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.     

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.     

Sedimentation Analysis of DNA from Irradiated and Unirradiated L Cells

DNA, released from unirradiated mouse L-cells gently lysed in a thin layer of 2% sucrose on top of an alkaline sucrose gradient, was found to sediment in a narrow band with a sedimentation coefficient of about 500S. Exposure of cells to increasing doses of X-rays (89-712 rads) continuously reduced the DNA sedimentation velocity until, after about 890 rads, the DNA appeared in a narrow peak with a sedimentation coefficient of approximately 180S. As the dose given to cells was increased beyond 890 rads, the sedimentation coefficient of the DNA released continued to decrease and the sedimentation profiles now broadened in a manner consistent with the random production of single-strand breaks in the DNA. The DNA released from unirradiated cells (500S) is thought to be loosely aggregated and only partially single stranded. It is presumed that cells exposed to low doses of radiation release DNA with marked reductions in sedimentation coefficient because single-strand breaks produced in the DNA aid the alkaline denaturation process. By using the system to be described, it has been possible to demonstrate DNA repair (rejoining of X-ray-induced single-strand breaks) during postirradiation incubation of cells given doses as low as 400 rads.     

Interpretation of thermodynamic non-ideality in sedimentation equilibrium experiments on proteins

This investigation re-examines theoretical aspects of the allowance for effects of thermodynamic non-ideality on the sedimentation equilibrium distribution for a single macromolecular solute, and thereby resolves the question of the constraints that pertain to the definition of the activity coefficient term in the basic sedimentation equilibrium expression. Sedimentation equilibrium results for ovalbumin are then presented to illustrate a simple procedure for evaluating the net charge (valence) of a protein from the magnitude of the second virial coefficient in situations where the effective radius of the protein can be assigned. Finally, published sedimentation equilibrium results on lysozyme are reanalysed to demonstrate the feasibility of employing the dependence of the second virial coefficient upon ionic strength to evaluate both the valence and the effective radius of the non-interacting solute.     

Boar acrosin, II: Amino acid composition, amino terminal residue and molecular weight estimations by ultracentrifugation.

The molecular weight of boar acrosin in neutral solution was estimated to be 41000 +/- 1000 by high-speed sedimentation equilibrium analysis. This result is in good agreement with the value found earlier[1] by sodium dodecylsulfate polyacrylamide gel electrophoresis. The sedimentation coefficeint of acrosin obtained by active enzyme centrifugation of partly purified preparations is in accordance with the sedimentation coefficient of the pure preparation estimated by conventional sedimentation velocity analysis. The sedimentation coefficient of acrosin is considerably decreased in slightly acidic solution (pH 4), indicating that changes in the tertiary structure occur upon acidification. The amino acid composition of the acrosin preparation homogeneous by electrophoretic and chromatographic criteria and in sedimentation studies was determined. Valine was found as the unique N-terminal amino acid. However, in microheterogeneous forms of acrosin, alanine and methionine were also detected in end group analysis.     

Turbidimetric ultracentrifugation. Application to the study of human serum very low density lipoprotein distributions.

In this communication it is shown that the sedimentation coefficient distribution may be accurately measured for very large particles using turbidimetric techniques and the ultraviolet-scanning analytical ultracentrifuge. A principal advantage is that turbidity is a function of the product of concentration and molecular weight; thus, large particles may be observed even when present in very small amounts. We propose to call this method of analysis "turbidimetric ultracentrifugation." We have used turbidimetric ultracentrifugation ot determine the sedimentation coefficient distribution for a sample of human serum very low density lipoproteins. This distribution is compared to that found with conventional schlieren techniques with good agreement.     

Sedimentation coefficient of polyoma virus DNA

The sedimentation coefficient of the twisted circular form of polyoma virus DNA is calculated from the Kirkwood sedimentation–diffusion equation, the structure being assumed to be a rigid double superhelix. Agreement with the experimental sedimentation coefficient can be obtained, with the use of an experimental value for the number of superhelical turns, when the pitch of the superhelix is intermediate between its minimal and maximal possible values. Another model, which has been proposed for polyoma DNA at low ionic strengths, may be visualized as a superhelical structure wound about a torus. Calculations of sedimentation coefficients for this model agree qualitatively with experimental data at ionic strengths Below 10^?2M.     

Kinetics of sedimentation in a density gradient

Two models of sedimentation in a density gradient are analyzed. The first is for sedimentation in cylindrical sector geometry and contains the assumption that diffusion can be neglected. The second treats sedimentation in a rectangular field and includes diffusion, although the boundaries are not treated exactly. In both of these models we approximate the time dependence of the gradient by a relaxation form. We derive exact results for both models. It is also shown that the sedimentation coefficient can be calculated from data by following the motion of the position of the maximum (or minimum) of the concentration gradient.     

