Effect of ionic strength on the diffusion coefficient of chondroitin sulfate and heparin measured by quasielastic light scattering

The normal modes for a mixture of charged macromolecules and electrolyte solution are calculated. We derive a generalized Debye relaxation time and the apparent diffusion coefficient of the macroion, which is shown to increase from its Stokes value, obtained in excess of added salt, with decreasing ionic strength. We test our result with experimental data for macromolecules with different charge densities: heparin and chondroitin sulfate. Besides, we show for this latter molecule that while the diffusion coefficient is increased, the scattered intensity is decreased but not by the same factor. Our results are compared with other theories developed in quasielastic light scattering.     

The concentration dependence of the diffusion coefficient for bovine pancreatic trypsin inhibitor: a dynamic light scattering study of a small protein

This paper reports the use of dynamic light scattering to investigate the concentration dependence of the diffusion coefficient for bovine pancreatic trypsin inhibitor (BPTI). BPTI is a small molecular weight protein (6511 Da) that has been the subject of numerous experimental studies. In addition to addressing questions that remain in the literature concerning the aggregation behavior of BPTI, we show that dynamic light scattering can be practically applied to proteins as small as BPTI, and that it can provide a useful means of parameterizing the solution behavior for proteins. We obtained values for the apparent diffusion coefficient of BPTI as a function of concentration over a range of pH values from 2.59 to 9.92 at an ionic strength of 0.3M, and over a range of ionic strength values from 0.1 to 0.5M at a pH of 7.0. The concentration dependence is linear for nearly all the conditions examined, even up to concentrations as high as 65 mg/mL. The average diffusion coefficient obtained at infinite dilution is 14.4 +/- 0.2 x 10(-7) cm2/s. This value agrees with that expected for a BPTI monomer hydrated with less than a monolayer of water. We used the theories of Felderhof, of Batchelor, and of Phillies, along with the DLVO theory to interpret the concentration dependence of the apparent diffusion coefficient. The variations observed with pH and ionic strength can be primarily attributed to screened coulombic interactions. In addition, there is an attractive interaction that is slightly stronger than the repulsive coulombic one, and that is essentially independent of pH and ionic strength. The attractive interactions appear to arise from nonspecific van der Waals interactions and do not lead to the formation of stable aggregates of BPTI.     

Protein interactions in solution characterized by light and neutron scattering: comparison of lysozyme and chymotrypsinogen.

The effects of pH and electrolyte concentration on protein-protein interactions in lysozyme and chymotrypsinogen solutions were investigated by static light scattering (SLS) and small-angle neutron scattering (SANS). Very good agreement between the values of the virial coefficients measured by SLS and SANS was obtained without use of adjustable parameters. At low electrolyte concentration, the virial coefficients depend strongly on pH and change from positive to negative as the pH increases. All coefficients at high salt concentration are slightly negative and depend weakly on pH. For lysozyme, the coefficients always decrease with increasing electrolyte concentration. However, for chymotrypsinogen there is a cross-over point around pH 5.2, above which the virial coefficients decrease with increasing ionic strength, indicating the presence of attractive electrostatic interactions. The data are in agreement with Derjaguin-Landau-Verwey-Overbeek (DLVO)-type modeling, accounting for the repulsive and attractive electrostatic, van der Waals, and excluded volume interactions of equivalent colloid spheres. This model, however, is unable to resolve the complex short-ranged orientational interactions. The results of protein precipitation and crystallization experiments are in qualitative correlation with the patterns of the virial coefficients and demonstrate that interaction mapping could help outline new crystallization regions.     

