Physicochemical studies on xylinan (acetan). III. Hydrodynamic characterization by analytical ultracentrifugation and dynamic light scattering

A laboratory-made sample of the polysaccharide xylinan (acetan) has been further characterized with respect to (i) purity, (ii) molar mass and polydispersity, and (iii) gross conformation by a combination of hydrodynamic measurements (sedimentation velocity and equilibrium analytical ultracentrifugation, viscometry, and dynamic light scattering) in aqueous NaCl (I = 0.10 mol·L⁻¹). Sedimentation velocity diagrams recorded using Schlieren optics revealed highly pure material sedimenting as a single boundary [s^o_20.w = 9.5 ± 0.7) S; k_s = (273 ± 112) mL/g]. The hypersharp nature of these boundaries is symptomatic of a polydisperse and highly nonideal (in the thermodynamic sense) system. Low speed sedimentation equilibrium in the analytical ultracentrifuge using Rayleigh interference optics and two different types of extrapolation procedure (involving point and whole-cell molar masses) gave a weight average molar mass M_w of (2.5 ± 0.5) × 10⁻⁶ g·mol⁻¹ and also a second virial coefficient, B = (2.8 ± 0.7) × 10⁻⁴ mL·mol·g⁻², both values in good agreement with those from light scattering-based procedures (Part II of this series). A dynamic Zimm plot from dynamic light scattering measurements gave a z-average translational diffusion coefficient D^o_20.w = (3.02 ± 0.05) × 10⁻⁸ cm²·s⁻¹ and the concentration-dependence parameter k_D = (370 ± 15) mL/g. Combination of s^o_20.w with D^o_20.w via the Svedberg equation gave another estimate for M_w of ≅ 2.4 × 10⁶ g/mol, again in good agreement. Both the Wales-van Holde ratio (k_s/[η]) ≅ 0.4 (with [η] = (760 ± 77) mL/g) and the ρ-parameter (ratio of the radius of gyration from static light scattering to the hydrodynamic radius from dynamic light scattering) as ρ > 2.0 all indicate an extended conformation for the macromolecules in solution. These findings, plus Rinde-type simulations of the sedimentation equilibrium data are all consistent with the interpretation in terms of a unimodal wormlike coil model performed earlier. © 1996 John Wiley & Sons, Inc.     

Structure of native proteoglycan aggregates from chick limb-bud chondrocytes

Laser light-scattering has been used to investigate the size of native proteoglycan aggregates (PGA-aA1) from day-8 chick limb-bud chondrocyte cultures isolated under associative extraction and purification conditions in 0.4M guanidinium chloride (GdnHCl) solution. Dynamic light-scattering measurements yielded a hydrodynamic radius, R_s, of 244 ± 10 nm for PGA-aA1 in 0.4M GdnHCl, and a weight-average molecular weight (M _w) of 150 ± 50 × 10⁶ was obtained from a Zimm plot. Disaggregation in 4.0M GdnHCl aqueous solution yielded proteoglycan subunits (PGS) with R_s = 39 ± 2 nm, M _w = 1.6 ± 0.3 × 10⁶, which reassembled in 0.4M GdnHCl to form “reconstituted native” aggregates (PGA-raA1) with R_s = 121 ± 6 nm, M _w = 17 ± 3 × 10⁶. A second specimen of PGA-aA1 had R_s = 192 ± 10 nm, M _w = 100 ± 10 × 10⁶. The latter value was estimated from an empirical relationship between M _w and R_s. After dissociation, this specimen reassembled to form PGA-raA1 with R_s = 85 ± 5 nm, M _w = 12 ± 1 × 10⁶. These data are compared with those for a specimen of reconstituted aggregate (PGA-A1) that had been extracted under dissociative conditions and then reaggregated by dialysis to 0.4M GdnHCl aqueous solution, for which R_s = 138 ± 9 nm, M _w = 45 ± 8 × 10⁶. From these values, we have calculated the weight-average number of subunits per aggregate N_w: 111 for PGA-aA1 and 12 for raA1 (70 and 7 for the second PGA-aA1 and PGA-raA1 specimen, respectively) as compared to 32 for PGA-A1. The numbers of subunits per aggregate were also determined from electron micrographs of spread specimens. The latter results show the same trends as those obtained by light scattering, but lead in each case to lower numbers of subunits per aggregate. These data demonstrate conclusively that PGA samples exhibit a higher degree of aggregation in solution than visualized in typical electron microscopy (EM) preparations, probably due to disaggregation during EM specimen preparation. Since N_w determined both by light scattering (LS) and by EM are larger for native versus reconstituted aggregate samples, our data point to a more compact aggregation of subunits along the hyaluronic acid (HA) chains in the former.     