Determination of Some Molecular Parameters of Tyrosine Hydroxylase From Rat Adrenal, Rat Striatum, and Human Pheochromocytoma

The molecular parameters of tyrosine hydroxylase (EC 1.14.16.2) from rat adrenal, rat striatum, and human pheochromocytoma were determined by combined gel filtration and sucrose gradient ultracentrifugation. The enzyme from rat adrenal has a calculated molecular weight of 228,000, a Stokes radius of 60.9 A, a sedimentation coefficient of 9.10S, and a frictional ratio of 1.39. The enzyme from rat striatum has a calculated molecular weight of 210,000, a Stokes radius of 54.3 A, a sedimentation coefficient of 9.38S, and a frictional ratio of 1.28. Tyrosine hydroxylase from human pheochromocytoma tissue has a calculated molecular weight of 255,000, a Stokes radius of 68.2 A, a sedimentation coefficient of 9.08S, and a frictional ratio of 1.50. These results indicate that the tyrosine hydroxylases from central and peripheral tissue in the rat are quite similar although the human enzyme appears to be significantly larger.     

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.     

Improved methods for fitting sedimentation coefficient distributions derived by time-derivative techniques

Time-derivative approaches to analyzing sedimentation velocity data have proven to be highly successful and have now been used routinely for more than a decade. For samples containing a small number of noninteracting species, the sedimentation coefficient distribution function, g(s *), traditionally has been fitted by Gaussian functions to derive the concentration, sedimentation coefficient, and diffusion coefficient of each species. However, the accuracy obtained by that approach is limited, even for noise-free data, and becomes even more compromised as more scans are included in the analysis to improve the signal/noise ratio (because the time span of the data becomes too large). Two new methods are described to correct for the effects of long time spans: one approach that uses a Taylor series expansion to correct the theoretical function and a second approach that creates theoretical g(s *) curves from Lamm equation models of the boundaries. With this second approach, the accuracy of the fitted parameters is approximately 0.1% and becomes essentially independent of the time span; therefore, it is possible to obtain much higher signal/noise when needed. This second approach is also compared with other current methods of analyzing sedimentation velocity data.     

Evaluation of diffusion coefficients by means of an approximate steady-state condition in sedimentation velocity distributions

This investigation examined the feasibility of manipulating the rotor speed in sedimentation velocity experiments to spontaneously generate an approximate steady-state condition where the extent of diffusional spreading is matched exactly by the boundary sharpening arising from negative s–c dependence. Simulated sedimentation velocity distributions based on the sedimentation characteristics for a purified mucin preparation were used to illustrate a simple procedure for determining the diffusion coefficient from such steady-state distributions in situations where the concentration dependence of the sedimentation coefficient, s = s⁰/(1 + Kc), was quantified in terms of the limiting sedimentation coefficient as c → 0 (s⁰) and the concentration coefficient (K). Those simulations established that spontaneous generation of the approximate steady state could well be a feature of sedimentation velocity distributions for many unstructured polymer systems because the requirement that Kc_oω²s⁰/D be between 46 and 183 cm⁻² is not unduly restrictive. Although spontaneous generation of the approximate steady state is also a theoretical prediction for structured macromolecular solutes exhibiting linear concentration dependence of the sedimentation coefficient, s = s⁰(1 − kc), the required value of k is far too large for any practical advantage to be taken of this approach with globular proteins.     

Binding Stoichiometry of the Gene 32 Protein of Phage T4 in the Complex with Single Stranded DNA Deduced from Boundary Sedimentation

Abstract

Short 145 base DNA fragments in complex with the helix destabilizing protein of bacteriophage T4, GP32, have been studied with boundary sedimentation. The sedimentation coefficient was determined as a function of concentration, protein-nucleic acid ratio, temperature and salt concentration. It can be concluded that the measured values reflect the properties of the saturated DNA-GP32 complex. A combination of the earlier obtained translational diffusion coefficient of the complex with the sedimentation coefficient yields its anhydrous molecular weight (M_w = 5.4 · 10^s D), which corresponds to a size of the binding site of 10 nucleotides per protein. This procedure is not sensitive to the presence of non-binding protein molecules and to the assumed protein concentration, and therefore, it seems more reliable than a determination from titration experiments.