Random coil scission rates determined by time-dependent total intensity light scattering: hyaluronate depolymerization by hyaluronidase

A recently developed theory of the light scattering by random coils undergoing random scission is applied to the digestion of hyaluronate by hyaluronidase. The time dependence of the scattered light from solutions undergoing digestion was monitored. Working at a high angle with high molecular weight hyaluronate allowed the use of a powerful approximation for determining initial velocities and the Henri-Michaelis-menten coefficients, without explicit knowledge of the hyaluronate molecular weight, radius of gyration, second virial coefficient, or polydispersity. Effects due to a molecular weight dependent second virial coefficient and to non-Gaussian behavior are briefly considered. Assays were performed over nearly two orders of magnitude in substrate concentration. The initial velocities are compared with those obtained by a standard reducing sugar assay, which was performed on identical samples. The main advantages of the light scattering assay procedure over the more traditional assays are that many relatively high-precision data points can be quickly and automatically collected with simple apparatus, and that the technique is most sensitive for the initial period of digestion, where the other assays are least sensitive. The shapes of the scattering curves also provide evidence that hyaluronate in these solutions is not a stable double strand and that the hyaluronidase cleaves bond randomly. The curves also indicate that enzyme deactivation occurs, which accounts for the lower velocities yielded by the slower reductimetric assay, which is measured over longer initial periods.     

Detection of monodisperse aggregates of a recombinant amelogenin by dynamic light scattering

Recombinant murine amelogenins M179 and M166 were expressed in Escherichia coli and purified. The aggregation properties of these amelogenins have been investigated in aqueous solutions as well as acetonitrile-containing solutions using dynamic light scattering. Dynamic light scattering provides direct measurement of the translational diffusion coefficient and hydrodynamic radius, and of an estimate of the molecular weight. Polydispersity and statistical parameters of how to interpret the analysis are also provided. Amelogenin aggregation was examined in solutions of a range of pH, ionic strengths, and protein concentrations. It was shown that at pH 7.8–8 and ionic strength of 0.02–0.05M the M179 molecules form monodispersed aggregates with hydrodynamic radii ranging from 15 to 19 nm. Analysis of hydrodynamic radii and size distribution of M179 aggregates in acetonitrile-containing solvents compared to that in aqueous solutions indicated a primary role for hydrophobic interactions in the association process of amelogenin molecules to form aggregates. Comparison between the aggregates formed by M179 and M166, which lacks the hydrophilic carboxy-terminal 13 residue sequence of M179, suggested that the self-assembly of amelogenin molecules to form stable and monodisperse aggregates requires the presence of the hydrophilic carboxy-terminal sequence of M179. © 1994 John Wiley & Sons, Inc.     

pH control of the third virial coefficient of hyaluronate solutions calculated from van der Waals forces by means of the Lifshitz-McLachlan susceptibility theory

Positive third virial coefficients and osmotic coefficients have been calculated for human umbilical cord hyaluronic acid solutions at pHs 6.0, 6.5, 7.0, 7.5, 8.0, and 8.5 and constant ionic strength 0.1. The calculations are based on experimental axial flow birefringence and radial linear dichroism data previously reported and the Lifshitz-McLachlan field theory of van der Waals forces. The second virial coefficients are negative, according to both this analysis and light scattering evidence, and reflect the tendency of hyaluronic acid to associate. This negativity denies the assumption of force additivity required by virial expansion theory.The results are in reasonable agreement with those of light scattering studies, and indicate the extreme nonideality of hyaluronate solutions with a high degree of pH control of osmotic pressure. The data are explained within the context of statistical mechanical and field theories of van der Waals forces, and the osmotic pressure of a solution is related to its optical properties. The numerical method used offers a way of exploring the applicability of modern interparticle force theory to biological systems.     

New evidence of the nonequilibrium nature of the "slow modes" of diffusion in polyelectrolyte solutions

The time-dependent behavior of the dissolution of polyelectrolyte powders in pure water and moderate ionic strength aqueous solvent was monitored by flowing dissolving material through an online filter, and then through a multiangle light scattering unit, a refractometer, and a capillary viscometer. When the polyelectrolytes were dissolved in solutions of moderate ionic strength, their dissolution behavior was similar to that of neutral polymers. When dissolved in pure water, however, there was consistently a small population of aggregates that appeared at the beginning of the dissolution process, which then rapidly diminished. For large pore filtration, the aggregates reached a final low level, and slowly disappeared over the span of many days, whereas for small pore filtration the aggregates disappeared completely over a scale of minutes. The real-time data, together with size exclusion chromatography analysis, shed light on previously unanswered questions concerning the nonequilibrium nature of this small population of polyelectrolyte aggregates in low ionic strength solutions, and its relation to the "extraordinary phase" of diffusion (or "slow modes"). Further evidence is also provided that both angular scattering maxima due to interpolyion correlations and the maximum of reduced viscosity vs polyion concentration ("electroviscous" effect) at low ionic strength are equilibrium properties that are unrelated to these aggregates.     