Measurement of diffusion coefficient and electrophoretic mobility with a quasielastic light-scattering–band-electrophoresis apparatus

We have constructed an apparatus for the simultaneous measurement of electrophoretic mobility, μ, and diffusion coefficient, D, of macromolecules and cells. It combines band electrophoresis in a vertical, sucrose-gradient stabilized column, with quasielastic laser light-scattering determination of the diffusion coefficient of the species within the band. The entire electrophoresis cell is scanned through the laser beam of the quasielastic laser light-scattering apparatus by a vertical translation stage. Total intensity light-scattering measurement at each point in the cell gives the macromolecular concentration at that point. Solvent viscosity and electrical potential are measured at each point in the cell. Application of this apparatus to resealed red blood cell ghosts and to bovine hemoglobin indicates that measurements of field, viscosity, and migration distance are reliable, and that electroosmosis is insignificant. Application to T4D bacteriophage gives μ_20,w = (?1.05 ± 0.05) × 10^?4 cm²/V sec and D_20,w = (3.35 ± 0.10) × 10^?8 cm²/sec for fiberless particles, and μ_20,w = ?(0.59 ± 0.03) × 10^?4 cm²/V sec and D_20,w = (2.86 ± 0.09) × 10^?8 cm²/sec for whole phage with 6 fibers. Approximate analysis of these results with the Henry electrophoresis theory for spheres in dicates that each fiber contributes about 193 positive charges to the phage particle, compared with 327 from amino-acid analysis. The advantages and disadvantages of this apparatus, relative to conventional electrophoresis and to electrophoretic light scattering, are discussed.     

Dynamic light scattering from collagen solutions. I. Translational diffusion coefficient and aggregation effects

Solutions of native collagen extracted from rat tail tendons in neutral salt solution have been studied by dynamic light scattering. The spectra obtained are consistent with the presence in solution of both single rod-shaped collagen molecules and aggregates of molecules. No contribution to the spectrum has been detected at any scattering angle from rotational diffusion of single molecules, although a measurable broadening effect is expected at high angles. The translational diffusion coefficient D of single molecules, calculated from the broader spectral component, shows an anomalous dependence on collagen concentration with a maximum value of D_20,w = 8.6 ± 0.2 × 10^?12 m²/sec near the concentration 0.04% by weight. Above 0.05% D falls linearly with increasing concentration and takes the value D _20,w = 8.1 ± 0.2 × 10^?12 m²/sec at 0.064% collagen.     

Histone-induced conformational changes in DNA as probed by quasi-elastic light scattering.

Quasi-elastic light scattering as measured by intensity fluctuation (self-beat) spectroscopy in the time domain can be profitably used to follow both the translational diffusion D and the dominant internal flexing mode τ_int of DNA and its complexes with various histones in aqueous salt solutions. Without histones, DNA is found to have D = 1.6 × 10^?8 cm²/sec and τ_int ? 5 × 10^?4 sec in 0.8 M NaCl, 2 M urea at 20°C. Total histone as well as fraction F2A induce supercoiling (D = 2.6 × 10^?8 cm²/sec, τ_int ? 2.8 × 10^?4 sec) whereas fraction F1 induces uncoiling (D = 1.0 × 10^?8 cm²/sec, τ_int ? 9.4 × 10^?4 sec). Upon increasing the salt concentration to 1.5 M the DNA–histone complex dissociates (D = 1.8 × 10^?8 cm²/sec). Upon decreasing the salt concentration to far below 0.8 M, the DNA–histone complex eventually precipitates as a chromatin gel.     

