Effect of Bending Strain on the Torsion Elastic Constant of DNA

The torsion constants of both circular and linear forms of the same 181 bp DNA were investigated by time-resolved fluorescence polarization anisotropy (FPA) of intercalated ethidium. The ratio of intrinsic ethidium binding constants of the circular and linear species was determined from the relative fluorescence intensities of intercalated and non-intercalated dye in each case. Possible changes in secondary structure were also probed by circular dichroism (CD) spectroscopy. Upon circularization, the torsion constant increased by a factor of 1.42, the intrinsic binding constant for ethidium increased by about fourfold, and the CD spectrum underwent a significant change. These effects are attributed to an altered secondary structure induced by the bending strain. Quantitative agreement between torsion constants obtained from the present FPA studies and previous topoisomer distribution measurements on circular DNAs containing 205 to 217 bp removes a long-standing apparent discrepancy between those two methods. After storage at 4°C for eight months, the torsion constant of the circular DNA increased by about 1.25-fold, whereas that of the linear DNA remained unchanged. For these aged circles, both the torsion constant and intrinsic binding constant ratio lie close to the corresponding values obtained previously for a 247 bp DNA by analyzing topoisomer distributions created in the presence of various amounts of ethidium. The available evidence strongly implies that torsion constants measured for small circular DNAs with less than 250 bp are specific to the altered secondary structure(s) therein, and are not applicable to linear and much larger circular DNAs with lower mean bending strains.     

Structure and Dynamics of Double Helices in Solution: Modes of DNA Bending

Abstract

The long range structure of DNA restriction fragments has been analysed by electro-optical measurements. The overall rotation time constants observed in a low salt buffer with monovalent ions is shown to decrease upon addition of Mg²⁺ or spermine. Since the circular dichroism and also the limiting value of the linear dichroism remain almost constant under these conditions, the effect is attributed to a change of the long range structure. According to a weakly bending rod model, the persistence length decreases from about 600 Å in the absence of Mg²⁺ or spermine to about 350 Å in the presence of these ions. The persistence length measured in the presence of Mg²⁺ is almost independent of temperature in the range of 10 to 40 °C. The nature of DNA bending is analysed by measurements of bending amplitudes and time constants from dichroism decay curves. The observed absence of changes in the bending amplitudes upon addition of Mg²⁺ or spermine, even though addition induces changes of the persistence length by a factor of 2, is hardly consistent with simple thermal bending. The combined results, including the remarkably small temperature dependence of persistence length and bending amplitude, can be explained by the existence of two bending effects: inherent curvature of DNA dominates at low temperature, whereas thermal bending prevails at high temperature. Analysis of bending amplitudes from dichroism decay curves according to an arc model provides an approximate measure for the degree of bending in restriction fragments. The model is consistent with the observed chain length dependence of bending amplitudes and provides an approximate curvature corresponding to a radius of ab out400Å. Thus the curvature observed in restriction fragments is similar to that observed for high molecular DNA condensed into toroids by addition of ions like spermine.

Particularly strong bending of DNA is induced by [CO(NH₃)₆]³⁺, indicated by an apparent persistence length of 200 Å and an increased bending amplitude together with a reduced limit value of the linear dichroism. This effect is attributed to the high charge density of this ion and potential site binding.     

On the origin of the temperature dependence of the supercoiling free energy.

Monte Carlo simulations using temperature-invariant torsional and bending rigidities fail to predict the rather steep decline of the experimental supercoiling free energy with increasing temperature, and consequently fail to predict the correct sign and magnitude of the supercoiling entropy. To illustrate this problem, values of the twist energy parameter (E(T)), which governs the supercoiling free energy, were simulated using temperature-invariant torsion and bending potentials and compared to experimental data on pBR322 over a range of temperatures. The slope, -dE(T)/dT, of the simulated values is also compared to the slope derived from previous calorimetric data. The possibility that the discrepancies arise from some hitherto undetected temperature dependence of the torsional rigidity was investigated. The torsion elastic constant of an 1876-bp restriction fragment of pBR322 was measured by time-resolved fluorescence polarization anisotropy of intercalated ethidium over the range 278-323 K, and found to decline substantially over that interval. Simulations of a 4349-bp model DNA were performed using these measured temperature-dependent torsional rigidities. The slope, -dE(T)/dT, of the simulated data agrees satisfactorily with the slope derived from previous calorimetric measurements, but still lies substantially below that of Duguet's data. Models that involve an equilibrium between different secondary structure states with different intrinsic twists and torsion constants provide the most likely explanation for the variation of the torsion constant with T and other pertinent observations.     

