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.     

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.     

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.     

Determination of the sedimentation coefficient distribution by least-squares boundary modeling

A new method is presented for the calculation of apparent sedimentation coefficient distributions g*(s) for the size-distribution analysis of polymers in sedimentation velocity experiments. Direct linear least-squares boundary modeling by a superposition of sedimentation profiles of ideal nondiffusing particles is employed. It can be combined with algebraic noise decomposition techniques for the application to interference optical ultracentrifuge data at low loading concentrations with significant systematic noise components. Because of the use of direct boundary modeling, residuals are available for assessment of the quality of the fits and the consistency of the g*(s) distribution with the experimental data. The method can be combined with regularization techniques based on F statistics, such as used in the program CONTIN, or alternatively, the increment of s values can be adjusted empirically. The method is simple, has advantageous statistical properties, and reveals precise sedimentation coefficients. The new least-squares ls-g*(s) exhibits a very high robustness and resolution if data acquired over a large time interval are analyzed. This can result in a high resolution for large particles, and for samples with a high degree of heterogeneity. Because the method does not require a high frequency of scans, it can also be easily used in experiments with the absorbance optical scanning system. Published 2000 John Wiley & Sons, Inc.     

Sizes and mass distributions of clathrin-coated vesicles from bovine brain

Clathrin-coated vesicles obtained from bovine brain have been studied by ultracentrifugation and dynamic light scattering techniques to provide information on their sedimentation and mass distributions and their average diffusion coefficients. "Uncoated" vesicles, obtained by removing the protein coat from coated vesicles, have been similarly characterized. For typical preparations, maximal values of approximately 210 and 95 S are observed for the sedimentation coefficients of coated and uncoated vesicles, respectively. Corresponding values for the average molecular weights, determined from values of average sedimentation and diffusion coefficients, are 49 X 10(6) and 13 X 10(6); values obtained by equilibrium sedimentation are 37.2 X 10(6) and 10.6 X 10(6). In order to obtain these results, some minor modifications of sedimentation and light-scattering techniques have been devised which may have application to other studies of size distributions of large particles.     

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.     

Physical properties of a genomic condensed chromatin fragment

We have studied the physical properties of a segment of condensed chromatin that lies upstream of the chicken beta-globin locus. This segment can be excised from an avian erythroleukemia cell line by restriction enzyme digestion and released from the nucleus as an essentially homogeneous fragment about 15.5 kbp long. Because of this homogeneity we could measure its sedimentation coefficient quite accurately by a combination of sucrose gradient and analytical ultracentrifugation. By measuring additionally the buoyant density of the cross-linked particle in CsCl we could deduce the total mass of the particle, hence its frictional coefficient, f, directly related to its shape. The measured value of f is consistent with a rod-like particle of the approximate length and diameter proposed earlier for the 30 nm chromatin fiber. The method is generally applicable to homogeneous particles of unique sequence at genomic abundance.     

Sedimentation studies of giant DNA molecules present in unsheared whole-cell lysates of D. melanogaster cells.

We have used band sedimentation in shallow density gradients of CsCl in the preparative centrifuge to analyze the distribution of sedimentation coefficients present in tritium labelled DNA from D. melanogaster cells. The cells were lysed according to the method of Kavenoff and Zimm to preserve very high molecular weight DNA. Sedimentation measurements have been carried out as a function of speed of centrifugation. The resulting distribution functions have been interpreted with the aid of the Zimm-Schumaker equation for the speed dependence of the sedimentation coefficient of very high molecular weight DNA. Low-speed centrifugation (3000 rpm) indicates that DNA molecules from the lysate are evenly distributed over values of S_20,w from 0 to 514S. This distribution is very sensitive to changes in speed of centrifugation and is transformed into a bimodal distribution at 12,080 rpm. Analysis of this transformation allows us to postulate that perhaps 55% of the DNA in the lysate may have molecular weights in excess of 40 × 10⁹ g/mol. Some of these molecules may also possess a variety of configurations including partially replicated branched structures.     

Lymphocyte-activating factor. I. Generation and physicochemical characterization.

