Hydrodynamic properties of human cervical-mucus glycoproteins in 6M-guanidinium chloride.

Cervical mucins and fragments thereof were studied by sedimentation-velocity, rotatory viscometry and laser light-scattering performed as photon-correlation spectroscopy as well as low-angle total-intensity measurements. The Mr of the whole mucins is 10 X 10(6)-15 X 10(6), whereas fragments obtained after reduction of disulphide bonds ('subunits') have Mr 2.1 X 10(6)-2.9 X 10(6), depending on the method used. Subsequent trypsin digestion of subunits afforded glycopeptides with Mr approx. 0.4 X 10(6). The high frictional ratio for the whole mucins is interpreted as a large degree of expansion. The Stokes radius calculated from the diffusion coefficient is approx. 110nm for the whole mucins, which is in agreement with that estimated from the radius of gyration (130nm) by using the concept of the equivalent hydrodynamic sphere. The ratio of the concentration-dependence parameter for the reciprocal sedimentation coefficient (Ks) to the intrinsic viscosity ( [eta] ) for the whole mucins is 1.42, suggesting that the individual macromolecule occupies a spheroidal domain in solution. The relationship between [eta] and Mr for whole mucins, subunits and T-domains suggests that they are linear flexible macromolecules behaving as somewhat 'stiff' random coils. This conclusion is supported by the relationships between the sedimentation coefficients, the diffusion coefficients and the Mr. The hydrodynamic behaviour of the mucins is thus close to that expected for coiling macromolecules entrapping a lot of solvent, which is consistent with the postulated polymeric structure.     

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.     

An improved approximate solution of the Lamm equation for the simultaneous estimation of sedimentation and diffusion coefficients from sedimentation velocity experiments

Sedimentation and diffusion coefficients are important parameters to describe size and shape of macromolecules in solution. The data can be obtained from sedimentation velocity experiments by a nonlinear fitting procedure using approximate solutions for the Lamm equation. Here, we present a modification of such a model function that was originally proposed by Fujita [H. Fujita, Mathematical Theory of Sedimentation Analysis, Wiley, New York, 1962]. The extended model function is well suitable to study low molecular mass compounds. The improvement of this solution given here is based on using an adjustable value for the explicit integration variable, z, the reduced radius. This modification leads to more accurate sedimentation and diffusion coefficients compared to using a constant value of 0.5 as used by Fujita. The advantage of our modification was demonstrated by the analysis of noise-free curves calculated using the finite element method, as well as experimental curves obtained for the peptides angiotensin I and II. The relatively low sedimentation and diffusion coefficients found for both substances indicate that the peptides exist as extended chains of about 3.65 nm (angiotensin I) or 3.04 nm length (angiotensin II) in solution. The lack of higher-order structure of the peptides that was derived also from CD spectra might facilitate receptor binding, and could be one reason for the fast proteolytic digestion of the free peptides.     

The evaluation of standard sedimentation coefficient in band sedimentation of macromolecules

Standardization in the calculation of the sedimentation coefficient of macromolecules by means of band techniques is discussed. When a sample of macromolecules suspended in a solvent is layered on to a denser bulk solution, the macromolecules do not sediment in this solution alone, but sediment in a mixture of bulk solution and sample solvent. This is caused by the diffusion between sample solvent and bulk solution. Experimental evidence of this process is shown during band sedimentation of ribosomes when the variation of the density and the viscosity along the cell is measured. The calculation shows that in the experimental conditions frequently used, standardization made in the usual way leads to a sedimentation coefficient which is largely overestimated; while standardization yields the correct coefficient if the diffusion effect of the sample solvent in to the bulk solution is taken into account, together with possible deuteration effects. A method to calculate the standard coefficient with the aid of a computer is proposed.     

Determination of sedimentation coefficients for small peptides.

