Hybrid colloid analysis combining analytical ultracentrifugation and flow-field flow fractionation

Ferritin, the iron storage protein, is an organic-inorganic hybrid colloid consisting of a hollow protein capsule, which is filled with ferrihydride with up to 4500 iron atoms. Owing to the varying iron content and the resulting density differences, as well as the protein oligomerization, a particle size distribution is superimposed with a density distribution, making a precise analysis of ferritin by analytical ultracentrifugation difficult. This study describes how the information of the sedimentation coefficient distribution can be combined with the diffusion coefficient distribution obtained from flow-field flow fractionation to yield the buoyant molar mass of the oligomers in the mixture, extending the information content of each individual analytical method. In addition, the sedimentation and diffusion coefficients are compatible with a simple hard-sphere aggregation model, suggesting that the ferritin oligomers up to the pentamer have a globular solution structure.Presented at the conference for Advances in Analytical Ultracentrifugation and Hydrodynamics, 8–11 June 2002, Grenoble, France     

Using prior knowledge in the determination of macromolecular size-distributions by analytical ultracentrifugation

Analytical ultracentrifugation has reemerged as a widely used tool for the study of ensembles of biological macromolecules to understand, for example, their size-distribution and interactions in free solution. Such information can be obtained from the mathematical analysis of the concentration and signal gradients across the solution column and their evolution in time generated as a result of the gravitational force. In sedimentation velocity analytical ultracentrifugation, this analysis is frequently conducted using high resolution, diffusion-deconvoluted sedimentation coefficient distributions. They are based on Fredholm integral equations, which are ill-posed unless stabilized by regularization. In many fields, maximum entropy and Tikhonov-Phillips regularization are well-established and powerful approaches that calculate the most parsimonious distribution consistent with the data and prior knowledge, in accordance with Occam's razor. In the implementations available in analytical ultracentrifugation, to date, the basic assumption implied is that all sedimentation coefficients are equally likely and that the information retrieved should be condensed to the least amount possible. Frequently, however, more detailed distributions would be warranted by specific detailed prior knowledge on the macromolecular ensemble under study, such as the expectation of the sample to be monodisperse or paucidisperse or the expectation for the migration to establish a bimodal sedimentation pattern based on Gilbert-Jenkins' theory for the migration of chemically reacting systems. So far, such prior knowledge has remained largely unused in the calculation of the sedimentation coefficient or molecular weight distributions or was only applied as constraints. In the present paper, we examine how prior expectations can be built directly into the computational data analysis, conservatively in a way that honors the complete information of the experimental data, whether or not consistent with the prior expectation. Consistent with analogous results in other fields, we find that the use of available prior knowledge can have a dramatic effect on the resulting molecular weight, sedimentation coefficient, and size-and-shape distributions and can significantly increase both their sensitivity and their resolution. Further, the use of multiple alternative prior information allows us to probe the range of possible interpretations consistent with the data.     

A model for sedimentation in inhomogeneous media. II. Compressibility of aqueous and organic solvents

The effects of solvent compressibility on the sedimentation behavior of macromolecules as observed in analytical ultracentrifugation are examined. Expressions for the density and pressure distributions in the solution column are derived and combined with the finite element solution of the Lamm equation in inhomogeneous media to predict the macromolecular concentration distributions under different conditions. Independently, analytical expressions are derived for the sedimentation of non-diffusing particles in the limit of low compressibility. Both models are quantitatively consistent and predict solvent compressibility to result in a reduction of the sedimentation rate along the solution column and a continuous accumulation of solutes in the plateau region. For both organic and aqueous solvents, the calculated deviations from the sedimentation in incompressible media can be very large and substantially above the measurement error. Assuming conventional configurations used for sedimentation velocity experiments in analytical ultracentrifugation, neglect of the compressibility of water leads to systematic errors underestimating sedimentation coefficients by approximately 1% at a rotor speeds of 45000 rpm, but increasing to 2-5% with increasing rotor speeds and decreasing macromolecular size. The proposed finite element solution of the Lamm equation can be used to take solvent compressibility quantitatively into account in direct boundary models for discrete species, sedimentation coefficient distributions or molar mass distributions. Using the analytical expressions for the sedimentation of non-diffusing particles, the ls-g*(s) distribution of apparent sedimentation coefficients is extended to the analysis of sedimentation in compressible solvents. The consideration of solvent compressibility is highly relevant not only when using organic solvents, but also in aqueous solvents when precise sedimentation coefficients are needed, for example, for hydrodynamic modeling.     

Velocity sedimentation of organelles at low centrifugal force in an isokinetic gradient.

