Twist Energy Parameter Research Articles

Supercoiled pseudocircular domains in single‐twisted DNAs under tension: Elastic constants and unwinding dynamics in complexes with topo I

Extension versus twist data of Koster et al. (Nature 2005, 434, 671-674) are analyzed to obtain C for the main-chain segments and the twist energy parameter (ET ) for the supercoiled pseudocircular (sp) domain(s) from which C is estimated via simulations. The torsional rigidity in the tension-free sp domain(s) (C = 163 fJ fm) is typical of the unstrained DNA and is less than half the value in the main-chain segments under tension (C = 350-410 fJ fm). Tension is suggested to induce a structural transition to a torsionally stiffer state. Data of Koster et al. for the rate of extension owing to unwinding of a covalent complex of DNA with human Topoisomerase Ib (H Topo I) are analyzed to determine the torque and rate of rotation from which an effective friction coefficient is obtained. A Langevin equation for the unwinding motion in a supercoiled DNA:H Topo I complex is solved to obtain the temporal trajectory of the average winding angle and the time-dependent distribution of winding angles. The mean rate constant for the religation reaction is estimated from the measured probability of reaction per turn. We predict that unwinding proceeds rather far during a single-cleavage and religation cycle, and is effectively completely equilibrated during the 3.2 cleavage and religation cycles that occur during each noncovalent binding and dissociation event. H Topo I is predicted to be completely processive as in accord with observations on calf-thymus Topo I (Brewood et al., Biochemistry 2010, 49, 3367-3380).

Calf-Thymus Topoisomerase I Equilibrates Metastable Secondary Structure Subsequent to Relaxation of Superhelical Stress

After relaxation of superhelical stress by various methods not involving topoisomerases, a long-lived metastable secondary structure with an anomalously low torsion elastic constant commonly prevails. The aim here is to ascertain whether such metastable secondary structure also results from the action of calf-thymus topoisomerase I (CT Topo I) on a native supercoiled DNA and, if so, whether the enzyme catalyzes its subsequent equilibration. The action of CT Topo I on supercoiled p30delta DNA was examined over a range of times from 10 min to 6 h. We verify that the enzyme operates in an almost completely processive manner, and at each time point determine the twist energy parameter, E(T), that governs the supercoiling free energy. E(T) is initially low, 533 +/- 60, and remains essentially constant up to at least 360 min, when no further CT Topo I is added. The activity of the rather dilute enzyme dies within approximately 60 min. During the 60 min after a second addition of fresh enzyme at either 60 or 120 min, E(T) rises up to a plateau at approximately 1100, which lies within the consensus equilibrium range, 1000 +/- 100. Over that same time period, the average peak spacing between the gel bands (corresponding to individual topoisomers) decreases somewhat with increasing time of exposure to active CT Topo I. After a third addition of fresh CT Topo I at 240 min, there is no further change in either E(T) or the average gel spacing. These and other observations indicate that active CT Topo I catalyzes the equilibration of a metastable secondary structure with abnormally low torsion and bending elastic constants that prevails after the initial release of superhelical stress. An observed temporal lag of this structural equilibration behind the relaxation of native superhelical DNAs suggests that it may require cleavage and religation events at multiple sites on the DNA. A novel analysis of the unwinding kinetics using literature data accounts for the almost complete processivity of the enzyme. The action of CT Topo I was also examined in the presence of 20 and 40 w/v% ethylene glycol (EG), which shift a secondary structure equilibrium toward an alternative state with altered torsion and bending elastic constants. The present results suggest that the usual metastable state coexists with the EG-induced state, and is equilibrated more rapidly than in the absence of EG.

