High-throughput dynamic light scattering method for measuring viscosity of concentrated protein solutions

We propose a new method to measure the viscosity of concentrated protein solutions in a high-throughput format. This method measures the apparent hydrodynamic radius of polystyrene beads with known sizes using a dynamic light scattering (DLS) system with a microplate reader. Glycerol solution viscosities obtained by the DLS method were in good agreement with those reported in the literature. Viscosity of the solutions of two monoclonal antibody molecules was acquired using both DLS and cone-and-plate techniques, and the results were comparable. The DLS method described here has the potential to be used in many aspects of protein characterization.     

Static and dynamic light scattering from dilute insulin solutions

Static and dynamic light-scattering measurements are reported on zinc-insulin at room temperature (21 ± l°C) and pH = 6.88 in 0.1M NaCl aqueous solution. The experiments were performed at very low concentration, in the range 0.12 × 10^?4 to 0.90 × 10^?4 g cm^?3. Within experimental error, we find no evidence for a critical micellar concentration in this system. The aggregation phenomenon starts immediately after preparation of the solutions, and takes several days to come to stable equilibrium. The concentration dependence of the diffusion coefficients, D _z, = D_o (1 — k_DC), is negative, and k_D was observed to decrease as a function of time, while the aggregate size was found to increase. The equivalent concentration coefficient, ?2BM _W, obtained from static light scattering, showed a similar behavior, and, within experimental error, was found to be numerically equal to k_D. From the relation found between the diffusion coefficient at infinite dilution and the molecular weight of the aggregates, log D₀ = ?0.240 log M _w ? 5.077, we deduce that the insulin aggregates are compact structures with a characteristic radius of 0.71 Å/(dalton)^1/3, surrounded by a hydration layer of a thickness of 8.0 Å. The equilibrium aggregation number is approximately 10.     

New methods for measuring macromolecular interactions in solution via static light scattering: basic methodology and application to nonassociating and self-associating proteins

A method for rapid detection and characterization of reversible associations of macromolecules in solution is presented. A programmable dual-syringe infusion pump is used to introduce a solution of time-varying composition into parallel flow cells for concurrent measurement of laser light scattering at multiple angles and ultraviolet-visible absorbance. An experiment lasting less than 15 min produces a large and information-rich set of data, consisting of several thousand values of the Rayleigh ratio as a function of solute concentration(s) and scattering angle. Using a novel treatment of the data, the entire data set may be equally rapidly analyzed in the context of models for self-association. Validation experiments conducted on previously characterized nonassociating and self-associating proteins yielded robust values for molecular weights in the range 10-330 kDa and equilibrium association constants for dimer formation in the range 2 x 10(3)-6 x 10(5) M(-1).     

Static light scattering to characterize membrane proteins in detergent solution

Determination of the oligomeric state or the subunit stoichiometry of integral membrane proteins in detergent solution is notoriously difficult, because the amount of detergent (and lipid) associated with the proteins is usually not known. Only two classical methods (sedimentation equilibrium centrifugation and static light scattering) can measure directly the absolute molecular mass of a protein present in a protein/detergent micelle, without any assumption on the amount of detergent bound, or the shape of the proteins. Here the theoretical background and practical aspects of static light scattering analysis of membrane proteins are reviewed using a number of examples from our lab to highlight potential pitfalls. A brief comparison with sedimentation equilibrium centrifugation is given and a detailed protocol of how we perform light scattering analyses is provided.     

Physicochemical properties of aqueous xanthan solutions: Static light scattering

The secondary structure of xanthan in solutions of relatively low salt concentration and at room temperature has been investigated using static light scattering experiments. Additional evidence has been found for a dimeric structure at 25°C in 0.01M NaCl. From the experimental z-average mean square (ms) radius of gyration, a value for the persistence length p has been estimated, taking explicitly into account the polydispersity of the three samples used, which has been established by gel permeation chromatography (GPC) measurements. The experimental particle scattering functions of the three samples are consistent with theoretical estimates for polydisperse systems with the same value of p = 65 ± 10 nm and the molar mass per unit length for a dimeric structure. This secondary structure remains unaffected by the ionic strength in the 0.005–0.0lM range. Partial aggregation seems to occur at higher NaCl concentrations. Light scattering and GPC data show that heating the xanthan 0.01M NaCl solutions to about 70°C considerably reduces the M_w of the low molar mass sample (2.3 × 10⁵-g·mol^?1), contrary to what is observed for the high molar mass sample (1.8 × 10⁶-g·mol^?1). These experimental findings can be accounted for by a partial temperature-induced dissociation of the xanthan dimers according to an all-or-none mechanism. © 1994 John Wiley & Sons, Inc.     

