Computer simulation of DNA supercoiling in a simple elastomechanical approximation

DNA supercoiling is both an interesting problem from the theoretical point of view and an important phenomenon affecting DNA functions in vivo. Experimentally, however, hardly more than the overall hydrodynamic shape, superhelical density, and enzymic or chemical reactivity of the parameters that are in some way related to DNA secondary and tertiary structure in the superhelical state can be determined. Consequently, it is highly desirable to build up models of DNA supercoiling that, on the one hand, match the above type of global data and, on the other, take advantage of the knowledge about DNA structure at lower levels of complexity, i.e., with linear DNA molecules and its synthetic models. One possible approach, presented here, deals with an extension of Fuller's and Benham's general ideas concerning an elastomechanical model of DNA supercoiling. We extend their model with an algorithm suitable for numerical calculations and construct a fast computer program, ROPASE , that displays the rod shapes as dependent on its elastic properties and applied stress. Development of this program made inevitable a detailed analysis of the input parameters found to be degenerate in the sense that not all of them should be considered variable to generate the whole set of possible solutions of the model. Many calculations were performed using ROPASE to test its properties and the properties of the elastomechanical model. Representative DNA shapes are presented.     

Statistical Mechanical Approach for Predicting the Transition to Non-B DNA Structures in Supercoiled DNA

Abstract

Supercoiling causes global twist of DNA structure and the supercoiled state has wide influence on conformational transition. A statistical mechanical approach was made for prediction of the transition probability to non-B DNA structures under torsional stress. A conditional partition function was defined as the sum over all possible states of the DNA sequence with basepair 1 and basepair n being in B-form helix and a recurrence formula was developed which expressed the partition function for basepair n with those for less number of pairs. This new definition permits a quick enumeration of every configuration of secondary structures. Energetic parameters of all conformations concerned, involving B-form, interior loop, cruciform and Z-form, were included in the equation. The probability of transition to each non-B conformation could be derived from these conditional partition functions. For treatment of effects of superhelicity, supercoiling energy was considered, and a twist of each conformation was determined to minimize the supercoiling energy. As the twist itself affects the transition probability, the whole scheme of equations was solved by renormalization technique. The present method permits a simultaneous treatment of serveral types of conformations under a common torsional stress.

A set of energetic parameters of DNA secondary structures has been chosen for calculation. Some DNA sequences were submitted to the calculation, and all the sequences that we submitted gave stable convergence. Some of them have been investigated the critical supercoil density for the transition to non-B DNA structures. Even though the reliability of the set of parameters was not enough, the prediction of secondary structure transition showed good agreement with reported observation. Hence, the present algorithm can estimate the probability of local conformational change of DNA under a given supercoil density, and also be employed to predict some specific sequences in which conformational change is sensitive to superhelicity.     

Experimental evaluation of the Liu–Beveridge dinucleotide step model of DNA structure

Methods for predicting DNA curvature have many possible applications. Dinucleotide step models describe DNA shape by characterization of helical twist, deflection angles and the direction of deflection for nearest neighbor base pairs. Liu and Beveridge have extended previous applications of dinucleotide step models with the development and qualitative validation of a predictive method for sequence-dependent DNA curvature (the LB model). We tested whether the LB model accurately predicts experimentally deduced curvature angles and helical repeat parameters for DNA sequences not in its training set, particularly when challenged with quantitative data and subtle sequence phasings. We examined a series of 17 well-characterized DNA sequences to compare electrophoretic and computational results. The LB model is superior to two other models in the prediction of helical repeat parameters. We observed a strong linear correlation between curvature magnitudes predicted using the LB model and those determined by electrophoretic ligation ladder experiments, although the LB model somewhat underestimated apparent curvature. With longer electrophoretic phasing probes the LB model slightly overestimated gel mobility anomalies, with modest deviations in predicted helical repeat parameters. Overall, our analyses suggest that the LB model provides reasonably accurate predictions for the electrophoretic behavior of DNA.     

DNA stem-loop structures in oligopurine-oligopyrimidine triplexes.

Closed circular DNA containing polypurine-polypyrimidine sequences can adopt a triple helical stem-loop structure under supercoiling pressure. We describe an automated procedure for building model loops and its application to the investigation of the polypyrimidine loop at the end of such a triple helical stem. All possible combinations of 3'-stacked and 5'-stacked structures have been examined for loops containing three, four, five, and six nucleotides. The lowest energy conformation is a four-membered loop with all bases stacked on the strand at the 3' end of the loop. The model predicts that sequences (GA)n, (GGGA)n and (GAAA)n should form the stem-loop structure more easily than (GGA)n and (GAA)n. It is also predicted that when a polypurine-polypyrimidine sequence converts from a double stranded structure to a triple stranded stem-loop, the most favorable conditions are those where an even number of basepairs makes the transition. Experimental tests of these predictions are also described.     