Light scattering during the hysteresis effect in poly(A)·2poly(U)

Light-scattering studies on buffered aqueous solutions of the triple-stranded polyribonucleic acid poly(A)·2poly(U) were carried out at neutral pH and during titration. At pH 7.1 and 22°C, a sample of commercially available polymer in 0.005M phosphate buffer gave a Zimm plot which yielded values for the weight-average molecular weight, M _w, of 874,000 ± 1800 g/mol, a root-mean-square radius, ρ of 930 ± 22 Å, and a second viral coefficient of 0.51 ± 0.05 × 10 ^?3 cm³g^?1 mol. The light-scattering data were also analyzed by serval linear and nonlinear least-squares programs which were devised to determine the model (e.g., rod, coil, or zigzag) which could best describe the shape of the molecule. It was found that a rodlike model, perhaps with a few bends, was in best overall agreement with the data. The assumption that the molecule is a thin rod leads to a value for the linear density of 206 g mol^?1 Å^?1 and a translation of 3.3 Å per residue. These values are also in close agreement with those expected for a triple-stranded, thin, base-stacked molecule. During titration from neutral pH with 0.1M HCl, the observed apparent molecular weight slowly increased until at about pH 3.5 a sudden, large increase (about 30-fold) occurred. The root-mean-square radius, on the other hand, after an initial small decrease (of about 25%), also exhibited a large increase (about 4-fold). Upon back titration with 0.1M NaOH, the molecular parameters did not retrace the original path, but instead exhibited hysteresis—the M _w and ρ _z are both larger on the basic branch than on the acid branch at a corresponding pH. A plot of long ρ _z against log(M _w) during the interval in which the high-moelcular-weight form was present (below pH 3.5 on the acid branch, and on the basic branch) gave a straight line with a slope of ?. This suggests that the aggregates were composed of some tens of rather open radom coils, presumably of poly(A)·poly(A), and that the hysteresis may be caused under conditions by the metastability of the entangled coils.     

Light-scattering spectroscopic study of polysaccharide protein conjugate

By combining gel permeation chromatography (GPC) and light-scattering spectroscopy, including photon correlation and angular distribution of absolute scattered intensity, we were able to characterize immunologically active Haemophilus influenzae type b polysaccharide (HIB Ps) bovine serum albumin (BSA) conjugates in terms of equivalent hydrodynamic radius r_h ～ (6.2 ± 0.6) × 10² Å, apparent radius of gyration r_g ～ (5.4 ± 0.3) × 10² Å, apparent molecular weight M_w ～ (3.5 ± 0.4) × 10⁶ g/mol, and a second virial coefficient A₂ ～ (1.9 ± 0.3) × 10^?4 cm³ mol/g². We could study the effects of each of the processes in the conjugate formation according to the following procedure: BSA (dialysis, modification, fractionation) + HIB Ps → HIB Ps/BSA conjugate (conjugate formation, fractionation). Narrow distributions of HIB Ps BSA conjugate formation can be achieved using fractionated BSA.     

Total intensity light scattering from short,optically anisotropic wormlike chains

Simple exact equations are derived for intensity light scattering from optically anisotropic wormlike chains in the absence of excluded volume. The results are valid at low scattering angles (q² 〈R²_G〉 ? 1) for all sormilke chains from rigid rods to random couils. The present work and an earlier theory [Nagai, K. (1972) Polym. J. 3 , 67–83] appear to be equivalent, although they were both derived using different methods. The present work is primarily concerned with short wormlike chains, since intensity light scattering from short fragments may provide valuable information about DNA flexibility. By using the results of this work to reanalyze some older light-scattering studies [Godfrey, J. E. & Eisenberg, H. (1976) Biophys. Chem. 5 , 301–318], it is shown that anisotropy corrections to polarized light-scattering measurements have been overcorrected in the past. It can be anticipated that future light-scattering experiments will determine the base-pair anisotropy.     

Joining of bacteriophage T4D heads and tails: A kinetic study by inelastic light scattering