Structural basis of eye lens transparency: light scattering by concentrated solutions of bovine alpha-crystallin proteins.

Short range order of the crystallins does account for the transparency of the eye lens. To explain the solution structure of this highly concentrated protein solution on a quantitative basis, the hydrodynamic structure and the interparticle interactions of the proteins have to be known. For that purpose, the light scattering of concentrated solutions of alpha-crystallin has been studied. Starting from the detailed knowledge of the solution parameters of alpha-crystallin in diluted solutions, the structure of concentrated solutions up to 360 mg/ml has been studied using light scattering. Our results indicate that subtle changes in the macromolecular structure such as optical anisotropy or structural asymmetry for part of the alpha-crystallins, which results in solute light-scattering heterogeneity, can dramatically increase the light scattering by the alpha-crystallins and cause solution opacity.     

Static and dynamic light scattering from aggregating particles

We use standard hydrodynamic and light scattering theories to calculate the total intensity and dynamic light scattering properties of random aggregates of spherical particles containing up to ten spheres. When the aggregates have dimensions comparable to the wavelength of light, intraaggregate interference effects can dramatically reduce the apparent size of the aggregates. These results could be significant in interpreting DNA condensation, protein polymerization, and other biomolecular aggregation reactions.     

X-Ray small-angle scattering from concentrated solutions of normal and sickle cell deoxyhemoglobin

X-ray small-angle scattering of human normal and sickle cell deoxyhemoglobin in aqueous solution was measured at various concentrations, including those approximating the intracellular. The calculated radius of gyration, determination of the overall shape, and Soulé-Porod plots all indicate a concentration-dependent difference in strength of interparticle forces between normal and sickle cell samples at high concentration.     

Dynamic light scattering from collagen solutions. I. Translational diffusion coefficient and aggregation effects

Solutions of native collagen extracted from rat tail tendons in neutral salt solution have been studied by dynamic light scattering. The spectra obtained are consistent with the presence in solution of both single rod-shaped collagen molecules and aggregates of molecules. No contribution to the spectrum has been detected at any scattering angle from rotational diffusion of single molecules, although a measurable broadening effect is expected at high angles. The translational diffusion coefficient D of single molecules, calculated from the broader spectral component, shows an anomalous dependence on collagen concentration with a maximum value of D_20,w = 8.6 ± 0.2 × 10^?12 m²/sec near the concentration 0.04% by weight. Above 0.05% D falls linearly with increasing concentration and takes the value D _20,w = 8.1 ± 0.2 × 10^?12 m²/sec at 0.064% collagen.     

Hierarchical selection theory and sex ratios I. General solutions for structured populations

Models of sex-ratio evolution in structured populations are derived with G.R. Price's covariance form for the hierarchical analysis of natural selection (1970, Nature 227, 520-521). Previous work on competition among related males for mates (local mate competition), competition among related females for a limiting resource (local resource competition), inbreeding, group selection, and asymmetry of genetic inheritance between males and females, are subsumed under a general formulation for sex-ratio biases in structured populations. I found that the evolutionarily stable strategy sex ratio (males:females) for diploids is 1 - rho m:1 - rho f, where rho m is the regression coefficient of relatedness of the controlling genotypes on males competing for mates, rho f is the regression of controlling genotypes on females that compete for a fixed, limiting resource, and there is no inbreeding. For inbreeding and no competition among females, the evolutionarily stable strategy is 1 - rho m:1 + rho mf, where rho mf is the regression of controlling genotypes on females' mates.     

