protein groups to elucidate the molecular basis of its effect on protein stability. Using the Trp-cage miniprotein as a model system, we report what we believe to be the first computation of changes in the preferential interaction coefficient of the protein upon urea denaturation from molecular-dynamics simulations and examine the contributions from the backbone and the side-chain groups. The preferential interaction is obtained from reversible folding/unfolding replica exchange molecular-dynamics simulations of Trp-cage in presence of urea, over a wide range of urea concentration. The increase in preferential interaction upon unfolding is dominated by the side-chain contribution, rather than the backbone. Similar trends are observed in simulations using two different force fields, Amber94 and Amber99sb, for the protein. The magnitudes of the side-chain and backbone contributions differ in the two force fields, despite containing identical protein-solvent interaction terms. The differences arise from the unfolded ensembles sampled, with Amber99sb favoring conformations with larger surface area and lower helical content. These results emphasize the importance of the side-chain interactions with urea in protein denaturation, and highlight the dependence of the computed driving forces on the unfolded ensemble sampled.     

The Dictyostelium discoideum 30,000-dalton protein is an actin filament- bundling protein that is selectively present in filopodia

The interaction with actin and intracellular localization of the 30,000-D actin-binding protein from the cellular slime mold Dictyostelium discoideum have been investigated to analyze the potential contributions of this protein to cell structure and movement. The formation of anisotropic cross-linked filament networks (bundles) containing actin and the 30,000-D protein has been observed by electron microscopy, light scattering, viscometry, and polarization microscopy. Cosedimentation experiments indicate that a maximum of one molecule of the 30,000-D protein can bind to 10 actin monomers in filaments with an apparent association constant of 1 X 10(7) liters/mol. Inhibition of the interaction of the 30,000-D protein with actin by either magnesium or calcium was observed by viscometry, light scattering, polarization microscopy, and direct binding assays. However, the concentration of magnesium required to diminish the interaction is greater than 100 times greater than that of calcium. The association constant of the 30,000-D protein for actin is 4.2 X 10(6) liters/mol, or less than 1 X 10(5) liters/mol in the presence of increased concentrations of either Mg2+ or Ca2+, respectively. Enzyme-linked immunoassays indicate that the 30,000-D protein comprises 0.04% of the protein in D. discoideum. Extensive interaction of the 30,000-D protein with actin in cytoplasm is predicted from these measurements of the concentration of this protein and its affinity for actin. The distribution of the 30,000-D protein was analyzed by immunofluorescence microscopy using mono-specific affinity-purified polyclonal antibody. The 30,000-D protein exhibits a diffuse distribution in cytoplasm, is excluded from prominent organelles, and is quite prominent in fine extensions protruding from the cell surface. The number, length, and distribution of these extensions containing the 30,000-D protein are similar to those of filopodia observed by scanning electron microscopy. To analyze the effects of cell thickness and the distribution of organelles on the immunofluorescence localization, fluorescein-labeled BSA was incorporated into the cytoplasm of living cells before fixation and staining using a sonication loading technique. The results indicate that the 30,000-D protein is selectively incorporated into filopodia. These results provide a clear distinction between the multiple actin-cross-linking proteins present in D. discoideum, and suggest that the 30,000-D protein contributes to organization of bundles of actin filaments in filopodia.     

Liquid diffraction analysis of the model membrane system. Egg lecithin + myelin protein (N-2).

The scattering from the model membrane system, egg lecithin + myelin protein (N-2), has been analyzed by liquid diffraction methods. It is found that by manipulating the protein-lipid ratio, the scattering domains of the protein and lipid can be identified. The multilayer contribution can also be identified by its position and concentration behavior in both the intensity pattern and its Fourier transform. When the multilayer and protein components are subtracted, the phospholipid scattering and an interaction term are left: these two can be resolved by a reasonable assessment of their relative magnitude in the boundary region where they overlap. The interaction term can then be used to determine the most probably position of the protein in the membrane. The deconvoluted protein and lipid transforms can then be combined in the proper way to obtain the electron density profiles. The resolution of the interaction term is not yet complete, but a method for accomplishing this is discussed.     