Lipopolysaccharide-activated murine peritoneal macrophages elaborate lymphocyte-activating factor (LAF) which is mitogenic for murine thymocytes. A method of LAF production is presented that permits the generation of a relatively homogeneous molecular species. LAF has an isoelectric point of 4.8 (range 4.7-4.9). The m.w. was determined by using several physical techniques. The apparent sedimentation coefficient (S20,w) was determined to be 2.0S by sucrose gradient ultracentrifugation. The Stokes (molecular) radius was determined by gel filtration on Sephadex G-75 to be 22 A (range 21.5 to 22.5); the calculated diffusion coefficient (D20,w) was 9.7 X 10(-7) cm2/sec (range 9.5 X 10(-7) to 9.9 X 10(-7). The buoyant density of LAF is 1.30 g/cm3 (range 1.27 to 1.33) as determined by CsCl isopycnic ultracentrifugation; the partial specific volume was estimated to be 0.72 (range 0.70 to 0.74). From these data, the m.w. was calculated to be 18,000 daltons (range 16,400 to 19,600) with the Svedberg equation. The frictional ratio was calculated to be 1.25.     

Large-scale purification, oligomerization equilibria, and specific interaction of the LexA repressor of Escherichia coli

A rapid large-scale procedure for the purification of the LexA repressor of Escherichia coli is described. This procedure allows one to get more than 100 mg of purified protein from 100 g of bacterial paste with a purity of at least 97%. This method is comparable to earlier, far more complicated purification procedures giving clearly smaller yields. It is shown that the LexA protein may be identified spectroscopically by a large A235/A280 ratio and very pronounced ripples in the absorption spectrum arising from a high amount of phenylalanine residues with respect to that of the other aromatic amino acids. Polyacrylamide gel electrophoresis has been used to study the specific interaction of LexA with a recA operator fragment. The quaternary structure of LexA has been studied by equilibrium ultracentrifugation and sedimentation velocity measurements. The sedimentation coefficient increases with increasing LexA concentration, indicating that LexA is involved in self-association. This finding has been confirmed by equilibrium ultracentrifugation. The results are best described by a monomer-dimer and a subsequent dimer-tetramer equilibrium, with an association constant of 2.1 X 10(4) M-1 for the dimer and 7.7 X 10(4) M-1 for the tetramer formation. These relatively small association constants determined under near-physiological pH and salt conditions suggest that in vivo LexA should be essentially in the monomeric state. The degree to which LexA decreases the electrophoretic mobility of a 175 base pair fragment harboring the recA operator suggests that the recA operator interacts nevertheless with a LexA dimer. However, our results may be also explained by the binding of a LexA monomer with a simultaneous bending of the DNA fragment.     

Lipid-induced aggregation of phospholipase A2: sucrose density gradient ultracentrifugation and crosslinking studies

The aggregation behavior of cobra venom (Naja naja naja) phospholipase A2 in the presence of lipids and Ca2+ was examined using ultracentrifugation and crosslinking techniques. Velocity sedimentation experiments were performed in sucrose gradients. The sedimentation coefficients of the cobra phospholipase A2 and various controls, including bovine serum albumin (BSA), malate dehydrogenase, carbonic anhydrase and pancreatic phospholipase A2, were calculated both in the presence and absence of ligands. The monomeric phospholipid, diheptanoylphosphatidylcholine, and the phospholipid analogue, dodecylphosphocholine (DPC), increased the sedimentation coefficient of the cobra phospholipase A2 from 2.2 S to 2.9 S, a value that is consistent with the formation of an enzyme dimer. The control proteins were unaffected by the presence of phospholipid, except for BSA, which apparently binds large amounts of DPC. Crosslinking experiments with glutaraldehyde showed that in the presence of diheptanoylphosphatidylcholine or DPC, the amount of crosslinked enzyme increased. Ca2+ had no effect on the aggregation state of the enzyme as measured by either technique. Both the ultracentrifugation data and crosslinking data are consistent with the hypothesis that the cobra venom phospholipase A2 exists as a dimer or higher-order aggregate in the presence of lipid substrate, although it is yet to be determined whether the functional subunit is a monomer, dimer or higher-order oligomer.     

Accounting for thermodynamic non-ideality in the Guinier region of small-angle scattering data of proteins

Hydrodynamic studies of the solution properties of proteins and other biological macromolecules are often hard to interpret when the sample is present at a reasonably concentrated solution. The reason for this is that solutions exhibit deviations from ideal behaviour which is manifested as thermodynamic non-ideality. The range of concentrations at which this behaviour typically is exhibited is as low as 1–2 mg/ml, well within the range of concentrations used for their analysis by techniques such as small-angle scattering. Here we discuss thermodynamic non-ideality used previously used in the context of light scattering and sedimentation equilibrium analytical ultracentrifugation and apply it to the Guinier region of small-angle scattering data. The results show that there is a complementarity between the radially averaged structure factor derived from small-angle X-ray scattering/small-angle neutron scattering studies and the second virial coefficient derived from sedimentation equilibrium analytical ultracentrifugation experiments.     

