Torsion Elastic Constant Research Articles

Effects of Sequence Changes on the Torsion Elastic Constant and Persistence Length of DNA. Applications of the Two-State Model.

Previous experimental studies of the effects of changes in sequence on the elastic constants and other properties of DNAs are analyzed using the recently parametrized two-state cooperative transition model. With appropriate assumptions regarding the relative preference of particular subsequences for the b and a states, the model gives an approximately quantitative account of the surprisingly large observed effects of replacing 25 bp of natural sequence near the middle of an ∼1100 bp DNA by 16 bp of alternating (CG)8 sequence on the fraction fb of base-pairs in the b-state and on the torsion elastic constant. This demonstrates the effect of the strong cooperativity of the transition to significantly influence the state of the DNA over surprisingly large domains of the flanking DNA. With appropriate assumptions regarding the disposition of nonrelaxing (permanent) and slowly relaxing bends between the a and b states, the two-state model resolves the discrepancy between experimental estimates of the magnitude of the nonrelaxing bends obtained from studies of synthetic straight and natural DNA sequences by cryo-electron microscopy on the one hand and by j-factors inferred from the kinetics of ligase cyclization of small ∼200 bp circular DNAs on the other. Approximately quantitative agreement with the experiments is again obtained.

Temperature-dependence of the bending elastic constant of DNA and extension of the two-state model. Tests and new insights

Review and analyses of the experimental data indicate that in nearly all cases bending elastic constants of the effective springs between bp of DNA actually undergo a net increase with increasing T from 278 to 315 K. The exceptions to this rule are bending elastic constants obtained from equilibrium topoisomer distributions of a 2686 bp pUC19 DNA by assuming a fixed T-independent value of the torsion elastic constant. When the same data are analyzed using measured T-dependent values of the torsion elastic constant, which decline with increasing T, a modest increase in bending elastic constant with increasing T is obtained. After revising the torsion elastic constants of the previously formulated two-state cooperative transition model to account for additional data, that model is fitted to the bending elastic constants reckoned from the aforementioned topoisomer distributions to determine the best-fit values for each state. The rather good fit implies a strong negative linear correlation between the inverse bending and inverse torsion elastic constants as T is varied. Predictions of the resulting two-state model, wherein each state has fixed bending and torsion elastic constants, agree surprisingly well with single-molecule relative extension and torque data. The same model also yields good agreement with numerous other experimental data. With increasing T the equilibrium is shifted from the (longer, torsionally stiffer, flexurally softer) b-state toward the (shorter, torsionally softer, flexurally stiffer) a-state. This transition is suggested to be the origin of the so-called broad pre-melting transition exhibited by many, but not all, DNAs.

Possible Origin of the Increased Torsion Elastic Constant of Small Circular DNAs: Bending-Induced Axial Tension

Deforming an intrinsically straight elastic rod into a circle is shown to introduce an axial tension that acts to extend the rod, much like an externally applied force. The response of a circular DNA to such axial tension was reckoned using a previously suggested model of a force-dependent cooperative transition between a shorter torsionally softer a conformation and a longer torsionally stiffer b conformation. Each of three earlier reported optimal sets of parameters, that well-fitted both relative extension vs force and torsion elastic constant vs force data on single DNAs under tension, was applied here to predict torsion elastic constants of the effective springs between base pairs for both linear and circular 181 bp and ∼210.8 bp DNAs under their respective conditions. Predicted values for both linear and circular species agreed well with their corresponding experimental values, which strongly suggests that the observed 1.4- to 1.5-fold enhancement of the torsion elastic constants upon circularization arises from such axial tension. Experimental torsion elastic constants lie in the range (6.4-6.6) × 10-19 J for these linear DNAs and in the range (9.1-9.9) × 10-19 J for the corresponding circles, significantly below the limiting value ∼12 × 10-19 J at tensions exceeding 4 pN.