Torsional rigidities of weakly strained DNAs

Measurements on unstrained linear and weakly strained large (> or =340 bp) circular DNAs yield torsional rigidities in the range C = 170-230 fJ fm. However, larger values, in the range C = 270-420 fJ fm, are typically obtained from measurements on sufficiently small (< or =247 bp) circular DNAs, and values in the range C = 300-450 fJ fm are obtained from experiments on linear DNAs under tension. A new method is proposed to estimate torsional rigidities of weakly supercoiled circular DNAs. Monte Carlo simulations of the supercoiling free energies of solution DNAs, and also of the structures of surface-confined supercoiled plasmids, were performed using different trial values of C. The results are compared with experimental measurements of the twist energy parameter, E(T), that governs the supercoiling free energy, and also with atomic force microscopy images of surface-confined plasmids. The results clearly demonstrate that C-values in the range 170-230 fJ fm are compatible with experimental observations, whereas values in the range C > or = 269 fJ fm, are incompatible with those same measurements. These results strongly suggest that the secondary structure of DNA is altered by either sufficient coherent bending strain or sufficient tension so as to enhance its torsional rigidity.     

Effect of temperature on DNA secondary structure in the absence and presence of 0.5 M tetramethylammonium chloride

Changes in the average secondary structures of three different linear DNAs over the premelting region from 5 to 60°C were investigated by measuring their CD spectra and also their torsion elastic constants (〈α〉) by time-resolved fluorescence polarization anisotropy. For one of these DNAs, the HaeII fragment of pBR322, the apparent diffusion coefficients [D_app (k)] at small and large scattering vectors (k) were also measured by dynamic light scattering. With increasing temperature, all three DNAs exhibited typical premelting changes in their CD spectra, and these were accompanied by 1.4- to 1.7-fold decreases in 〈α〉. Also for the 1876 base pair fragment, D_app(k) at large scattering vectors, which is sensitive to the dynamic bending rigidity, decreased by 17%, even though there was no change at small scattering vectors, where D_app(k) = D₀ is the translational diffusion coefficient of the center-of-mass. These observations demonstrate conclusively that the premelting CD changes of these DNAs are associated with a significant change in average secondary structure and mechanical properties, though not in persistence length. In the presence of 0.5 M tetramethylammonium chloride (TMA-Cl) the premelting change in CD is largely suppressed, and the corresponding changes in 〈α〉 and D_app(k) at large scattering vectors are substantially diminished. These observations suggest that TMA-Cl, which binds preferentially to A · T-rich regions and stabilizes those regions (relative to G · C-rich regions) against melting, effectively stabilizes the prevailing low-temperature secondary structure sufficiently that the DNA is effectively trapped in that state over the temperature range observed. © 1998 John Wiley & Sons, Inc. Biopoly 45: 503–515, 1998     

Evidence for allosteric transitions in secondary structure induced by superhelical stress