Direct fitting of sedimentation velocity data with numerical solutions of the Lamm equations has been exploited to obtain sedimentation coefficients for single solutes under conditions where solvent and solution plateaus are either not available or are transient. The calculated evolution was initialized with the first experimental scan and nonlinear regression was employed to obtain best-fit values for the sedimentation and diffusion coefficients. General properties of the Lamm equations as data analysis tools were examined. This method was applied to study a set of small peptides containing amphipathic heptad repeats with the general structure Ac-YS-(AKEAAKE)nGAR-NH2, n = 2, 3, or 4. Sedimentation velocity analysis indicated single sedimenting species with sedimentation coefficients (s(20,w) values) of 0.37, 0.45, and 0.52 S, respectively, in good agreement with sedimentation coefficients predicted by hydrodynamic theory. The described approach can be applied to synthetic boundary and conventional loading experiments, and can be extended to analyze sedimentation data for both large and small macromolecules in order to define shape, heterogeneity, and state of association.     

Translational diffusion coefficient of cycloamylose in aqueous sodium hydroxide

Seven cyclic (1 --> 4)-alpha-D-glucan (cycloamylose) samples ranging in weight-average molecular weight from 5 x 10(3) to 1.8 x 10(4) and gamma-cyclodextrin have been studied by sedimentation equilibrium in dimethylsulfoxide (at 25 degrees C) and by dynamic light scattering in 0.5 N aqueous sodium hydroxide (at 25 degrees C), a good solvent for linear amylose. The measured translational diffusion coefficients D in the aqueous NaOH agree fairly closely with previous Monte Carlo results for cyclic (1 --> 4)-alpha-D-glucan chains with excluded volume, when correction is made for the effects of bead diameter and fluctuating hydrodynamic interaction (HI) on the Kirkwood theory on which the computation of D was based. These D data are also explained almost quantitatively by Yamakawa and Fujii's expression for the associated KP ring (based on the Kratky-Porod wormlike chain) with the molecular parameters for linear amylose if the fluctuating HI and excluded-volume effects are taken into account. It is concluded that the translational diffusion behavior of cycloamylose in the aqueous NaOH is consistent with the conformational characteristics derived from the conformational energy of maltose and dilute-solution data for linear amylose.     

Diffusion and electrophoretic mobility of single-stranded RNA from molecular dynamics simulations

Hydrodynamic properties of small single-stranded RNA homopolymers with three and six nucleotides in free solution are determined from molecular dynamics simulations in explicit solvent. We find that the electrophoretic mobility increases with increasing RNA length, consistent with experiment. Diffusion coefficients of RNA, corrected for finite-size effects and solvent viscosity, agree well with those estimated from experiments and hydrodynamic calculations. The diffusion coefficients and electrophoretic mobilities satisfy a Nernst-Einstein relation in which the effective charge of RNA is reduced by the charge of transiently bound counterions. Fluctuations in the counterion atmosphere are shown to enhance the diffusive spread of RNA molecules drifting along the direction of the external electric field. As a consequence, apparent diffusion coefficients measured by capillary zone electrophoresis can be significantly larger than the actual values at certain experimental conditions.     

Skeletal structure of clathrin triskelion in solution: experimental and theoretical approaches

The physicochemical properties of the clathrin triskelion were determined by dynamic and static light-scattering and sedimentation analyses in Tris and triethanolamine (TEA) buffers of about pH 8, in which the clathrin triskelion has been found to be in different conformational states by electron microscopy [Heuser, J., & Kirchhausen, T. (1985) J. Ultrastruct. Res. 92, 1-27]. Dynamic light-scattering measurements provided diffusion coefficients (D0(20,w)) of 1.22 x 10(-7) and 1.23 x 10(-7) cm2/s, and ultracentrifugal analysis gave sedimentation coefficients (S0(20,w)) of 8.39 and 8.32 S in Tris and TEA buffer, respectively. The average Stokes radius of the protein was determined to be 175 A from its diffusion and sedimentation coefficients and its molecular weight. Static light-scattering analysis provided molecular weights of 6.58 x 10(5) and 6.41 x 10(5) and radii of gyration of 311 and 301 A in the respective buffers. These results indicate that the clathrin triskelion has a similar conformation in the two buffers. For clarification of the skeletal structure of the clathrin triskelion in solution, the physicochemical parameters were calculated by using two models in which the clathrin arms are bent at various angles in a plane, on the basis of the Bloomfield approximation and a formula derived to estimate the radius of gyration of proteins consisting of various structural units. Values for the Stokes radius, diffusion and sedimentation coefficients, and radius of gyration in the ranges of 178-170 A, (1.20-1.26) x 10(-7) cm2/s, 8.26-8.66 S, and 316-266 A, respectively, were obtained with these models with the arms bent in the range of 0-60 degrees.(ABSTRACT TRUNCATED AT 250 WORDS)     