We have used inelastic laser light scattering to study the kinetics of the spontaneous assembly of heads and tails of bacteriophage T4D to form noninfectious tail fiberless particles. For interpretation of the kinetics, it was first necessary to determine the physical properties of the strongly scattering phage parts. For heads, these are D_{20,w = 3.60 × 10⁻⁸cm²/s, 820,w = 1025 S, M = 1.76 × 10⁸}. For tail fiberless particles, D_20,w = 3.14 × 10⁻⁸cm²/s, 8_20,w = 968 S, and M = 1.95 × 10⁸. The kinetics of the head-tail joining process was followed by measuring the time variation of the homodyne scattering autocorrelation function. This was interpreted as a sum of exponentials whose decay constants were known from the scattering angle and the diffusion coefficients, and whose amplitudes were related to the concentrations of reactants and products. Scattering experiments at 22 °C gave a bimolecular rate constant of 1.02 × 10⁷m⁻¹ s⁻¹, while infectivity assays at 30 °C gave a rate constant of 1.28 × 10⁷. Adjustment of both rate constants to 20 °C, assuming diffusion controlled reaction, gave 0.97 × 10⁷ and 0.98 × 10⁷m⁻¹ s⁻¹, respectively. This rate is about $\text{1}\text{500}$ that predicted by Smoluchowski theory for a diffusion controlled reaction between two spherical particles; the discrepancy is largely explicable from orientational factors.     

Translational diffusion coefficient of α-chymotrypsinogen A by laser-light-scattering spectroscopy

The translational diffusion coefficient of a pure sample of α-chymotrypsinogen A is measured by laser light scattering to give a value of D_20,w⁰ = (8.40 ± 0.15) × 10^?7 cm²/sec.     

Light scattering studies of supercoiled and nicked DNA

Static and dynamic light scattering measurements were made of solutions of pGem1a plasmids (3730 base pairs) in the relaxed circular (nicked) and supercoiled forms. The static structure factor and the spectrum of decay modes in the autocorrelation function were examined in order to determine the salient differences between the behaviors of nicked DNA and supercoiled DNA. The concentrations studied are within the dilute regime, which is to say that the structure and dynamics of an isolated DNA molecule were probed. Static light scattering measurements yielded estimates for the molecular weight M, second virial coefficient A₂, and radius of gyration R_G. For the nicked DNA, M = (2.8 ± 0.4) × 10⁶g/mol, A₂ = (0.9 ± 0.2) × 10⁻³ mol cm³/g², and R_G = 90 ± 3 nm were obtained. For the supercoiled DNA, M = (2.5 ± 0.4) × 10⁶ g/mol, A₂ = (1.2 ± 0.2) × 10⁻³ mol cm³/g², and R_G = 82 ± 2.5 nm were obtained. The static structure factors for the nicked and supercoiled DNA were found to superpose when they were scaled by the radius of gyration. The intrinsic stiffness of DNA was evident in the static light scattering data. Homodyne intensity autocorrelation functions were collected for both DNAs at several angles, or scattering vectors. At the smallest scattering vectors the probe size was comparable to the longest intramolecular distance, while at the largest scattering vectors the probe size was smaller than the persistence length of the DNA. Values of the self-diffusion coefficients D were obtained from the low-angle data. For the nicked DNA, D = (2.9 ± 0.3) × 10⁻⁸ cm²/s, and for the supercoiled DNA, D = (4.11 ± 0.21) × 10⁻⁸ cm²/s. The contribution to the correlation function from the internal dynamics of the DNA was seen to result in a strictly bimodal decay function. The rates of the faster mode Γ_int, reached plateau values at low angles. For the nicked DNA, Γ_int = 2500 ± 500 s⁻¹, and for the supercoiled DNA, Γ_int = 5000 ± 500 s⁻¹. These rates correspond to the slowest internal relaxation modes of the DNAs. The dependence of the relaxation rates on scattering vector was monitored with the aid of cumulants analysis and compared with theoretical predictions for the semiflexible ring molecule. The internal mode rates and the dependence of the cumulants moments reflected the difference between the nicked DNA and the supercoiled DNA dynamical behavior. The supercoiled DNA behavior seen here indicates that conformational dynamics might play a larger role in DNA behavior than is suggested by the notion of a branched interwound structure. © 1996 John Wiley & Sons, Inc.     

Inelastic light scattering studies of solutions of the chloroplast coupling factor (CF1) at high and low ionic strength

The translational diffusion coefficient of CF₁ at low and high protein concentration as well as at different ionic strength (0.05 – 1.65 M) wsa determined by means of quasi-elastic light scattering experiments. The diffusion coefficient changes from D_20,w^o = 3.12 × 10^?7 cm² · sec^?1 at 0.05 M, pH 7.8, 20°C, to D_20,w^o = 3.52 × 10^?7 cm² · sec^?1 at 1.6 M, pH 7.8, 20°C. At high enzyme concentration (20 mg/ml) and under crystallization conditions (Paradies, BBRC 91: 685, 1979) CF₁ behaves as a solution of “true” hard spheres, whereas at low salt concentration the ionic atmosphere has a larger spatial extent, resulting in a higher effective hydrodynamic radius (R_H = 65 Å).     

