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.

The distribution of end-to-end distances of the weakly bending rod model.

The weakly bending rod model is an approximation to a worm-like chain in the limit where the ratio L(0)/P of the contour length L(0) to the persistence length P is not too large. The range of validity of the weakly bending rod model is investigated by deriving analytical expressions for its distribution of end-to-end distances P(L) and its moments and numerically comparing the results with corresponding values for the worm-like chain model. No general, closed form analytical expression for either P(L) or the average length of a worm-like chain exists, so those quantities are obtained by Monte Carlo simulations. Exact analytical expressions for and for the worm-like chain are employed in the comparison of the computed moments. Moments calculated for the approximate distributions of Daniels and Yamakawa and Stockmayer are also compared with the others. In addition, P(L) and its moments for the alternative model of Winkler et al. are compared with the others. The weakly bending rod model gives a reasonably good account of both P(L) and , m = 1,2,4, over the range L(0)/P /= 1.0. In contrast, the alternative model of Winkler et al. yields rather poor results in the rodlike domain.

Dynamic bending rigidity of a 200-bp DNA in 4 mM ionic strength: a transient polarization grating study.

DNA may exhibit three different kinds of bends: 1) permanent bends; 2) slowly relaxing bends due to fluctuations in a prevailing equilibrium between differently curved secondary conformations; and 3) rapidly relaxing dynamic bends within a single potential-of-mean-force basin. The dynamic bending rigidity (kappa(d)), or equivalently the dynamic persistence length, P(d) = kappa(d)/k(B)T, governs the rapidly relaxing bends, which are responsible for the flexural dynamics of DNA on a short time scale, t < or = 10(-5) s. However, all three kinds of bends contribute to the total equilibrium persistence length, P(tot), according to 1/P(tot) congruent with 1/P(pb) + 1/P(sr) + 1/P(d), where P(pb) is the contribution of the permanent bends and P(sr) is the contribution of the slowly relaxing bends. Both P(d) and P(tot) are determined for the same 200-bp DNA in 4 mM ionic strength by measuring its optical anisotropy, r(t), from 0 to 10 micros. Time-resolved fluorescence polarization anisotropy (FPA) measurements yield r(t) for DNA/ethidium complexes (1 dye/200 bp) from 0 to 120 ns. A new transient polarization grating (TPG) experiment provides r(t) for DNA/methylene blue complexes (1 dye/100 bp) over a much longer time span, from 20 ns to 10 micros. Accurate data in the very tail of the decay enable a model-independent determination of the relaxation time (tau(R)) of the end-over-end tumbling motion, from which P(tot) = 500 A is estimated. The FPA data are used to obtain the best-fit pairs of P(d) and torsion elastic constant (alpha) values that fit those data equally well, and which are used to eliminate alpha as an independent variable. When the relevant theory is fitted to the entire TPG signal (S(t)), the end-over-end rotational diffusion coefficient is fixed at its measured value and alpha is eliminated in favor of P(d). Neither a true minimum in chi-squared nor a satisfactory fit could be obtained for P(d) anywhere in the range 500-5000 A, unless an adjustable amplitude of azimuthal wobble of the methylene blue was admitted. In that case, a well-defined global minimum and a reasonably good fit emerged at P(d) = 2000 A and (1/2) = 25 degrees. The discrimination against P(d) values <1600 A is very great. By combining the values, P(tot) = 500 A and P(d) = 2000 A with a literature estimate, P(pb) = 1370 A, a value P(sr) = 1300 A is estimated for the contribution of slowly relaxing bends. This value is analyzed in terms of a simple model in which the DNA is divided up into domains containing m bp, each of which experiences an all-or-none equilibrium between a straight and a uniformly curved conformation. With an appropriate estimate of the average bend angle per basepair of the curved conformation, a lower bound estimate, m = 55 bp, is obtained for the domain size of the coherently bent state. Previous measurements suggest that this coherent bend is not directional, or phase-locked, to the azimuthal orientation of the filament.

Manifestations of slow site exchange processes in solution NMR: a continuous Gaussian exchange model.