Interactions of lysozyme in concentrated electrolyte solutions from dynamic light-scattering measurements

The diffusion of hen egg-white lysozyme has been studied by dynamic light scattering in aqueous solutions of ammonium sulfate as a function of protein concentration to 30 g/liter. Experiments were conducted under the following conditions: pH 4-7 and ionic strength 0.05-5.0 M. Diffusivity data for ionic strengths up to 0.5 M were interpreted in the context of a two-body interaction model for monomers. From this analysis, two potential-of-mean-force parameters, the effective monomer charge, and the Hamaker constant were obtained. At higher ionic strength, the data were analyzed using a model that describes the diffusion coefficient of a polydisperse system of interacting protein aggregates in terms of an isodesmic, indefinite aggregation equilibrium constant. Data analysis incorporated multicomponent virial and hydrodynamic effects. The resulting equilibrium constants indicate that lysozyme does not aggregate significantly as ionic strength increases, even at salt concentrations near the point of salting-out precipitation.     

Interaction of tobacco mosaic virus and tobacco mosaic virus protein with bovine serum albumin.

Bovine serum albumin (BSA) causes tobacco mosaic virus (TMV) to crystallize at pH values where both have negative charges. The amount of albumin required to precipitate the virus varies inversely with ionic strength of added electrolyte. At pH values above 5, the precipitating power is greatest when BSA has the maximum total, positive plus negative, charge. Unlike early stages of the crystallization of TMV in ammonium sulfate-phosphate solutions, which can be reversed by lowering the temperature, the precipitation of TMV by BSA is not readily reversed by changes in temperature. The logarithm of the apparent solubility of TMV in BSA solutions, at constant ionic strength of added electrolyte, decreases linearly with increasing BSA concentration. This result and the correlation of precipitating power with total BSA charge suggest that BSA acts in the manner of a salting-out agent. The effect of BSA on the reversible entropy-driven polymerization of TMV protein (TMVP) depends on BSA concentration, pH, and ionic strength. In general, BSA promotes TMVP polymerization, and this effect increases with increasing BSA concentrations. The effect is larger at pH 6.5 than at pH 6. Even though increasing ionic strength promotes polymerization of TMVP in absence of BSA, the effect of increasing ionic strength from 0.08 to 0.18 at pH 6.5 decreases the polymerization-promoting effect of BSA. Likewise, the presence of BSA decreases the polymerization-promoting effect of ionic strength. The polymerization-promoting effect of BSA can be interpreted in terms of a process akin to salting-out. The mutual suppression of the polymerization-promoting effects of BSA and of electrolytes by each other can be partially explained in terms of salting-in of BSA.     

Ultracentrifugation of concentrated biopolymer solutions and effect of ascorbate

Highly concentrated solutions of bovine methemoglobin, human transferrin, proteoglycan-protein complex from bovine cartilage, and human hyaluronate were run to equilibrium in the preparative ultracentrifuge. The mass fraction, wo, of water in the compact part of the sediment ("the pellet") was studied as a function of the centrifugal force, ionic strength and pH. For the proteins, wo was close to 0.4 and varied only slightly on variation of the ionic strength and the force. For the proteoglycan-protein complex, wo was close to unity at low force but decreased sharply with increasing force, a finding which agrees well with the specific physical properties of the cartilage matrix. For hyaluronate, wo exceeded 0.8 even at the highest forces, but decreased sharply with increasing ionic strength. There appeared to be a relationship between wo and the carbohydrate mass fraction, wc, of the dry polymer material, wo increasing linearly with wc at 440,000g. A series of biologically or pharmacologically interesting substances was tested for a possible effect on wo of hyaluronate, and it was found that the addition of ascorbate (0.2 g/liter) caused a reduction of 0.040 in wo, independent of the force at which this parameter was measured. Simultaneously, the sedimentation coefficient was doubled. These findings suggest that, on reacting with ascorbate, the hyaluronate molecule changes from a random coil to a more compact molecule.     