A Structural Transition in Duplex DNA Induced by Ethylene Glycol

The twist energy parameter ( E T) that governs the supercoiling free energy, and the linking difference (Delta l) are measured for p30delta DNA in solutions containing 0-40 w/v % ethylene glycol (EG). A plot of E T vs -ln a w, where a w is the water activity, displays the full (reverse) sigmoidal profile of a discrete structural transition. A general theory for the effect of added osmolyte on a cooperative structural transition between two duplex states, 1 right arrow over left arrow 2, is formulated in terms of parameters applicable to individual base-pair subunits. The resulting fraction of base pairs in the 2-state ( f 2 (0)) is incorporated into expressions for the effective torsion and bending elastic constants, the effective twist energy parameter ( E T (eff)), and the change in intrinsic twist (delta l 0). Fitting the expression for E T (eff) to the measured E T values yields reasonably unambiguous estimates of E T 1 and E T 2 , the midpoint value (ln a w) 1/2, and the midpoint slope ( partial differential E T/ partial differential ln a w) 1/2, but does not yield unambiguous estimates of the equilibrium constant ( K 0), the difference in DNA-water preferential interaction coefficient (DeltaGamma), or the inverse cooperativity parameter ( J). Fitting a noncooperative model (assumed J = 1.0) to the data yields K 0 = 0.067 and DeltaGamma = -30.0 per base pair (bp). Essentially equivalent fits are provided by models with a wide range of correlated J, DeltaGamma, and K 0 values. Other results favor DeltaGamma in the range -1.0 to 0, which then requires K 0 > or = 0.914, and a cooperativity parameter, 1/ J > or = 30.0 bp. The measured delta l 0 and circular dichroism (CD) at 272 nm are found to be compatible with curves predicted using the same f 2 (0) values that best-fit the E T data. At least 7-10% of the base pairs are inferred to exist in the 2-state in 0.1 M NaCl in the complete absence of added osmolyte. Compared with the 1-state, the 2-state has a approximately 2.0- to 2.1-fold greater torsion elastic constant, a approximately 0.70-fold smaller bending elastic constant, a approximately 0.91-fold smaller E T value, a approximately 0.2% lower intrinsic twist, a somewhat lower CD near both 272 and 245 nm, and less water and/or more EG in its neighborhood. However, the relative change in preferential interaction coefficient associated with the transition is likely rather slight.

Estimation of the Persistence Length of DNA from the Torsion Elastic Constant and Supercoiling Free Energy: Effect of Ethylene Glycol

Two different methods are proposed to estimate the persistence length ( P) of DNA from the measured torsion elastic constant (alpha) and the twist energy parameter ( E T ) that governs the supercoiling free energy. The first method involves Monte Carlo simulations and reversible-work calculations of E T for model DNAs that possess the measured alpha and selected trial values of P. Comparison of the computed E T values with the experimental value allows estimation of P (or equivalently the bending elastic constant (kappa beta)) by interpolation. A far simpler, though less accurate, alternative is to solve a previously conjectured analytical relation connecting E T , alpha, kappa beta (or P), and an unknown "constant" ( B). The present simulations are used to ascertain the optimum value of B and to assess the validity and accuracy of that relation. Within the simulation errors, P values obtained from the measured alpha and E T via this analytical expression agree with those determined from the simulations and E T values reckoned from the input alpha and kappa beta by this analytical expression agree with the corresponding simulated values. Although B is found to be insensitive to variation in alpha, it appears to decline slightly with increasing kappa beta. The original analytical expression is modified to take this apparent variation of B with kappa beta into account. By using this modified analytical relation to estimate P (from the measured alpha and E T ) or E T (from the input alpha and kappa beta), much closer agreement is obtained respectively with the values of P or E T obtained from the simulations. As specific examples, these methods are applied to determine P in 0 and 20 w/v % ethylene glycol, which has been shown to induce a structural transition in duplex DNA.

The effect of changes in the bulk dielectric constant on the DNA torsional properties

The effect of changes in the bulk dielectric constant on the DNA torsional properties was evaluated from plasmid circularization reactions. In these reactions, pUC18 previously linearized by EcoRI digestion was recircularized with T4 DNA ligase. The bulk dielectric constant of the reaction medium was decreased by the addition of different concentrations of neutral solutes: ethylene glycol, glycerol, sorbitol, and sucrose, or increased by the addition of glycine. The topoisomers generated by the ligase reaction were resolved by agarose-gel electrophoresis. The DNA twist energy parameter (kappa), which is an apparent torsional constant, was determined by linearization of the Gaussian topoisomers' distribution. It was observed that the twist energy parameter for the given solutes is almost linearly dependent on the bulk dielectric constant. In the reaction buffer, the twist energy parameter was determined to be 1100 +/- 100. By decreasing the dielectric constant to 74 with the addition of sorbitol, the value of the parameter reaches kappa = 900 +/- 100, whereas the addition of ethylene glycol leads to kappa = 400 +/- 50. Upon addition of glycine, which resulted in a dielectric constant equal to 91, the value of the twist energy parameter increased to kappa = 1750 +/- 100.

Torsional Rigidities of Weakly Strained DNAs

Measurements on unstrained linear and weakly strained large (≥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 (≤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 ≥ 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.

Effects of ethylene glycol on the torsion elastic constant and hydrodynamic radius of p30δ 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.

Effects of small neutral osmolytes on the supercoiling free energy and intrinsic twist of p30delta DNA.