Theory of single-molecule controlled rotation experiments, predictions, tests, and comparison with stalling experiments in F1-ATPase

A recently proposed chemomechanical group transfer theory of rotary biomolecular motors is applied to treat single-molecule controlled rotation experiments. In these experiments, single-molecule fluorescence is used to measure the binding and release rate constants of nucleotides by monitoring the occupancy of binding sites. It is shown how missed events of nucleotide binding and release in these experiments can be corrected using theory, with F1-ATP synthase as an example. The missed events are significant when the reverse rate is very fast. Using the theory the actual rate constants in the controlled rotation experiments and the corrections are predicted from independent data, including other single-molecule rotation and ensemble biochemical experiments. The effective torsional elastic constant is found to depend on the binding/releasing nucleotide, and it is smaller for ADP than for ATP. There is a good agreement, with no adjustable parameters, between the theoretical and experimental results of controlled rotation experiments and stalling experiments, for the range of angles where the data overlap. This agreement is perhaps all the more surprising because it occurs even though the binding and release of fluorescent nucleotides is monitored at single-site occupancy concentrations, whereas the stalling and free rotation experiments have multiple-site occupancy.

A possible cooperative structural transition of DNA in the 0.25-2.0 pN range.

The measured effective torsional rigidities of single twisted DNAs under various tensions conflict with theoretical predictions of Moroz and Nelson (MN) at low forces in the 0.25-2.0 pN range. However, MN theory was recently shown to agree well with effective torsional rigidities obtained from simulations, indicating that MN theory is valid down to 0.25 pN for a filament with a constant intrinsic torsional rigidity. Here MN theory is used with an assumed persistence length, 50 nm, to obtain the force-dependent intrinsic torsional rigidity of the filament at each force from its measured effective torsional rigidity. The resulting values rise ∼1.8-fold with increasing force from 0.25 to 2.0 pN. Unexpected behavior of the relative extensions of the untwisted DNAs of Mosconi et al. is noted, and ascribed to a small increase in contour length with force over the 0.18-2.0 pN range. The variations of both the intrinsic torsional rigidity and rise per base pair (bp) with force are suggested to arise from a force-induced shift of a cooperative equilibrium between two conformations with different rises per bp. A two-state nearest-neighbor model is formulated, and ranges of optimal parameters are determined by fitting the model to the experimental differences in rise per bp as a function of force. Optimal adjustment of the torsion elastic constants of the two states enables the same optimal model(s) with fixed parameters to provide reasonably good fits of the experimental torsion elastic constant data. The results reconcile single-molecule measurements on DNAs under tension with numerous results from fluorescence polarization anisotropy, topoisomer distributions, X-ray scattering of DNAs with attached gold colloids, and other kinds of measurements.

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.

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.

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 [1,2] [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 ( α) from FPA measurements on such short DNAs is examined in detail. The difficulty is illustrated by two (fictitious) 24 bp DNAs with ∼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 α 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, α, 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 α is obtained, but that best-fit α 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 α, 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 ( α, R H, and L) is obtained for a model, wherein all DNAs have the same typical input α=5.9×10 −12 dyn cm, R H=10.0 Å, and L=27 (3.4)+2.7=94.5 Å, 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 Å, and L=94.5 Å, but a ∼3-fold range of α-values. It is concluded that, in the absence of reliable independent estimates of r 0 for every DNA, the α-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.

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.

Torsional constant of 27-mer DNA oligomers of different sequences

We have studied the torsional elastic constant ( α) of short DNA (27mer) oligomers of various sequence by fluorescence polarization anysotropy (FPA) measurements. The lowest α values were found in samples with sequence rich in AA dinucleotides or containing the alternating d(A–T)·d(A–T) motif. The torsional rigidity of our DNA samples was compared to that calculated according to the current values of twist angle fluctuations derived for ten dinucleotide steps by recent analyses of DNA crystal structure database. The values of torsional rigidity derived from crystals are higher than our experimental ones, obtained by FPA analysis, suggesting that packing force in crystals may notably hinder the dinucleotide twist angle fluctuations that occur in solution. This behaviour is more evident for samples containing AA, TA and AT steps. In all the samples there is about a twofold change of the α value in the 10–40 °C range. An activation enthalpy (Δ H #) of about 17.4 kJ mol −1, on average, was obtained for the temperature dependence of eight of the ten samples studied. A correlation with the stacking energy is discussed.