Mast-cell granules and polystyrene microspheres (0.600 and 1.011 micrometer in diameter) were sedimented in a previously described [Pretlow (1971) Anal. Biochem. 41, 248--255] isokinetic gradient in a low-speed centrifuge. For the analytical velocity sedimentation of organelles, this gradient offers several advantages over gradients that are commonly used for the sedimentation of organelles: (a) the density gradient (0.0008 g.ml-1.cm-1) is small, and the effective densities of organelles will change relatively little during sedimentation; (b) the densities at all points in the gradient (1.017--1.027 g/ml) are less than those in gradients commonly used for the sedimentation of organelles, the effective densities of sedimenting organelles are consequently relatively large, and the effect of density as a determinant of velocity of sedimentation is less limiting than in conventional gradients; (c) the small slope of the gradient is associated with a relatively slow increase in the viscosity encountered by the sedimenting organelle; (d) the iso-osmotic gradient is not significantly affected by the gradient medium (Ficoll), and the osmolarity can be adjusted to the desired value by the selection of an appropriate salt solution as the solvent for the Ficoll; (e) the gradient will be isokinetic for particles of densities similar to most organelles. An ultracentrifuge is not required for work with this gradient.     

Macro and micro rate zonal analytical centrifugation of polydisperse and slowly diffusing sedimenting systems in isovolumetric density gradients. Application to cartilage proteoglycans

A method to study the polydispersity of zonally sedimenting and slowly diffusing macromolecules or particles in isokinetic or isovolumetric density gradients is presented. First, a brief theory is given for predicting the zonal profile after a "triangular" (or "inverse") zone is centrifuged. This type of zone is essential to preserve hydrodynamic stability of the very slowly diffusing polydisperse solutes. It is proven, both by semitheoretical considerations and by computer calculations, that the resulting concentration profile of macrosolute is almost identical with that obtainable with a rectangular zone coextensive with the triangular one and carrying the same total mass. Next, practical procedures are described for the convectionless layering of very small triangular zones (50 microL or less). The linearity and stability of the zones are experimentally tested and verified. Finally, the method is applied to cartilage proteoglycan preparations that included either the monomeric molecules only or both the monomeric and the aggregated ones. The zonal results are compared with those obtained by using conventional boundary sedimentation. The two sets of results are seen to coincide fairly well, thus proving that the present technique can add to preparative zonal centrifugation the analytical precision of boundary sedimentation. A multimodal polydisperse system is suggested to describe the aggregated proteoglycan macromolecules.     

On the analysis of protein self-association by sedimentation velocity analytical ultracentrifugation

Analytical ultracentrifugation is one of the classical techniques for the study of protein interactions and protein self-association. Recent instrumental and computational developments have significantly enhanced this methodology. In this paper, new tools for the analysis of protein self-association by sedimentation velocity are developed, their statistical properties are examined, and considerations for optimal experimental design are discussed. A traditional strategy is the analysis of the isotherm of weight-average sedimentation coefficients s(w) as a function of protein concentration. From theoretical considerations, it is shown that integration of any differential sedimentation coefficient distribution c(s), ls-g(*)(s), or g(s(*)) can give a thermodynamically well-defined isotherm, as long as it provides a good model for the sedimentation profiles. To test this condition for the g(s(*)) distribution, a back-transform into the original data space is proposed. Deconvoluting diffusion in the sedimentation coefficient distribution c(s) can be advantageous to identify species that do not participate in the association. Because of the large number of scans that can be analyzed in the c(s) approach, its s(w) values are very precise and allow extension of the isotherm to very low concentrations. For all differential sedimentation coefficients, corrections are derived for the slowing of the sedimentation boundaries caused by radial dilution. As an alternative to the interpretation of the isotherm of the weight-average s value, direct global modeling of several sedimentation experiments with Lamm equation solutions was studied. For this purpose, a new software SEDPHAT is introduced, allowing the global analysis of several sedimentation velocity and equilibrium experiments. In this approach, information from the shape of the sedimentation profiles is exploited, which permits the identification of the association scheme and requires fewer experiments to precisely characterize the association. Further, under suitable conditions, fractions of incompetent material that are not part of the reversible equilibrium can be detected.     

Characterization of heterologous protein-protein interactions using analytical ultracentrifugation.

Methods for quantitative characterization of heterologous protein-protein interactions by means of analytical ultracentrifugation (AUC) include sedimentation equilibrium, tracer sedimentation equilibrium, sedimentation velocity, and analytical band sedimentation. Fundamental principles governing the behavior of macromolecules in a centrifugal field are summarized, and the application of these principles to the interpretation of data obtained from each type of experiment is reviewed. Instrumentation and software for the acquisition and analysis of data obtained from different types of AUC experiments are described.     