The effects of site exchange due to slow conformational changes in rapidly rotating molecules in solution are examined in detail. Significant gaps in the currently available theory are filled. The effects of site exchange on the lineshape, decay of a simple spin-echo, decay of the even echoes in a Carr-Purcell-Meiboom-Gill (CPMG) pulse-sequence, and decay of the transverse magnetization in a resonant spin-locking field are investigated. Both trajectory and stochastic operator approaches are formulated and shown to be completely equivalent whenever the dynamics of population transfers among the inequivalent sites is governed by either a stationary or a nonstationary Markov process. A nonstationary Markov process may result from Brownian dynamics (a stationary Markov process) in a larger conformational space that contains the subspace of inequivalent sites. A continuous Gaussian exchange model is formulated in which a nucleus undergoes continuous one-dimensional motion in a harmonic potential well that is located in a linear chemical shift gradient. The effects of this Gaussian exchange model on the lineshape, simple spin-echo decay, and decay of the even echoes of a CPMG pulse train are treated rigorously via the trajectory approach. Compact analytical expressions are obtained for the relevant correlation functions in each case. The relevant decays are found to be exponential in the very short time and long time limits, which are not necessarily experimentally significant in any given case. In the fast exchange limit the relevant decays are exponential at all times, and explicit formulas are given for their decay rates. In the long time limit, all discrete multisite models with the same intrinsic Ro2 at every site are shown to be completely equivalent to a continuous Gaussian model with appropriate relaxation time and variance of the Larmor frequency. The effects of this Gaussian exchange model on the decay of the transverse magnetization in a resonant spin-locking field are treated heuristically by a trajectory approach. The intrinsic contribution (Ro1rho) of rapid rotations and dipole-dipole interactions to relax the transverse magnetizations of two nuclei of the same kind in the presence of a (nearly) resonant spin-locking field is also derived and found to be practically the same as the intrinsic contribution, Ro2, of those same rotations to the simple and CPMG spin-echo decay rates and linewidth. Literature data for the linewidth, decay rate of the CPMG even spin-echoes, and R(1rho) decay rate for the A9-H2 protons of adenines at the central TpA step in the sequence, 5'-GCAGGTTTAAACCTCG-3', are analyzed using the Gaussian exchange model to assess the time-scale and variance of the site exchange process as well as the intrinsic Ro2 rate. Although a single Gaussian exchange process with appropriate parameters can fit these three A9-H2 data rather well, this particular "solution" cannot be reconciled with NMR relaxation data on other protons in the same DNA molecule. Rather good agreement with all of the observations is obtained by using a model of two concurrent Gaussian exchange processes, whose relaxation times, tau = 7 and 460 micros, differ in time-scale by a factor of 65. The insensitivity of R1rho in the presence of a fast site exchange process to much slower concurrent site exchange processes is explicitly demonstrated. Protocols for detecting and characterizing a second slow site exchange process are suggested.

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 degrees C were investigated by measuring their CD spectra and also their torsion elastic constants () by time-resolved fluorescence polarization anisotropy. For one of these DNAs, the Haell fragment of pBR322, the apparent diffusion coefficients [Dapp(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 . Also for the 1876 base pair fragment, Dapp(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 Dapp(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 and Dapp(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.

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.

Comparison of hard-cylinder and screened Coulomb interactions in the modeling of supercoiled DNAs.

A 1000 base pair (bp) model supercoiled DNA is simulated using spherical screened Coulomb interactions between subunits on one hand and equivalent hard-cylinder interactions on the other. The amplitudes, or effective charges, of the spherical screened Coulomb electrostatic potentials are chosen so that the electrostatic potential surrounding the middle of a linear array of 2001 subunits (31.8 A diameter) closely matches the solution of the nonlinear Poisson-Boltzmann equation for a cylinder with 12 A radius and the full linear charge density of DNA at all distances beyond the 24 A hard-core diameter. This superposition of spherical screened Coulomb potentials is practically identical to the particular solution of the cylindrical linearized Poisson-Boltzmann equation that matches the solution of the nonlinear Poisson-Boltzmann equation at large distances. The interaction energy between subunits is reckoned from the effective charges according to the standard DLVO expression. The equivalent hard-cylinder diameter is chosen following Stigter's protocol for matching second virial coefficients, but for the full linear charge density of DNA. The electrostatic persistence length of the model with screened Coulomb interactions is extremely sensitive to the (arbitrarily) chosen subunit length at the higher salt concentrations. The persistence length of the hard-cylinder model is adjusted to match that of the screened Coulomb model for each ionic condition. Simulations for a superhelix density sigma = -0.05 using a spherical screened Coulomb interaction plus a 24 A hard-cylinder core (SCPHC) potential indicate that the radius of gyration of this 1000 bp DNA actually undergoes a slight increase as the NaCl concentration is raised from 0.01 to 1.0M. Thus, merely softening the potential from hard-cylinder to screened Coulomb form does not produce a large decrease in radius of gyration with increasing NaCl concentration for DNAs of this size. Radii of gyration, static structure factors, and diffusion coefficients obtained using the equivalent hard-cylinder (EHC) potential agree well with those obtained using the SCPHC potential in 1.0M NaCl, but in 0.1M NaCl the agreement is not as good, and in 0.01M NaCl the agreement is definitely unsatisfactory. These conclusions differ in significant respects from those obtained in previous studies.