Static and dynamic light scattering from dilute insulin solutions

Static and dynamic light-scattering measurements are reported on zinc-insulin at room temperature (21 ± l°C) and pH = 6.88 in 0.1M NaCl aqueous solution. The experiments were performed at very low concentration, in the range 0.12 × 10^?4 to 0.90 × 10^?4 g cm^?3. Within experimental error, we find no evidence for a critical micellar concentration in this system. The aggregation phenomenon starts immediately after preparation of the solutions, and takes several days to come to stable equilibrium. The concentration dependence of the diffusion coefficients, D _z, = D_o (1 — k_DC), is negative, and k_D was observed to decrease as a function of time, while the aggregate size was found to increase. The equivalent concentration coefficient, ?2BM _W, obtained from static light scattering, showed a similar behavior, and, within experimental error, was found to be numerically equal to k_D. From the relation found between the diffusion coefficient at infinite dilution and the molecular weight of the aggregates, log D₀ = ?0.240 log M _w ? 5.077, we deduce that the insulin aggregates are compact structures with a characteristic radius of 0.71 Å/(dalton)^1/3, surrounded by a hydration layer of a thickness of 8.0 Å. The equilibrium aggregation number is approximately 10.     

Translational and rotational diffusion of tobacco mosaic virus from polarized and depolarized light scattering

The translational and rotational dynamics of tobacco mosaic virus in sodium phosphate buffer (pH =7.5) solutions has been investigated by polarized and depolarized light scattering Rayleigh linewidth studies. For concentrations ranging from 1.75 × 10^?4 g ml^?1 to 0.25 × 10^?4 g ml^?1 the translational diffusion coefficient (D_T) has been found to be slightly concentration dependent and extrapolation to zero concentration gives D₀^20°C = 0.34 ± 0.01 × 10^?7 cm²S^?1. A full analysis of the polarized spectra obtained at high and low scattering angles and the depolarized spectra at near zero scattering angles has enabled these techniques to be compared and the rotational diffusion constant D_R to be determined. At a solution concentration of 1.75 × 10^?4 g ml^?1 a mean value is found to be D_R^20°C = 350 ± 30s^?1. These values of D_T and D_R are in approximate agreement with calculations based on models of the tobacco mosaic virus molecule as a cylindrical rod.     

Stages of bacteriophage lambda head morphogenesis: physical analysis of particles in solution

Intermediates in the morphogenesis of bacteriophage lambda are characterized in solution by classical light-scattering, using a modified version of the Zimm plot procedure, by quasi-elastic light-scattering and analytical ultracentrifugation. Partial specific volumes are determined simultaneously with molecular weights by a variant of the conventional combination of sedimentation and diffusion constants. Our measurements were performed within a short time and allowed the characterisation of metastable intermediates.Comparison of hydration of DNA-containing and empty heads shows that dehydration plays a minor role in the stabilisation of the DNA within the heads. The molecular weight of the scaffolding protein is 4 × 10⁶, about twice the value estimated so far. Enlargement of preheads (21% and 13% increase in dry and hydrodynamic radius, respectively) leaves the molecular weight unchanged, whereas the volume of hydration water increases from 70% to 90% of the total hydrodynamic volume. Addition of protein pD to the enlarged preheads leads to a further increase in the radius, indicating that pD is attached to the outside of the protein shell.In order to determine simultaneously the molecular weight and the partial specific volume of large and sometimes labile structures, such as a virus, the conventional sedimentation-diffusion method is modified by measuring sedimentation and diffusion coefficients in buffers containing different amounts of ²H₂O. If diffusion coefficients are determined by quasi-elastic light-scattering, experiments can be performed in a few hours. In addition, the method allows a check on the sample for changes in the frictional coefficient due, for instance, to DNA abortively ejected from a virus preparation. This method is described in the Appendix.     