Histidine-tag-directed chromophores for tracer analyses in the analytical ultracentrifuge

Many recombinant proteins carry an oligohistidine (His(X))-tag that allows their purification by immobilized metal affinity chromatography (IMAC). This tag can be exploited for the site-specific attachment of chromophores and fluorophores, using the same metal ion-nitrilotriacetic acid (NTA) coordination chemistry that forms the basis of popular versions of IMAC. Labeling proteins in this way can allow their detection at wavelengths outside of the absorption envelopes of un-modified proteins and nucleic acids. Here we describe use of this technology in tracer sedimentation experiments that can be performed in a standard analytical ultracentrifuge equipped with absorbance or fluorescence optics. Examples include sedimentation velocity in the presence of low molecular weight chromophoric solutes, sedimentation equilibrium in the presence of high concentrations of background protein and selective labeling to simplify the assignment of species in a complex interacting mixture.     

Macromolecular size-and-shape distributions by sedimentation velocity analytical ultracentrifugation

Sedimentation velocity analytical ultracentrifugation is an important tool in the characterization of macromolecules and nanoparticles in solution. The sedimentation coefficient distribution c(s) of Lamm equation solutions is based on the approximation of a single, weight-average frictional coefficient of all particles, determined from the experimental data, which scales the diffusion coefficient to the sedimentation coefficient consistent with the traditional s approximately M(2/3) power law. It provides a high hydrodynamic resolution, where diffusional broadening of the sedimentation boundaries is deconvoluted from the sedimentation coefficient distribution. The approximation of a single weight-average frictional ratio is favored by several experimental factors, and usually gives good results for chemically not too dissimilar macromolecules, such as mixtures of folded proteins. In this communication, we examine an extension to a two-dimensional distribution of sedimentation coefficient and frictional ratio, c(s,f(r)), which is representative of a more general set of size-and-shape distributions, including mass-Stokes radius distributions, c(M,R(S)), and sedimentation coefficient-molar mass distributions c(s,M). We show that this can be used to determine average molar masses of macromolecules and characterize macromolecular distributions, without the approximation of any scaling relationship between hydrodynamic and thermodynamic parameters.     

Boundary centrifugation in isovolumetric and isokinetic cesium sulfate density gradients: application to cartilage proteoglycans and other macromolecules

A boundary sedimentation methodology is described that avoids plateau dilution and simplifies the calculation of centrifugal parameters. The technique is designed for the preparative ultracentrifuge and uses a newly developed sectorial cell. It is based on previous developments of the transport method and depends on isokinetic or isovolumetric Cs2SO4 density and viscosity gradients. These gradients are prepared with a single-chamber mixing device, and the only two parameters required for their calculations are presented in a tabulated form for general use with most available rotors and cell sizes. Conditions are specified (1) to assure that the density and shape of the sedimenting molecules remain invariant through the selected electrolytic gradient, (2) to monitor the gradient profiles, and (3) to verify attainment of isokinetic or isovolumetric sedimentations. A set of equations is presented to calculate the average and transport sedimentation coefficients and the differential sedimentation coefficient distribution for both the isokinetic and isovolumetric centrifugal regimes. The method was applied to slowly diffusing polydisperse proteoglycan monomers, to a paucidisperse DNA from bacteriophage PM2, and to a diffusible monodisperse system (purified bovine serum albumin). In all cases, the expected results were obtained.     

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.     

The size and shape of amylopectin: a study using analytical ultracentrifugation

Starch was isolated from a range of wheat cultivars grown under various conditions. The starches were known to produce pastes having contrasting rheological properties when heated. Solutions of the starch in dimethyl sulphoxide were investigated by analytical ultracentrifugation. Sedimentation coefficients and normalized weight-frequency distributions of limiting sedimentation-coefficients were determined. The sedimentation-coefficient data confirmed the weight-average molar mass of amylopectin in dimethyl sulphoxide to be ∼10⁷, irrespective of the source of the starch. The sedimentation-coefficient values were also combined with diffusion-coefficient data and evaluated according to hydrodynamic theory, this indicated that amylopectin has a flat-sheet or disc-like structure with semi-major and semi-minor axes of 45 and 1.2 nm, respectively. The distributions of sedimentation coefficients of the amylopectin samples were all similar, being unimodal, symmetrical, and having peak-width half-heights of ∼60 S. The amylopectin obtained after removal of amylose by chemical fractionation was shown to be representative of the total amylopectin in starch.     