The question of long-range allosteric transitions in DNA.

The question of long-range allosteric transitions of DNA secondary structure and their possible involvement in transcriptional activation is discussed in the light of new results. A variety of recent evidence strongly supports a fluctuating long-range description of DNA secondary structure. Balanced equilibria between two or more different secondary structures, and the occurrence of very large domain sizes, have been documented in several instances. Long-range allosteric effects stemming from changes in sequence or secondary structure over a small region of the DNA have been observed to extend over distances up to hundreds of base pairs in some cases. The discovery that coherent bending strain beyond a threshold level in small (N < or = 250 base pairs (bp)] circular DNAs significantly alters the DNA secondary structure has important implications, especially for transcriptional activators that either bend the DNA directly or are involved in the formation of DNA loops of sufficiently small size (N < or = 250 bp). Whether the RNA polymerase is activated primarily via protein: protein contacts, as is widely believed, or instead via a bend-induced allosteric transition of the DNA in such a small loop, is now an open question. Binding of the transcriptional activator Sp1 to linear DNA induces a remarkably long-range change in its secondary structure, and catabolite activator protein binding to a supercoiled DNA behaves similarly, though possibly for different reasons. Compelling evidence for a bend-induced long-range structural transmission effect of the transcriptional activator integration host factor on RNA polymerase activity was recently reported. These results may augur a new paradigm in which allosteric transitions of duplex DNA, as well as of the proteins, are involved in the regulation of transcription.

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 (> or approximately 0.1 M) and superhelix density (> or approximately-0.05) cause circular DNAs to adopt highly extended, tightly interwound configurations, in which the strands are laterally contiguous along almost their entire length. Millimolar levels of MgCl2 reportedly 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 p30 delta 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 (Rg) decreased substantially, which indicates that p30 delta adopts a more compact structure. This contradicts the cryo-EM studies, where molecular extension and Rg both 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 (Dplat) 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 average Do values and scattered intensity ratios, [symbol: see text]I (zero) [symbol: see text]/[symbol: see text] l(k) [symbol: see text], were calculated. Agreement between simulations and experiments in regard to [symbol: see text] I(O) [symbol: see text] /[symbol: see text] I(k) [symbol: see text], D(zero) and the supercoiling free energy, delta Gsc (delta l), is remarkably good for the most extensively studied p30 delta 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 A. When 4 mM Mg2+ was added to native supercoiled p30 delta in 0.1 M NaCl, Rg decreased, D(zero) increased, and the longest internal relaxation rate (1/tau 2(zero)) 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 p30 delta 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 degrees C. Structures identical to those seen in cryo-EM are in fact the equilibrium structures in the simulations at -50 degrees C, and the estimated time for equilibration (2.3 x 10(-6) second) is much smaller than the estimated time for vitrification (1 x 10(-4) second).

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 degrees 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.

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 x 10(-19) dyne cm2, and persistence length, P = 500 A. 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 (delta l) exhibit two minima, one corresponding to slightly writhed circles and one to slightly underwrithed figure-8's, whenever delta l lies in the transition region. The free energies of the two minima are equal when delta lc = 1.35, which defines the midpoint of the transition. At this midpoint, the free energy barrier between the two minima is found to be delta Gbar = (0.20) kBT at 298 K. Curves of mean potential energy vs writhe at fixed linking difference similarly exhibit two minima for delta l values in the transition region, and the two minimum mean potential energies are equal when delta l = 1.50. At the midpoint writhe, delta lc = 1.35, the difference in mean potential energy between the minimum free energy figure-8 and circle states is (1.3) kBT, and the difference in their entropies is 1.3 kB. 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 delta l values from 0.85 to 1.85. The twist energy parameter (ET), 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.