Purification and properties of the polymeric fatty acid synthetase from a filamentous fungus.

Fatty acid synthetase was purified from the filamentous fungus, Aspergillus fumigatus to a specific activity of 4000--5000 munits/mg protein. Its purity was established by its appearance in electron micrographs, on sodium dodecyl sulphate polyacrylamide gels and by analytical ultracentrifugation, and also by its behaviour upon sucrose gradient centrifugation. This enzyme comprises two large polypeptides with molecular weights of 190 000 and 186 000. Evidence from electron microscopy indicates that it consists of three equivalent loops of protein. It dissociates into different-sized circular subunits on ageing or upon dissolution in buffer of low ionic strength. Differences in properties between this fungal synthetase and that found in yeast have been noted and relate, for example, to inhibition by acetyl CoA and malonyl-CoA, cold-lability and pH optimum. The synthetase from A. fumigatus, purified by different procedures, consistently exists in two forms of similar specific activity, with sedimentation coefficients approx. 40 S and 60 S. Synthetase activity present in crude extracts has been identified as a very heavy component with sedimentation coefficient greater than 100 S.     

Sedimentation analysis of noninteracting and self-associating solutes using numerical solutions to the Lamm equation.

The potential of using the Lamm equation in the analysis of hydrodynamic shape and gross conformation of proteins and reversibly formed protein complexes from analytical ultracentrifugation data was investigated. An efficient numerical solution of the Lamm equation for noninteracting and rapidly self-associating proteins by using combined finite-element and moving grid techniques is described. It has been implemented for noninteracting solutes and monomer-dimer and monomer-trimer equilibria. To predict its utility, the error surface of a nonlinear regression of simulated sedimentation profiles was explored. Error contour maps were calculated for conventional independent and global analyses of experiments with noninteracting solutes and with monomer-dimer systems at different solution column heights, loading concentrations, and centrifugal fields. It was found that the rotor speed is the major determinant for the shape of the error surface, and that global analysis of different experiments can allow substantially improved characterization of the solutes. We suggest that the global analysis of the approach to equilibrium in a short-column sedimentation equilibrium experiment followed by a high-speed short-column sedimentation velocity experiment can result in sedimentation and diffusion coefficients of very high statistical accuracy. In addition, in the case of a protein in rapid monomer-dimer equilibrium, this configuration was found to reveal the most precise estimate of the association constant.     

Physical properties of nucleoprotein cores from adenovirus type 5.

Analytical ultracentrifugation, thermal denaturation, and electron microscopy have been used to study nucleoprotein core particles, obtained from disrupted type 5 adenovirus and partially purified on glycerol density gradients. Electron microscopy at low salt concentrations has shown that the cores are homogeneous particles with characteristic structures, which vary with conditions of observation from a fairly loose network of fibers to a highly condensed, compact particle. Sedimentation measurements in the analytical ultracentrifuge, both by boundary and by band techniques, show that the cores are relatively homogeneous in solution and have sedimentation coefficients near 185 S at low salt concentrations, about 243 S in 1 or 2 M NaCl, and 376 S in 1 mM MgCl2. Correlation of sedimentation data with electron microscopic observations suggests that the 185 S particle has a loose, fibrous structure, while the faster species are more highly condensed particles. The melting temperature of the cores in 5 mM Tris/HCl is 79 degrees C, which is 10 degrees C higher than the Tm for purified, viral DNA. This indicates that the protein enhances the stability of DNA in the nucleoprotein complex.     

Characterization of ribonucleic acids from Rhizophlyctis rosea zoospores

Summary The nucleotide composition of ribosomal, soluble and total ribonucleic acids (RNA) from the zoospores of Rhizophlyctis rosea was determined. The base ratios for ribosomal, soluble, and total RNA were 49.16, 51.79 and 49.97 moles percent, guanylic acid (G) and cytidylic acid (C) respectively. The distribution of the nucleotides in ribosomal RNA differed slightly from those determined in other fungi and microorganisms. The amount of uridylic acid in soluble RNA was very high, while the GC content was unexpectedly low. Ribosomes were characterized with respect to their mean sedimentation coefficient, under high magnesium (0.01 M) concentrations, in the analytical ultracentrifuge, and by a linear sucrose-density gradient centrifugation. The particles had an average of 82 S by the sucrose-density gradient method, and an average of 78 S by the analytical ultracentrifugation technique.     