An externally adjustable motor-driven Rayleigh slit assembly for the analytical ultracentrifuge

Precise alignment of the Rayleigh optical system of the Beckman Instruments Model E analytical ultracentrifuge is prerequisite to the performance of difference sedimentation velocity, difference sedimentation equilibrium, and high-speed equilibrium ultracentrifugation. One of the components required for precise alignment is an adjustable Rayleigh slit assembly. An externally adjustable assembly has been developed which offers some advantages over previous designs. The rotational movement is motor driven, allowing external adjustment by a single operator, who can monitor visually changes in the fringe pattern while the rotor is spinning. Installation of the slit assembly is simple and requires no permanent modifications of the armor plate, since the slit assembly is attached directly to the collimating lens holder. The slit assembly can be removed and replaced easily whenever the collimating lens is cleaned. The alignment procedure, involving rotation of both slit assembly and cylinder lens, can be carried out in less than 3 hr.     

Differential interferometry in the analytical ultracentrifuge. II. General applications

Various ways of applying differential interferometry to ultracentrifugal analyses are examined and several analytical techniques are established. In transport and moving boundary methods, the sedimentation coefficient is more precisely determined in the differential interference system than in the schlieren optical system because fringe measurement accuracy is much higher in the former system. Compared to interference and absorption optics, the differential interferometer provides a more exact s value in the transport method since an accurate calculation procedure can be adopted. Moreover, the following advantages of differential interferometry are noted. Determination of the initial solute concentration, which must be done in the usual interference method, is unnecessary in this sedimentation equilibrium method. Regardless of the partial loss of solute from the observed system due to rapid precipitation or adsorption to the cell wall during centrifugation, the molecular weight of the rest of the solute can be determined exactly. The diffusion coefficient can be determined accurately by fringe displacement analysis at the hinge point during the transient state. Together with the molecular weight and diffusion coefficient, the partial specific volume and sedimentation coefficient of a solute can be obtained from the result of a single low-speed centrifugation when the sample solutions in H₂O and D₂O are compared.     

The Sedimentation Pattern of D-Glucose-6-Phosphate Dehydrogenase from Bovine Fetal and Adult Erythrocytes

Erythrocytes from bovine fetuses contain about 2.4 times higher D-glucose-6-phosphate dehydrogenase activities than erythrocytes from adult cows and bulls. Studying whether this is due to the existence of a special fetal type of enzyme or an increased amount of enzyme in fetal erythrocytes, the sedimentation coefficients of the enzymes have been estimated by s-zonal ultracentrifugation, and compared to normal and deficient human erythrocyte D-glucose-6-phosphate dehydrogenase, s-zonal ultracentrifugations have been performed with a computer optimized isokinetic sucrose gradient. The mainlines in the program used for calculation of sedimentation coefficients are described. Bovine fetal and adult erythrocyte D-glucose-6-phosphate dehydrogenase was found to have the same sedimentation coefficient of 7.4 S which is different from the sedimentation coefficient of 6.4 S of both human types of the enzyme. The sedimentation coefficients of 6-phospho-D-gluconate dehydrogenase from bovine fetal, bovine adult and human erythrocytes were 6 S for all three types of this enzyme. By cellulose acetate electrophoresis bovine fetal and adult D-glucose-6-phosphate dehydrogenase show the same mobility, again differing from the normal and deficient human type. The results of these experiments show that bovine fetal and adult erythrocytic D-glucose-6-phosphate dehydrogenase with respects to molecular parameters are closely related and perhaps identical enzymes.     

Separation of epithelial cells from suspensions of cells from the hamster parotid gland in an isokinetic density gradient of Ficoll in tissue culture medium.

Epithelial cells were separated from suspensions of hamster parotid cells by velocity sedimentation in an isokinetic gradient and by isopycnic sedimentation. Epithelial cells were 48.1 ± 18.0% of the cells in the starting sample suspensions of cells from the disaggregated hamster parotid glands. The purest gradient fractions following velocity sedimentation in a previously described isokinetic gradient contained 98.8 ± 1.8% epithelial cells. The purest fractions obtained from isopycnic sedimentation contained 99.9 ± 0.2% epithelial cells. Purification of parotid epithelial cells by velocity sedimentation in the isokinetic gradient seems preferable to purification using isopycnic centrifugation because a larger proportion of the epithelial cells are obtained in the zone of the gradient which contains highly purified epithelial cells and because velocity sedimentation requires lower centrifugal forces for a shorter period of time.     

