Frictional coefficients of multisubunit structures. I. Theory

The theory of Kirkwood for the translational frictional coefficients of structures composed of subunits has been generalized in two ways in order to consider aggregates of nonidentical subunits. One of these generalizations fails when the sizes of subunits are too disparate; the other, derived from a surface shell distribution of frictional elements, is effective over the whole range of relative sizes. It is shown that, in the limit of a continuous surface distribution, a shell model reproduces Stoke's law for a sphere. Comparison is made between the frictional coefficients of spheres, ellipsoids, and rods modeled by finite numbers of subunits and by continuous shells of frictional elements, and those calculated from other theories. Agreement is generally good, though the shell model for prolate ellipsoids of revolution deviates by a few per cent from the Perrin value.     

Hydrodynamics of macromolecular complexes. III. Bacterial viruses

We have calculated the translational and rotational frictional coefficients of structures related to T2 and T4 bacteriophage, using the theoretical framework developed in the preceding two papers. The structures considered were models for tail-fiberless phage, and for whole phage with fibers in the extended and retracted portions. We also computed and compared with the experiment the changes in translational frictional coefficient produced by successive addition of 1–6 fibers to the fiberless particle. Agreement with experimental results is markedly improved over previous theoretical efforts, especially with respect to the effect of tail-fiber extension. Some significant discrepancies remain, however, in the comparison of fiber-retracted and fiberless phage.     

Structural and enzymatic studies of the T4 DNA replication system. I. Physical characterization of the polymerase accessory protein complex

In this study, we have investigated the structural and physical properties of the bacteriophage T4 DNA polymerase accessory proteins. We find that T4 gene 44 and 62 proteins associate to form a tight, highly homogeneous complex, containing four gene 44 protein subunits and one gene 62 protein subunit. The molecular mass of the complex is 163,700 daltons. Sedimentation results suggest that the complex is quite asymmetric, with a prolate ellipsoid axial ratio of about 5:1. This protein complex is known to carry a DNA-dependent ATPase activity; we show by photoaffinity labeling that the ATP-binding sites reside in the gene 44 protein subunits of the complex. Equilibrium sedimentation and chemical cross-linking studies indicate that the T4 gene 45 protein self-associates to form a trimer in solution. This trimer species also appears to be quite asymmetric, showing an axial ratio for a prolate ellipsoid of about 6:1, assuming normal hydration.     

Low angle light scattering studies on whole, half, and quarter molecules of T2 bacteriophage DNA.

Static light scattering measurements have been made at angles as low as 8 degrees on whole, half, and quarter molecules of native, T2 bacteriophage DNA in 0.195 M Na+. The fragments were obtained by high-speed stirring of the native DNA, and fractionated on methylated-albumin-kieselguhr columns. Accompanying measurements of sedimentation coefficients and intrinsic viscosities were made. Because linear extrapolations of light scattering data above 8 degrees for these samples were suspect, the measurements were analyzed by fitting curves calculated from the theory of wormlike coils to experimental curves at c = 0. Results showed that the excluded volume parameter, epsilon, must be used in analyzing the scattering curves; a reasonable value of epsilon was 0.08, in agreement with that found for T7 DNA (Harpst, J. A. 1980. Biophys. Chem. 11:295-302). The persistence length of all three DNAs in this paper was 50 +/- 5 nm, showed no dependence on molecular weight, but was somewhat below that reported previously for T7 DNA (60 nm). Theoretical curves calculated with the preceding parameters had a clear upward curvature in scattering envelopes below 8 degrees for quarter and half molecules, but such curvature was minimal for whole T2 DNA, so that linear extrapolations of experimental data above 8 degrees gave a molecular weight and root-mean-square radius which were nearly the same as those from theory. The molecular weight and radius for whole T2, derived from the comparison of theory and experiment, were 115 X 10(6) and 1,224 nm, respectively. The measurements on T2 DNA were clearly at the upper limit of current techniques.     

Subunits of the alkaline phosphatase of Bacillus licheniformis: chemical, physicochemical, and dissociation studies.