An automated method for rapid determination of diffusion coefficients via measurements of boundary spreading

The use of a simple device by which a layer of solvent may be deposited onto a solution of an optically absorbing solute in a cylindrical quartz tube, without substantial mixing of solution and solvent, is described. The spreading of the boundary thus formed may be monitored as a function of time using an automated absorbance scanning device previously described [A. K. Attri and A. P. Minton (1983) Anal. Biochem. 133, 142-152]. A semiautomatic procedure for determining the diffusion coefficient from the time dependence of the shape of the boundary is described and is particularly well-suited for real-time data analysis with a laboratory microcomputer. The diffusion coefficients of several proteins have been measured using the technique reported, and the results are generally in good agreement with values reported in the literature. The feasibility of using this technique in combination with a previously described method for measuring the sedimentation coefficient [A. K. Attri and A. P. Minton (1984) Anal. Biochem. 136, 407-415] to rapidly determine the molecular weight of a protein is established.     

The concentration dependence of transport processes: A general description applicable to the sedimentation,translational diffusion,and viscosity coefficients of macromolecular solutes

The transport coefficients of macromolecular solutes are normally extrapolated to “infinite dilution” to remove the effects of concentration-dependence terms, for which no satisfactory general treatment has been available. It is shown that a simple general treatment for the concentration-dependence effect can be derived, applicable to limiting concentrations in the absence of charge effects or other forms of specific interactions between the solute particles. The relationships derived are of considerable practical significance for the characterization of the size and conformation of natural and synthetic polymers.     

Peptide self-association in aqueous trifluoroethanol monitored by pulsed field gradient NMR diffusion measurements

Defining the self-association state of a molecule in solution can be an important step in NMR-based structure determination. This is particularly true of peptides, where there can be a relatively small number of long-range interactions and misinterpretation of an intermolecular NOE as an intramolecular contact can have a dramatic influence on the final calculated structure. In this paper, we have investigated the use of translational self-diffusion coefficient measurements to detect self-association in aqueous trifluoroethanol of three peptides which are analogues of the C-terminal region of human neuropeptide Y. Experimentally measured diffusion coefficients were extrapolated to D⁰, the limiting value as the peptide concentration approaches zero, and then converted to D_20,w, the diffusion coefficient after correction for temperature and the viscosity of the solvent. A decrease in D_20,w of about 16% was found for all three peptides in aqueous TFE (30% by volume) compared with water, which is in reasonable agreement with the expected decrease upon dimerisation, the presence of which was indicated by sedimentation equilibrium measurements. Apparent molecular masses of these peptides in both solutions were also calculated from their diffusion coefficients and similar results were obtained. Several potential internal standards, including acetone, acetonitrile, dimethylsulfoxide and dioxane, were assessed as monitors of solution viscosity over a range of trifluoroethanol concentrations. Compared with independent measurements of viscosity, acetonitrile was the most accurate standard among these four. The practical limitations of a quantitative assessment of peptide self-association from translational diffusion coefficients measured by PFGNMR, including the calculation of apparent molecular mass, are also discussed.     

A method for measuring sedimentation and diffusion of macromolecules in capillary tubes by total intensity and quasi-elastic light-scattering techniques.

