The effect of intrinsic curvature on conformational properties of circular DNA.

Both thermal fluctuations and the intrinsic curvature of DNA contribute to conformations of the DNA axis. We looked for a way to estimate the relative contributions of these two components of the double-helix curvature for DNA with a typical sequence. We developed a model and Monte Carlo procedure to simulate the Boltzmann distribution of DNA conformations with a specific intrinsic curvature. Two steps were used to construct the equilibrium conformation of the model chain. We first specified the equilibrium DNA conformation at the base pair level of resolution, using a set of the equilibrium dinucleotide angles and DNA sequence. This conformation was then approximated by the conformation of the model chain consisting of a reduced number of longer, straight cylindrical segments. Each segment of the chain corresponded to a certain number of DNA base pairs. We simulated conformational properties of nicked circular DNA for different sets of equilibrium dinucleotide angles, different random DNA sequences, and lengths. Only random sequences of DNA generated with equal probability of appearance for all types of bases at any site of the sequence were used. The results showed that for a broad range of intrinsic curvature parameters, the radius of gyration of DNA circles should be nearly independent of DNA sequence for all DNA lengths studied. We found, however, a DNA properly that should strongly depend on DNA sequence if the double helix has essential intrinsic curvature. This property is the equilibrium distribution of the linking number for DNA circles that are 300-1000 bp in length. We found that a large fraction of the distributions corresponding to random DNA sequences should have two separate maxima. The physical nature of this unexpected effect is discussed. This finding opens new opportunities for joined experimental and theoretical studies of DNA intrinsic curvature.     

Ring closure probabilities for DNA fragments by Monte Carlo simulation

The rate of ligation of DNA molecules into circular forms depends on the ring closure probability, commonly called the j-factor, which is a sensitive measure of the extent to which thermal fluctuations contribute to bending and twisting of DNA molecules in solution. We present a theoretical treatment of the cyclization equilibria of DNA that employs a special Monte Carlo method for generating large ensembles of model DNA chains. Using this method, the chain length dependence of the j-factor was calculated for molecules. in the size range 250 to 2000 base-pairs. The Monte Carlo results are compared with recent analytical theory and experimental data. We show that a value of 475 A for the persistence length of DNA, close to values measured by a number of other methods, is in excellent agreement with the cyclization results. Preliminary applications of the Monte Carlo method to the problem of systematically bent DNA molecules are presented. The calculated j-factor is shown to be very sensitive to the amount of bending in these fragments. This fact suggests that ligase closure measurements of systematically bent DNA molecules should be a useful method for studying sequence-directed bending in DNA.     

Curved DNA

A priori considerations and the concept of the sequence-dependent local curving of the DNA axis. Experimental evidence: electric dichroism (relaxation time measurements); anomalous electrophoretic mobility and gel-filtration of some restriction fragments of DNA; one-sided binding of the nucleosomal DNA to the mica surface. Theoretical predictions concerning the nucleotide sequences of the curved DNA. Discovery of the dinucleotide periodicity in the chromatin DNA. The sequence periodicity as a tool for mapping of the nucleosomes along the sequences. Preferential binding of the histone octamers to the curved pieces of DNA--sequence analysis predictions and comparison with experiments: Theoretical and experimental estimates of the tilt and roll angles for different combinations of the neighboring base-pairs. Inherent sequence-dependent curvature and apparent persistence length of DNA.     