Previous studies suggest that the global secondary structures of native supercoiled and equilibrium linear DNAs may differ somewhat. Recent evidence also indicates that metastable secondary structure commonly persists following complete relaxation of the superhelical stress by intercalating dyes or by the action of topoisomerase I. In this work, the torsion constants (alpha) of pBR322, pUC8 and M13mp7 (replicative form) DNAs are determined by time-resolved fluorescence polarization anisotropy at various times subsequent to linearization. In all three cases, the torsion constants are relatively low immediately after linearization, and evolve for eight to ten weeks before reaching their apparent equilibrium values. It is shown in detail how the persistence of metastable secondary structure, subsequent to relaxation of superhelical stress, necessarily implies that one or more transitions in equilibrium secondary structure are induced as the superhelix density is varied from zero to native, or vice versa. Samples of pUC8 dimer (5434 base-pairs) with different superhelix densities are prepared by the action of topoisomerase I in the presence of various amounts of ethidium. Their median linking number differences are determined by standard band counting methods. The translational diffusion coefficient (Do) and the plateau diffusion coefficient (Dplat) characterizing internal motions over short distances (225 A) are determined by dynamic light-scattering. The torsion constant (alpha) between base-pairs and the circular dichroism spectrum are also measured for each sample. Curves of Dplat, Do, alpha and molar ellipticity ([theta]) (at the minimum near 250 nm) versus superhelix density (sigma) are constructed. The curve of Do versus sigma is very similar to that for sedimentation coefficient versus sigma for simian virus 40 (SV40) and polyoma DNAs. The curves of Dplat, Do, alpha and [theta] versus sigma show that, with increasing negative superhelix density, a structural transition occurs near sigma = -0.020 to an intermediate state with low torsion constant, and a second structural transition occurs near sigma = -0.035 to a state that exhibits more normal properties by sigma = -0.048. These data are consistent with the hypothesis that supercoiling induces two successive allosteric transitions to alternative global secondary structures. The data are much less consistent with the hypothesis that supercoiling induces some radical secondary structure at one or a few sites of small extent at sigma = -0.020, and at other sites at sigma = -0.035, or with hypotheses based on changes in tertiary structure alone.(ABSTRACT TRUNCATED AT 400 WORDS)     

Effect of ethidium on the torsion constants of linear and supercoiled DNAs.

The torsion elastic constants (alpha) of linear pBR322 (4363 bp) and pUC8 (2717 bp) DNAs and supercoiled pBR322 and pJMSII (4375 bp) DNAs are measured in 0.1 M NaCl as a function of added ethidium/base-pair (EB/BP) ratio by studying the fluorescence polarization anisotropy (FPA) of the intercalated ethidium. The time-resolved FPA is measured by using a picosecond dye laser for excitation and time-correlated single photon counting detection. Previously developed theory for the emission anisotropy is generalized to incorporate rotations of the transition dipole due to excitation transfer. The excitation transfers are simulated by a Monte Carlo procedure (Genest et al., Biophys. Chem. 1 (1974) 266-278) and the consequent rotations of the transition dipole are superposed on the Brownian rotations. After accounting for excitation transfer, the torsion constants of the linear DNAs are found to be essentially independent of intercalated ethidium up to a binding ratio r = 0.10 dye/bp. Dynamic light scattering measurements on linear pUC8 DNA confirm that the torsion constant is independent of binding ratio up to r = 0.20 dye/bp. If alpha d denotes the torsion constant between ethidium and a base-pair, and alpha 0 that between two base-pairs, then our data imply that alpha d/alpha 0 lies in the range 0.65 to 1.64 with a most probable value of 1.0. The torsion constants of supercoiled DNAs decrease substantially with increasing binding ratio even after accounting for excitation transfer. At the binding ratio r* = 0.064, where the superhelix density vanishes and superhelical strain is completely relaxed, the torsion constant of the supercoiled pBR322 DNA/dye complex lies below that of the corresponding linear DNA/dye complex by about 30%. This contradicts the conventional view according to which linear, nicked circular, and supercoiled DNA/dye complexes with r = r* should coexist with the same concentration of free dye, display the same distribution of bound dye, and exhibit identical secondary structures, twisting and bending rigidities, and FPA dynamics. These and other observations imply the existence of metastable secondary structure in freshly relaxed supercoiled DNAs. A tentative explanation is presented for these and other unexpected observations on supercoiled DNAs.     

Can reliable torsion elastic constants be determined from FPA data on 24 and 27 base-pair DNAs?