Light scattered from a macromolecular solution in a capillary tube is used to determine both the sedimentation and translational diffusion coefficients. The capillary tube is spun in a preparative centrifuge, removed, and placed in a light-scattering photometer equipped with a scanning mechanism. The intensity distribution of scattered light along the tube represents the concentration profile in the tube and provides the measure of boundary migration. The sedimentation coefficient is determined from this measure and the applied centrifugal field. The diffusion coefficient is obtained from a time-autocorrelation analysis of fluctuations in intensity of light scattered from any fixed point of the profile. These coefficients were obtained for two monodisperse systems, R17 bacteriophage and 28s ribosomal rat liver RNA. The molecular weights obtained from ratios of these coefficients are in good agreement with literature values. In the sedimentation analysis, deviations from linearity between boundary displacement and applied field were found to be less than 1%. This precision confirms that the boundary is stable for the capillary geometry even in the absence of a preformed density gradient. The sedimentation coefficients of identical samples were also measured with the Spinco Model E analytical ultracentrifuge; results of the two methods agree to within 4%. As a consequence of the capillary tube geometry and light-scattering detection, sedimentation coefficients can be obtained from sample volumes of less than 100 μl. This detection techniques is thus far demonstrated to be at least an order of magnitude more sensitive than Schlieren optics, thereby useful when uv absorption is not applicable. For diffusion measurements there are also several inherent advantages. The diffusion coefficient is obtained from the identical sample, and scanning provides the capability to measure D from various parts of the sedimentation profiles and thereby directly explore concentration dependence, homogeneity, and integrity of the sample. The capillary tube with a layer of silicone oil over the sample and centrifugation provides an effective method to cleanse the solution and trap all dust.     

Preparation of subtilisin BPN' and dextran conjugates

The conditions for subtilishine BPN' binding with bromocyanogen activated dextranes have been selected. The dependence of the enzyme activity and stability from pH and temperature levels has been studied. The stability of a modified enzyme during storage in solution is increased as compared with that of the native enzyme due to a decrease in the autolysis rate. On the basis of diffusion coefficients and sedimentation constants of conjugates, absolute values of their molecular weights have been computed.     

Band centrifugation of macromolecules in self-generating density gradients. II. Sedimentation and diffusion of macromolecules in bands

Three approaches to the simultaneous sedimentation and diffusion of hands or zones of noninteracting homogeneous macromolecules are examined: (1) The authors' method of moments: (2) the transport me of Sehumaker and Rosenbloom; and (3) the stochastic solution of the Lamm equation due to Gehatia and Katehalski. All three methods indicate that the motion of the maximum of the hand may be used to evaluate the sedimentation coefficient. The moment, method provides relations which appear to be useful for measuring diffusion coefficients. Relations are given for the analysis of resolved components. The problem of measuring sedimentation coefficients of macromolecules with concentration-dependent sedimentation coefficients is examined. Methods are described for evaluating the sedimentation coefficient in these systems and for obtaining the sedimentation coefficient at infinite dilution. Methods are described for determining the weight-average sedimentation coefficient in Multi-component systems, and the differential and integral distribution of sedimentation coefficients of macromolecules with low-diffusion coefficients.     

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.     

Fractionation of a hyaluronic acid preparation in a density gradient. Some properties of the hyaluronic acid

1. Hyaluronic acid was isolated from ox synovial fluid by sedimentation equilibrium in a caesium chloride density gradient (Silpananta, Dunstone & Ogston, 1967). The product was almost free from chondroitin sulphate and from protein. 2. Its composition did not differ significantly from that of the carbohydrate part of the protein-containing material isolated by filtration. Its physicochemical properties and molecular configuration were similar, except for its viscosity, which showed markedly reduced concentration-dependence and shear-dependence. This suggests that the associated protein tends to form links between molecules of hyaluronic acid. 3. The accurate measurement of viscosity at very low velocity gradient, by use of the damping of oscillations in a Couette viscometer, is described. 4. A method is described for measuring, approximately, the thermodynamic non-ideality of a solute from the shape of its schlieren curve at sedimentation equilibrium in a density gradient. 5. A value for the partial specific volume of hyaluronic acid in dilute salt solution was calculated from its isopycnic density in a caesium chloride gradient.     