Orientation relaxation of DNA restriction fragments and the internal mobility of the double helix

The orientation relaxation of 15 DNA restriction fragments (43-4361 base-pairs) is characterized by measurements of linear dichroism using high electric field pulses. The off-field relaxation of fragments of 84 base-pairs or less can be described by single exponentials, which are related to the transverse rotational diffusion of the helix. Fragments of 95 base-pairs or greater exhibit an additional fast component with time constants around 100 ns for fragments of approx. 100 base-pairs, increasing with chain length to about 700 ns for a fragment with 258 base-pairs. The amplitude of this process increases from virtually zero at low fields (approximately equal to 10 kV) to a substantial limit contribution at high fields. According to these results, we suggest that electric fields induce stretching of the DNA fragments from a weakly bent to a more straight form and that the fast component reflects the internal mobility of the DNA chain. The slow off-field components of the orientation are discussed in terms of different models. The data up to helix lengths of about 400 base-pairs can be described by the 'weakly bending rod' model from Hearst using 3.4 A rise per base-pair and 13 A axial radius of the helix. Both the weakly bending rod according to Hearst and the 'wormlike chain' according to Hagerman and Zimm provide a persistence length of 500 A. The on-field relaxation is slower than the corresponding off-field process at low field strengths, but the on-field process is accelerated substantially at high electric fields. These observations are compared with model calculations of Schwarz.     

Topological measurement of an A-tract bend angle: variation of duplex winding

The rotational variant method of Lutter et al. was developed to measure the bend angle induced when a protein binds to DNA. To measure the intrinsic bend conferred by a sequence of six adenine bases (an A6 tract), the method was modified by relaxing at high temperature to remove the bend. We describe here an alternative approach that involves unwinding the duplex DNA between adjacent bends in plasmids containing tandemly repeated blocks of A-tracts. This method measures the topological difference contributed by adjacent bends when they are in two different rotational settings, and therefore does not require reference to a straight state. The interbend DNA was unwound by use of the intercalator chloroquine, or, alternatively, by raising the temperature in the relaxation reaction. The effect of this unwinding is to change the pitch of the superhelix of the tandem repeats from which the bend angle is measured. The result is a bend angle value that is consistent with that measured using the bend-straightening version of the method. This version offers several advantages that complement the conventional bent versus straight approach.     

Gapped DNA and cyclization of short DNA fragments

We use the cyclization of small DNA molecules, approximately 200 bp in length, to study conformational properties of DNA fragments with single-stranded gaps. The approach is extremely sensitive to DNA conformational properties and, being complemented by computations, allows a very accurate determination of the fragment's conformational parameters. Sequence-specific nicking endonucleases are used to create the 4-nt-long gap. We determined the bending rigidity of the single-stranded region in the gapped DNA. We found that the gap of 4 nt in length makes all torsional orientations of DNA ends equally probable. Our results also show that the gap has isotropic bending rigidity. This makes it very attractive to use gapped DNA in the cyclization experiments to determine DNA conformational properties, since the gap eliminates oscillations of the cyclization efficiency with the DNA length. As a result, the number of measurements is greatly reduced in the approach, and the analysis of the data is greatly simplified. We have verified our approach on DNA fragments containing well-characterized intrinsic bends caused by A-tracts. The obtained experimental results and theoretical analysis demonstrate that gapped-DNA cyclization is an exceedingly sensitive and accurate approach for the determination of DNA bending.     

MPD and DNA Bending in Crystals and in Solution

Bending of 15 to 24° is observed within crystal structures ofB-DNA duplexes, is strongly sequence-dependent, and exhibits no correlation with the concentration of MPD (2-methyl-2,4-pentanediol) in the crystallizing solution. Two types of bends are observed: facultative bends or flexible hinges at junctions between regions of G·C and A·T base-pairs, and a persistent and almost obligatory bend at the center of the sequence R-G-C-Y. Only A-tracts are characteristically straight and unbent in every crystal structure examined to date. A detailed examination of normal vector plots for individual strands of a double helix provides an explanation, in terms of the stacking properties of guanine and adenine bases. The effect of high MPD concentrations, in both solution and crystal, is to decrease local bending somewhat without removing it altogether. MPD gel retardation experiments provide no basis for choosing among the three models that seek to explain macroscopic curvature of DNA by means of microscopic bending: junction bending, bent A-tracts, or bent general- sequence DNA. Crystallographic data on the straightness of A-tracts, the bendability of non-A sequences, and the identity of inclination angles in A-tract and non-A-tractB-DNA support only the general-sequence bending model. The pre-melting transition observed in A-tract DNA probably represents a relaxation of stiff adenine stacks to a flexible conformation more typical of general-sequence DNA.     

