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.     

Probing the Elasticity of DNA on Short Length Scales by Modeling Supercoiling under Tension

The wormlike-chain (WLC) model is widely used to describe the energetics of DNA bending. Motivated by recent experiments, alternative, so-called subelastic chain models were proposed that predict a lower elastic energy of highly bent DNA conformations. Until now, no unambiguous verification of these models has been obtained because probing the elasticity of DNA on short length scales remains challenging. Here we investigate the limits of the WLC model using coarse-grained Monte Carlo simulations to model the supercoiling of linear DNA molecules under tension. At a critical supercoiling density, the DNA extension decreases abruptly due to the sudden formation of a plectonemic structure. This buckling transition is caused by the large energy required to form the tightly bent end-loop of the plectoneme and should therefore provide a sensitive benchmark for model evaluation. Although simulations based on the WLC energetics could quantitatively reproduce the buckling measured in magnetic tweezers experiments, the buckling almost disappears for the tested linear subelastic chain model. Thus, our data support the validity of a harmonic bending potential even for small bending radii down to 3.5 nm.     

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.     

Bending and flexibility of methylated and unmethylated EcoRI DNA

We used cyclization kinetics experiments and Monte Carlo simulations to determine a structural model for a DNA decamer containing the EcoRI restriction site. Our findings agree well with recent crystal and NMR structures of the EcoRI dodecamer, where an overall bend of seven degrees is distributed symmetrically over the molecule. Monte Carlo simulations indicate that the sequence has a higher flexibility, assumed to be isotropic, compared to that of a "generic" DNA sequence. This model was used as a starting point for the investigation of the effect of cytosine methylation on DNA bending and flexibility. While methylation did not affect bend magnitude or direction, it resulted in a reduction in bending flexibility and under-winding of the methylated nucleotides. We demonstrate that our approach can augment the understanding of DNA structure and dynamics by adding information about the global structure and flexibility of the sequence. We also show that cyclization kinetics can be used to study the properties of modified nucleotides.     

Statistical mechanics of sequence-dependent circular DNA and its application for DNA cyclization

DNA cyclization is potentially the most powerful approach for systematic quantitation of sequence-dependent DNA bending and flexibility. We extend the statistical mechanics of the homogeneous DNA circle to a model that considers discrete basepairs, thus allowing for inhomogeneity, and apply the model to analysis of DNA cyclization. The theory starts from an iterative search for the minimum energy configuration of circular DNA. Thermodynamic quantities such as the J factor, which is essentially the ratio of the partition functions of circular and linear forms, are evaluated by integrating the thermal fluctuations around the configuration under harmonic approximation. Accurate analytic expressions are obtained for equilibrium configurations of homogeneous circular DNA with and without bending anisotropy. J factors for both homogeneous and inhomogeneous DNA are evaluated. Effects of curvature, helical repeat, and bending and torsional flexibility in DNA cyclization are analyzed in detail, revealing that DNA cyclization can detect as little as one degree of curvature and a few percent change in flexibility. J factors calculated by our new approach are well consistent with Monte Carlo simulations, whereas the new theory has much greater efficiency in computations. Simulation of experimental results has been demonstrated.     

Effects of the nucleoid protein HU on the structure, flexibility, and ring-closure properties of DNA deduced from Monte Carlo simulations

The histone-like HU (heat unstable) protein plays a key role in the organization and regulation of the Escherichia coli genome. The nonspecific nature of HU binding to DNA complicates analysis of the mechanism by which the protein contributes to the looping of DNA. Conventional models of the looping of HU-bound duplexes attribute the changes in biophysical properties of DNA brought about by the random binding of protein to changes in the effective parameters of an ideal helical wormlike chain. Here, we introduce a novel Monte Carlo approach to study the effects of nonspecific HU binding on the configurational properties of DNA directly. We randomly decorated segments of an ideal double-helical DNA with HU molecules that induce the bends and other structural distortions of the double helix find in currently available X-ray structures. We find that the presence of HU at levels approximating those found in the cell reduces the persistence length by roughly threefold compared with that of naked DNA. The binding of protein has particularly striking effects on the cyclization properties of short duplexes, altering the dependence of ring closure on chain length in a way that cannot be mimicked by a simple wormlike model and accumulating at higher-than-expected levels on successfully closed chains. Moreover, the uptake of protein on small minicircles depends on chain length, taking advantage of the HU-induced deformations of DNA structure to facilitate ligation. Circular duplexes with bound HU show much greater propensity than protein-free DNA to exist as negatively supercoiled topoisomers, suggesting a potential role of HU in organizing the bacterial nucleoid. The local bending and undertwisting of DNA by HU, in combination with the number of bound proteins, provide a structural rationale for the condensation of DNA and the observed expression levels of reporter genes in vivo.     

