Two theories relating the translational and rotational diffusion coefficients Dt and Dr of a rod‐like macromolecule to its length and diameter, proposed by Broersma [J. Chem. Phys. 74, 6989 (1981)], and Tirado and Garcia de la Torre [J. Chem. Phys. 71, 2581 (1979); 73, 1986 (1980)] are shown to predict different values of the coefficients for a particle of given dimensions. Next, we use the two theories to analyze existing experimental data of sedimentation coefficients s and translational and rotational diffusion coefficients of short DNA fragments, and obtain values of the hydrated diameter of DNA d which is treated as an adjustable parameter. The results are compared with the expected value, d≂26A. This comparison favors clearly the Tirado–Garcia de la Torre theory in the case of Dt and s. For Dr, and using a rise per base pair r=3.4 A, this theory gives best agreement for all the data examined, while when r=3.3 A, the agreement depends on the source of data.

Comparison of theories for the translational and rotational diffusion coefficients of rod‐like macromolecules. Application to short DNA fragments

Thermal denaturation of DNA molecules: A comparison of theory with experiment

This review should demonstrate that polyelectrolyte solutions are currently advancing to a fascinating topic in polymer science. The increasing effort in analytical theory, simulations and experiments is about to result in a deeper, fundamental understanding of the interacting macroions and of the conformational properties of flexible polyions. As these “simple” problems have still not been completely solved, new challenges have already emerged, such as the effect of polyion chain architecture (polyelectrolyte stars, combs, rings, μ-gels), the effect of bivalent or multivalent metal ions bound to the polyelectrolyte chain (intramolecular cross-linking, polyion coil collapse), and the complex field of surfactant-polyion and polyanion-polycation complexes. In comparison with the growing technical importance of such complex ionic systems, the fundamental academic research in this area has hardly started yet.

Polyelectrolytes in solution

The free solution mobility of DNA has been measured by capillary electrophoresis in the two buffers most commonly used for DNA gel electrophoresis, Tris-borate-EDTA (TBE) and Tris-acetate-EDTA (TAE). The capillaries were coated with polymers of either of two novel acrylamide monomers, N-acryloylaminoethoxyethanol or N-acryloylaminopropanol, both of which are stable at basic pH and effectively eliminate the electroendosmotic mobility due to the capillary walls. The free solution mobility of DNA in TAE buffer was found to be (3.75 +/- 0.04) x 10(-4) cm2 V-1 s-1 at 25 degrees C, independent of DNA concentration, sample size, electric field strength, and capillary coating, and in good agreement with other values in the literature. The free solution mobility was independent of DNA molecular weight from approximately 400 base pairs to 48.5 kilobase pairs, but decreased monotonically with decreasing molecular weight for smaller fragments. Surprisingly, the free solution mobility of DNA in TBE buffer was found to be (4.5 +/- 0.1) x 10(-4) cm2 V-1 s-1, about 20% larger than observed in TAE buffer, presumably because of the formation of nonspecific borate-deoxyribose complexes.

The free solution mobility of DNA.

Single biomolecules in free solution have long been of interest for detailed study by optical methods, but Brownian motion prevents the observation of one single molecule for extended periods. We have used an anti-Brownian electrokinetic (ABEL) trap to trap individual protein molecules in free solution, under ambient conditions, without requiring any attachment to beads or surfaces. We also demonstrate trapping and manipulation of single virus particles, lipid vesicles, and fluorescent semiconductor nanocrystals.

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Suppressing Brownian motion of individual biomolecules in solution

The apparent diffusion coefficient Dapp(K) of a single sample of linear ϕ29 DNA (Mr = 11.5 × 106) has been measured as a function of K2 from 0.21 × 1010 to 20 × 1010 cm−2 at a variety of temperatures from −0.5 to +70°C. Dapp(K) scales closely as T/η at every value of K2. All of these data are simulated by a particular Rouse-Zimm model comprised of a constant number of subchains with constant rms subchain extension b = 1057 A and an apparent subchain diffusion coefficient Dplat that scales at T/η from −0.5 to +70°C. It is inferred from these results that any temperature dependence of the flexural and torsional rigidities of DNA must be rather weak. A less firm inference is that these rigidities actually increase slightly with temperature, possibly in proportion to T, which is weak T dependence in this context. These findings eliminate the possibility that spontaneous transient opening of the DNA structure has any significant effect on the flexural and torsional rigidities of the DNA filament. A review of the most pertinent available data from other experiments concerning spontaneous transient opening of the DNA is presented. The formaldehyde kinetics data do not unequivocally implicate an open base-pair intermediate and provide only an upper limit to the fraction of open base pairs. An alternative nonopening model with a protonated doorway state is proposed to accommodate the hydrogen-exchange data. It is concluded that there is presently no incontrovertible evidence for a fraction of unstacked open base pairs greater than about 10−4.

Temperature dependence of the dynamic light scattering of linear phi 29 DNA: implications for spontaneous opening of the double-helix.

