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Development of an ultracentrifuge technique to determine the adhesion and friction properties between particles and surfaces.

The extension of a centrifuge technique to measure adhesion and friction forces to an ultracentrifuge has been described. The equipment and procedure provide many experimental possibilities of which the adhesion of single particles to flat compacted powder surfaces has been used to measure the adhesion and friction force of starch microspheres to microcrystalline cellulose. The equipment used allows the positioning of the adhesion samples in the rotor in such a way that any angle between the centrifugal force vector and the flat sample surface can be obtained, and hence both adhesion and friction forces can be measured. The adhesion strength between starch microspheres and microcrystalline cellulose could initially be increased by applying a higher press-on force. However, a maximum plastic deformation and hence maximum contact area between the spheres and the surfaces was eventually reached, and any further application of press-on force appeared to lead only to more elastic deformation and hence not to an increase in adhesion strength. The friction between the starch microspheres and the compacted microcrystalline cellulose surfaces at a maximum deformation of the spheres is still very low, so that starch microspheres could be used as excipient in mixtures including microcrystalline cellulose for example in tabletting.

Adhesiveness↗

Multidimensional proteomic analysis of photosynthetic membrane proteins by liquid extraction-ultracentrifugation-liquid chromatography-mass spectrometry.

The membrane protein components of photosystem I (PSI) and II (PSII) from different species were prefractionated by liquid extraction and sucrose gradient ultracentrifugation and subsequently analyzed by reversed-phase high-performance liquid chromatography-electrospray ionization-mass spectrometry (RP-HPLC-ESI-MS) using poly-(styrene-divinylbenzene)-based monolithic capillary columns. The analytical method was shown to be very flexible and enabled the identification of antenna proteins as well as most of the proteins of the reaction center from PSI and PSII in various plant species with few RP-HPLC-ESI-MS analyses necessitating only minor adaptations in the gradients of acetonitrile in 0.05% aqueous trifluoroacetic acid. The membrane proteins, ranging in molecular mass (Mr) from 4196 (I protein) to more than 80,000 (PSI A/B) as well as isoforms were identified on the basis of their intact Mr and comparison with Mr deduced from known DNA or protein sequences. High quality mass spectra enabled the identification and quantitation of the nonphosphorylated and phosphorylated reaction center subunits D1, D2, and CP43 of PSII, containing five to seven membrane-spanning alpha-helices. Because of its high flexibility and suitability for proteins having a very wide range of Mr and hydrophobicities, the method is generally applicable to the analysis of complex mixtures of membrane proteins.

Arabidopsis↗

Interaction of the DNA-binding domain of Drosophila heat shock factor with its cognate DNA site: a thermodynamic analysis using analytical ultracentrifugation.

Heat shock transcription factor (HSF) mediates the activation of heat shock genes by binding to its cognate sites with high affinity and specificity. The high-affinity binding of HSF is dependent on the formation of an HSF homotrimer, which interacts specifically with the heat shock response element (HSE), comprised of 3 inverted repeats of the 5-bp sequence NGAAN. In order to investigate the thermodynamic basis of the interaction between HSF and HSE, we have overexpressed and purified a polypeptide (dHSF(33-163)) encompassing only the DNA-binding domain of HSF from Drosophila and analyzed its binding to DNA by equilibrium analytical ultracentrifugation using a multiwavelength scan technique. We demonstrate that dHSF(33-163) can bind as a monomer with 1:1 stoichiometry to a synthetic 13-bp DNA containing a single NGAAN sequence. The values of the thermodynamic parameters obtained from the temperature dependence of the equilibrium binding constants indicate that the changes of free energy for the binding of dHSF(33-163) to the wild-type site and a mutant DNA site are predominantly characterized by substantial negative changes of enthalpy. Binding to the wild-type DNA is characterized by a significant positive change of entropy, whereas binding to the mutant DNA is distinguished by a negative change of entropy of comparable magnitude. The binding to the mutant DNA was also highly sensitive to increasing salt concentrations, indicating a dominance of ionic interactions. The sequence-specific, 1:1 binding of dHSF(33-163) to the NGAAN sequence provides a basis for the analysis of higher order interactions between HSF trimers and the HSE.