Probing the Conformational Distributions of Subpersistence Length DNA

We have measured the bending elasticity of short double-stranded DNA (dsDNA) chains through small-angle x-ray scattering from solutions of dsDNA-linked dimers of gold nanoparticles. This method, which does not require exertion of external forces or binding to a substrate, reports on the equilibrium distribution of bending fluctuations, not just an average value (as in ensemble fluorescence resonance energy transfer) or an extreme value (as in cyclization), and in principle provides a more robust data set for assessing the suitability of theoretical models. Our experimental results for dsDNA comprising 42-94 basepairs are consistent with a simple wormlike chain model of dsDNA elasticity, whose behavior we have determined from Monte Carlo simulations that explicitly represent nanoparticles and their alkane tethers. A persistence length of 50 nm (150 basepairs) gave a favorable comparison, consistent with the results of single-molecule force-extension experiments on much longer dsDNA chains, but in contrast to recent suggestions of enhanced flexibility at these length scales.     

Topological distributions and the torsional rigidity of DNA. A Monte Carlo study of DNA circles

Distributions of the linking number of circular DNA molecules, defined as the sum of twist and the writhing number, are obtained by Monte Carlo simulations of small, randomly closed DNA circles. We estimate the relative contributions of fluctuations in twist and writhe to the linking number distribution, as functions of DNA size. Published experimental data on topoisomer distributions in circular DNA molecules are interpreted to estimate the torsional rigidity of DNA in solution. We show that ignoring the writhe component of the linking number distribution, even for DNA circles as small as 250 base-pairs, leads to an underestimate for the torsional stiffness of the double helix. The value of the torsional modulus obtained from this analysis, C = 3.4 X 10(-19) erg cm, is from 10 to 40% larger than that estimated by others and more than twice as large as the values obtained from fluorescence depolarization or other time-resolved spectroscopic measurements. We also develop further the theoretical treatment of ring closure probabilities for DNA described in the previous article. It is shown that the torsional part of the ring closure probability, phi 0,1 (tau 0) is a periodic function of DNA length that contributes strongly to the ring closure probability for short chains but makes negligible contributions for chains over 1000 base-pairs in length.     

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.     

Magnitude and direction of DNA bending induced by screw-axis orientation: influence of sequence, mismatches and abasic sites

DNA-bending flexibility is central for its many biological functions. A new bending restraining method for use in molecular mechanics calculations and molecular dynamics simulations was developed. It is based on an average screw rotation axis definition for DNA segments and allows inducing continuous and smooth bending deformations of a DNA oligonucleotide. In addition to controlling the magnitude of induced bending it is also possible to control the bending direction so that the calculation of a complete (2-dimensional) directional DNA-bending map is now possible. The method was applied to several DNA oligonucleotides including A(adenine)-tract containing sequences known to form stable bent structures and to DNA containing mismatches or an abasic site. In case of G:A and C:C mismatches a greater variety of conformations bent in various directions compared to regular B-DNA was found. For comparison, a molecular dynamics implementation of the approach was also applied to calculate the free energy change associated with bending of A-tract containing DNA, including deformations significantly beyond the optimal curvature. Good agreement with available experimental data was obtained offering an atomic level explanation for stable bending of A-tract containing DNA molecules. The DNA-bending persistence length estimated from the explicit solvent simulations is also in good agreement with experiment whereas the adiabatic mapping calculations with a GB solvent model predict a bending rigidity roughly two times larger.     

Conformational and thermodynamic properties of supercoiled DNA.

We used Monte Carlo simulations to investigate the conformational and thermodynamic properties of DNA molecules with physiological levels of supercoiling. Three parameters determine the properties of DNA in this model: Kuhn statistical length, torsional rigidity and effective double-helix diameter. The chains in the simulation resemble strongly those observed by electron microscopy and have the conformation of an interwound superhelix whose axis is often branched. We compared the geometry of simulated chains with that determined experimentally by electron microscopy and by topological methods. We found a very close agreement between the Monte Carlo and experimental values for writhe, superhelix axis length and the number of superhelical turns. The computed number of superhelix branches was found to be dependent on superhelix density, DNA chain length and double-helix diameter. We investigated the thermodynamics of supercoiling and found that at low superhelix density the entropic contribution to superhelix free energy is negligible, whereas at high superhelix density, the entropic and enthalpic contributions are nearly equal. We calculated the effect of supercoiling on the spatial distribution of DNA segments. The probability that a pair of DNA sites separated along the chain contour by at least 50 nm are juxtaposed is about two orders of magnitude greater in supercoiled DNA than in relaxed DNA. This increase in the effective local concentration of DNA is not strongly dependent on the contour separation between the sites. We discuss the implications of this enhancement of site juxtaposition by supercoiling in the context of protein-DNA interactions involving multiple DNA-binding sites.     