Band centrifugation of macromolecules in self-generating density gradients. III. Conditions for convection-free band sedimentation

The conditions for convection-free hand sedimentation are analyzed in terms of the negative density gradients associated with the leading edge of a band and the positive density gradients generated during the experiment. The amount of material necessary to perform a band-centrifugation experiment depends on the diffusion coefficient of the macromolecules, which determines the rate at which the concentration at band maximum decreases, and on the extinction coefficient at the wavelength of observation. The maximum negative gradients in bands of macromolecules with diffusion and extinction coefficients typical of proteins, nucleic acids, and viruses are calculated. Positive density gradients generated by diffusion of small molecules between the thin lamella and the bulk solution are calculated for bulk solutions such us 1M NaCl or 95% D₂O. These “diffusion gradients” are generally adequate to stabilize bands of the above macromolecules. Positive density gradients generated by sedimentation of salts within the bulk solution may be significant in providing stability near the bottom of the cell. The effects of inadequate stabilizing gradients are discussed, and are found to cause forward spreading of the band.     

Size-distribution analysis of macromolecules by sedimentation velocity ultracentrifugation and lamm equation modeling

A new method for the size-distribution analysis of polymers by sedimentation velocity analytical ultracentrifugation is described. It exploits the ability of Lamm equation modeling to discriminate between the spreading of the sedimentation boundary arising from sample heterogeneity and from diffusion. Finite element solutions of the Lamm equation for a large number of discrete noninteracting species are combined with maximum entropy regularization to represent a continuous size-distribution. As in the program CONTIN, the parameter governing the regularization constraint is adjusted by variance analysis to a predefined confidence level. Estimates of the partial specific volume and the frictional ratio of the macromolecules are used to calculate the diffusion coefficients, resulting in relatively high-resolution sedimentation coefficient distributions c(s) or molar mass distributions c(M). It can be applied to interference optical data that exhibit systematic noise components, and it does not require solution or solvent plateaus to be established. More details on the size-distribution can be obtained than from van Holde-Weischet analysis. The sensitivity to the values of the regularization parameter and to the shape parameters is explored with the help of simulated sedimentation data of discrete and continuous model size distributions, and by applications to experimental data of continuous and discrete protein mixtures.     

The use of sedimentation coefficients to distinguish between models for protein oligomers.

The sedimentation coefficients of proteins are dependent on their sizes, shapes and densities and on the density and viscosity of the solvent. However, when the sedimentation coefficients of an oligomeric protein and its protomer are measured under the same experimental conditions, the ratio of the two coefficients depends only on the protomer shape and the mode of aggregation. This property, which we shall call the sedimentation ratio, therefore provides a way of distinguishing between models for oligomeric proteins. To allow examination of the behaviour of the sedimentation ratio, sedimentation coefficients are calculated for a comprehensive range of protomer shapes and modes of aggregation in hexameric systems using equations derived by Kirkwood. As illustrations of the method the resulting sedimentation ratios are compared with experimental values for insulin and arthroped hemocyanin, which eliminates many of the possible structures for these proteins. When experimental estimates of degree of hydration and molecular dimensions are also considered, all but a group of virtually identical structures are eliminated for the insulin hexamer and a single most likely structure remains for arthropod hemocyanin. The insulin structure is in good agreement with that determined by X-ray crystallography while the hemocyanin hexameric structure is a hexagonal prism formed by the cyclic aggregation of prolate ellipsoids of axial ratio about 2.5 : 1.     

Distribution and diffusion of solutes in articular cartilage

An experimental study was made on the distribution of solutes between articular cartilage and external solution, and on their diffusivity in cartilage. The solutes were classed as small ions, small uncharged molecules, and uncharged molecules of increasing size ranging from glucose to hemoglobin. The distribution of sodium and chloride ions obeys the Donnan equilibrium when cartilage is equilibrated in physiological saline solution. However, in cartilage immersed in dilute solution the concentration of chloride ions is higher than predicted. This is probably due to the presence in cartilage of some microscopic regions depleted of mucopolysaccharide in which the Donnan exclusion does not operate. The molal distribution coefficients of small uncharged molecules like urea are close to unity, which indicates that all water in cartilage seems to behave as solvent water. For larger molecules the distribution as well as the diffusion coefficients decrease with increase in molecular weight and are very sensitive to variations in fixed charge density. The results have been interpreted on the basis of the “steric exclusion” principle. The largest molecules which can penetrate into cartilage are of the size of the hemoglobin molecule.