Animals↗

Three-dimensional model and quaternary structure of the human eye lens protein gamma S-crystallin based on beta- and gamma-crystallin X-ray coordinates and ultracentrifugation.

A 3-dimensional model of the human eye lens protein gamma S-crystallin has been constructed using comparative modeling approaches encoded in the program COMPOSER on the basis of the 3-dimensional structure of gamma-crystallin and beta-crystallin. The model is biased toward the monomeric gamma B-crystallin, which is more similar in sequence. Bovine gamma S-crystallin was shown to be monomeric by analytical ultracentrifugation without any tendency to form assemblies up to concentrations in the millimolar range. The connecting peptide between domains was therefore built assuming an intramolecular association as in the monomeric gamma-crystallins. Because the linker has 1 extra residue compared with gamma B and beta B2, the conformation of the connecting peptide was constructed by using a fragment from a protein database. gamma S-crystallin differs from gamma B-crystallin mainly in the interface region between domains. The charged residues are generally paired, although in a different way from both beta- and gamma-crystallins, and may contribute to the different roles of these proteins in the lens.

Amino Acid Sequence↗

An optical thermometer for direct measurement of cell temperature in the Beckman instruments XL-A analytical ultracentrifuge.

An optical thermometer has been evaluated for use in the Beckman Instruments Optima XL-A Analytical Ultracentrifuge. A thermochromic solution of CoCl2.6H2O was used as the temperature sensing material. The dehydration of CoCl2.6H2O is temperature dependent resulting a highly temperature dependent absorption peak at 660 nm. Spectra of 0.1 M CoCl2.6H2O in an alcohol-water mixture were measured at different temperature settings of the XL-A. The spectra of the same CoCl2.6H2O solutions were measured on a Beckman Instruments DU-650 spectrophotometer with a calibrated thermocouple attached to the cuvette. A standard curve was constructed by plotting the area under the spectrum from 450 to 750 nm as a function of the thermocouple temperature. Spectra were obtained on the XL-A at various temperature settings and integrated over the same range. This method allows direct comparison of the cell temperature to the value displayed on the console panel of the XL-A.

Thermometers↗

A new data analysis method to determine binding constants of small molecules to proteins using equilibrium analytical ultracentrifugation with absorption optics.

In principle, equilibrium analytical ultracentrifugation (AU) can be used to quantify the binding stoichiometry and affinity between small-molecule ligands and proteins in aqueous solution. We show here that heteromeric binding constants can be determined using a data-fitting procedure which utilizes a postfitting computation of the total amount of each component in the centrifuge cell. The method avoids overconstraining the fitting of the radial concentration profiles, but still permits unique binding constants to be determined using measurements at a single wavelength. The computational program is demonstrated by applying it to data obtained with mixtures of a 500-Da molecule and interleukin-2, a 16-kDa protein. The 1:1 binding stoichiometry and heteromeric dissociation constants (K(ab)) determined from centrifuge data at two different wavelengths are within the 4-9 microM range independently determined from a functional assay. Values for K(ab) have been obtained for ligands with affinities as weak as 500 microM. This AU method is applicable to compounds with significant UV absorbance (approximately 0.2) at concentrations within approximately 5- to 10-fold of their K(ab). The method, which has been incorporated into a user procedure for IgorPro (Wavemetrics, Oswego, OR), is included as supplementary material.

Inhibitory Concentration 50↗

Association states of the transcription activator protein NtrC from E. coli determined by analytical ultracentrifugation.