Effect of anisotropy of the bending rigidity on the supercoiling free energy of small circular DNAs.

In principle, the supercoiling free energy of a small circular DNA will be enhanced by increasing the anisotropy of its bending potential at constant persistence length. The magnitude of this effect is investigated by Monte Carlo simulation using an extension of a previously proposed algorithm. The supercoiling free energy at 298 K is simulated for circular DNAs containing N = bp with torsion constant alpha = 5.8 X 10(-12) dyne cm, persistence lengths P = 500 A and 10,000 A, and a range of anisotropies of the bending potential from rho = 1.0 to 16.0. The apparent torsion constants, reckoned from these supercoiling free energies by assuming an isotropic bending potential, are found to increase by less than 3% as the input anisotropy increases from 1.0 to 16.0 When P = 500 A, the apparent torsion constant never rises significantly above the input value over the entire range of input anisotropies. When P = 10,000 A, the apparent torsion constant rises only about 3% above the input value for anisotropies rho = 8.0 and 16.0. Evidently, anisotropy of the bending potential cannot account for the fact that the torsion constants reported for small circular DNAs exceed those reported for long linear DNAs by a factor of 1.6 or more.

Monte Carlo simulations of supercoiling free energies for unknotted and trefoil knotted DNAs.

A new Monte Carlo (MC) algorithm is proposed for simulating inextensible circular chains with finite twisting and bending rigidity. This new algorithm samples the relevant Riemann volume elements in a uniform manner, when the constraining potential vanishes. Simulations are performed for filaments comprising 170 subunits, each containing approximately 28 bp, which corresponds to a DNA length of 4770 bp. The bending rigidity is chosen to yield a persistence length, P = 500 A, and the intersubunit potential is taken to be a hard-cylinder potential with diameter d = 50 A. This value of d yields the same second virial coefficient as the electrostatic potential obtained by numerical solution of the Poisson-Boltzmann equation for 150 mM salt. Simulations are performed for unknotted circles and also for trefoil knotted circles using two different values of the torsional rigidity, C = (2.0 and 3.0) x 10(-19) dyne cm2. In the case of unknotted circles, the simulated supercoiling free energy varies practically quadratically with linking difference delta l. The simulated twist energy parameter ET, its slope dET/dT, and the mean reduced writhe /delta l for C = 3 x 10(-19) dyne cm2 all agree well with recent simulations for unknotted circles using the polygon-folding algorithm with identical P, d, and C. The simulated ET vs. delta l data for C = 2.0 x 10(-19) dyne cm2 agree rather well with recent experimental data for p30 delta DNA (4752 bp), for which the torsional rigidity, C = 2.07 x 10(-19) dyne cm2, was independently measured. The experimental data for p30 delta are enormously more likely to have arisen from C = 2.0 x 10(-19) than from C = 3.0 x 10(-19) dyne cm2. Serious problems with the reported experimental assessments of ET for pBR322 and their comparison with simulated data are noted. In the case of a trefoil knotted DNA, the simulated value, (ET)tre, exceeds that of the unknotted DNA, (ET)unk, by approximately equal to 1.40-fold at magnitude of delta l = 1.0, but declines to a plateau about 1.09-fold larger than (ET)unk when magnitude of delta l > or = 15. Although the predicted ratio, (ET)tre/(ET)unk approximately equal to 1.40, agrees fairly well with recent experimental measurements on a 5600-bp DNA, the individual measured ET values, like some of those reported for pBR322, are so large that they cannot be simulated using P = 500 A, d = 50 A, and any previous experimental estimate of C.

Position-dependent internal motions and effective correlation times for magnetization transfer in DNA.

An effective correlation time that accounts for position dependence of the combined local angular motions and collective twisting and bending deformations, as well as for anisotropic uniform rotation, is defined in terms of the magnetization-transfer rate and expressed in terms of molecular parameters. Application to measured magnetization-transfer rates from H6 to H5 of cytosine in cases where all other relevant data, including the uniform rotational diffusion coefficients, are known, suggests that the amplitude of local angular motion, as well as that due to collective deformations, is significantly greater for a penultimate base pair than for base pairs near the center of the molecule, and that such amplitudes might be approximately transferable from one molecule to another. Protocols are suggested for using estimated ratios of effective correlation times in the initial calibrations of internuclear distances and in the subsequent structure-refinement process.