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 ( κ d), or equivalently the dynamic persistence length, P d = κ d /k B T, governs the rapidly relaxing bends, which are responsible for the flexural dynamics of DNA on a short time scale, t ≤ 10 −5 s. However, all three kinds of bends contribute to the total equilibrium persistence length, P tot, according to 1/P tot ≅ 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 μs. 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 μs. Accurate data in the very tail of the decay enable a model-independent determination of the relaxation time ( τ R) of the end-over-end tumbling motion, from which P tot = 500 Å is estimated. The FPA data are used to obtain the best-fit pairs of P d and torsion elastic constant ( α) values that fit those data equally well, and which are used to eliminate α 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 α 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 Å, 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 Å and 〈 δζ 2〉 1/2 = 25°. The discrimination against P d values <1600 Å is very great. By combining the values, P tot = 500 Å and P d = 2000 Å with a literature estimate, P pb = 1370 Å, a value P sr = 1300 Å 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.

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.

Dynamic twisting correlations in a model DNA with uniform torsion elastic constant.

The extent to which the twisting motions of two separate subunits (base pairs) in an elastic filament are correlated is discussed in terms of the two-point correlation function of their azimuthal angular displacements C(Delta,t) identical with <(phi(m)(t) - phi(m)(0))(phi(n)(t) - phi(n)(0))>, where m,n are the sequential subunit indices and Delta = |m - n| is their absolute difference. An approximate expression is derived for C(Delta,t) for an infinitely long model DNA from the analytical theory developed previously to treat the decay of the fluorescence polarization anisotropy of intercalated ethidium. C(Delta,t) is numerically evaluated as a function of Delta for a range of times (20, 40, 60, 80, 100, and 120 ns) for a model DNA with a typical torsion elastic constant. By t = 120 ns, significant dynamic correlations are observed to extend over a domain (Delta) several hundred base pairs. Copyright 1999 John Wiley & Sons, Inc.

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 (<alpha>) 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 <alpha>. 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 <alpha> 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.

Torsional dynamics and orientation of DNA--DAPI complexes.

The flexibility of calf thymus DNA and several polynucleotides was measured using the anisotropy decay of DAPI bound to DNA, a minor groove probe. DNA torsional dynamics were analyzed using the Schurr model [Allison, S. A., & Schurr, J. M. (1979) Chem. Phys. 41, 35-44] in the infinite polymer length approximation. Time-resolved fluorescence depolarization was measured using a frequency-double mode-locked dye laser and frequency-domain acquisition methods. At very high P/D ratios, the anisotropy decay is dominated by DNA torsional dynamics. The recovered values of the torsional elastic constant were in good agreement with literature values obtained using other DNA probes. The exact knowledge of the angle between the probe emission dipole transition moment and the helix axis is critical for the determination of the polymer elastic constant. At low P/D ratios, energy transfer between dye molecules strongly contributes to the anisotropy decay. We have developed a statistical model that describes the anisotropy decay, when the correct geometrical factors are included. At low P/D ratios the anisotropy decay is dominated by fluorescence homotransfer. In this regime, it is possible to determine the orientation of the dye molecule with respect to the polymer with accuracy. The values obtained for the distance and orientation of the DAPI molecules in solution using the fluorescence measurements are in excellent agreement with those from the crystal structure of the oligonucleotides-DAPI complex by Dickerson's group [Larsen T.A., Goodsell, D. S., Cascio, D., Grzeskowiak, K., & Dickerson, R. E. (1989) J. Biomol. Struct. Dyn. 7, 477-491].

Investigation of the influence of cytosine methylation on DNA flexibility.

To test the influence of pyrimidine methyl groups on DNA flexibility and helix repeat, two sets of 14 mixed sequence DNA molecules, spanning a range of lengths from 158 to 180 base pairs, were cyclized with T4 DNA ligase. The two sets differed only in that the Cyt-5 positions of all cytosines (80-90 cytosine residues per molecule) were fully methylated in the members of one set. Determination of the molar cyclization factors, persistence lengths, helix repeats, and torsional elastic constants revealed no significant differences between the two sets. These results imply that, at least for mixed sequence DNA, the biological consequences of cytosine methylation are likely to derive from either local structural distortions in the helix, which do not propagate as altered twist, or from direct protein-methyl cytosine interactions.