Molecular mechanics studies on poly(purine).poly(pyrimidine) sequences in DNA: polymorphism and local variability

Energy minimization has been carried out on three poly(purine).poly(pyrimidine) sequences--d(G)10.d(C)10, d(A)10.d(T)10, and d(AG)5.d(CT)5--using the molecular mechanics program AMBER (Assisted Model Building and Energy Refinement). In order to extensively scan the conformational space available, five different helical models were studied, three of them being right-handed helices while the other two were left helical. For all three sequences the right-handed A- and B-type helices are energetically slightly preferred over the left helices, but the energy difference between the various right-handed helices is only marginal. A detailed analysis has been carried out to characterize the local structural variability in the refined structures, both in terms of torsion angles as well as other parameters such as base-pair tilt, wedge roll, and wedge tilt, etc. All three sequences exhibit similar structural features for a particular form, but both the forms A and B show significant deviations from fiber models. In particular, the A-form structures have higher unit rise (2.7 A), and lower unit twist (31 degrees) and base-pair tilt (12 degrees), compared to the fiber model, which has corresponding values of 2.56 A, 32.7 degrees, and 20 degrees, respectively. All these changes indicate that the refined models are closer to the A-form structure observed in crystals of oligonucleotides. In the refined B-for models, the helical parameters are close to the fiber B-form, although the torsion angles show considerable variations. None of the three sequences examined, including the d(A)n.d(T)n sequence, show any pronounced curvature for the B-form structure.     

Packing features of the all-AT oligonucleotide d(AAATTT)

We describe the packing features of the oligonucleotide duplex d(AAATTT)2, as determined by X-ray diffraction. There is little information on sequences that only contain A and T bases. The present structure confirms that these sequences tend to pack as a helical arrangement of stacked oligonucleotides in a B conformation with Watson-Crick hydrogen bonding. Our results demonstrate that the virtual TA base step between stacked duplexes has a negative twist that improves base stacking. This observation is consistent with the low stability of TA base steps in B-form DNA.     

Sensitivity of NMR internucleotide distances to B-DNA conformation: underlying mechanics.

Nuclear magnetic resonance (NMR) spectroscopy, combining correlated spectroscopy (COSY) coupling constant measurements with nuclear Overhauser effect spectroscopy (NOESY) interatomic distances, should make it possible to determine an averaged solution structure for DNA oligomers. However, even if such data could be obtained with high accuracy, it is not clear which structural parameters of DNA would be determined. Here, the relationships between measurable internucleotide distances and helical parameters are systematically studied through molecular modelling. Investigations are carried out using four representative sequences, (ACGT)n, (TCGA)n, (AGCT)n and (TGCA)n, composed of repeated tetranucleotides belonging to oligomers previously studied by NMR. Correlations between interatomic distances become evident and strong connections between distances and inter-base helical parameters are observed. Results imply that twist, roll, shift and slide values can be accurately determined from NMR data. Sequence independent mechanical coupling which link backbone and sugar conformations to helical twist are also described.     

The potentially Z-DNA-forming sequence d(GTGTACAC) crystallizes as A-DNA

(GT)n/(CA)n sequences have stimulated much interest because of their frequent occurrence in eukaryotic DNA and their potential for forming the left-handed Z-DNA structure. We here report the X-ray crystal structure of a self-complementary octadeoxynucleotide, d(GTGTACAC), at 2.5 A resolution. The molecule adopts a right-handed double-helical conformation belonging to the A-DNA family. In this alternating purine-pyrimidine DNA minihelix the roll and twist angles show alternations qualitatively consistent with Calladine's rules. The average tilt angle of 9.3 degrees is between the values found in A-DNA (19 degrees) and B-DNA (-6 degrees) fibers. It is envisaged that such intermediate conformations may render diversity to genomic DNA. The base-pair tilt angles and the base-pair displacements from the helix axis are found to be correlated for the known A-DNA double-helical fragments.     

Identification of a DNA structural motif that includes the binding sites for Sp1, p53 and GA-binding protein.

We have analyzed predicted helical twist angles in the 21-bp repeat region of the SV40 genome, using a semi-empirical model previously shown to accurately predict backbone conformations. Unexpectedly, the pattern of twist angles characteristic of the six GC-boxes is repeated an additional five times at positions that are regularly interspersed with the six GC-box sequences. These patterns of helical twist angles are associated with a second, imperfectly-repeated sequence motif, the TR-box 5'-RRNTRGG. Unrelated DNA sequences that interact with trans-acting factors (p53 and GABP) exhibit similar twist angle patterns, due to elements of the general form 5'-RRRYRRR that occur as interspersed arrays with a spacing of 10-11 bp and an offset of 4-6 bp. Arrays of these elements, which we call pyrimidine sandwich elements (PSEs), may play an important role in the interaction of trans-acting factors with DNA control regions. In 13 human proto-oncogenes analyzed, we identified 31 PSE arrays, 11 of which were in the 5'-flanking regions of the genes. The most extensive array was found in the promoter region of the K-ras gene. Extending over 80 bp of DNA, it contained 16 PSEs that showed an average deviation from the SV40 criterion pattern of angles of only 1.2 degrees.     