Both theory and experiments are employed to investigate the effects of small neutral osmolytes on the average intrinsic twist (l0), the torsion and bending elastic constants, and the twist energy parameter (ET) that governs the supercoiling free energy. The experimental data for ethylene glycol and acetamide at 37 degrees C suggest, and are interpreted in terms of, a model wherein the DNA exhibits an equilibrium between two distinct conformational states that possess different numbers of bound water molecules and exhibit different intrinsic twists and torsion and bending elastic constants. Expressions are derived to relate the effective ET and l0 to the equilibrium constant, water activity (aw), and number (n) of bound water molecules released per cooperative domain undergoing the two-state transition. The variations of l0 and ET with -ln(aw) are similar for acetamide and ethylene glycol at 37 degrees C. Fitting the theory to those data yields the range n = 103-125 for ethylene glycol and n = 71-113 for acetamide, depending on the assumed value of ET for the dehydrated state. The cooperative domain size of the two-state transition is estimated to exceed about 25-30 base pairs (bp). Between 0 and 19.4 w/v % ethylene glycol, the torsion elastic constant, measured by time-resolved fluorescence polarization anisotropy (FPA), increases by 1.37-fold, whereas the measured ET decreases by 1.15-fold over that same range. The implied decrease in bending rigidity over that range is by a factor of about 0.7. The variations of l0 and ET with increasing -ln(aw) due to added ethylene glycol at 37 degrees C are far smaller than the corresponding variations observed previously at 14 and 15 degrees C. However, at 21 degrees C, upon adding either ethylene glycol or acetamide, l0 and ET initially decline steeply with increasing -ln(aw), with slopes possibly comparable to those seen at 14 and 15 degrees C, but then flatten out and follow curves similar to those at 37 degrees C. Possible origins of such mixed behavior are discussed. The effects of betaine at both 37 and 21 degrees C differ qualitatively and quantitatively in various respects from those of ethylene glycol and acetamide. Upon adding sucrose, l0 initially jumps to higher plateaus at both 37 and 21 degrees C, but its effects on ET cannot be reliably assessed, due to the limited range of -ln(aw).

Monte Carlo Simulations of Locally Melted Supercoiled DNAs in 20 mM Ionic Strength

Mesoscopic models of unmelted and locally melted supercoiled DNAs in 20 mM ionic strength are simulated over a range of linking difference from Δ ℓ = 0 to −26 turns, or superhelix density from σ = 0 to −0.062. A domain containing m = 0, 28, or 56 melted basepairs (out of 4349 total) is modeled simply by a region of suitable length with substantially reduced torsion and bending elastic constants. Average structural properties are calculated from the saved configurations, and a reversible work protocol is used to calculate the supercoiling free energy, Δ G sc . The cross-writhe between duplex and melted regions (defined herein) is found to be negligibly small. The total writhe, radius of gyration, and ordered elements of the diagonalized inertial tensor are found to be nearly universal functions of the residual linking difference ( 〈 Δ ℓ r 〉 ) associated with the duplex region, independent of m. However, deformability of the tertiary structure, as manifested by the variance of those same properties, is not a universal function of 〈 Δ ℓ r 〉 , but depends upon m. Δ G sc varies with 〈 Δ ℓ r 〉 more strongly than 〈 Δ ℓ r 〉 2 due to the low ionic strength. The twist energy parameter, E T , obtained from the simulated Δ G sc , 〈 Δ ℓ r 〉 , and net twisting strain of the melted region, 〈 T D 〉 , is found to be independent of m, hence also of the torsion and bending elastic constants of the melted region. However, E T increases linearly with − 〈 Δ ℓ r 〉 , which leads to 1), a small overestimation of E T for any given 〈 Δ ℓ r 〉 , when E T is determined from the observed Δ ℓ and 〈 Δ ℓ r 〉 by the protocol of Bauer and Benham; and 2), a significant enhancement of the apparent slope, ⁡ − ⁡ d E T / d T , obtained via the protocol of Bauer and Benham, relative to the actual slope at fixed 〈 Δ ℓ r 〉 . After taking these two effects into account, the theoretical and experimental E T values and − ⁡ d E T / d T values agree rather well. For the larger Δ ℓ , the melted regions are found preferentially in the linker domains between interwound arms, rather than in the apical regions at the ends of interwound arms.

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.

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.

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.

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 <w>/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.

