Conformational and Thermodynamic Properties of Supercoiled DNA

The intrinsic viscosity of biological macromolecules. Progress in measurement, interpretation and application to structure in dilute solution.

https://febs.onlinelibrary.wiley.com/doi/pdf/10.1111/j.1432-1033.1988.tb14425.x

Nucleic acids and nuclear magnetic resonance.

The DNA double helix exhibits local sequence-dependent polymorphism at the level of the single base pair and dinucleotide step. Curvature of the DNA molecule occurs in DNA regions with a specific type of nucleotide sequence periodicities. Negative supercoiling induces in vitro local nucleotide sequence-dependent DNA structures such as cruciforms, left-handed DNA, multistranded structures, etc. Techniques based on chemical probes have been proposed that make it possible to study DNA local structures in cells. Recent results suggest that the local DNA structures observed in vitro exist in the cell, but their occurrence and structural details are dependent on the DNA superhelical density in the cell and can be related to some cellular processes.

Local supercoil-stabilized DNA structures.

From the first high-resolution structure of a repressor bound specifically to its DNA recognition sequence it has been shown that the phage 434 repressor protein binds as a dimer to the helix. Tight, local interactions are made at the ends of the binding site, causing the central four base pairs (bp) to become bent and overtwisted. The centre of the operator is not in contact with protein but repressor binding affinity can be reduced at least 50-fold in response to a sequence change there. This observation might be explained should the structure of the intervening DNA segment vary with its sequence, or if DNA at the centre of the operator resists the torsional and bending deformation necessary for complex formation in a sequence dependent fashion. We have considered the second hypothesis by demonstrating that DNA stiffness is sequence dependent. A method is formulated for calculating the stiffness of any particular DNA sequence, and we show that this predicted relationship between sequence and stiffness can explain the repressor binding data in a quantitative manner. We propose that the elastic properties of DNA may be of general importance to an understanding of protein-DNA binding specificity.

Importance of DNA stiffness in protein-DNA binding specificity.

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.

Evidence for allosteric transitions in secondary structure induced by superhelical stress.

Optical anisotropy data spanning a very wide time range are analyzed using a recently developed theory for filamentous macromolecules that can bend, twist, and also admit overdamped local libration (or wobble) of the chromophore. A rapid relaxation in the fluorescence polarization anisotropy (FPA) near 10−10 s is fitted well by superimposing isotropic wobble of the chromophore (7° rms polar and azimuthal amplitude) on the long-wavelength twisting and bending motions that characterize the relaxation at longer times but not by the latter alone. Moreover, the decay of the FPA from 0.5 to 150 ns cannot be satisfactorily fitted by chromophore wobble in an otherwise rigid DNA and must be assigned primarily to twisting, as noted previously.



Data from 26 ns to 20 μs for 600 base-pair DNA are accurately fitted with only a single adjustable scaling factor when the tumbling correlation function is taken to be the empirical electric birefringence decay function of Elias and Eden. The Barkley-Zimm (BZ) tumbling correlation for very long filaments appears to decay too rapidly and results in significant overestimation of the depolarization for t ≤ 300 ns. In the range of the FPA experiments (t ≥ 150 ns), equally good fits with equally uniform torsion constants are obtained for long DNAs, whether one assumes the BZ tumbling correlation function or neglects tumbling entirely, but the best-fit torsion constant (actually the product of the torsion constant and friction factor) is increased by the factor 1.9 when the BZ result is used with a persistence length of a = 500 A. The BZ bending theory is compared with other experimental data, and also with a simulation at very short times with mixed results. Present uncertainties regarding the tumbling dynamics and the friction factor for azimuthal rotation allow the torsion constant to be as much as 3.8 times larger than the initial estimate of Thomas et al. Apparent torsion constants obtained from relative ligase kinetics measurements are also briefly discussed.

Rotational dynamics of DNA from 10−10 to 10−5 seconds: Comparison of theory with optical experiments

The conformation and internal dynamics of supercoiled pUC 8 DNA (2717 bp) are examined by dynamic light scattering, and the magnitude and uniformity of its torsional rigidity are determined using time-resolved fluorescence polarization anisotropy of intercalated ethidium dye. Neither measurement gives any indication of an appreciably reduced bending or twisting rigidity, or anomalously rapid internal motions. For 31P, in supercoiled pUC 8, we measure T2 = (2.0 ± 0.5) × 10−3 s. This lies within the range of present theoretical estimates obtained using normal rigidities. The proton linewidths observed for pUC 8 and pBR322 (4363 bp) DNAs are within a factor of 2–3 of those similarly estimated assuming ordinary rigidities.



According to Bendel, Laub and James [(1982) J. Am. Chem. Soc.104, 6748–6754], supercoiled pIns36 DNA (7200 bp) exhibits an astonishingly long T2 = 1.17 s for 31P, a slowest rotational relaxation time, τ = 5 × 10−9 s, and an enormously reduced bending rigidity. Serious questions raised by these findings are examined here. The 5 × 10−9 s slowest rotational relaxation time is shown to be physically inadmissible.



The nmr relaxation theory developed previously by Allison, Shibata, Wilcoxon, and Schurr [(1982) Biopolymers21, 729–762], is modified to incorporate new results for deformable filaments, which directly introduce the highly nonexponential tumbling correlation function for reorientation of the local helix axis. Essential requirements for a complete calculation of R2, including estimation of the tumbling correlation function and evaluation of the still unknown DIP/CSA cross-term, are described in detail. Slow coil-deformation modes analogous to the Rouse-Zimm modes of linear DNAs are shown to make an important, if not dominant, contribution to the R2 relaxation rate. Geometrical parameters in the theory are chosen to provide good agreement with literature data for 600-bp linear DNA. Using this theory and an informed guess for the tumbling correlation function, we find that the 31P-nmr relaxation data of Bendel et al., if correct, necessarily impose on their DNA one or more extreme properties, such as enormously reduced bending or twisting rigidities. In contrast, the same theory yields reasonable agreement with the T2 reported here for 31P in supercoiled pUC 8 DNA when its rigidities are assumed to be quite ordinary.

Deformational dynamics and NMR relaxation of supercoiled DNAs.

A theory explicitly allowing the possibility of aggregation of multistrand biopolymers is proposed. It is found that the same secondary bonds responsible for stabilizing the native structure at low temperature will promote aggregation in the thermal denaturation region for sufficiently long chains. A requirement for both open and zippered regions dictates that the aggregation region does not extend far below Tm. However, its width, or extension on the high-temperature side of Tm, is a strongly increasing function of chain length and also of the cooperativity parameter. The present theoretical results obtained for DNA and collagen with almost no adjustable parameters are in good qualitative agreement with a number of previously poorly understood experimental observations. The significance of such a spontaneous aggregation phenomenon for genetic recombination is noted.

John H. Shibata

Papers

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

Evidence for allosteric transitions in secondary structure induced by superhelical stress.

Rotational dynamics of DNA from 10−10 to 10−5 seconds: Comparison of theory with optical experiments

Deformational dynamics and NMR relaxation of supercoiled DNAs.

A theory of aggregation in the thermal denaturation region of multistrand biopolymers