Nonequivalence of second virial coefficients from sedimentation equilibrium and static light scattering studies of protein solutions

Experimental data for ovalbumin and lysozyme are presented to highlight the nonequivalence of second virial coefficients obtained for proteins by sedimentation equilibrium and light scattering. Theoretical considerations confirm that the quantity deduced from sedimentation equilibrium distributions is B(22), the osmotic second virial coefficient describing thermodynamic nonideality arising solely from protein self-interaction. On the other hand, the virial coefficient determined by light scattering is shown to reflect the combined contributions of protein-protein and protein-buffer interactions to thermodynamic nonideality of the protein solution. Misidentification of the light scattering parameter as B(22) accounts for published reports of negative osmotic second virial coefficients as indicators of conditions conducive to protein crystal growth. Finally, textbook assertions about the equivalence of second virial coefficients obtained by sedimentation equilibrium and light scattering reflect the restriction of consideration to single-solute systems. Although sedimentation equilibrium distributions for buffered protein solutions are, indeed, amenable to interpretation in such terms, the same situation does not apply to light scattering measurements because buffer constituents cannot be regarded as part of the solvent: instead they must be treated as non-scattering cosolutes.     

Dynamic light scattering microscopy. A novel optical technique to image submicroscopic motions. I: theory

The theoretical basis of an optical microscope technique to image dynamically scattered light fluctuation decay rates (dynamic light scattering microscopy) is developed. It is shown that relative motions between scattering centers even smaller than the optical resolution of the microscope are sufficient to produce significant phase variations resulting in interference intensity fluctuations in the image plane. The timescale and time dependence for the temporal autocorrelation function of these intensity fluctuations is derived. The spatial correlation distance, which reports the average distance between constructive and destructive interference in the image plane, is calculated and compared with the pixel size, and the distance dependence of the spatial correlation function is derived. The accompanying article in this issue describes an experimental implementation of dynamic light scattering microscopy.     

Electrophoretic determination of sulfhydryl groups and its application to complex protein samples, in vitro protein synthesis mixtures, and cross-linked proteins

Without prior fractionation, the number of sulfhydryl groups of individual polypeptides in a protein mixture can be determined, provided their molecular weights and approximate isoelectric points are known. Urea-denatured protein samples are reacted with iodoacetamide and iodoacetate in a modified version of Creighton's procedure. After separation by sodium dodecyl sulfate - polyacrylamide gel electrophoresis and isoelectric focusing, the number of sulfhydryl groups is determined by counting the protein bands which have additional negative charges. This method requires little material and provides an additional parameter, besides the molecular weight and isoelectric point, for the identification and characterization of a protein. The sensitivity may be enhanced for nonradioactive proteins by using 14C-labeled iodoacetamide and iodoacetate. The procedure has been applied to prokaryotic in vitro protein synthesis mixtures, bacterial membrane protein, and trypsin-cleaved or chemically cross-linked subunits of the F1 ATPase from Escherichia coli.     

The solution behavior of poly-L-proline: I. Light scattering studies in water and concentrated aqueous neutral salt solutions

The solution bebavior of poly-L -proline Form II has been studied in water and aqueous salt solutions by both elastic and quasi-elastic light -scattering techniques. The results of this study suggest that polyproline Form II can exist in water at 24 °C as an associated polymer complex and that certain salts which do not appear to affect the helix integrity, e.g., guanidinium-HCl, resutl in dissociation of the aggregate. Other neutral salts, of the variety effective in mediating unfolding of the Form II helix (e.g., 4M NaClO₄) also induce aggregate dissociation, but 4M CaCl₂ results in enhanced aggregation of polyproline. Kinetic experiments indicate that a time of 20 hours is necessary for the completion of the “large” to “small” transformation (at 22°C) which is induced by the addition of 4M NaClO₄. Thus it appears that neutral salts additives in aqueous solutions of polyproline influence both the state of aggregation and the conformation of this polymer.     