Solubility relationships in binary mixtures of hemoglobin variants: Application to the “gelationrd of sickle-cell hemoglobin

A thermodynamic treatment of solubility in binary mixtures of hemoglobin variants is presented. It is shown that the reported dependence of the minimum gelling concentration in five binary mixtures of the variants S, C_Harlem' Korle-Bu and A may be satisfactorily accounted for using the derived solubility relations together with simple models relating structure to interaction energies in the condensed phase.     

Quantitation of protein-protein interactions by thermal stability shift analysis

Thermal stability shift analysis is a powerful method for examining binding interactions in proteins. We demonstrate that under certain circumstances, protein-protein interactions can be quantitated by monitoring shifts in thermal stability using thermodynamic models and data analysis methods presented in this work. This method relies on the determination of protein stabilities from thermal unfolding experiments using fluorescent dyes such as SYPRO Orange that report on protein denaturation. Data collection is rapid and straightforward using readily available real-time polymerase chain reaction instrumentation. We present an approach for the analysis of the unfolding transitions corresponding to each partner to extract the affinity of the interaction between the proteins. This method does not require the construction of a titration series that brackets the dissociation constant. In thermal shift experiments, protein stability data are obtained at different temperatures according to the affinity- and concentration-dependent shifts in unfolding transition midpoints. Treatment of the temperature dependence of affinity is, therefore, intrinsic to this method and is developed in this study. We used the interaction between maltose-binding protein (MBP) and a thermostable synthetic ankyrin repeat protein (Off7) as an experimental test case because their unfolding transitions overlap minimally. We found that MBP is significantly stabilized by Off7. High experimental throughput is enabled by sample parallelization, and the ability to extract quantitative binding information at a single partner concentration. In a single experiment, we were able to quantify the affinities of a series of alanine mutants, covering a wide range of affinities (～ 100 nM to ～ 100 μM).     

Stopped-flow studies of myelin basic protein association with phospholipid vesicles and subsequent vesicle aggregation

When mixed with vesicles containing acidic phospholipids, myelin basic protein causes vesicle aggregation. The kinetics of this vesicle cross-linking by myelin basic protein was investigated by using stopped-flow light scattering. The process was highly cooperative, requiring about 20 protein molecules per vesicle to produce a measurable aggregation rate and about 35 protein molecules per vesicle to produce the maximum rate. The maximum aggregation rate constant approached the theoretical vesicle-vesicle collisional rate constant. Vesicle aggregation was second order in vesicle concentration and was much slower than protein-vesicle interaction. The highest myelin basic protein concentration used here did not inhibit vesicle aggregation, indicating that vesicle cross-linking occurred through protein-protein interactions. In contrast, poly(L-lysine)-induced vesicle aggregation was easily inhibited by increasing peptide concentrations, indicating that it did cross-link vesicles as a peptide monomer. The myelin basic protein:vesicle stoichiometry required for aggregation and the low affinity for protein dimerization suggested that multiple protein cross-links were needed to form a stable aggregate. Stopped-flow fluorescence was used to estimate the kinetics of myelin basic protein-vesicle binding. The half-times obtained suggested a rate constant that approached the theoretical protein-vesicle collisional rate constant.     

The influence of a protein on water dynamics in its vicinity investigated by molecular dynamics simulation

A system containing the globular protein ubiquitin and 4,197 water molecules has been used for the analysis of the influence exerted by a protein on solvent dynamics in its vicinity. Using Voronoi polyhedra, the solvent has been divided into three subsets, i.e., the first and second hydration shell, and the remaining bulk, which is hardly affected by the protein. Translational motion in the first shell is retarded by a factor of 3 in comparison to bulk. Several molecules in the first shell do not reach the diffusive regime within 100 ps. Shell-averaged orientational autocorrelation functions, which are also subject to a retardation effect, cannot be modeled by a single exponential time law, but are instead well-described by a Kohlrausch-Williams-Watts (KWW) function. The underlying distribution of single-molecule rotational correlation times is both obtained directly from the simulation and derived theoretically. The temperature dependence of reorientation is characterized by a strongly varying correlation time, but a virtually temperature-independent KWW exponent. Thus, the coupling of water structure relaxation with the respective environment, which is characteristic of each solvation shell, is hardly affected by temperature. In other words, the functional form of the distributions of single-molecule rotational correlation times is not subject to a temperature effect. On average, a correlation between reorientation and lifetimes of neighborhood relations is observed. © 1996 Wiley-Liss, Inc.