An Exact theoretical expression for the apparent diffusion coefficient Dapp(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. Dapp(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 A and the rotational diffusion coefficient DR = 318s−1, yield also Δ ≡ D∥ − D⊥ = (1.79 ± 0.38) × 10−8 cm2/s. The experimental data closely follow the curve of Dapp(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.

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

The pertinent correlation function for nmr dipolar relaxation of 31P by its neighboring protons in DNA is derived for a comparatively realistic model of the internal Brownian motions. These motions include the collective torsional deformation modes of the elastic filament, uncoupled local overdamped reorienting motions of the P-H vectors in harmonic potential wells within the nucleotide unit, and the compartively slow end-over-end rotations of the local helix axis. These latter slow axial tumbling motions essentially completely determine T2 but have virtually no effect on T1 or the nuclear Overhauser effect (NOE), which are governed almost exclusively by rapid torsional deformations and local reorientations on the nanosecond time scale. The essential behavior of the relevant correlation function for the collective torsional motions has recently been determined experimentally in this laboratory using the decay of fluorescence polarization anisotropy of bound ethidium dye [J. C. Thomas et al. (1980) Biophys. Chem.12, 177–180]. By using that result to carry out nmr relaxation calculations for various amplitudes and time constants of the uncoupled local motions and comparing them with the experimental data, it can be demonstrated that (within this model of purely dipolar relaxation), only rather small rms amplitudes of local reorientations (<7°) occur and that their relaxation times are near 1 ns. Contrary to previous conclusions in the literature, the collective torsional deformation modes actually make the dominant contribution to T1 and NOE. At t = 1 ns the total rms azimuthal displacement of the P-H vector in this model is 19.5°, which results from a superposition of torsional deformations with rms displacement 18.2° and uncoupled local motions with rms displacement 7°. The contribution of pure chemical shift anisotropy (CSA) to the 1/T1 relaxation rate is calculated for the first time for the case when torsional deformation modes predominate, and it is predicted to be 46% of the corresponding dipolar relaxation rate or 31% of the total relaxation rate. Unusual magnetic field strength dependence of the pure CSA and dipolar contributions is predicted to arise as a consequence of the collective torsional deformation modes. This seriously weakens empirical arguments in favor of a small (<10%) CSA contribution. In any case, a detailed interpretation of T1 and NOE incorporating both dipolar and CSA relaxation must await the evaluation of the CSA:dipolar interference term, or crossterm, contribution to the relaxation rate. The contribution of pure CSA to 1/T2 relaxation is likewise calculated for the case when local reorienting motions are negligible; it is found to be ≲16% of the corresponding dipolar relaxation rate for the comparatively short (300–600-base-pair) DNA fragments of interest. For high-molecular-weight DNAs we predict that the slow Rouse-Zimm coil-deformation modes will dominate 1/T2 relaxation and the linewidth. Dynamic light-scattering and other evidence is presented that the remarkable loss of nmr signal from DNA on addition of ethidium bromide, as reported by Hogan and Jardetzky, is actually a consequence of phase separation in such concentrated solutions. A pronounced decrease in T2, due to greatly hindered axial tumbling in the more concentrated phase, is advanced as a plausible line-broadening explanation for the apparent loss of nmr signal from DNA in that phase.

NMR relaxation in DNA. I. The contribution of torsional deformation modes of the elastic filament.

Electrophoretic light scattering (ELS) is employed to determine the electrophoretic mobilities μE and apparent diffusion coefficients DELS obtained from ELS linewidths for three samples of poly(L‐lysine)HBr (PLL) of degree of polymerization n=406, n=946, and n=2273 as a function of salt (Cs) and polyion (Cp) concentration. Dynamic light scattering (DLS) is used to determine apparent diffusion coefficients Dapp of these same PLL samples in the absence of the applied field. The polyelectrolyte system exhibits an ordinary to extraordinary phase transition at low salt concentrations that is manifested by a more than 50‐fold decrease in Dapp as well as a twofold decrease in scattered intensity. In the extraordinary phase, the DELS values are typically very small, though still somewhat (frequently twofold) larger than Dapp. When the salt concentration is raised to enter the ordinary phase DELS remains small, less than one tenth of Dapp, in the low‐salt end of the ordinary phase, but increases with increasing Cs...

Electrophoretic light scattering studies of poly(L‐lysine) in the ordinary and extraordinary phase. Effects of salt, molecular weight, and polyion concentration

Jess Wilcoxon

Papers

Temperature dependence of the dynamic light scattering of linear phi 29 DNA: implications for spontaneous opening of the double-helix.

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

NMR relaxation in DNA. I. The contribution of torsional deformation modes of the elastic filament.

Electrophoretic light scattering studies of poly(L‐lysine) in the ordinary and extraordinary phase. Effects of salt, molecular weight, and polyion concentration

Validity of stokes' law for polystyrene latex spheres