Torsion elastic constants obtained from fluorescence polarization anisotropy (FPA) measurements on fifty-three 24 and 27 base-pair (bp) DNAs were recently reported [F. Pedone, F. Mazzei, D. Santoni, Sequence-dependent DNA torsional rigidity: a tetranucleotide code, Biophys. Chem. 112 (2004) 77-88; F. Pedone, F. Mazzei, M. Matzeu, F. Barone, Torsional constant of 27-mer DNA oligomers of different sequences, Biophys. Chem. 94 (2001) 175-184]. The problem of extracting reliable torsion elastic constants (alpha) from FPA measurements on such short DNAs is examined in detail. The difficulty is illustrated by two (fictitious) 24 bp DNAs with approximately 5-fold different torsion elastic constants and 10% different initial anisotropies (r(0)), which exhibit practically indistinguishable anisotropy decays for all t>1 ns. FPA data were simulated for 24 bp DNAs with different input values of alpha and r(0) in the presence and absence of Poisson noise, and were fitted using different choices of the adjustable and fixed parameters. Experimental data for a 24 bp DNA were fitted in a similar manner. For either the simulated or experimental FPA data, it was not possible to determine both the initial anisotropy, r(0), and the torsion elastic constant, alpha, in a reliable (i.e. statistically significant) manner in the presence of Poisson noise. When r(0) is assumed to be fixed at any particular value in the fitting protocol, a unique best-fit value of alpha is obtained, but that best-fit alpha is extremely sensitive to small deviations of the assumed fixed value of r(0) away from the input r(0)-value of the simulated data. Pedone et al. fitted their FPA data by assuming that r(0)=0.360, and adjusting alpha, the hydrodynamic radius (R(H)), and effective length (L). In fact, the reported best-fit values of R(H) and L lay significantly outside their expected ranges. When this same fitting protocol is applied to simulated data for 27 bp DNAs, better overall agreement with the reported experimental values (alpha, R(H), and L) is obtained for a model, wherein all DNAs have the same typical input alpha=5.9 x 10(-12) dyn cm, R(H)=10.0 A, and L=27 (3.4)+2.7=94.5 A, but a 1.00- to 1.13-fold range of r(0)-values, than for the model of Pedone et al., wherein all DNAs have the same input r(0)=0.360, R(H)=10.0 A, and L=94.5 A, but a approximately 3-fold range of alpha-values. It is concluded that, in the absence of reliable independent estimates of r(0) for every DNA, the alpha-values reported for 24 and 27 bp DNAs cannot be regarded as experimentally justified. The reliability of the torsion elastic constants reported for the 136 distinct tetranucleotide steps, which are inferred from the values reported for the fifty-three 24 and 27 bp DNAs, is also briefly discussed.     

Thermodynamics of the first transition in writhe of a small circular DNA by Monte Carlo simulation

Monte Carlo simulations are employed to investigate the thermodynamics of the first transition in writhe of a circular model filament corresponding to a 468 base-pair DNA. Parameters employed in these simulations are the torsional rigidity, C = 2.0 × 10⁻¹⁹ dyne cm², and persistence length, P = 500 Å. Intersubunit interactions are modeled by a screened Coulomb potential. For a straight line of subunits this accurately approximates the nonlinear Poisson-Boltzmann potential of a cylinder with the linear charge density of DNA. Curves of relative free energy vs writhe at fixed linking difference (Δ1) exhibit two minima, one corresponding to slightly writhed circles and one to slightly underwrithed figure-8's, whenever Δ1 lies in the transition region. The free energies of the two minima are equal when Δ1_c = 1.35, which defines the midpoint of the transition. At this midpoint, the free energy barrier between the two minima is found to be ΔG_bar = (0.20) k_BT at 298 K. Curves of mean potential energy vs writhe at fixed linking difference similarly exhibit two minima for Δ1 values in the transition region, and the two minimum mean potential energies are equal when Δ1 = 1.50. At the midpoint writhe, Δ1_c = 1.35, the difference in mean potential energy between the minimum free energy figure-8 and circle states is (1.3) k_BT, and the difference in their entropies is 1.3 k_B. Thus, the entropy of the minimum free energy figure-8 state significantly exceeds that of the circle at the midpoint of the transition. The first transition in writhe is found to occur over a rather broad range of Δ1 values from 0.85 to 1.85. The twist energy parameter (E_T), which governs the overall free energy of supercoiling, undergoes a sigmoidal decrease, while the translational diffusion coefficient undergoes a sigmoidal increase, over this same range. The static structure factor exhibits an increase, which reflects a decrease in radius of gyration associated with the circle to figure-8 transition. © 1996 John Wiley & Sons, Inc.     