Anisotropic elastic bending models of DNA

Simplified elastic rod models of DNA were developed in which the rigidity of DNA is sequence dependent and asymmetrical, i.e. the bending is facilitated towards the major groove. By subjecting the models to bending load in various directions perpendicular to the longitudinal axis of DNA, the bending deformation and the average conformation of the models can be estimated using finite element methods. Intrinsically curved sequence motifs [(aaaattttgc)_n, (tctctaaaaaatatataaaaa)_n] are found to be curved by this modelling procedure whereas the average conformation of homopolymers and straight motifs [(a)_n, (atctaatctaacacaacaca)_n] show negligible or no curvature. This suggests that sequence dependent asymmetric rigidity of DNA can provide an explanation in itself for intrinsic DNA curvature. The average rigidity of various DNA sequences was calculated and a good correlation was found with such quantities as the free energy change upon the binding of the Cro repressor, the base stacking energy and the thermal fluctuations at room temperature.     

Analysis of DNA bending by transient electric birefringence

Transient electric birefringence has been used to analyze DNA bending in six restriction fragments containing 171, 174, 207, 263, 289, and 471 bp in three different low ionic strength buffers. The target fragments contain sequences corresponding to the apparent bend centers in pUC19 and Litmus 28, previously identified by the circular permutation assay (Strutz, K.; Stellwagen, N. C. Electrophoresis 1996, 17, 989-995). The target fragments migrate anomalously slowly in polyacrylamide gels and exhibit birefringence relaxation times that are shorter than those of restriction fragments of the same size, taken from nonbent regions of the same plasmids. Apparent bend angles ranging from 30 degrees to 41 degrees were calculated for the target fragments by tau-ratio method. The bend angles of four of the target fragments were independent of temperature from 4 degrees C to 20 degrees C, but decreased when the temperature was increased to 37 degrees C. The bend angles of the other two target fragments were independent of temperature over the entire range examined, 4 degrees -37 degrees C. Hence, the thermal stability of sequence-dependent bends in random-sequence DNA is variable. The bend angles of five of the six target fragments were independent of the presence or absence of Mg2+ ions in the solution, indicating most of the target fragments were stably bent or curved, rather than anisometrically flexible. Restriction fragments containing 219 and 224 bp, with sequences somewhat offset from the sequence of the 207 bp fragment, were also studied. Comparison of the tau-ratios of these overlapping fragments allowed both the bend angle and bend position to be independently determined. These methods should be useful for analyzing sequence-dependent bending in other random-sequence DNAs.     

Self-attraction and natural curvature in null DNA

Forces of self-attraction inherent in DNA are unmasked when its ionic charge is neutralized. On the global level, self-attraction operates between segments to condense null (charge-neutralized) DNA into a segment-rich particle. Locally, self-attraction tends to contract an individual segment along its axis. If certain conditions are satisfied, the compressed segment buckles outward from the original line of the axis. Its most stable shape is then curved, or, as an extreme case, even completely folded. Buckling conditions are derived and shown to be met by DNA, thus explaining the high degree of ordered curvature and folding in the observed morphologies of condensed null DNA. The central concept employed is the buckling persistence length. It is evaluated for null DNA (40-50 bp) and agrees with experimental data (less than 60 bp). It helps in understanding the observed cooperative unit in the condensation/decondensation equilibrium (about 60 bp) and the observed size of digestion fragments unstable in the condensed phase (about 80 bp). The root-mean-square thermal compression/extension fluctuation in DNA is estimated at about 0.1 A/bp.     