Effect of ethidium binding and superhelix density on the supercoiling free energy and torsion and bending constants of p30 delta DNA.

Topoisomer distributions created by the action of topoisomerase I on p30 delta DNA in the presence of various concentrations of ethidium are measured and analyzed using recently developed theory to obtain the twist energy parameter (ET) that governs the free energy of supercoiling in each case. Competitive dialysis experiments to investigate the relative affinity of ethidium for linear and supercoiled DNAs at different binding ratios are assayed fluorometrically and the results are analyzed using related theory. The topoisomer distributions and fluorescence intensity ratios agree well with the theory, which is based on the assumption that the supercoiling free energy varies quadratically with the effective linking difference, regardless of ethidium binding or superhelix density. The topoisomer distribution experiments alone yield an average best-fit value, ET = 950 +/- 80, independent of ethidium binding ratio from r = 0 to 0.082, while the combined topoisomer distribution and ethidium binding experiments yield an average best-fit value, ET = 1030 +/- 90, which is essentially independent of ethidium binding ratio from r = 0 to 0.082 and superhelix density from sigma = 0 to (-)0.053. One may conclude that the supercoiling free-energy-varies quadratically with effective linking difference over the entire range of observed ethidium binding ratios and superhelix densities. The independently measured torsion constant (alpha) of p30 delta DNA is likewise essentially independent of superhelix density and ethidium binding ratio. The observed invariance of ET and alpha implies that the bending constant kappa beta is similarly invariant to superhelix density and ethidium binding ratio. The apparently ideal behavior displayed by p30 delta DNA is not exhibited by pBR322 DNA, which is discussed in the following companion paper.

Effect of ethidium binding and superhelix density on the apparent supercoiling free energy and torsion constant of pBR322 DNA.

The value of the twist energy parameter (ET) of pBR322 is determined near zero superhelix density from topoisomer distributions created under various conditions. The resulting value, ET = 1155 +/- 65, at 37 degrees C is essentially unaffected by adding 10 mM Mg2+, or by changing the kind of Topo I from chicken-red-cell to calf-thymus. This value significantly exceeds that (ET = 950 +/- 80) measured for p30 delta DNA under identical conditions by the same method in the preceding paper. Decreasing the temperature from 37 to 21 degrees C yields a slightly larger value, ET = 1340 +/- 130, but the statistical significance of the increase is marginal. Attempts to determine reliable ET values for pBR322 at higher superhelix densities by ethidium binding were frustrated by the fact that good fits of the equilibrium dialysis results could not be achieved using a single value of ET. Moreover, the curves of apparent ET versus binding ratio r vary considerably from one preparation to another, and for a given preparation vary with time after cell lysis up to about seven weeks, after which they settle in to nearly reproducible behavior. The apparent ET values obtained from competitive dialysis experiments are typically rather low (ET approximately 700) for small r and nearly native superhelix density, and rise up to 1300 to 1500 with increasing binding ratio (up to r = 0.055) and decreasing negative superhelix density.(ABSTRACT TRUNCATED AT 250 WORDS)

A model for the binding of E. coli single-strand binding protein to supercoiled DNA.

A model is proposed for the binding of E. coli single strand binding protein (SSB) to supercoiled DNA. The basic tetrameric binding units of SSB are assumed to bind in pairs to the complementary single strands of a locally melted region. The cooperativity of the binding includes contributions from both protein-protein and base-pair stacking interactions. Each bound SSB tetramer is assumed to unwind l = 34 bp, which implies an unwinding angle of 3.27 turns. The resulting loss of superhelical strain is the essential driving force for binding SSB to supercoiled DNAs. All molecular parameters entering into the theory are estimated from available data, except for the composite binding constant (Ka), which is adjusted to best-fit the theory to the fluorescence quenching (FQ) and diffusion coefficient (D0) data of Langowski et al. Very good fits are obtained with optimum values of Ka that are consistent with estimates from other data. This binding model predicts several noteworthy features. (1) SSB binds essentially always in a single contiguous stack on a supercoiled plasmid, and relative fluctuations in stack length are quite small, in agreement with results of electron microscopy studies. (2) The progressive loss of superhelical strain with increasing bound ligand decreases the affinity of the DNA for SSB. This anti-cooperativity offsets the cooperativity of the binding and causes apparent saturation of the binding at rather low binding ratios. Consequently, over the limited span of the measurements, the FQ data can also be satisfactorily fitted by a non-cooperative model comprising a small number of independent sites. (3) When SSB binds to a population of different topoisomers, the distribution of linking differences of the resulting complexes is extremely narrow. Thus, SSB acts to level any differences in superhelical strain in a population of topoisomers. Finally, the effects of restricting binding to a region comprising only part of the plasmid are assessed.