The alkaline phosphatase (orthophosphoric monoester phosphydrolase, EC 3.1.3.1) of Bacillus licheniformis MC14 was studied in an attempt to determine the number of subunits contained in the 120,000-molecular-weight native enzyme. Two moles of arginine was liberated per mole of native enzyme by carboxypeptidases A and B in the presence of sodium dodecyl sulfate. The effect on the native enzyme of progressively lowering the solvent buffer pH was monitored by determining the molecular weight by sedimentation equilibrium analysis, the sedimentation coefficient, the frictional coefficient, and the percent alpha-helix content of the enzyme. The alkaline phosphatase dissociates into two subunits around pH 4. At pH 2.8 a further decrease in S value, but no change in molecular weight, is observed, indicating a change in conformation. The frictional coefficients and percent alpha-helix content agree with this interpretation. A subunit molecular weight of 59,000 was calculated from sodium dodecyl sulfate gels.     

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.     

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.     

Hydrodynamic properties of macromolecular complexes. I. Translation

We have developed an improved theory for calculating the translational frictional coefficients of rigid macromolecular complexes composed of unequal spherical subunits. The Yamakawa hydrodynamic interaction tensor, which improves on the Oseen tensor by taking account of the finite sizes of the frictional subunits, has been generalized to accomodate nonidentical subunits. Iterative numerical methods are described for solving the set of simultaneous hydrodynamic interaction equations, thus avoiding preaveraging. The theory is applied to prolate ellipsoids of revolution, to lollipops, and to dumbbells, and comparison is made with earlier, more approximate theories.     

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.     

Physicochemical characterization of Rhesus low density lipoproteins.

The serum low density lipoprotein (LDL; p 1.019-1.050 g/ml) of the normal Macaca mulatta monkey (rhesus), kept on a low-fat Purina primate chow diet, was isolated by ultracentrifugal flotation, and its physicochemical properties were compared with those previously reported for human LDL. Rhesus LDL was found to be chemically similar to human LDL. The values for the sedimentation (S25, w-O) and diffusion (D25,w-O) coefficients were 7.09 S and 2.50 times 10- minus-7 cm-2 sec- minus-1, respectively. The intrinsic viscosity was 3.40 ml g- minus-1. The partial specific volume of rhesus LDL, determined in an Anton Paar precision density meter, was 0.960 ml g- minus-1. Molecular weights, calculated from a combination of S-O and D-O and of S-O and [n], were in agreement with the weight-average molecular weight, Mw, of 2.29 times 10-6 obtained by high-speed sedimentation equilibrium. In addition, a Z-average molecular weight, Mz, of 2.73 times 10-6 was calculated because curvature in the graphs of log c vs. r-2 indicated that rhesus LDL was heterogeneous. From the frictional ratio of 1.02, a maximum hydration of 0.1 g of H2O/g of lipoprotein was obtained. On electron micrographs, rhesus LDL appeared spherical with a mean diameter of 196 A, which was substantiated by hydrodynamic analysis.     

Buoyant density sedimentation of macromolecules in sodium iothalamate density gradients.

Nucleic acids, bacteriophages, phage capsids, and a DNA-capsid complex have been centrifuged to an equilibrium buoyant density in sodium iothalamate density gradients. Nucleic acids have comparatively high hydrations and are less dense than proteins in these gradients. Sodium iothalamate gradients can be used to separate DNA from RNA, single-chain DNA from double-chain DNA and to separate bacteriophage T7 and λ deletion mutants from the respective wild-type phage.The DNA packaged in bacteriophage T7 appears to be less hydrated than free DNA in sodium iothalamate gradients. There is evidence that the hydration of DNA packaged in phage T7 is restricted by the volume of the phage head. The total volume of phage T7 was estimated to be 1.32 × 10⁻¹⁶ ml. The volume available to package phage T7 DNA was estimated to be 2.2 times the volume of the B form of T7 DNA.     

Effect of centrifuge speed on the sedimentation of high-molecular-weight bacteriophage G DNA

Large molecular weight bacteriophage G DNA, about five times larger than T2 DNA, was used to test Zimm's theory [(1974) Biophys. Chem. 1 , 279–291] for the effect of rotor speed on the sedimentation of large linear monodisperse DNA. Sedimentation profiles from neutral sucrose gradinets at low and high rotor speeds show G DNA sedimenting from 1.8 to 0.7 times as fast as T2 DNA. Experimental measurements indicate that the sedimentation coefficient of G DNA decreases with increasing rotor speed about as fast as predicted by theory.     