A model for sedimentation in inhomogeneous media. I. Dynamic density gradients from sedimenting co-solutes

Macromolecular sedimentation in inhomogeneous media is of great practical importance. Dynamic density gradients have a long tradition in analytical ultracentrifugation, and are frequently used in preparative ultracentrifugation. In this paper, a new theoretical model for sedimentation in inhomogeneous media is presented, based on finite element solutions of the Lamm equation with spatial and temporal variation of the local solvent density and viscosity. It is applied to macromolecular sedimentation in the presence of a dynamic density gradient formed by the sedimentation of a co-solute at high concentration. It is implemented in the software SEDFIT for the analysis of experimental macromolecular concentration distributions. The model agrees well with the measured sedimentation profiles of a protein in a dynamic cesium chloride gradient, and may provide a measure for the effects of hydration or preferential solvation parameters. General features of protein sedimentation in dynamic density gradients are described.     

The subunits of human hexosaminidase A.

Previous studies of the subunit structure of hexosaminidase gave ambiguous results, but suggested that the enzyme was composed of six equally sized subunits. Dissociation of hexosaminidase A with p-chloromercuribenzoate produces an alkylated fragment with mol.wt. approx. 50000, which is converted into hexosaminidase S by treatment with dithiothreitol. Treatment of native hexosaminidase A with sodium dodecylsulphate results in the formation of a large and a small fragment. However, although the native enzyme has a sedimentation coefficient of 5.8S, dissociation by S-carboxymethylation and maleic anhydride treatment results in subunits exhibiting a single schlieren boundary on analytical ultracentrifugation with a sedimentation coefficient of 2.18S. These results indicate that the enzyme is composed of four subunits, each with molwt. approx. 25000-27000. The mol.wt. of the native enzymes is calculated to be approx. 110000. Our data are consistent with the subunit structures of hexosaminidases A, B and S as being alpha2beta2, beta4 and alpha4 respectively.     

Anomalous sedimentation behaviour of the e-coli ribosomal system: 50S-30S ⇄ 50S + 30S

An experimental and theoretical study has been made into the effect of association-dissociation reactions on the sedimentation of the E. coli ribosomal system 50S-30S ⇄ 50S + 30S. It has been found that(a) the sedimentation pattern is strongly dependent on the rotor speed;(b) the ratio of components as measured using high-speed ultracentrifugation (30000–40000 r.p.m.) is independent of rotor speed; and(c) the speed of ultracentrifugation has a strong effect on the sedimentation coefficient of the ribosomal system as determined by the mean square second moment.The results of this paper demonstrate that ribosome sedimentation at low-speed ultracentrifugation is affected by some artefactual processes. A theoretical analysis of the experimental findings has shown that the observed effects cannot be attributed to the effect of the association-dissociation reaction not to the pressure dependence of the equilibrium constant of that reaction.On the other hand, at high-speed ultracentrifugation the ribosomal system sediments as a heterogeneous mixture of non-interacting components. Consequently, the shape of the boundary in this case will reflect the equilibrium composition of the ribosomal system.     

Variable-Field Analytical Ultracentrifugation: I. Time-Optimized Sedimentation Equilibrium

Sedimentation equilibrium (SE) analytical ultracentrifugation (AUC) is a gold standard for the rigorous determination of macromolecular buoyant molar masses and the thermodynamic study of reversible interactions in solution. A significant experimental drawback is the long time required to attain SE, which is usually on the order of days. We have developed a method for time-optimized SE (toSE) with defined time-varying centrifugal fields that allow SE to be attained in a significantly (up to 10-fold) shorter time than is usually required. To achieve this, numerical Lamm equation solutions for sedimentation in time-varying fields are computed based on initial estimates of macromolecular transport properties. A parameterized rotor-speed schedule is optimized with the goal of achieving a minimal time to equilibrium while limiting transient sample preconcentration at the base of the solution column. The resulting rotor-speed schedule may include multiple over- and underspeeding phases, balancing the formation of gradients from strong sedimentation fluxes with periods of high diffusional transport. The computation is carried out in a new software program called TOSE, which also facilitates convenient experimental implementation. Further, we extend AUC data analysis to sedimentation processes in such time-varying centrifugal fields. Due to the initially high centrifugal fields in toSE and the resulting strong migration, it is possible to extract sedimentation coefficient distributions from the early data. This can provide better estimates of the size of macromolecular complexes and report on sample homogeneity early on, which may be used to further refine the prediction of the rotor-speed schedule. In this manner, the toSE experiment can be adapted in real time to the system under study, maximizing both the information content and the time efficiency of SE experiments.