Very low-angle light scattering. A characterization method for high-molecular-weight DNA

A very low-angle light-scattering photometer is described with respect to optical features, scattering cell, correction factors, and absolute calibration in the angular range 2°–35°. An improved microfiltration apparatus was used to obtain essentially dust-free aqueous solutions for very low-angle light scattering. The instrument was calibrated with silicotungstic acid, an absolute molecular-weight standard, and the calibration was confirmed with the use of several secondary standards. Very low-angle light-scattering measurements were made to determine the weight-average molecular weight M?_r and z-average radius of gyration R_g,z of a commerical preparation of calf-thymus DNA. Microfiltration of the solutions allowed measurements down to 6°. The value M?_r = 20.0 × 10⁶ obtained by extrapolating 6°–9° data to 0° is more than three times that from 30°–75° data (6.38 × 10⁶) but ～20% smaller than that from 10–35° data (23.7 × 10⁶). The experimental errors in M?_r and R_g,z are estimated to be ±8% and ±14%, respectively. Combined 6°–75° data from two photometers fit well a theoretical scattering curve for a model wormlike coil of the same M?_r as the DNA sample.     

Isolation,characterization, and magnesium-induced self-association kinetics of discrete aggregates of RecA protein from Escherichia coli

Dynamic and static intensity light scattering techniques were employed to identify conditions allowing preparation of homogeneous solutions of distinct oligomeric states of RecA protein. These hydrodynamically distinguishable oligomer populations of RecA protein were obtained in homogeneous pure quantities sufficient for physical studies. Results indicate two fairly narrow distributions of RecA oligomers comprised on average of 42 ± 3 and 18 ± 1 RecA monomers. These structures, denoted RecA₄₂ and RecA₁₈, respectively, could be obtained reproducibly in milligram quantities and were stable for at least one week. This enabled reliable characterizations of their hydrodynamic properties by dynamic and total intensity light scattering. These measurements revealed RecA₄₂ had an average translational diffusion coefficient, D₂₀(L) = 8 ± 2 × 10⁻⁸ cm²/s, molecular weight, M_r = 1.6 ± 0.1 × 10⁶, and radius of gyration, R_G = 465 ± 29 Å. The smaller aggregate, RecA₁₈, had D₂₀(S) = 20.5 ± 2.5 × 10⁻⁸ cm²/s. M_r = 7.0 ± 0.4 × 10⁵, and R_G = 300 ± 20 Å. Heating RecA₁₈ at 37°C overnight resulted in conversion to a species with hydrodynamic properties indistinguishable from RecA₄₂, called RecA_18/42. Conversion of RecA₄₂ to RecA₁₈ occurred almost instantaneously by 50% dilution at 38°C or very slowly with incubation at 4°C for at least 39 days. Self-association reactions of the three starting oligomeric states (RecA₁₈, RecA₄₂, and RecA_18/42) induced by MgCl₂ were monitored at several temperatures by dynamic light scattering. Results of these experiments provided evaluations of kinetic activation parameters of the self-association reactions. The activation parameters found for each starting oligomeric state of the protein were significantly different, revealing the variable influence of MgCl₂ on the activation barriers to RecA self-association. Highly aggregated equilibrium solutions that ultimately form in solutions of each starting oligomeric species, incubated in MgCl₂ at 38°C for four days, were characterized by total intensity light scattering. Interpretations of these data in terms of characteristic behavior of random polymers suggests the surface morphologies of these highly associated equilibrium states formed from RecA₄₂ and RecA_18/42 are similar but contrast with that of RecA₁₈. Calculated values of the translational diffusion coefficient D₀ were obtained for oligomeric structures modeled as helical arrays of connected monomer spheres. Best agreement with experimentally determined diffusion coefficients required that constituent monomer spheres of RecA₄₂ have radii 33–40% larger than the monomer spheres of RecA₁₈. Results suggest the hydrodynamically distinct oligomeric forms of RecA may reside in conformational states with different surface exposure of hydrophobic residues, which results in substantial differences in local solvation/hydration. © 1996 John Wiley & Sons, Inc.     