A test of the model-free formulas. Effects of anisotropic rotational diffusion and dimerization.

The effects of anisotropy of rotational diffusion and extent of dimerization on the performance of the simple and extended model-free formulas are investigated. Numerically exact 15N NMR R1, R2, and NOE data are simulated for cylindrically symmetric species and also for mixtures of spherical monomers and dimers with the same internal dynamics. The relevant internuclear vectors are assumed to move in isotropic deflection potentials fixed at different orientations in the molecule and to exhibit a single relaxation time in their internal correlation functions. The simple model-free formula is fitted to these simulated data in order to obtain the best-fit order parameter and internal relaxation time for each nucleus. Fitting is accomplished by the standard data-analysis protocol, in which a single common global correlation time is adjusted, and also by an alternative protocol, in which the global correlation time is adjusted separately for each nucleus. The extended model-free formula is likewise fitted to these same data. With noise-free data, the simple model-free formula and standard protocol yield remarkably good best-fit internal motion parameters up to moderate anisotropies (r = D parallel/D perpendicular = 2.0), but some or many of the NMR relaxation data are not fitted well even for quite modest anisotropies (r = 1.3). The extended model-free formula yields an improved fit to the NMR data, but predicts substantial amplitudes of nonexistent slow internal motions (tau approximately greater than 0.2 ns) for many of the nuclei for all r > or = 1.3. The simple model-free formula with the alternate protocol yields even better internal motion parameters than the standard protocol and also an excellent fit to the NMR relaxation data. The best-fit global correlation time for each nucleus corresponds very closely to the theoretical correlation time defined herein. Knowledge of these times would allow one not only to estimate the anisotropy of diffusion but also in favorable cases to infer the existence of slow internal motions. Inclusion of typical statistical errors in R1, R2, and NOE, or modest exchange contributions to R2, seriously degrades the performance of the simple model-free formula with either protocol, especially in regard to the internal relaxation times, which can exhibit very large deviations from their input value even for spherical diffusors. When the fraction of monomers existing as dimers lies in the range 0.1 < or = fd < or = 0.8, none of the three model-free approaches tested yields reliable internal motion parameters.

Circularization of small DNAs in the presence of ethidium: a theoretical analysis.

A rigorous theory is developed for ethidium binding to linear and circular DNAs and for the ratios of topoisomers produced upon ligation of an equilibrium population of noncovalently closed circles in the presence of ethidium. Assuming an unwinding angle theta E = 26 degrees for intercalated ethidium, optimum values of the intrinsic binding constant, KE = 7.16 x 10(4) M-1, the intrinsic twist, l0 = 23.746 turns, and twist energy parameter, Et = 5250, are obtained by fitting the present theory to the data of Shore and Baldwin [(1993) Journal of Molecular Biology, Vol. 170, pp. 983-1007] for a 247 base pair DNA. A very good fit is achieved with these optimum values, but a poor fit results when the parameters estimated by Shore and Baldwin are employed in the same theory. Three assumptions employed in the analysis of Shore and Baldwin are found to be not strictly valid. Adoption of the present substantially larger Et value as representative of their short DNAs would allow the Et vs N data of Shore and Baldwin to conform to the shape predicted by Shimada and Yamakawa [(1985) Journal of Molecular Biology, Vol. 184, pp. 319-329] and Frank-Kamenetskii et al. [(1985) Journal of Biomolecular Structure and Dynamics, Vol. 2, pp. 1005-1012], and would imply that all of their DNAs exist in a substantially stiffer than normal state.