The transcription activator protein NtrC (nitrogen regulatory protein C) can catalyze the transition of E. coli RNA polymerase complexed with the sigma54 factor (RNAP.sigma54) from the closed complex (RNAP.sigma54 bound at the promoter) to the open complex (melting of the promoter DNA). This process involves phosphorylation of NtrC, assembly of a multimeric NtrC complex at the enhancer DNA sequence, interaction of this complex with promoter bound RNAP. sigma54 via DNA looping, and hydrolysis of ATP. We have used analytical ultracentrifugation to study the different NtrC association states and to derive hydrodynamic models for the conformation of the various NtrC species. The following results were obtained. (i) The unphosphorylated wild-type protein formed a dimer with a measured molecular weight of 102(+/-3) kDa, which compares to a calculated molecular weight of 54 kDa for a monomer (concentration range studied 2 to 8 microM NtrC monomer). (ii) In the unphosphorylated state one NtrC dimer was bound to one binding site as determined with DNA oligonucleotide duplexes containing one or two binding sites (concentration range studied 50 to 1000 nM NtrC dimer). (iii) The data obtained at protein concentrations that were below the concentration of binding sites indicate that binding to the DNA duplex with two binding sites occurred with essentially no cooperativity. The experiments were conducted in the absence of ATP. (iv) The phosphorylated protein formed a specific complex at the DNA duplex with the enhancer sequence (two NtrC binding sites) that consisted of four dimers (concentration range studied 100 to 1000 nM NtrC dimer). (v) The formation of this octameric complex was highly cooperative, and the data suggest that two DNA strands could bind simultaneously to this complex. (vi) From the sedimentation data a model was derived in which the NtrC dimer adopts a V shaped structure with the DNA binding domains being located at the bottom and the two receiver domains at the top of the V. In this conformation higher order NtrC complexes can be stabilized by interaction between the phosphorylated receiver domain and the central activation domain of different NtrC dimers.

Bacterial Proteins↗

Studies on the structure and mechanism of a bacterial protein toxin by analytical ultracentrifugation and small-angle neutron scattering.

Pneumolysin, an important virulence factor of the human pathogen Streptococcus pneumoniae, is a pore-forming toxin which also possesses the ability to activate the complement system directly. Pneumolysin binds to cholesterol in cell membrane surfaces as a prelude to pore formation, which involves the oligomerization of the protein. Two important aspects of the pore-forming activity of pneumolysin are therefore the effect of the toxin on bilayer membrane structure and the nature of the self-association into oligomers undergone by it. We have used analytical ultracentrifugation (AUC) to investigate oligomerization and small-angle neutron scattering (SANS) to investigate the changes in membrane structure accompanying pore formation. Pneumolysin self-associates in solution to form oligomeric structures apparently similar to those which appear on the membrane coincident with pore formation. It has previously been demonstrated by us using site-specific chemical derivatization of the protein that the self-interaction preceding oligomerization involves its C-terminal domain. The AUC experiments described here involved pneumolysin toxoids harbouring mutations in different domains, and support our previous conclusions that self-interaction via the C-terminal domain leads to oligomerization and that this may be related to the mechanism by which pneumolysin activates the complement system.SANS data at a variety of neutron contrasts were obtained from liposomes used as model cell membranes in the absence of pneumolysin, and following the addition of toxin at a number of concentrations. These experiments were designed to allow visualization of the effect that pneumolysin has on bilayer membrane structure resulting from oligomerization into a pore-forming complex. The structure of the liposomal membrane alone and following addition of pneumolysin was calculated by the fitting of scattering equations directly to the scattering curves. The fitting equations describe scattering from simple three-dimensional scattering volume models for the structures present in the sample, whose dimensions were varied iteratively within the fitting program. The overall trend was a thinning of the liposome surface on toxin attack, which was countered by the formation of localized structures thicker than the liposome bilayer itself, in a manner dependent on pneumolysin concentration. At the neutron contrast match point of the liposomes, pneumolysin oligomers were observed. Inactive toxin appeared to bind to the liposome but not to cause membrane alteration; subsequent activation of pneumolysin in situ brought about changes in liposome structure similar to those seen in the presence of active toxin. We propose that the changes in membrane structure on toxin attack which we have observed are related to the mechanism by which pneumolysin forms pores and provide an important perspective on protein/membrane interactions in general. We discuss these results in the light of published data concerning the interaction of gramicidin with bilayers and the hydrophobic mismatch effect.

Amino Acid Sequence↗

Folded-back solution structure of monomeric factor H of human complement by synchrotron X-ray and neutron scattering, analytical ultracentrifugation and constrained molecular modelling.