Ultrasonic storage modulus as a novel parameter for analyzing protein-protein interactions in high protein concentration solutions: correlation with static and dynamic light scattering measurements

The purpose of this work was to establish ultrasonic storage modulus (G') as a novel parameter for characterizing protein-protein interactions (PPI) in high concentration protein solutions. Using an indigenously developed ultrasonic shear rheometer, G' for 20-120 mg/ml solutions of a monoclonal antibody (IgG(2)), between pH 3.0 and 9.0 at 4 mM ionic strength, was measured at frequency of 10 MHz. Our understanding of ultrasonic rheology indicated decrease in repulsive and increase in attractive PPI with increasing solution pH. To confirm this behavior, dynamic (DLS) and static (SLS) light scattering measurements were conducted in dilute solutions. Due to technical limitations, light scattering measurements could not be conducted in concentrated solutions. Mutual-diffusion coefficient, measured by DLS, increased with IgG(2) concentration at pH 4.0 and this trend reversed as pH was increased to 9.0. Second virial coefficient, measured by SLS, decreased with increasing pH. These observations were consistent with the nature of PPI understood from G' measurements. Ultrasonic rheology, DLS, and SLS measurements were also conducted under conditions of increased ionic strength. The consistency between rheology and light scattering analysis under various solution conditions established the utility of ultrasonic G' measurements as a novel tool for analyzing PPI in high protein concentration systems.     

Correlation between biological activity of 30 S subunits of Escherichia coli ribosomes and their conformation changes revealed by optical mixing spectroscopy

Spectral analysis of light scattered from solutions of 30 S subunits was performed by the method of regularization of the inverse spectral problem. The subunits observed under ionic conditions which preserved their biological activity (200 mM NH4Cl at 1 mM MgCl2) revealed a monodisperse pattern of scattering with diffusion constant D = (1.83 +/- 0.10) X 10(-7) cm2/s. The polydispersity and compaction of 30 S subunits were observed under inactivation ionic conditions (30 mM NH4Cl at 1 mM MgCl2). The number of compacted particles correlates with the irreversible loss of biological activity, the ability of 30 S subunits to bind specific tRNA.     

Hyaluronate diffusion in semidilute solutions

Analysis of the mutual diffusion coefficient of hyaluronate reveals that it rapidly increases with increasing concentration or decreasing ionic strength. The mutual diffusion coefficients analyzed by boundary relaxation in the analytical ultracentrifuge by either Raleigh interference optics or absorption optics (through the use of fluorescein-labeled hyaluronate) yielded similar values. The theoretical treatment of the mutual diffusion coefficient has been analyzed in terms of experimentally measured intradiffusion coefficients and thermodynamic virial coefficients. Only approximate agreement between theory and experiment was found. The concept of formation of transient statistical network structures in semidilute solutions of hyaluronate was applied to evaluate a critical concentration at which network formation occurs. This has been discussed in relation to the marked decrease in the intradiffusion coefficient of hyaluronate with concentration. The formation of network structures in hyaluronate was found not to preclude the hyaluronate undergoing extremely rapid rates of mutual diffusion (with diffusion coefficients ～30 × 10^?11 m² s¹) under conditions of relatively large initial chemical potential gradients. Measurements of the unidirectional flux of hyaluronate for nonzero gradients demonstrated their marked sensitivity to the magnitude of the concentration difference across the boundary. An experimental feature of the unidrectional diffusion coefficients of hyaluronate is that they may be analyzed purely in terms of mutual and intradiffusion processes. The backflux diffusion coefficient (describing the flux against the imposed concentration gradient) appeared identical with the intradiffusion coefficient. The analysis of the various sources of errors made in this study suggests that the magnitude of the diffusion coefficients measured may be regarded only as approximate.     