Relating independent measures of DNA curvature: electrophoretic anomaly and cyclization efficiency

Electrophoretic methods are often used to measure DNA curvature and protein-induced DNA bending. Though convenient and widely-applied, quantitative analyses are generally limited to assays for which empirical calibration standards have been developed. Alternatively, solution-based cyclization of short DNA duplexes allows analysis of DNA curvature and bending from first principles, but a detailed understanding of this assay is still lacking. In this work, we demonstrate that calibration with an independent electrophoretic assay of DNA curvature permits interpretation of cyclization assay results in a quantitatively meaningful way. We systematically measure intrinsic DNA curvature in short duplexes using a well-established empirical ligation ladder assay. We then compare the results to those obtained from the analysis of the distribution of circular products obtained in simple enzymatic cyclization assays of the same duplexes when polymerized. A strong correlation between DNA curvature estimates from these two assays is obtained for DNA fragments between 150-300 bp in length. We discuss how this result might be used to improve quantitative analysis of protein-mediated bending events evaluated by cyclization methods. Our results suggest that measurements of DNA curvature obtained under similar conditions, in solution and in an acrylamide gel matrix, can be compared directly. The ability to correlate results of these simple assays may prove convenient in monitoring DNA curvature and flexibility.     

Influence of DNA length on spermine-induced condensation. Importance of the bending and stiffening of DNA

Using DNA restriction fragments of 258 to 4362 base-pairs, we have investigated the influence of the DNA length on the condensation process induced by spermine, with the aid of electric dichroism measurements. The 258- and 436 bp fragments condensed into rod-like particles, while the fragments of 748 bp or more condensed into torus-shaped particles. Our results suggest that a DNA molecule longer than the circumference of the toroids observed previously (680 bp) is required to serve as a nucleus for the growth of the condensed particles. The toroids were more stable in the electric field than the rod-shaped particles, suggesting that rapid fluctuations of the bound spermine counterions can provide one of the main attractive forces yielding to the condensation process. Relaxation time data for the 436 bp fragment revealed that the structure of DNA was altered at a spermine concentration as low as one-tenth of that required for condensation: the DNA became bent in the presence of spermine. Moreover, the field strength dependence of the relaxation times, as well as the fitting of the decay curves at 12.5 kV/cm, showed an increase of the stiffness of the DNA double helix upon spermine addition. We estimated that, in the case of DNA condensation by spermine, a decrease in the measured persistence length may occur, irrespective of the DNA flexibility, owing to the bending of the DNA molecule.     

Influence of DNA length on spermine-induced condensation: Importance of the bending and stiffening of DNA

Using DNA restriction fragments of 258 to 4362 base-pairs, we have investigated the influence of the DNA length on the condensation process induced by spermine, with the aid of electric dichroism measurements. The 258- and 436 bp fragments condensed into rod-like particles, while the fragments of 748 bp or more condensed into torus-shaped particles. Our results suggest that a DNA molecule longer than the circumference of the toroids observed previously (680 bp) is required to serve as a nucleus for the growth of the condensed particles. The toroids were more stable in the electric field than the rod-shaped particles, suggesting that rapid fluctuations of the bound spermine counterions can provide one of the main attractive forces yielding to the condensation process. Relaxation time data for the 436 bp fragment revealed that the structure of DNA was altered at a spermine concentration as low as one-tenth of that required for condensation: the DNA became bent in the presence of spermine. Moreover, the field strength dependence of the relaxation times, as well as the fitting of the decay curves at 12.5 kV/cm, showed an increase of the stiffness of the DNA double helix upon spermine addition. We estimated that, in the case of DNA condensation by spermine, a decrease in the measured persistence length may occur, irrespective of the DNA flexibility, owing to the bending of the DNA molecule.     