Effect of polyethylene glycol on the supercoiling free energy of DNA

The supercoiling free energy of pUC19 DNA [2686 base pairs (bp)] was measured in various concentrations of PEG 8000 (polyethylene glycol; molecular weight 8000) by the topoisomer distribution method. The effective twist energy parameter (E(T)) that governs the supercoiling free energy declined linearly by 1.9-fold with increasing w/v % PEG from 0 to 7.5%, which lies below the threshold for intermolecular condensation. In principle, PEG could affect E(T) either via an osmotic exclusion mechanism or by altering the torsion elastic constant, bending rigidity, or self-repulsions of the DNA. Possible alterations of the DNA secondary structure and torsion elastic constant were assessed by CD spectroscopy and time-resolved fluorescence polarization anisotropy of intercalated ethidium. Up to 7.5% PEG, the secondary structure of the DNA remained largely unaltered, as evidenced by (1) the absence of any significant change in the CD spectrum, (2) an extremely small relative decrease (-0.0013) in intrinsic twist, and (3) a negligibly small change in the torsion elastic constant. The observed reduction in E(T) cannot be ascribed primarily to a decrease in torsion elastic constant, and most likely does not stem from a decrease in bending rigidity either. The decrease in medium dielectric constant due to PEG should increase the self-repulsions, and thereby increase E(T), which is opposite to the observed trend. Instead, the observed decline in E(T) is attributed to an osmotic exclusion mechanism. The change in molar volume excluded to the PEG (Delta V(ex)), when the linking difference converts from Delta l = 0 to Delta l = +/-1, was determined from the observed E(T) value and PEG osmotic pressure at each concentration. The experimental Delta V(ex) values agree well with theoretical estimates reckoned for a simple osmotic exclusion model, in which PEG is excluded by hard-core interactions from a concentric cylindrical volume around every duplex segment. The difference in volume excluded to PEG between the Delta l = 0 and the Delta l = +/-1 topoisomers is attributed entirely to the approximately 0.7 additional writhe "crossing" of two duplex strands at roughly 90 degrees, which is known to occur in the latter species. When the separation between the duplex centers at the "crossing" was adjusted so that the theoretical estimate of Delta V(ex) matched the experimental value at each PEG concentration, a value near 5.7 nm was obtained in each case. The invariance and plausible magnitude of this mean separation at the crossing provide strong support for this simple osmotic exclusion model. An alternative model, in which the PEG is excluded from the entire coil envelope of the DNA out to its radius of gyration, perhaps because it decreases the local dielectric constant, was also considered. The estimated difference in excluded volume in that case exceeds the experimental value by a factor of nearly 10(4), and could be ruled out on that basis.     

Torsional dynamics and rigidity of fractionated poly(dGdC)

Time-resolved fluorescence polarization anisotropy measurements were performed on two fractionated samples of duplex poly(dGdC) containing 230 (+40, ?30) base pairs (bp) and 590 ± 40 bp. Deconvolution using the intermediate zone formula for the twisting correlation functions (which is not valid for such short DNAs) yields apparent torsion constants for these two samples that are disparate and, in any case, too low. By similarly deconvoluting simulated data constructed from the correct twisting correlation functions, it can be inferred that these two samples actually exhibit the same torsion constant, α = (4.0 ± 0.4) × 10^?12 dyn cm. Within the experimental uncertainties, this value is the same as that reported previously from this laboratory for linear ?29 and linearized M13mp7 DNAs. The 590-bp sample exhibited a peculiar evolution of its apparent torsional rigidity from a very high initial value, \documentclass{article}\pagestyle{empty}\begin{document}$ \hat \alpha $\end{document} = (11 ± 1) × 10^?12 dyn cm, to a normal value over a period of several months, during which time many very small fragments appeared to be dissociated from, or annealed out, of the predominant high-molecular-weight species. Possible interpretations of these observations are discussed.     

Effects of chloroquine on the torsional dynamics and rigidities of linear and supercoiled DNAs at low ionic strength