Skeletal muscle myosin subfragment-1 induces bundle formation by actin filaments

As is well known, the light scattering intensity of F-actin solutions increases immediately upon formation of the rigor complex with subfragment-1 (S-1). We have found that after the initial rise in scattering, there is a further gradual increase in scattering (we call it "super-opalescence"). Fluorescence and electron microscopic observations of acto-S-1 solutions showed that super-opalescence results from formation of actin filament bundles once S-1 binds to F-actin. The actin bundles possessed transverse stripes with a periodicity of about 350 A, which suggested that in the bundles actin filaments are arranged in parallel register. The rate of the initial process of bundle formation (i.e. side-by-side dimerization) could be approximately estimated by measuring the initial rate of super-opalescence (V0). V0 had a maximum (V0m) at a molar ratio of S-1 to actin of 1;6-1;7, regardless of the actin concentration, pH (6-8.5), Mg2+ concentration (up to 5 mM), or ionic strength (up to 0.3 M KC1). Lower pH, higher Mg2+ concentration, and higher ionic strength increased V0m; V0 was proportional to the square of the actin concentration, regardless of the solution conditions.     

The behaviour of lung surfactant in electrolyte solutions

Surface and electrokinetic properties of purified calf lung surfactant in various electrolyte solutions were determined. Surface properties were pH dependent in distilled water and the surfactant performed as a good lung surfactant only below pH 4. In more physiological media it was pH insensitive over the range 2-8.5. In distilled water at pH 6 its surface properties improved when NaCl was added up to 20 mM; above this concentration it had the surface properties required to stabilise alveoli. The surface properties of surfactant in distilled water were also restored by certain cations (Ca2+, Mg2+, Mn2+, Cd2+ and Ni2+) but not others (Na+, K+, La3+ and Fe3+) when added to an ionic strength of 5.6 mM. Cations that restored its surface activity also reduced the surface charge density on the surfactant particles. Aggregation of surfactant by various metal chlorides was studied by light scattering measurements and bore no relation to surface activity or the charge on the particles. Aggregation of surfactant particles by Ca2+, Cd2+ and Mn2+ was instantly reversed by addition of excess EGTA. The influence of electrolytes on the surface properties of lung surfactant is explained in terms of the electrostatic forces operating in the system.     

Electrostatic interactions modulate the conformation of collagen I

The pH- and electrolyte-dependent charging of collagen I fibrils was analyzed by streaming potential/streaming current experiments using the Microslit Electrokinetic Setup. Differential scanning calorimetry and circular dichroism spectroscopy were applied in similar electrolyte solutions to characterize the influence of electrostatic interactions on the conformational stability of the protein. The acid base behavior of collagen I was found to be strongly influenced by the ionic strength in KCl as well as in CaCl(2) solutions. An increase of the ionic strength with KCl from 10(-4) M to 10(-2) M shifts the isoelectric point (IEP) of the protein from pH 7.5 to 5.3. However, a similar increase of the ionic strength in CaCl(2) solutions shifts the IEP from 7.5 to above pH 9. Enhanced thermal stability with increasing ionic strength was observed by differential scanning calorimetry in both electrolyte systems. In line with this, circular dichroism spectroscopy results show an increase of the helicity with increasing ionic strength. Better screening of charged residues and the formation of salt bridges are assumed to cause the stabilization of collagen I with increasing ionic strength in both electrolyte systems. Preferential adsorption of hydroxide ions onto intrinsically uncharged sites in KCl solutions and calcium binding to negatively charged carboxylic acid moieties in CaCl(2) solutions are concluded to shift the IEP and influence the conformational stability of the protein.     