Determination of the extent of DNA bending by an adenine-thymine tract

We determined the magnitude of the bend induced in DNA by an adenine-thymine tract by measuring the rate of cyclization of DNA oligonucleotides containing phased A tracts. A series of linear multimers with 2-bp single-stranded ends, in which the (A.T)6 tracts are separated by CG2-3C sequences and are positioned 10 and 11 bp apart alternately, were prepared from 21 bp long synthetic duplexed deoxyoligonucleotides. The cyclization rates of the multimers (105-210 bp) and the bimolecular association rate of the 84 bp long multimer were measured in the presence of DNA ligase. From the rate constants of the cyclization and bimolecular association reactions, ring closure probabilities were obtained for the multimers. The systematically bent molecules were simulated by Monte Carlo methods, and the ring closure probabilities were calculated for a given set of junction bend angles. By comparing the calculated values of ring closure probabilities to experimental values and adjusting the junction bend angles to fit experimental values, the extent of bending at the junctions (or the extent of bending for an adenine tract) was determined. We conclude that an A6 tract bends the DNA helix by 17-21 degrees.     

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.     

The contribution of transient counterion imbalances to DNA bending fluctuations

A two-sided model for DNA is employed to analyze fluctuations of the spatial distribution of condensed counterions and the effect of these fluctuations on transient bending. We analyze two classes of fluctuations. In the first, the number of condensed counterions on one side of the DNA remains at its average value, while on the other side, counterions are lost to bulk solution or gained from it. The second class of fluctuations is characterized by movement of some counterions from one side of the DNA to the other. The root-mean-square fluctuation for each class is calculated from counterion condensation theory. The amplitude of the root-mean-square fluctuation depends on the ionic strength as well as the length of the segment considered and is of the order 5-10%. Both classes of fluctuation result in transient bends toward the side of greater counterion density. The bending amplitudes are approximately 15% of the total root-mean-square bends associated with the persistence length of DNA. We are thus led to suggest that asymmetric fluctuations of counterion density contribute modestly but significantly toward the aggregate of thermalized solvent fluctuations that cause bending deformations of DNA free in solution. The calculations support the idea that counterions may exert some modulating influence on the fine structure of DNA.     

Sequence-dependent DNA structure: a database of octamer structural parameters

We have constructed the potential energy surfaces for all unique tetramers, hexamers and octamers in double helical DNA, as a function of the two principal degrees of freedom, slide and shift at the central step. From these potential energy maps, we have calculated a database of structural and flexibility properties for each of these sequences. These properties include: the values of each of the six step parameters (twist roll, tilt, rise, slide and shift), for each step of the sequence; flexibility measures for both decrease and increase in each property value from the minimum energy conformation for the central step; and the deviation from the path of a hypothetical straight octamer. In an analysis of structural change as a function of sequence length, we observe that almost all DNA tends to B-DNA and becomes less flexible. A more detailed analysis of octamer properties has allowed us to determine the structural preferences of particular sequence elements. GGC and GCC sequences tend to confer bistability, low stability and a predisposition to A-form DNA, whereas AA steps strongly prefer B-DNA and inhibit A-structures. There is no correlation between flexibility and intrinsic curvature, but bent DNA is less stable than straight. The most difficult deformation is undertwisting. The TA step stands out as the most flexible sequence element with respect to decreasing twist and increasing roll. However, as with the structural properties, this behavior is highly context-dependent and some TA steps are very straight.     

Intrinsic bends and integration host factor binding at F plasmid oriT.

F plasmid oriT DNA extending from the F kilobase coordinate 66.7 (base pair [bp] 1 on the oriT sequence map) rightward to bp 527 was analyzed for intrinsic bends (by permutation assays) and for binding of integration host factor (IHF) (by gel retardation and DNase footprinting). Intrinsic bending of the 527-bp fragment (bend center approximately at bp 240) was represented as a composite of at least two components located near bp 170 and near bp 260. IHF bound primarily to a site extending from bp 165 to 195 and with lower affinity to a site extending from bp 287 to 319. The intrinsic curvature and sequences to which IHF binds (IHF is known to bend DNA) may play a structural role in oriT function.