Factor H (FH) is a regulatory cofactor for the protease factor I in the breakdown of C3b in the complement system of immune defence, and binds to heparin and other polyanionic substrates. FH is composed of 20 short consensus/complement repeat (SCR) domains, for which the overall arrangement in solution is unknown. As previous studies had shown that FH can form monomeric or dimeric structures, X-ray and neutron scattering was accordingly performed with FH in the concentration range between 0.7 and 14 mg ml(-1). The radius of gyration of FH was determined to be 11.1-11.3 nm by both methods, and the radii of gyration of the cross-section were 4.4 nm and 1.7 nm. The distance distribution function P(r) showed that the overall length of FH was 38 nm. The neutron data showed that FH was monomeric with a molecular mass of 165,000(+/-17,000) Da. Analytical ultracentrifugation data confirmed this, where sedimentation equilibrium curve fits gave a mean molecular mass of 155,000(+/-3,000) Da. Sedimentation velocity experiments using the g*(s) derivative method showed that FH was monodisperse and had a sedimentation coefficient of 5.3(+/-0.1) S. In order to construct a full model of FH for scattering curve and sedimentation coefficient fits, homology models were constructed for 17 of the 20 SCR domains using knowledge of the NMR structures for FH SCR-5, SCR-15 and SCR-16, and vaccinia coat protein SCR-3 and SCR-4. Molecular dynamics simulations were used to generate a large conformational library for each of the 19 SCR-SCR linker peptides. Peptides from these libraries were combined with the 20 SCR structures in order to generate stereochemically complete models for the FH structure. Using an automated constrained fit procedure, the analysis of 16,752 possible FH models showed that only those models in which the 20 SCR domains were bent back upon themselves were able to account for the scattering and sedimentation data. The best-fit models showed that FH had an overall length of 38 nm and is flexible. This length is significantly less than a predicted length of 73 nm if the 20 SCR structures had been arranged in an extended arrangement. This outcome is attributed to several long linker sequences. These bent-back domain structures may correspond to conformational flexibility in FH and enable the multiple FH binding sites for C3 and heparin to come into close proximity.

Amino Acid Sequence↗

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.

Kinetics↗

Complexes prepared from protein A and human serum, IgG, or Fc gamma fragments: characterization by immunochemical analysis of ultracentrifugation fractions and studies on their interconversion.

Protein A of Staphylococcus aureus is an Fc receptor for IgG that has been used as a therapeutic reagent to treat cancer in humans and experimental animals. We used ultracentrifugation combined with analysis of isolated fractions by radioimmunoprecipitation and competitive radioimmunoassay with chicken antibodies that bind free protein A or protein A in complexes but do bind free immunoglobulin reagents to localize and characterize the types of complexes formed with different molar ratios of 125I-protein A and human 131I-IgG alone or in serum, and 131I-Fc gamma fragments. This approach offers a distinct advantage over direct counting of radioactivity in the fractions because resolution of complexes and free reagents is much improved. With excess 131I-IgG or 131I-Fc, all the 125I-protein A is present only in complexes that contained 4 molecules of immunoglobulin reagent and 2 molecules of protein A (4:2 complexes), whereas with excess 125I-protein A the stoichiometry of the complexes was 1:1. We have also shown the preformed 4:2 and 1:1 complexes will interconvert in the presence of added excess protein A or IgG, respectively, and that fresh IgG will exchange with IgG or Fc gamma in preformed complexes. Because protein A has been found to elute from an immobilized reagent used in serotherapy of human cancer and is present in a large excess of IgG, the 4:2 complexes may play an active role in the tumoricidal or toxic reactions observed.

Antigen-Antibody Complex↗

In vivo localization of Ga-citrate in rat liver as determined by cell fractionation with isopycnic rate-zonal ultracentrifugation.

The in vivo behaviour of Ga-67 citrate was studied, using a rat liver model, and the mechanisms of cellular uptake were investigated by observing the time course of the radionuclide in subcellular liver cell fractions. Modified continuous ultracentrifugation was used to successively fractionate the homogenates according to isopycnic and rate-zonal principles. To collect the cell nuclei, a special technique, which consisted of supplementing the outer sucrose layer with cesium chloride to increase density, was applied to trap nuclei with isopycnic equilibrium. We isolated nuclei, mitchondria, lysosomes and peroxysomes, microsomes, and the cell supernatant in a sufficiently purified state. By this method, the in vivo localization of Ga-67 was studied. At 30 min after intravenous injection, radioactivity was found mainly in the cell supernatant, the radioactivity peak corresponded to 5 S. However, after 24 h, the radioactivity was localized in the heavier fraction containing lysosomes and heavy endoplasmic reticulum. No intranuclear localization was observed. In spite of the difficulty in completely separating the lysosomal fraction from heavy endoplasmic reticulum, our results suggest the participation of heavy endoplasmic reticulum in gallium localization.