The magnitude and uniformity of the torsion elastic constant (alpha) of linear and supercoiled pBR322 DNAs are measured in 3 mM Tris as a function of added chloroquine/basepair ratio (chl/bp) by studying the fluorescence polarization anisotropy of intercalated ethidium dye. The time-resolved FPA is measured using a picosecond dye-laser for excitation and time-correlated single-photon counting detection. For both linear and supercoiled DNAs, alpha remains uniform except at the very highest chl/bp ratio examined. For the linear DNA, alpha decreases from 5.0 x 10(-12) dyne-cm at chl/bp = 0 to about 3.5 x 10(-12) dyne-cm at chl/bp = 0.5, and remains at that value up to chl/bp = 5, whereupon it increases back up to its original value. For the supercoiled DNA, alpha remains constant at about 5.2 x 10(-12) dyne-cm from chl/bp = 0 up to chl/bp = 5, whereupon it increases in parallel with the linear DNA. The effect of chloroquine on the secondary structure, torsion constant, and torsional dynamics evidently differs substantially between linear and supercoiled DNAs, even under conditions where the supercoiled DNA is completely relaxed and both DNAs bind the same amount of dye. This strongly contradicts any notion that the local structures of linear and relaxed supercoiled DNA/dye complexes with the same binding ratio are identical. The increase in apparent alpha at chl/bp = 5 for both DNAs may be due to stacking of the chloroquine in the major groove and consequent stiffening of the filament.     

Structure and dynamics of double helices in solution: modes of DNA bending

The long range structure of DNA restriction fragments has been analysed by electro-optical measurements. The overall rotation time constants observed in a low salt buffer with monovalent ions is shown to decrease upon addition of Mg2+ or spermine. Since the circular dichroism and also the limiting value of the linear dichroism remain almost constant under these conditions, the effect is attributed to a change of the long range structure. According to a weakly bending rod model, the persistence length decreases from about 600 A in the absence of Mg2+ or spermine to about 350 A in the presence of these ions. The persistence length measured in the presence of Mg2+ is almost independent of temperature in the range of 10 to 40 degrees C. The nature of DNA bending is analysed by measurements of bending amplitudes and time constants from dichroism decay curves. The observed absence of changes in the bending amplitudes upon addition of Mg2+ or spermine, even though addition induces changes of the persistence length by a factor of 2, is hardly consistent with simple thermal bending. The combined results, including the remarkably small temperature dependence of persistence length and bending amplitude, can be explained by the existence of two bending effects: inherent curvature of DNA dominates at low temperature, whereas thermal bending prevails at high temperature. Analysis of bending amplitudes from dichroism decay curves according to an arc model provides an approximate measure for the degree of bending in restriction fragments. The model is consistent with the observed chain length dependence of bending amplitudes and provides an approximate curvature corresponding to a radius of about 400 A. Thus the curvature observed in restriction fragments is similar to that observed for high molecular DNA condensed into toroids by addition of ions like spermine. Particularly strong bending of DNA is induced by [Co(NH3)6]3+, indicated by an apparent persistence length of 200 A and an increased bending amplitude together with a reduced limit value of the linear dichroism. This effect is attributed to the high charge density of this ion and potential site binding.     

Crystallization and characterization of the recombinant human Clara cell 10-kDa protein

Crystals of recombinant human Clara cell 10-kDa protein were grown both from ammonium sulfate and polyethylene glycol (PEG) solutions. Crystals grown from ammonium sulfate solution have been characterized by X-ray diffraction studies as monoclinic with the space group C2 and lattice constants a = 69.2 Å, b = 83.0 Å, c = 58.3 Å, and β = 99.7°. The monoclinic crystals diffract to beyond 2.5 Å. Some of the crystals grown from PEG were of a similar habit to those grown from ammonium sulfate, but others were triclinic with the space group P1 and cell constants a = 40.3 Å, b = 46.3 Å, c = 51.3 Å, α = 117.7°, β = 102.3°, and γ = 71.4°. These crystals diffract to beyond 3.2 Å. © 1994 Wiley-Liss, Inc.     

An electrostatic model for the dielectric effects,the adsorption of multivalent ions,and the bending of B-DNA