Understanding apparent DNA flexibility enhancement by HU and HMGB architectural proteins

Understanding and predicting the mechanical properties of protein/DNA complexes are challenging problems in biophysics. Certain architectural proteins bind DNA without sequence specificity and strongly distort the double helix. These proteins rapidly bind and unbind, seemingly enhancing the flexibility of DNA as measured by cyclization kinetics. The ability of architectural proteins to overcome DNA stiffness has important biological consequences, but the detailed mechanism of apparent DNA flexibility enhancement by these proteins has not been clear. Here, we apply a novel Monte Carlo approach that incorporates the precise effects of protein on DNA structure to interpret new experimental data for the bacterial histone-like HU protein and two eukaryotic high-mobility group class B (HMGB) proteins binding to ∼ 200-bp DNA molecules. These data (experimental measurement of protein-induced increase in DNA cyclization) are compared with simulated cyclization propensities to deduce the global structure and binding characteristics of the closed protein/DNA assemblies. The simulations account for all observed (chain length and concentration dependent) effects of protein on DNA behavior, including how the experimental cyclization maxima, observed at DNA lengths that are not an integral helical repeat, reflect the deformation of DNA by the architectural proteins and how random DNA binding by different proteins enhances DNA cyclization to different levels. This combination of experiment and simulation provides a powerful new approach to resolve a long-standing problem in the biophysics of protein/DNA interactions.     

Phased adenine tracts in double-stranded RNA do not induce sequence-directed bending

Tracts of four to six adenines phased with the DNA helix produce a sequence-directed bending of the helix axis. Here, using gel electrophoresis and electron microscopy (EM), we have asked whether a similar motif will induce bending in a duplex RNA helix. Single-stranded RNAs were transcribed either from short synthetic DNA templates or from Crithidia fasciculata kinetoplast bent DNA, and the complementary single-stranded RNAs were annealed to produce duplex RNA molecules containing blocks of four to six adenines. Electrophoresis on polyacrylamide gels revealed no retardation of the RNAs containing phased blocks of adenines relative to duplex RNAs lacking such blocks. Examination by EM showed most of the molecules to be straight or only slightly bent. Thus, in contrast to DNA duplexes, phased adenine tracts do not induce sequence-directed bending in double-stranded RNA. Analysis of the distribution of molecule shapes for the highly bent C. fasciculata DNA showed that the adenine blocks do not act cooperatively to induce DNA bending and that the molecules must equilibrate between a spectrum of bent shapes.     

Uranyl photoprobing of nonbent A/T- and bent A-tracts. A difference of flexibility?

In this study, we have systematically compared the uranyl photocleavage of a range of bent A-tracts and nonbent TA-tracts as well as interrupted A-tracts. We demonstrate that uranyl photocleavage of A-tracts and TA-tracts is almost identical, indicating a very similar minor groove conformation. Furthermore, a 10 base pair A-tract is divided into two independent tracts by an intervening TA or GC step. Uranyl probing also clearly distinguishes the bent A4T4 and the nonbent T4A4 sequences as adopting different structures, and our interpretation of the data is consistent with a structure for the bent A4T4 sequence that resembles a continuous A-tract, whereas the nonbent T4A4 sequences are closer to two independent and opposite A-tracts that cancel each other in terms of macroscopic bending. Finally, we also note that even single TA and TAT steps are highly sensitive to uranyl photocleavage and propose that in addition to average minor groove width, uranyl also senses DNA helix flexibility/deformability. Thus, the structural difference of TA-tracts and A-tracts may to a large extent reflect a difference in flexibility, and DNA curvature may consequently require a rigid narrow minor groove conformation that creates distinct A-tract-B-DNA junctions as the predominant cause of the bending.     

Geometry of mediating protein affects the probability of loop formation in DNA

Recent single molecule experiments have determined the probability of loop formation in DNA as a function of the DNA contour length for different types of looping proteins. The optimal contour length for loop formation as well as the probability density functions have been found to be strongly dependent on the type of looping protein used. We show, using Monte Carlo simulations and analytical calculations, that these observations can be replicated using the wormlike-chain model for double-stranded DNA if we account for the nonzero size of the looping protein. The simulations have been performed in two dimensions so that bending is the only mode of deformation available to the DNA while the geometry of the looping protein enters through a single variable which is representative of its size. We observe two important effects that seem to directly depend on the size of the enzyme: 1), the overall propensity of loop formation at any given value of the DNA contour length increases with the size of the enzyme; and 2), the contour length corresponding to the first peak as well as the first well in the probability density functions increases with the size of the enzyme. Additionally, the eigenmodes of the fluctuating shape of the looped DNA calculated from simulations and theory are in excellent agreement, and reveal that most of the fluctuations in the DNA occur in regions of low curvature.     