Animals↗

Ultracentrifugal analysis of the junction complexes of the red cell membrane cytoskeletal network: application to hereditary spherocytosis and metabolically depleted cells.

A method has been developed for the assessment of the number of spectrin dimer units associated with each actin protofilament junction, in the membrane cytoskeletal network (i.e. the degree of branching) of the red cell. Ghosts are first exposed to elevated temperature at low ionic strength to dissociate some 65% of the spectrin tetramers (that link the network junctions) into dimers, without causing their release from the actin filaments. Non-ionic detergent is then added to solubilize the membrane itself with its intrinsic proteins, so as to liberate the cytoskeletal material, and the mixture is immediately examined in the analytical ultracentrifuge. The predominant components observed are isolated junctions (20 S), free spectrin dimers and the residual undissociated cytoskeletal material, with very minor components, probably corresponding to multiple junctions, linked by spectrin tetramers. The junction boundary is homogeneous within the accuracy of measurement and is taken to correspond to a complex containing six spectrin dimers, known to predominate in situ. About 17% of the total network is liberated in this form and 12% as free spectrin dimers. In hereditary spherocytosis both the size of the junction complex (as reflected by its sedimentation coefficient) and the proportion of the complex and of free spectrin liberated are indistinguishable from normal values. We conclude that the reported deficit of spectrin in hereditary spherocytosis is not reflected by a lower degree of branching of the network, and, if the membrane area is not correspondingly reduced, this must mean that the junctions are more widely spaced and the spectrin tetramers therefore more extended. In metabolically depleted cells, in which the cytoskeletal proteins are known to be extensively dephosphorylated, there is no change in the sedimentation pattern and thus no detectable loss of spectrin from the junctions or weakening in the cohesion of the cytoskeletal network.

Actins↗

Calcium and temperature regulation of the stability of the human platelet integrin GPIIb/IIIa in solution: an analytical ultracentrifugation study.

The human platelet integrin GPIIb/IIIa (228 kDa), a Ca-dependent heterodimer formed by the alpha IIb subunit (GPIIb, 136 kDa) and the beta 3 subunit (GPIIIa, 92 kDa), serves as the fibrinogen receptor at the surface of activated platelets. The degree of dissociation of the GPIIb/IIIa heterodimer (s degrees 20*, 8.9 S) into its constituent glycoproteins (GPIIb, 5.8 S; and GPIIIa, 3.9 S) has been assessed by analytical ultracentrifugation in Triton X100 buffers, and its Ca(2+)- and temperature-dependence correlated with Ca(2+)-binding to GPIIb/IIIa and its temperature dependence. At 21 degrees C half-maximal dissociation of GPIIb/IIIa occurs at 5.5 +/- 2.5 x 10(-8) M Ca2+, very close to the dissociation constant of the high affinity Ca-binding site of GPIIb/IIIa (Kd1 8 +/- 3 x 10(-8) M) (Rivas and González-Rodriguez, 1991) and much lower than the Kd of the 3.4 medium affinity Ca-binding sites (Kd2 4 +/- 1.5 x 10(-5) M), which seems to demonstrate that the stability of the heterodimer in solution at room temperature is regulated by the degree of saturation of the high-affinity Ca-binding site. At 4 degrees C, the stability of the heterodimer is apparently Ca(2+)-independent, while at room and physiological temperatures (15-37 degrees C) the degree of dissociation of the heterodimer is regulated by the degree of dissociation of the high- and medium-affinity Ca-binding sites, respectively.(ABSTRACT TRUNCATED AT 250 WORDS)

Calcium↗

A comparison of simplified methods for lipoprotein quantification using the analytic ultracentrifuge as a standard.

Two simplified methods for quantitative lipoprotein analysis have been calibrated and compared with each other using analytic ultracentrifugation as a standard reference procedure. The first method was the Friedewald procedure and the second was an automated agarose gel electrophoresis system. Both procedures offer comparable quantitative lipoprotein analysis with potential for large scale screening purposes at low cost ($4.00-$5.00 per analysis). There were advantages and limitations to both procedures. The Friedwald procedure can be used on frozen sera but requires 3 ml sera. In contrast, the electrophoresis system must be used with fresh serum but requires only 50 mul serum and the electrophoretic slides may be quantitatively analyzed several years retrospectively.