Caldesmon. Molecular weight and subunit composition by analytical ultracentrifugation

A wide range of values has been reported for the subunit and molecular weights of smooth muscle caldesmon. There have also been conflicting reports concerning whether caldesmon is a monomer or dimer. We attempted to resolve these uncertainties by determining the molecular weight of chicken gizzard smooth muscle caldesmon using the technique of sedimentation equilibrium in the analytical ultracentrifuge. Unlike previous methods that have been used to estimate the molecular weight of caldesmon, the molecular weight determined by equilibrium sedimentation does not depend upon assumptions about the shape of the molecule. We concluded that caldesmon in solution is monomeric with a molecular mass of 93 +/- 4 kDa, a value that is much less than those previously reported in the literature. This new value, in conjunction with sedimentation velocity experiments, led to the conclusion that caldesmon is a highly asymmetric molecule with an apparent length of 740 A in solution. The mass of a cyanogen bromide fragment, with an apparent mass of 37 kDa from sodium dodecyl sulfate-polyacrylamide gel electrophoresis, was determined to be 25.1 +/- 0.6 kDa using sedimentation equilibrium. These results imply that the reported molecular weights of other fragment(s) of caldesmon have also been overestimated. We have determined an optical extinction coefficient for caldesmon (E1%(280 nm) = 3.3) by determining its concentration from its refractive index which was measured in the analytical ultracentrifuge. From the above values of the molecular weight and the extinction coefficient, we redetermined that the caldesmon molecule has two cysteines and recalculated the stoichiometric molar ratio of actin/tropomyosin/caldesmon in the smooth muscle thin filament to be 28:4:1.     

Analysis of interacting biopolymer systems by analytical ultracentrifugation

Many of the functions of biological macromolecules are based on specific interactions. Extended concentration dependent studies of sedimentation coefficients or molecular masses of biopolymers are highly useful for describing the different kinds of association phenomena. These studies allow one to determine the partial concentrations of monomers and associates or reactants and complexes in self-associating systems or heterologous associations, respectively. Furthermore, in combination with corresponding measurements of biological activity these data allow one to estimate the individual activity parameters of components involved in equilibrium processes. The study of self-association and heterologous association using analytical ultracentrifugation, some recent developments therein, and its application to different examples are outlined here. Accepted: 18 October 1996     

The stiffness of dsRNA: hydrodynamic studies on fluorescence-labelled RNA segments of bovine rotavirus.

The sedimentation coefficients of dsRNA segments of bovine rotavirus were determined in the analytical ultracentrifuge. The eleven segments were separated by preparative gel electrophoresis, and isolated by elution from gel pieces. The RNA was labelled by the intercalating fluorescent dye ethidium bromide at a ratio bound dye per base pair between 0.003 to 0.018. The analytical ultracentrifuge was equipped with a fluorescence recording optics. Sedimentation coefficients could be determined with amounts of RNA as little as 8 ng. All sedimentation coefficients were extrapolated to zero-concentration, zero-dye binding, and zero-impurities from the preparative gel electrophoresis. The hydrodynamic model of flexible cylinders was applied for the interpretation of the sedimentation coefficients. All dsRNA segments of rotavirus (663-3409 base pairs) and the dsRNA5 of cucumber mosaic virus (335 base pairs) fit the model of a "worm-like" or flexible cylinder with a persistence length of 1125 A and a hydrated diameter of 30 A. The results are compared with data from the literature on the persistence lengths of the B- and Z-forms of dsDNA and of viroids.     

Fluorescence detection for the XLI analytical ultracentrifuge

Analytical ultracentrifugation (AUC) provides first-principle hydrodynamic and thermodynamic information concerning the size, shape and interactions of macromolecules. The fundamental measurement needed in AUC is the macromolecular concentration as a function of radial position and time. Currently, the Beckman Coulter XLI analytical ultracentrifuge may be equipped with absorbance and refractive detectors, which provide complementary concentration determinations. For detecting trace quantities of materials, fluorescence detection offers unique advantages over either absorbance or interference detection. A prototype fluorescence detector for the XLI analytical ultracentrifuge has been developed and its characteristics determined. An Ar(+) laser provides a continuous 488-nm excitation beam. Radial resolution is achieved by scanning the focused beam along a radial axis. Detection of the fluorescence signal uses a co-axial, front-face optical configuration to reduce inaccuracies in the concentration caused by inner filter effects. A high-speed A/D data acquisition system allows the fluorescence intensity to be monitored continuously and at a sufficiently high angular resolution so that at any radial position the intensities from all of the samples may be acquired at each revolution. The fluorescence detector is capable of detecting concentrations as low as 300 pM for fluorescein-like labels. The radial resolution of the fluorescence detector is comparable to that of the absorbance system. Both sedimentation velocity and sedimentation equilibrium measurements may be made with the fluorescence detector. Results are presented comparing data acquired using the fluorescence with those acquired using the absorbance detector.