Sequence-dependent flexibility in promoter sequences

The non-neighbor interactions between base-pairs were taken into account to calculate the angular parameters (Omega, rho and tau) describing the orientation of successive base-pair planes and the translation parameters (D(y)) along the long axis of base-pair steps for 36 independent tetramers. A statistical mechanical model was proposed to predict the DNA flexibility that is mainly related to the thermal fluctuations at individual base-pair steps. The DNA flexibility can be described by the root-mean-square deviation of the end-to-end distance of DNA helical structure. The present model was then used to investigate the extreme flexible pattern in prokaryotic and eukaryotic promoter sequences. The results demonstrated several extreme flexible regions related to functionally important elements exist both in prokaryotic promoters and in eukaryotic promoters, DNA flexibility and AT content are highly correlated. The probabilities finding flexibility pattern in promoter sequences were also estimated statistically. The biological implications were discussed briefly.     

Theoretical model of the B-Z transition in DNA with an arbitrary sequence

A statistical-mechanical model is suggested that makes it possible to describe the B-Z transition in DNA with an arbitrary sequence of nucleotides. The key point consists in allowance for the fact that each base pair can assume one of the two states with different energies. One of these states corresponds to the standard Z-form with purines in the syn conformation and pyrimidines in the anti conformation. However, in natural DNA sequences such standard base-pair conformations should be interrupted by energetically unfavorable conformations (syn for pyrimidines and anti for purines). Open regions and cruciform structures are also allowed for in the model. The probabilities of formation of the Z-form stretches, open regions and cruciform structures have been calculated for different values of parameters for pBR322 and pAO3 DNA.     

Topoisomerase II, not topoisomerase I, is the proficient relaxase of nucleosomal DNA

Eukaryotic topoisomerases I and II efficiently remove helical tension in naked DNA molecules. However, this activity has not been examined in nucleosomal DNA, their natural substrate. Here, we obtained yeast minichromosomes holding DNA under (+) helical tension, and incubated them with topoisomerases. We show that DNA supercoiling density can rise above +0.04 without displacement of the histones and that the typical nucleosome topology is restored upon DNA relaxation. However, in contrast to what is observed in naked DNA, topoisomerase II relaxes nucleosomal DNA much faster than topoisomerase I. The same effect occurs in cell extracts containing physiological dosages of topoisomeraseI and II. Apparently, the DNA strand-rotation mechanism of topoisomerase I does not efficiently relax chromatin, which imposes barriers for DNA twist diffusion. Conversely, the DNA cross-inversion mechanism of topoisomerase II is facilitated in chromatin, which favor the juxtaposition of DNA segments. We conclude that topoisomerase II is the main modulator of DNA topology in chromatin fibers. The nonessential topoisomerase I then assists DNA relaxation where chromatin structure impairs DNA juxtaposition but allows twist diffusion.     

Elucidating a key intermediate in homologous DNA strand exchange: structural characterization of the RecA-triple-stranded DNA complex using fluorescence resonance energy transfer

The RecA protein of Escherichia coli plays essential roles in homologous recombination and restarting stalled DNA replication forks. In vitro, the protein mediates DNA strand exchange between single-stranded (ssDNA) and homologous double-stranded DNA (dsDNA) molecules that serves as a model system for the in vivo processes. To date, no high-resolution structure of the key intermediate, comprised of three DNA strands simultaneously bound to a RecA filament (RecA-tsDNA complex), has been reported. We present a systematic characterization of the helical geometries of the three DNA strands of the RecA-tsDNA complex using fluorescence resonance energy transfer (FRET) under physiologically relevant solution conditions. FRET donor and acceptor dyes were used to label different DNA strands, and the interfluorophore distances were inferred from energy transfer efficiencies measured as a function of the base-pair separation between the two dyes. The energy transfer efficiencies were first measured on a control RecA-dsDNA complex, and the calculated helical parameters (h approximately 5 A, Omega(h) approximately 20 degrees ) were consistent with structural conclusions derived from electron microscopy (EM) and other classic biochemical methods. Measurements of the helical parameters for the RecA-tsDNA complex revealed that all three DNA strands adopt extended and unwound conformations similar to those of RecA-bound dsDNA. The structural data are consistent with the hypothesis that this complex is a late, post-strand-exchange intermediate with the outgoing strand shifted by about three base-pairs with respect to its registry with the incoming and complementary strands. Furthermore, the bases of the incoming and complementary strands are displaced away from the helix axis toward the minor groove of the heteroduplex, and the bases of the outgoing strand lie in the major groove of the heteroduplex. We present a model for the strand exchange intermediate in which homologous contacts preceding strand exchange arise in the minor groove of the substrate dsDNA.     