Small angle neutron and x-ray scattering studies of concentrated protein solutions. II. Cytochrome C

Small angle neutron scattering (SANS) and small angle x-ray scattering (SAXS) techniques were used to study two series of concentrated protein solutions containing horse heart cytochrome C (a spherical protein molecule with hydrated diameter σ_H = 32.6 Å and pI = 10.2) at pD = 2.9 and 11.9, respectively. The concentration of the protein ranges from 1.2 to 24 g/dL. A titration experiment was made to determine the protein charge (Z_t) for each sample. Since the form factor of the protein was already determined from a previous experiment [C. F. Wu and S. H. Chen (1987) J. Chem. Phys. 87 , 6199–6205] at pD = 6.8, the present series of experiments was used to test the effect of protein charge on the interparticle structure factor. It is demonstrated that the absolute values of both SANS and SAXS cross sections can be calculated with a theory (called the generalized one-component macroion theory) of the interparticle structure factor, which contains a single unknown parameter, the effective protein charge Z_p. Comparison of Z_t and Z_p thus obtained shows that when the bare surface charge density of the protein calculated by using Z_t exceeds about 3 μC/cm², Z_p becomes much smaller than Z_t. This is interpreted as a charge renormalization phenomenon similar to that known to occur for highly charged polystyrene latex particles in aqueous solution [S. Alexander, P. M. Chaikin, P. Grant, G. J. Morales, and P. Pincus (1984) J. Chem. Phys. 80 , 5776–5781].     

Protein-protein association in polymer solutions: from dilute to semidilute to concentrated

In a typical cell, proteins function in the crowded cytoplasmic environment where 30% of the space is occupied by macromolecules of varying size and nature. This environment may be simulated in vitro using synthetic polymers. Here, we followed the association and diffusion rates of TEM1-beta-lactamase (TEM) and the beta-lactamase inhibitor protein (BLIP) in the presence of crowding agents of varying molecular mass, from monomers (ethylene glycol, glycerol, or sucrose) to polymeric agents such as different polyethylene glycols (PEGs, 0.2-8 kDa) and Ficoll. An inverse linear relation was found between translational diffusion of the proteins and viscosity in all solutions tested, in accordance with the Stokes-Einstein (SE) relation. Conversely, no simple relation was found between either rotational diffusion rates or association rates (k(on)) and viscosity. To assess the translational diffusion-independent steps along the association pathway, we introduced a new factor, alpha, which corrects the relative change in k(on) by the relative change in solution viscosity, thus measuring the deviations of the association rates from SE behavior. We found that these deviations were related to the three regimes of polymer solutions: dilute, semidilute, and concentrated. In the dilute regime PEGs interfere with TEM-BLIP association by introducing a repulsive force due to solvophobic preferential hydration, which results in slower association than predicted by the SE relation. Crossing over from the dilute to the semidilute regime results in positive deviations from SE behavior, i.e., relatively faster association rates. These can be attributed to the depletion interaction, which results in an effective attraction between the two proteins, winning over the repulsive force. In the concentrated regime, PEGs again dramatically slow down the association between TEM and BLIP, an effect that does not depend on the physical dimensions of PEGs, but rather on their mass concentration. This is probably a manifestation of the monomer-like repulsive depletion effect known to occur in concentrated polymer solutions. As a transition from moderate to high crowding agent concentration can occur in the cellular milieu, this behavior may modulate protein association in vivo, thereby modulating biological function.     

Quasi-elastic laser light scattering from solutions and gels of hemoglobin S.

Quasi-elastic light scattering has been used to examine solutions and gels of deoxyhemoglobin S. The autocorrelation function is found to decay with a characteristic exponential relaxation which can be ascribed to the diffusion of monomer (64,000 molecular weight) hemoglobin S molecules. In the absence of polymers, the relaxation time is in good agreement with previous measurements of the diffusion coefficient for solutions of normal human hemoglobin. In the presence of the polymer phase, a large (greater than 200-fold) increase in the scattered intensity is observed but no contribution to the decay of the autocorrelation function from the motion of the aligned polymer phase can be detected. Heterodyning between the time-independent scattering amplitude from the polymers and the time-dependent scattering of the diffusing monomers results in a twofold increase in the relaxation time arising from monomer diffusion.