We have studied electrostatic properties of DNA with a discrete charge model consisting of a cylindrical dielectric core with a radius of 8 Å and a dielectric constant D_i = 4, surrounded by two helical strings of phosphate point charges at 10 Å from the axis, immersed in an aqueous medium with dielectric constant D_w = 78.54. Eliminating the dielectric core makes potentials in the phosphate surface less negative by about 0.5 kT/e. Salt effects are evaluated for the model without a dielectric core, using the shielded Coulomb potential. Smearing the phosphate charges increases their potential by about 2.5 kT/e, due mostly to the self-potential of the smeared charge. Potentials in the center of the minor and major grooves vary less than 0.02 kT/e along their helical path. The potential in the center of the minor groove is from 1.0 to 1.7 kT/e, more negative than in the center of the major groove, depending on dielectric core and salt concentration. So multivalent cations and also larger cationic ligands, such as some antibiotics, are likely to adsorb in the minor groove, in agreement with earlier computations by A. and B. Pullman. Dielectric effects on the surface potential and the local potential variations are found to be relatively small. Bending of DNA is studied by placing a multivalent cation, M^Z+, in the center of the minor or major groove, curving DNA around it for a certain length, and calculating the free energy difference between the bent and the straight configuration. Boltzmann averaged bending angles, 〈β〉, are found to be maximal in 0.03M monovalent salt, for a length of about 50 or 25 Å of curved DNA when an M^Z+ ion is adsorbed in the minor or the major groove, respectively. When the dielectric constant of water is used throughout the calculation, we find maximal bends of 〈β〉 = 11° for M²⁺ and 〈β〉 = 16° for M³⁺ in the minor groove, 〈β〉 = 13° for M³⁺ in the major groove. The absence of bends in DNA adsorbed to mica in the presence of Mg salts supports the role of Mg²⁺ in “ion bridging” between DNA and mica. The treatment of the effective dielectric constant between two points outside a dielectric cylinder in water is appended. © 1998 John Wiley & Sons, Inc. Biopoly 46: 503–516, 1998     

Effects of Na+and Mg2+on the Structures of Supercoiled DNAs: Comparison of Simulations with Experiments

Recent cryo-electron microscopy (cryo-EM) results suggest that sufficient NaCl concentration (≤0.1 M) and superhelix density (≤−0.05) cause circular DNAs to adopt highly extended, tightly interwound configur ations, in which the strands are laterally contiguous along almost their entire length. Millimolar levels of MgCl₂reportedly act synergistically with NaCl to produce similar conformations. However, Monte Carlo simulations with purely repulsive interduplex forces failed to reproduce such structures. In the present work, solution measurements of particular physical properties were performed both to characterize the effects of Na⁺and Mg²⁺on DNA structure and to provide quantitative tests of Monte Carlo simulations of circular DNAs. Supercoiled p30δ DNAs in 10 mM Tris plus 0, 0.122, and 0.1 M NaCl, and 0.1 M NaCl plus 4 mM Mg²⁺were examined by static and dynamic light scattering (LS and DLS), time- resolved fluorescence polarization anisotropy (FPA) of intercalated ethidium, and circular dichroism (CD) spectroscopy. Upon addition of 0.122 M NaCl, the radius of gyration (R_g) decreased substantially, which indicates that p30δ adopts a more compact structure. This contradicts the cryo-EM studies, where molecular extension andR_gboth increase upon adding 0.1 M NaCl. In 0.1 M NaCl, the torsion constant measured by FPA is practically invariant to superhelix density, and the plateau diffusion coefficient at large scattering vector (D_plat) is likewise nearly the same at both relaxed and native superhelix densities. Such invariance is difficult to reconcile with any transition from relaxed circles to tightly interwound structures with laterally contiguous strands. Metropolis Monte Carlo simulations were performed to generate canonically distributed sets of structures, from which averageD₀values and scattered intensity ratios,〈I(0)〉/〈I(k)〉, were calculated. Agreement between simulations and experiments in regard to 〈I(0)|〉/〈I(k)〉,D₀and the supercoiling free energy, ΔG_sc(Δl ), is remarkably good for the most extensively studied p30δ samples. The simulated structures exhibit no sign of very tight interwinding with extensive lateral contacts, but instead exhibit most probable superhelix diameters of 85 to 90 Å. When 4 mM Mg²⁺was added to native supercoiled p30δ in 0.1 M NaCl,R_gdecreased,D₀increased, and the longest internal relaxation rate (1/τ₂(0)) increased, all of which indicate a further overall contraction of the molecular envelope. The torsion constant exhibited a slight increase that is hardly statistically significant. In this case, agreement between the simulations and experiments was only semi-quantitative for most samples investigated, although the predicted contraction was exhibited by all five samples of p30δ and one of pBR322 DNA. The simulated structures in 0.1 M NaCl plus 4 mM Mg²⁺again showed no sign of extensive lateral contacts. A plausible explanation is proposed for the highly extended, tightly interwound structures seen in cryo-EM, and explicitly tested by Monte Carlo simulations of a 1000 bp circular DNA at +25 and −50°C. Structures identical to those seen in cyro-EM are in fact the equilibrium structures in the simulations at −50°C, and the estimated time for equilibration (2.3×10⁻⁶second) is much smaller than the estimated time for vitrification (1×10⁻⁴second).     