The contribution of phosphate-phosphate repulsions to the free energy of DNA bending

DNA bending is important for the packaging of genetic material, regulation of gene expression and interaction of nucleic acids with proteins. Consequently, it is of considerable interest to quantify the energetic factors that must be overcome to induce bending of DNA, such as base stacking and phosphate–phosphate repulsions. In the present work, the electrostatic contribution of phosphate–phosphate repulsions to the free energy of bending DNA is examined for 71 bp linear and bent-form model structures. The bent DNA model was based on the crystallographic structure of a full turn of DNA in a nucleosome core particle. A Green's function approach based on a linear-scaling smooth conductor-like screening model was applied to ascertain the contribution of individual phosphate–phosphate repulsions and overall electrostatic stabilization in aqueous solution. The effect of charge neutralization by site-bound ions was considered using Monte Carlo simulation to characterize the distribution of ion occupations and contribution of phosphate repulsions to the free energy of bending as a function of counterion load. The calculations predict that the phosphate–phosphate repulsions account for ~30% of the total free energy required to bend DNA from canonical linear B-form into the conformation found in the nucleosome core particle.     

Electric dichroism and bending amplitudes of DNA fragments according to a simple orientation function for weakly bent rods

The linear dichroism is calculated for DNA fragments in their thermal bending equilibrium. These calculations are given for relatively short fragments, where bent molecules can be described by an arc model. Using the measured value of 350 A for the persistence length, the limit dichroism (corresponding to complete alignment) decreases due to thermal bending, e.g., for a fragment with 100 base pairs to 80% of the value expected for straight molecules. Thermal bending should lead to a strong continuous decrease of the dichroism with increasing chain length, which is not observed, however, in electric dichroism experiments due to electric stretching. The influence of the electric field on the bending equilibrium is described by a contribution to the bending energy, which is calculated from the movement of charge equivalents against the potential gradient upon bending. The charge equivalents, which are assigned to the helix ends, are derived from the dipole moments causing the stationary degree of orientation. By this procedure the energy term inducing DNA stretching is given for induced, permanent, and saturating induced dipole models without introduction of any additional parameter. The stationary dichroism at a given electric field strength is then calculated according to an arc model by integration over all angles of orientation of helix axes or chords with respect to the field vector, and at each of these angles the contribution to the dichroism is calculated by integration over all helices with different degrees of bending. Orientation functions obtained by this procedure are fitted to dichroism data measured for various restriction fragments. Optimal fits are found for an induced dipole model with saturation of the polarizability. The difference between orientation functions with and without electric stretching is used to evaluate dichroism bending amplitudes. Both chain length and field strength dependence of bending amplitudes are consistent with experimental amplitudes derived from the dichroism decay in low salt buffers containing multivalent ions like Mg2+, spermine, or [CoNH3)6]3+. Bending amplitudes can be used to evaluate the persistence length from electrooptical data obtained for a single DNA restriction fragment. Bending and stretching effects are considerable already at relatively low chain length, and thus should not be neglected in any quantitative evaluation of experimental data.     

An evolutionary Monte Carlo algorithm for predicting DNA hybridization

Many DNA-based technologies, such as DNA computing, DNA nanoassembly and DNA biochips, rely on DNA hybridization reactions. Previous hybridization models have focused on macroscopic reactions between two DNA strands at the sequence level. Here, we propose a novel population-based Monte Carlo algorithm that simulates a microscopic model of reacting DNA molecules. The algorithm uses two essential thermodynamic quantities of DNA molecules: the binding energy of bound DNA strands and the entropy of unbound strands. Using this evolutionary Monte Carlo method, we obtain a minimum free energy configuration in the equilibrium state. We applied this method to a logical reasoning problem and compared the simulation results with the experimental results of the wet-lab DNA experiments performed subsequently. Our simulation predicted the experimental results quantitatively.     

Amplified stretch of bottlebrush-coated DNA in nanofluidic channels

The effect of a cationic-neutral diblock polypeptide on the conformation of single DNA molecules confined in rectangular nanochannels is investigated with fluorescence microscopy. An enhanced stretch along the channel is observed with increased binding of the cationic block of the polypeptide to DNA. A maximum stretch of 85% of the contour length can be achieved inside a channel with a cross-sectional diameter of 200 nm and at a 2-fold excess of polypeptide with respect to DNA charge. With site-specific fluorescence labelling, it is demonstrated that this maximum stretch is sufficient to map large-scale genomic organization. Monte Carlo computer simulation shows that the amplification of the stretch inside the nanochannels is owing to an increase in bending rigidity and thickness of bottlebrush-coated DNA. The persistence lengths and widths deduced from the nanochannel data agree with what has been estimated from the analysis of atomic force microscopy images of dried complexes on silica.