Adult↗

Analytic ultracentrifuge calibration and determination of lipoprotein-specific refractive increments.

Accurate quantification of the major classes and subfractions of human serum lipoproteins is an important analytical need in the characterization and evaluation of therapy of lipid and lipoprotein abnormalities. For calibrating the analytic ultracentrifuge (AnUC), we routinely use a Beckman calibration wedge cell with parallel scribed lines 1 cm apart. Such a cell gives a rectangular pattern in the schlieren diagram, which determines magnification and also provides an area corresponding to an invariant refractive increment. We have independently validated this wedge calibration cell using a special boundary-forming cell in which 1.174% sucrose is overlayered with distilled water. Comparing wedge cell area with extrapolated zero time boundary area refractive increment gives agreement to within less than 1%, corresponding to a refractive increment error of +/- 0.00002 delta n. Complete calibration for AnUC analysis of lipoproteins also requires accurate determination of the specific refractive increments (SRI) of the major lipoprotein classes, namely low density lipoprotein (LDL) and high density lipoprotein (HDL). These are measured in the density in which they are analyzed, i.e., 1.061 g/ml for LDL and 1.200 g/ml for HDL. Five fresh serum samples were fractionated for total LDL and total HDL and their SRI determined. Total lipoprotein mass was determined using precise CHN elemental analysis and compositional analyses. The results yielded corrected SRI of 0.00142 and 0.00135 delta n/g/100 ml for LDL and HDL. Thus, our current values using 0.00154 and 0.00149 delta n/g/100 ml underestimate LDL and HDL by 9% and 11%. Corrections of all previous LDL and HDL AnUC data can be made using appropriate factors of 1.087 and 1.106.

Humans↗

Evaluation of the rapid micromethod for ultracentrifugal separation of labeled plasma lipoproteins.

The fractionations of plasma lipoproteins by 2 methods were compared to evaluate the rapid separation (Airfuge) method for lipoprotein distribution studies. When [125I] labeled very low density, low density, and high density lipoproteins (VLDL, LDL, HDL), were separately centrifuged in buffers at d = 1.006, 1.06 or 1.2 g/ml by the conventional ultracentrifuge and the Airfuge, separations of the fractions in the Airfuge were incomplete at both 5 C and 24 C, especially at d = 1.006. [3H] Benzo (a)pyrene, when added to plasma, associates with the plasma proteins and lipoproteins, especially LDL. Compared to the standard techniques, the Airfuge method greatly overestimated its distribution into VLDL. The distribution of [3H] vitamin D3 into the VLDL plus LDL fraction was also overestimated by the Airfuge procedure. It is concluded that caution should be observed in quantitative studies of lipoproteins in the Airfuge. A careful comparison of the distribution into or fractionation of lipoproteins by the 2 methods should always precede any quantitative determinations involving the Airfuge.

Humans↗

Correlation of SEC/MALLS with ultracentrifuge and viscometric data for chitosans.

Attempts have been made to correlate estimates of molecular weight for a group of cationic polysaccharides known as chitosans between the highly popular technique of size-exclusion chromatography coupled to multi-angle laser light scattering, "SEC-MALLS", and the less convenient but more established technique of sedimentation equilibrium in the analytical ultracentrifuge. Four pharmaceutical grade chitosans of various molecular weights and degrees of acetylation (4-30%) were chosen. Better correlation than previous was achieved, although some batch variability was observed. Despite the broad spectrum in degree of acetylation, a log s degrees(20,w) versus log Mw scaling plot appeared to fit a straight line with power-law exponent b=0.25 +/- 0.04, i.e. between the limits of rod (0.15) and coil (0.4-0.5), although this may be the average of a lower b value at low Mw and higher b at high Mw. With regard to viscosity, a logeta versus logMw scaling plot appeared to also fit a straight line with power-law exponent a=0.96 +/- 0.10, again between the coil (0.5-0.7) and rod (1.8) limits.

Centrifugation, Density Gradient↗