Dynamic bending rigidity of DNA

Rapidly relaxing components in the decay of the transient electric dichroism of DNA restriction fragments were reported by Diekmann et al. [(1982) Biophys. Chem. 15, 263-270] and P?rschke et al. [(1987) Biopolymers 26, 1971-1974]. These are analyzed using a new normal mode theory for weakly bending rods and assigned to bending. The longest bending relaxation times for fragments with 95-250 base pairs coincide with the theoretical curve calculated for a dynamic bending rigidity corresponding to a dynamic persistence length Pd = 2100 A. Analysis of the relative amplitudes of fast and slow components following weak orienting pulses is also consistent with a rather large dynamic persistence length. The enhancement of the relative amplitude of the fast component in large electric fields is attributed to steady-state bending of initially perpendicular DNAs by the field. Several reasons are proposed why the dynamic bending rigidity is 4 times larger than the apparent static bending rigidity inferred from equilibrium persistence length measurements on the same fragments.     

Calculated compression,bending, shearing,torsion, and base-tilting force constants of B- and A-form poly(dG)·poly(dC)

Force constants associated with large-scale motions of the DNA double-helical homopolymer poly(dG)·poly(dC) are projected out of a long-range atom–atom Coulomb force field. Force constants for both B- and A-conformations have been calculated. Using the Coulomb interaction as previously incorporated into our DNA normal mode calculations, we obtain the forces determined by this long-range interaction. These include compression, bending, shearing, torsion, and base tilting. We show, quantitatively, how the shearing and torsional transverse interactions fall off with intercell distance more rapidly than the compressional (longitudinal) interactions. Reasonable values for the elastic moduli of B- and A-DNA are calculated. An important prediction of the present interaction theory is that although the single adjustable strength parameter in the Coulomb force field was chosen so as to reproduce an experimental value for the longitudinal sound velocity, the transverse torsional potential resulting from this fitted force field is in excellent agreement with results reported from supercoiling data and fluorescence measurements.     

Effects of ethylene glycol on the torsion elastic constant and hydrodynamic radius of p30delta DNA

Upon increasing the concentration of ethylene glycol (EG) at 37 degrees C, the twist energy parameter, E(T), which governs the supercoiling free energy, was recently found to undergo a decreasing (or reverse) sigmoidal transition with a midpoint near 20 w/v % EG. In this study, the effects of adding 20 w/v % EG on the torsion elastic constant (alpha) of linear p30delta DNA and on the hydrodynamic radius (R(H)) of a synthetic 24 bp duplex DNA were examined at both 40 and 20 degrees C. The time-resolved fluorescence intensity and fluorescence polarization anisotropy (FPA) of intercalated ethidium were measured in order to assess the effects of 20 w/v % EG on: (1) alpha; (2) R(H); (3) the lifetimes of intercalated and non-intercalated dye; (4) the amplitude of dye wobble in its binding site; and (5) the binding constant for intercalation. The effects of 20 w/v % EG on the circular dichroism (CD) spectrum of the DNA and on the emission spectrum of the free dye were also measured. At 40 degrees C, addition of 20 w/v % EG caused a substantial (1.27- to 1.35-fold) increase in alpha, a significant change in the CD spectrum, and a very small, marginally significant increase in R(H), but little or no change in the amplitude of dye wobble in its binding site or the lifetime of intercalated dye. Together with previously reported measurements of E(T), these results imply that the bending elastic constant of DNA is significantly decreased by 20 w/v % EG at 40 degrees C. At 20 degrees C, addition of 20 w/v % EG caused a marginally significant decrease in alpha and very little change in any other measured properties. Also at 20 degrees C, addition of 30 w/v % betaine caused a marginally significant increase in alpha and significant but modest change in the CD spectrum, but very little change in any other properties.