Dynamic light scattering from thin rigid rods: Anisotropy of translational diffusion of tobacco mosaic virus

An Exact theoretical expression for the apparent diffusion coefficient D_app(K) of a thin rigid rod with arbitrary anisotropy of its translational diffusion diffusion coefficient is derived from the first cumulant of its dynamic structure factor. D_app(K) is predicted to reach a limiting plateau value at extermely large values of KL, where K is the scattering vector and L the rod length. Howerver, that limiting plateau value is approached only very slowly along a quasi-plateau with a very gradual slope. Dynamic light-scattering studies have been performed on tobacco mosaic virus from K² = (0.4–20) × 10¹⁰ cm^?2 using 632-8-nm laser radiation. The present data yield D₀ = (4.19 ± 0.10) × 10^?8 cm²/s (corrected to 20,w conditions) and, with literature data to establish L = 2980 Å and the rotational diffusion coefficient D_R = 318s^?1, yield also Δ ≡ D_∥ ? D_⊥ = (1.79 ± 0.38) × 10^?8 cm²/s. The experimental data closely follow the curve of D_app(K) vs K² calcuated for these parameters. The present value of D₀ substantially exceeds all previous dynamic light-scattering values, but is in good aggreement with previous sedimentation data, which were confirmed for the presemt sample. The anisotropy ratio Δ/D₀ = 0.43 ± 0.09 is in accord with theoretical predictions based on the modified Kirkwood algorithm, despite the fact the D₀ lies significantly below its corresponding theoretical value. The present data largely predlude the possibility that both D₀ and Δ/D₀ could simultaneously match their theoretical predictions. We present a detailed comparison of the experimental data with the calculations of Tirado and Garcia de la Torre based on the modified Kirkwood algorithm and with the Broersma formulas.     

Dielectric relaxation of DNA solutions. II

Real and imaganiry parts of complex dielectric constant of dilute solutions of DNA in 10^?3M NaCl with molecular weight ranging from 0.4 × 10⁶ to 4 × 10⁶ were measured at frequencies from 0.2 Hz to 30 kHz. Dielectric increments Δε were obtained from Cole-Cole plots and relaxation times τ_D from the loss maximum frequency. The τ_D of all samples agrees well with twice of the maximum viscoelastic relexation time in the Zimm theory, indicating that the low-frequency dielectric relaxiation should be ascribed to be the rotation of DNA. The rms dipole moment, which was obtained from Δε, agree well with that calculated from the counterion fluctuation theory. The dielectric increment was found to be greatly depressed in MgCl₂, which is resonably interpreted in terms of a strong binding of Mg⁺⁺ ions with DNA.     

A critical evaluation of models for complex molecular dynamics: application of NMR studies of double- and single-stranded DNA

The nature of internal and overall motions in native (double-stranded) and denatured (single-stranded) DNA fragments 120–160 base pairs (bp) long is examined by molecular-dynamics modeling using ¹³C-nmr spin-relaxation data obtained over the frequency range of 37–125 MHz. The broad range of ¹³C frequencies is required to differentiate among various models. Relatively narrow linewidths, large nuclear Overhauser enhancements (NOEs), and short T₁ values all vary significantly with frequency and indicate the presence of rapid, restricted internal motions on the nanosecond time scale. For double-stranded DNA monomer fragments (147 bp, 24 Å diam at 32°C), the overall motion is that of an axially symmetric cylinder (τ_x = ～10^?6 s;τ_Z = ～1.8 × 10^?8s), which is in good agreement with values calculated from hydrodynamic theory (τ_x = ～1.8 × 10^?6 s; τ_Z = ～2.7 × 10^?8 s). The DNA internal motion can be modeled as restricted amplitude internal diffusion of individual C? H vectors of deoxyribose methine carbons C1′, C3′, and C4′, either with conic boundary conditions (τ_w = ～4 × 10^?9 s, θ_cone = ～21°) or as a bistable jump (τ_A = τ_B = ～2 × 10^?9 s, θ = ～15°). We discuss the critical role in molecular-dynamics modeling played by the angle (β) that individual C? H vectors make with the long axis of the DNA helix. Heat denaturation brings about increases in both the rate and amplitude of the internal motion (described by the wobble model with τ_W = ～0.2 × 10^?9 s, θ_cone = ～50°), and overall motion is affected by becoming essentially isotropic (τ_x = τ_Z = ～5 × 10^?8 s) for the single-stranded molecules. Since ¹³C-nmr data obtained at various DNA concentrations for C2′ of the deoxyribose ring is not described well by the above models, a new model incorporating an additional internal motion is proposed to take into account the rapid, extensive, and weakly coupled motion of C2′.