Similar sedimentation measurements were performed with tRNA-complexes containing 76 nucleotides. The translational diffusion coefficient can be calculated from the measured rotational diffusion coefficient and assuming the same hydrodynamic diameter for this complex as obtained for the 145 b DNA complex. The molecular weight derived from the data then also leads to a binding site size of about 10 nucleotides. This suggests that also the short tRNA-complex forms an open, strongly solvated structure, as was proposed for the 145 b DNA-GP32 complex.     

Nonequivalence of second virial coefficients from sedimentation equilibrium and static light scattering studies of protein solutions

Experimental data for ovalbumin and lysozyme are presented to highlight the nonequivalence of second virial coefficients obtained for proteins by sedimentation equilibrium and light scattering. Theoretical considerations confirm that the quantity deduced from sedimentation equilibrium distributions is B(22), the osmotic second virial coefficient describing thermodynamic nonideality arising solely from protein self-interaction. On the other hand, the virial coefficient determined by light scattering is shown to reflect the combined contributions of protein-protein and protein-buffer interactions to thermodynamic nonideality of the protein solution. Misidentification of the light scattering parameter as B(22) accounts for published reports of negative osmotic second virial coefficients as indicators of conditions conducive to protein crystal growth. Finally, textbook assertions about the equivalence of second virial coefficients obtained by sedimentation equilibrium and light scattering reflect the restriction of consideration to single-solute systems. Although sedimentation equilibrium distributions for buffered protein solutions are, indeed, amenable to interpretation in such terms, the same situation does not apply to light scattering measurements because buffer constituents cannot be regarded as part of the solvent: instead they must be treated as non-scattering cosolutes.     

Physico-chemical and serological study of agglutinogen 3 of B. pertussis]

Results of immunoelectrophoresis, gel-filtration and sedimentation analysis showed the preparation of agglutinogen 3 of B. pertussis to be homogenous. The principal physico-chemical characteristics of agglutinogen 3 (sedimentation constant, diffusion coefficient, molecular weight) were determined.     

Streptolysin O: Sedimentation Coefficient and Molecular Weight Determinations

The sedimentation coefficient of streptolysin O as determined by sucrose density gradient ultracentrifugation is 3.7S. An approximate molecular weight of 60,500 was calculated from the sedimentation velocity, and a similar value was obtained by Sephadex gel filtration. There was no measurable difference in the sedimentation coefficient of streptolysin O in either the active or reversibly inactive forms, indicating that there were at most only minor conformational differences between the two forms.     

Haemoglobin from the tadpole shrimp, Lepidurus apus lubbocki Characterization of the molecule and determination of the number of polypeptide chains.

Haemoglobin from the tadpole shrimp, Lepidurus apus lubbocki, was found to have a sedimentation coefficient (s020,w) of 19.3 +/- 0.2 S and a molecular weight, as determined by sedimentation equilibrium, of 798000 +/- 20000. The amino acid composition showed the lack of cysteine and cystine residues. A haem content of 3.55 +/- 0.03% was determined, corresponding to a minimal mol.wt. of 17400 +/- 200. The pH-independence in the range pH 5-11 of the sedimentation coefficient indicates a relatively high stability of the native molecule. Sodium dodecyl sulphate/polyacrylamide-gel electrophoresis gave one band with mobility corresponding to a mol.wt. of 34000 +/- 1500. The molecular weight of the polypeptide chain was determined to be 32800 +/- 800 by sedimentation equilibrium in 6 M-guanidinium chloride and 0.1 M-2-mercaptoethanol. The findings indicate that Lepidurus haemoglobin is composed of 24 identical polypeptide chains, carrying two haem groups each.     

A specific binding protein for 17beta-estradiol in retired breeder rat ventral prostate

A specific binding protein for 17β-estradiol has been detected in ventral prostate of normal retired breeder rats using sucrose density gradient techniques. The protein has an approximate sedimentation coefficient of 3. 5S. It is distinguishable from serum proteins which bind 17β-estradiol on the basis of binding specificity and sedimentation coefficient. It is also distinct from the cytoplasmic androgen binding protein known to be present in rat ventral prostate.     

Molecular weight determination of glyoxalated RNA by sedimentation centrifugation

A rapid, reliable sedimentation centrifugation technique has been developed to measure the molecular weights of rather large glyoxalated RNAs. A distinctive feature of this method is that the glyoxalated RNAs can be analyzed in sucrose gradients containing no denaturant. This feature allowed us to compute the sedimentation coefficients of glyoxalated RNAs by a comparison with those of native, untreated RNA markers. These values then were used to obtain accurate molecular weight estimates by applying the linear log-log relation between the molecular weight of an RNA and its sedimentation coefficient.