Effect of ethidium binding and superhelix density on the supercoiling free energy and torsion and bending constants of p30δ DNA

Topoisomer distributions created by the action of topoisomerase I on p30δ DNA in the presence of various concentrations of ethidium are measured and analyzed using recently developed theory to obtain the twist energy parameter ( E T) 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, E T = 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, E T = 1030 ± 90, which is essentially independent of ethidium binding ratio from r = 0 to 0.082 and superhelix density from σ = 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 (α) of p30δ DNA is likewise essentially independent of superhelix density and ethidium binding ratio. The observed invariance of E T and α implies that the bending constant κ β is similarly invariant to superhelix density and ethidium binding ratio. The apparently ideal behavior displayed by p30δ 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 ( E T) of pBR322 is determined near zero superhelix density from topoisomer distributions created under various conditions. The resulting value, E T = 1155 ± 65, at 37°C is essentially unaffected by adding 10 mM Mg 2+, or by changing the kind of Topo I from chicken-red-cell to calf-thymus. This value significantly exceeds that ( E T = 950 ± 80) measured for p30δ DNA under indentical conditions by the same method in the preceding paper. Decreasing the temperature from 37 to 21°C yields a slightly larger value, E T = 1340 ± 130, but the statistical significance of the increase is marginal. Attempts to determine reliable E T 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 E T. Moreover, the curves of apparent E T 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 E T values obtained from competitive dialysis experiments are typically rather low ( E T ∼ 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. The observed trend of apparent E T values extrapolates to a still larger value at r ≈ 0.07, σ = 0, which significantly exceeds the value obtained from topoisomer distributions near r = 0, σ = 0. These findings cast considerable doubt on the reliability of apparent E T values obtained for pBR322 by ethidium binding studies. The differences between pBR322 and p30δ are attributed to one or more different secondary conformations that prevails over part of the pBR322 sequence, and to the metastable prevalence of one or more of those as dye is added. In the case of pBR322 DNA, the torsion constant, molar ellipticity at 250 nm, and plateau diffusion coefficient from dynamic light scattering at K = 4.5 × 10 5 cm −1 all vary with superhelix density in a similar way, showing dips at σ = −0.010 and jumps at σ = −0.037. This behavior, which is similar to that observed previously for pUC8 dimer DNA, suggests that two successive transitions in secondary structure are induced in pBR322 by increasing negative superhelix density. The possible role of such structural transitions in the contrasting behaviors of pBR322 and p30δ is discussed.

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.

Interaction of chloroquine with linear and supercoiled DNAs. Effect on the torsional dynamics, rigidity, and twist energy parameter.

The magnitude and uniformity of the torsion elastic constant (alpha) of linear pBR322 DNA and supercoiled pBR322 DNAs with high-twist (sigma = -0.083) and normal-twist (sigma = -0.48) are measured in 0.1 M NaCl as a function of added chloroquine/base-pair ratio (chl/bp) by studying the fluorescence polarization anisotrophy (FPA) of intercalated ethidium dye. The time-resolved FPA is measured by using a picosecond dye laser for excitation and time-correlated single-photon counting detection. A general theory is developed for the binding of ligands that unwind superhelical DNAs, and the simultaneous binding of two different intercalators is treated in detail. The equilibrium constant (K) for binding chloroquine to linear pBR322 DNA and the number (r) of bound chloroquines per base pair are determined from the relative amplitude ratio of the slow (normally intercalated) and fast (free) components in the decay of the (probe) ethidium fluorescence intensity as a function of chl/bp. For chloroquine binding to supercoiled pBR322 DNAs, the intrinsic binding constant is assumed to be the same as for the linear DNA, but the twist energy parameter ET (N times the free energy to change the linking number from 0 to 1 in units of kBT) is regarded as adjustable. Using the best-fit ET, the binding ratios r are calculated for each chl/bp ratio. Twist energy parameters are also determined for ethidium binding to these supercoiled DNAs by competitive dialysis. For chloroquine binding, we obtain ET = 360 and 460 respectively for the normal-twist and high-twist supercoiled DNAs. For ethidium binding the corresponding values are ET = 280 +/- 70 and 347 +/- 50. Like other dye-binding values, these are substantially lower than those obtained by ligation methods. In the absence of chloroquine, the torsion constants of all three DNAs are virtually identical, alpha = (5.0 +/- 0.4) x 10(-12) dyn.cm. For linear pBR322 DNA, the magnitude and uniformity of alpha remain unaltered by intercalated chloroquine up to r = 0.19. This finding argues that the FPA is not significantly relaxed by diffusion of any kinks or solitons. If alpha d denotes the torsion constant between a dye 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 0.65-1.64, with a most probable value of 1.0.(ABSTRACT TRUNCATED AT 400 WORDS)