Physical characterization of lumazine proteins from Photobacterium

The physicochemical properties of Photobacterium lumazine proteins have been investigated. The molecular weights obtained by several physical techniques are in good agreement, and the averages are 2% and 8% higher than the minimum molecular weights from amino acid and ligand content. The average molecular weights, sedimentation coefficients, and molecular radii are respectively the following: Photobacterium leiognathi lumazine protein, 21 200 +/- 300, 2.18 S, and 22.9 A; Photobacterium phosphoreum lumazine protein, 21 300 +/- 500, 2.16 S, and 23.0 A. The hydrations of the lumazine proteins, estimated in several ways, indicate less hydration for P. leiognathi than for P. phosphoreum. The frictional ratios corrected for hydration give axial ratios less than 1.3 for both lumazine proteins. These values agree with those obtained by a combination of rotational and translational frictional parameters and elimination of the common hydrated volume terms. There is insufficient area on the exterior surface to accommodate hydration when the lumzine proteins are considered as smooth-surfaced ellipsoids. The required surface area can be accommodated however by surface roughness with a minimum of 30% internal water.     

Use of difference boundary sedimentation velocity to investigate nonspecific protein-nucleic acid interactions

The difference boundary sedimentation velocity technique of Schachman and co-workers is demonstrated to be applicalbe to the measurement of binding constants (Kobsd) in the range 10(2)-10(5) M(-1) for the nonspecific interactions of proteins with DNA. The difference technique can reproducibly detect a 2% change in the sedimentation coefficient of the DNA upon binding ligands, corresponding to average extents of association as low as 10 molecules of protein (in the cases of Escherichia coli lac repressor and E. coli RNA polymerase) per molecule of bacteriophage T7 DNA. At these low binding densities, it is plausible to assume that the primary effect of ligand binding is on the buoyant mass of the complex and not on the frictional coefficient of the flexible DNA coil. Binding constants calculated by using this assumption agree well with literature values for the nonspecific interactions of RNase and lac repressor proteins with double-stranded DNA. Advantages of the method are that it is relatively rapid, requires the optical detection of the DNA only, and can be performed on small amounts of sample. The method appears useful for surveying (to an accuracy of +/-50% in Kobsd or +/-10% in log Kobsd) the effects of solution variables on Kobsd of protein-DNA interactions. Applications of the method to the nonspecific interactions of RNA polymerase core and holoenzymes with T7 DNA are discussed.     

Structure of initiation factor eIF-3 from rat liver. Hydrodynamic and electron microscopic investigations

On the basis of hydrodynamic, electron microscopic and biochemical investigations a new model of the structure of initiation factor eIF-3 is proposed. From sedimentation and diffusion coefficients of 16.35 S and 2.13 X 10(-7) cm2/s, respectively, as well as from sedimentation equilibrium measurements, a molecular mass of about 650 kDa was determined for isolated eIF-3. This is in agreement with molecular mass estimations by sodium dodecyl sulphate gel electrophoresis. A partial specific volume of 0.723 cm3/g was determined by means of the amino acid composition and the specific volume increments of the amino acids. From this value and from the molecular mass, a volume of 780 nm3 was calculated for eIF-3. In electron micrographs of isolated eIF-3, images with triangular profiles and side lengths of 14 nm, 16 nm, and 17 nm have been observed. Taking into account the calculated volume and considering the triangular image as one face of the particle, it is suggested that eIF-3 has the shape of a flat triangular prism with a height of about 7 nm and the above-mentioned side-lengths. This model is in agreement with results of electron microscopic investigations of eIF-3 in native small ribosomal subunits [Lutsch, G., Benndorf, R., Westermann, P., Bommer, U.-A. & Bielka, H. (1986) Eur. J. Cell Biol. 40/2, in press]. The high frictional ratio of about 1.7 also supports eIF-3 to be rather of a flat than of a globular shape.     

Light scattering and hydrodynamic properties of linear and circular bacteriophage lambda DNA

Low-angle light scattering, sedimentation velocity, and intrinsic viscosity measurements have been made on circular and linear forms of lambda (λ) bacteriophage DNA. Available equations, used to relate hydrodynamic parameters of both forms to the molecular weight, give relatively consistent values of particle weights which essentially agree with the light-scattering results. An average molecular weight of (34 ± 3) × 10⁶ for λ DNA was obtained in good agreement with literature values of (31–33) × 10⁶. The linear λ DNA has a larger root-mean-square radius than the circular molecule, when determined by light scattering, but the difference does not appear to be us large as expected from hydrodynamic data. The two forms also show significantly different angular distrbutions of scattered light intensities which agree only qualitatively with those derived from existing theory. The light-scattering results suggest that further experiments and modifications of available theories should be undertaken.     