Packing Features of the all-AT Oligonucleotide d(AAATTT)

Abstract

We describe the packing features of the oligonucleotide duplex d(AAATTT)₂, as determined by X-ray diffraction. There is little information on sequences that only contain A and T bases. The present structure confirms that these sequences tend to pack as a helical arrangement of stacked oligonucleotides in a B conformation with Watson-Crick hydrogen bonding. Our results demonstrate that the virtual TA base step between stacked duplexes has a negative twist that improves base stacking. This observation is consistent with the low stability of TA base steps in B-form DNA.     

Conformational analysis of stiff chiral polymers with end-constraints

We present a Lie-group-theoretic method for the kinematic and dynamic analysis of stiff chiral polymers with end constraints. The first is to determine the minimum energy conformations of stiff polymers with end constraints and the second is to perform normal mode analysis based on the determined minimum energy conformations. In this paper, we use concepts from the theory of Lie groups and principles of variational calculus to model such polymers as inextensible or extensible chiral elastic rods with coupling between stiffnesses. This method is general enough to include any stiffness and chirality parameters in the context of elastic filament models with the quadratic elastic potential energy function. As an application of this formulation, the analysis of DNA conformations is discussed. We demonstrate our method with examples of DNA conformations in which topological properties such as writhe, twist and linking number are calculated from the results of the proposed method. Given these minimum energy conformations, we describe how to perform the normal mode analysis. The results presented here build both on recent experimental work in which DNA mechanical properties have been measured and theoretical work in which the mechanics of non-chiral elastic rods has been studied.     

Interaction of berenil with the tyrT DNA sequence studied by footprinting and molecular modelling. Implications for the design of sequence-specific DNA recognition agents.

We have developed a technique of partially-restrained molecular mechanics enthalpy minimisation which enables the sequence-dependence of the DNA binding of a non-intercalating ligand to be studied for arbitrary sequences of considerable length (greater than = 60 base-pairs). The technique has been applied to analyse the binding of berenil to the minor groove of a 60 base-pair sequence derived from the tyrT promoter; the results are compared with those obtained by DNAse I and hydroxyl radical footprinting on the same sequence. The calculated and experimentally observed patterns of binding are in good agreement. Analysis of the modelling data highlights the importance of DNA flexibility in ligand binding. Further, the electrostatic component of the interaction tends to favour binding to AT-rich regions, whilst the van der Waals interaction energy term favours GC-rich ones. The results also suggest that an important contribution to the observed preference for binding in AT-rich regions arises from lower DNA perturbation energies and is not accompanied by reduced DNA structural perturbations in such sequences. It is therefore concluded that those modes of DNA distortion favourable to binding are probably more flexible in AT-rich regions. The structure of the modelled DNA sequence has also been analysed in terms of helical parameters. For the DNA energy-minimised in the absence of berenil, certain helical parameters show marked sequence-dependence. For example, purine-pyrimidine (R-Y) base pairs show a consistent positive buckle whereas this feature is consistently negative for Y-R pairs. Further, CG steps show lower than average values of slide while GC steps show lower than average values of rise. Similar analysis of the modelling data from the calculations including berenil highlights the importance of DNA flexibility in ligand binding. We observe that the binding of berenil induces characteristic responses in different helical parameters for the base-pairs around the binding site. For example, buckle and tilt tend to become more negative to the 5'-side of the binding site and more positive to the 3'-side, while the base steps at either side of the centre of the site show increased twist and decreased roll.     

Exploring polymorphisms in B-DNA helical conformations

The traditional mesoscopic paradigm represents DNA as a series of base-pair steps whose energy response to equilibrium perturbations is elastic, with harmonic oscillations (defining local stiffness) around a single equilibrium conformation. In addition, base sequence effects are often analysed as a succession of independent XpY base-pair steps (i.e. a nearest-neighbour (NN) model with only 10 unique cases). Unfortunately, recent massive simulations carried out by the ABC consortium suggest that the real picture of DNA flexibility may be much more complex. The paradigm of DNA flexibility therefore needs to be revisited. In this article, we explore in detail one of the most obvious violations of the elastic NN model of flexibility: the bimodal distributions of some helical parameters. We perform here an in-depth statistical analysis of a very large set of MD trajectories and also of experimental structures, which lead to very solid evidence of bimodality. We then suggest ways to improve mesoscopic models to account for this deviation from the elastic regime.