The use and development of the dynamic light-scattering method to investigate supramolecular structures in aqueous solutions of bacterial lipopolysaccharides

The temperature dependence of the scattering intensity, average size, and size distribution for supramolecular particles in aqueous solutions of lipopolysaccharides from Azospirillum bacteria was investigated by dynamic light scattering. Relationships were obtained that made it possible to comparatively estimate the mass–volume concentration of the biopolymeric substance in suspensions and the number concentration of supramolecular particles with their size and degree of polydispersity taken into account. In the range from 0 to 60°C, two types of the temperature dependence of scattering intensity were found: (a) with an irregular spasmodic change in scattering intensity and with considerable heterogeneity of the systems with respect to particle size and (b) with a smoother character of this dependence with considerably decreased heterogeneity of the suspensions. In the ranges of the latter type, whose location depended on what strain was used to isolate lipopolysaccharides, it proved to be possible to correctly determine the parameters of the supramolecular particles (of the supposedly formed micellar phase) by dynamic light scattering. The revealed statistically significant differences in the size and the concentration of the micellar particles are explained by their dependence on the peculiarities of the chemical structure of lipopolysaccharides. Atomic-force microscopy was used for an independent morphological estimation of the preparations, yielding good agreement with the dynamic light-scattering results.     

Quasielastic light scattering by biopolymers. V. Interparticle interactions between polynucleosomes

Quasielastic light scattering and electrophoretic light scattering experiments were performed on chicken erythrocyte polynucleosome solutions at various temperatures and ionic strengths. The apparent diffusion coefficient, D_app, was found to depend on the scattering vector K. In general, D_app can be described as a damped oscillatory function of K in the ionic strength range of 10 to 60 mM and over the temperature range of 10 to 40°C. Electrophoretic light scattering studies on total digest chromatin samples indicate the apparent charge on the polynucleosomes increases as the ionic strength is lowered from 10 to 1 mM. These data are interpreted in terms of fluctuations in the surface charge distribution of the polyion and subsequent inducement of an asymmetric distribution of small ions about the polyion. These fluctuation components lead to the formation of “clusters” of polyions.     

Influence of the ionic strength on the heat-induced aggregation of the globular protein beta-lactoglobulin at pH 7

The influence of the ionic strength on the structure of beta-lactoglobulin aggregates formed after heating at pH 7 has been studied using static and dynamic light scattering. The native protein depletion has been monitored using size exclusion chromatography. Above a critical association concentration (CAC) well-defined clusters are formed containing about 100 monomers. The CAC increases with decreasing ionic strength. The so-called primary aggregates associate to form self similar semi-flexible aggregates with a large scale structure that is only weakly dependent on the ionic strength. The local density of the aggregates increases with increasing ionic strength. At a critical gel concentration, Cg, the size of the aggregates diverges. Cg decreases from 100 g/l without added salt to 1 g/l at 0.4M NaCl. For C > Cg the system gels except at high ionic strength close to Cg where the gels collapse under gravity and a precipitate is formed.     

Aggregates and other particles as the origin of the “extraordinary” diffusional phase in polyelectrolyte solutions

The “extraordinary” diffusional phase (EP) at low ionic strength, and the conditions for 1 its removability by filtration were investigated for dilute solutions of the following linear polyelectrolytes: poly(L -lysine), heparin, chondroitin-6-sulfate, hyaluronate, polystyrene sulfonate, and variably ionized polyacrylamide. The EP was not present for all the different types studied, and for heparin, for example, the phase was present only for samples from certain sources. In all cases the phase was removable by filtration through sufficiently small pore-size membranes. Once filtered, the EP remained absent for over one week. It is concluded that the extraordinary diffusional phase consists of fairly stable polyelectrolyte aggregates, and sometimes also includes other very small particulate impurities. These aggregates and other small particles are thought to be present, or at least nascent, in the dry polyelectrolyte material, so that their properties may depend critically on the manner in which such dry material is produced. Tests for “reversibility” of the EP by cycling between high and low C_s by dialysis further confirm these conclusions. The evidence is thus against the EP representing any type of temporal aggregates or local ordering, at least for the linear polyelectrolytes studied in this work Rather, due to the extremely feeble scattering of ordinary polyelectrolytes at low ionic strength, the weak scattering from residual aggregates and other particles, not removed by ordinary filtration and centrifugation procedures, give autocorrelable scattering signals with long decay times. The “loss” of the extraordinary phase as ionic strength increases appears to be due simply to the weak EP scattering signal getting buried in the sharply increasing scattering from the ordinary polyelectrolyte phase. Model calculations based on experimental data support this latter conclusion. © 1992 John Wiley & Sons, Inc.