Lambda-repressed mutants of bacteriophage T5. II. Physiological characterization.

Physiological properties of bacteriophage T5 gene A1 mutants, whose growth is inhibited in λ lysogens, and designated T5 lr, have been studied. In the presence of λ gene rex, which is responsible for lr growth inhibition, gene A1 product is synthesized and functional. However, several physiological defects were observed: phage DNA synthesis is inhibited; late phage-induced proteins are synthesized in markedly decreased amounts after a delay of about 15 minutes; phage DNA transfer into the host goes beyond the first-step transfer fragment but, in most bacteria, is interrupted after penetration of about 55% of the genome. Relationships between these different defects are discussed.     

Sedimentation behavior of chloroplast ribosomes from Chlamydomonas reinhardtii.

The identity of peaks generated by chloroplast ribosomes of Chlamydomonas reinhardtii were determined by zone velocity sedimentation on sucrose density gradients, and analysis of distribution of ribosomal RNAs in the gradients. The sedimentagion coefficient of the principal peak was 66-70 S (usually 69 S), in good agreement with previously reported values for chloroplast ribosomes of C. reinhardtii, and other organisms. The fast sedimenting side of the 69 S peak contained an excess of chloroplast large subunit. When ribosome dissociation was prevented by sedimentation at low velocity, by aldehyde fixation, or by the presence of nascent polypeptide chains, the principal peak had a sedimentation coefficient of about 75 S. Thus the 69 S peak was an artifact caused by dissociation during centrifugation. Peaks that contained chloroplast ribosomal RNAs were also observed at '60 S' and '45 S' when chloroplast ribosomes were centrifuged unfixed at high velocity. The amounts of '60 S' and '45 S' components were decreased by centrifugation at low speed, or fixation, but sedimentation coefficients remained unchanged. The '60 S', and '45 S' components were identified as large, and small subunits of chloroplast ribosomes, respectively. The artifacts produced by centrifugation of chloroplast ribosomes, are similar to the artifacts produced by centrifuging ribosomes of Escherichia coli. Similar explanations appear to apply to both. We concluded that the 69 S chloroplast ribosome peak occurs because of dissociation of 'tight' couples, and incomplete separation of subunits. Subunit peaks (60 S and 45 S) arise from free subunits, and/or from dissociation of 'loose' couples.     

Hydrodynamic theory of swimming of flagellated microorganisms.

A theory of the type commonly used in polymer hydrodynamics is developed to calculate swimming properties of flagellated microorganisms. The overall shape of the particle is modeled as an array of spherical beads which act, at the same time, as frictional elements. The fluid velocity field is obtained as a function of the forces acting at each bead through Oseen-type, hydrodynamic interaction tensors. From the force and torque equilibrium conditions, such quantities as swimming velocity, angular velocity, and efficiency can be calculated. Application is made to a spherical body propelled by a helical flagellum. A recent theory by Lighthill, and earlier formulations based on tangential and normal frictional coefficients of a curved cylinder, CT and CN, are analyzed along with our theory. Although all the theories predict similar qualitative characteristics, such as optimal efficiency and the effect of fluid viscosity, they lead to rather different numerical values. In agreement with Lighthill, we found the formalisms based on CN and CT coefficients to be somewhat inaccurate, and head-flagellum interactions are shown to play an important role.     

Hydrodynamic properties of macromolecular complexes. V. Improved calculation of rotational diffusion coefficient and intrinsic viscosity

In our previous calculations of rotational diffusion coefficients and intrinsic viscosities of macromolecular complexes modeled by arrays of spherical subunits [J. G. de la Torre & V. A. Bloomfield, Biopolymers 16 , 1765, 1779 (1977); 17 , 1605 (1978)], results were poor when the dominant subunit was located near the center of frictional resistance. A simple means of correcting this flaw, which gives satisfactorily accurate results with little increase in computation time, is to replace the single large subunit with an array of smaller ones. We have examined trigonal bipyramidal, octahedral, and cubic arrays of spheres whose radii were chosen to give the same total volume or the same rotational diffusion coefficient as the parent sphere. These all give similar results, so the details of the modeling are not important. Results obtained using this stratagem are in much better agreement with the theories of Perrin and Simha for short prolate ellipsoids of revolution, and with experimental measurements of rotational diffusion coefficients of T-even bacteriophage without fibers or with fibers retracted. We have also extended our previous calculations to consider phage with various numbers of fibers attached.