Theoretical analysis of the helix-coil transition in positively superhelical DNA at high temperatures

DNA superhelicity

Closing each strand of a DNA duplex upon itself fixes its linking number L. This topological condition couples together the secondary and tertiary structures of the resulting ccDNA topoisomer, a constraint that is not present in otherwise identical nicked or linear DNAs. Fixing L has a range of structural, energetic and functional consequences. Here we consider how L having different integer values (that is, different superhelicities) affects ccDNA molecules. The approaches used are primarily theoretical, and are developed from a historical perspective. In brief, processes that either relax or increase superhelicity, or repartition what is there, may either release or require free energy. The energies involved can be substantial, sufficient to influence many events, directly or indirectly. Here two examples are developed. The changes of unconstrained superhelicity that occur during nucleosome attachment and release are examined. And a simple theoretical model of superhelically driven DNA structural transitions is described that calculates equilibrium distributions for populations of identical topoisomers. This model is used to examine how these distributions change with superhelicity and other factors, and applied to analyze several situations of biological interest.

Single-molecule insights into torsion and roadblocks in bacterial transcript elongation

During transcription, RNA polymerase (RNAP) translocates along the helical template DNA while maintaining high transcriptional fidelity. However, all genomes are dynamically twisted, writhed, and decorated by bound proteins and motor enzymes. In prokaryotes, proteins bound to DNA, specifically or not, frequently compact DNA into conformations that may silence genes by obstructing RNAP. Collision of RNAPs with these architectural proteins, may result in RNAP stalling and/or displacement of the protein roadblock. It is important to understand how rapidly transcribing RNAPs operate under different levels of supercoiling or in the presence of roadblocks. Given the broad range of asynchronous dynamics exhibited by transcriptional complexes, single-molecule assays, such as atomic force microscopy, fluorescence detection, optical and magnetic tweezers, etc. are well suited for detecting and quantifying activity with adequate spatial and temporal resolution. Here, we summarize current understanding of the effects of torsion and roadblocks on prokaryotic transcription, with a focus on single-molecule assays that provide real-time detection and readout.

Torsion-mediated interaction between adjacent genes

DNA torsional stress is generated by virtually all biomolecular processes involving the double helix, in particular transcription where a significant level of stress propagates over several kilobases. If another promoter is located in this range, this stress may strongly modify its opening properties, and hence facilitate or hinder its transcription. This mechanism implies that transcribed genes distant of a few kilobases are not independent, but coupled by torsional stress, an effect for which we propose the first quantitative and systematic model. In contrast to previously proposed mechanisms of transcriptional interference, the suggested coupling is not mediated by the transcription machineries, but results from the universal mechanical features of the double-helix. The model shows that the effect likely affects prokaryotes as well as eukaryotes, but with different consequences owing to their different basal levels of torsion. It also depends crucially on the relative orientation of the genes, enhancing the expression of eukaryotic divergent pairs while reducing that of prokaryotic convergent ones. To test the in vivo influence of the torsional coupling, we analyze the expression of isolated gene pairs in the Drosophila melanogaster genome. Their orientation and distance dependence is fully consistent with the model, suggesting that torsional gene coupling may constitute a widespread mechanism of (co)regulation in eukaryotes.

Temperature dependence of the DNA double helix at the nanoscale: structure, elasticity, and fluctuations

Biological organisms exist over a broad temperature range of -15°C to +120°C, where many molecular processes involving DNA depend on the nanoscale properties of the double helix. Here, we present results of extensive molecular dynamics simulations of DNA oligomers at different temperatures. We show that internal basepair conformations are strongly temperature-dependent, particularly in the stretch and opening degrees of freedom whose harmonic fluctuations can be considered the initial steps of the DNA melting pathway. The basepair step elasticity contains a weaker, but detectable, entropic contribution in the roll, tilt, and rise degrees of freedom. To extend the validity of our results to the temperature interval beyond the standard melting transition relevant to extremophiles, we estimate the effects of superhelical stress on the stability of the basepair steps, as computed from the Benham model. We predict that although the average twist decreases with temperature in vitro, the stabilizing external torque in vivo results in an increase of ∼1°/bp (or a superhelical density of Δσ ≃ +0.03) in the interval 0-100°C. In the final step, we show that the experimentally observed apparent bending persistence length of torsionally unconstrained DNA can be calculated from a hybrid model that accounts for the softening of the double helix and the presence of transient denaturation bubbles. Although the latter dominate the behavior close to the melting transition, the inclusion of helix softening is important around standard physiological temperatures.

Bubble statistics and positioning in superhelically stressed DNA

We present a general framework to study the thermodynamic denaturation of double-stranded DNA under superhelical stress. We report calculations of position- and size-dependent opening probabilities for bubbles along the sequence. Our results are obtained from transfer-matrix solutions of the Zimm-Bragg model for unconstrained DNA and of a self-consistent linearization of the Benham model for superhelical DNA. The numerical efficiency of our method allows for the analysis of entire genomes and of random sequences of corresponding length (10(6)-10(9) base pairs). We show that, at physiological conditions, opening in superhelical DNA is strongly cooperative with average bubble sizes of 10(2)-10(3) base pairs (bp), and orders of magnitude higher than in unconstrained DNA. In heterogeneous sequences, the mean degree of base-pair opening is self-averaging, while bubble localization and statistics are dominated by sequence disorder. Compared to random sequences with identical GC-content, genomic DNA has a significantly increased probability to open large bubbles under superhelical stress. These bubbles are frequently located directly upstream of transcription start sites.

Strand separation in negatively supercoiled DNA

We consider Benham's model for strand separation in negatively supercoiled circular DNA, and study denaturation as function of the linking difference density kappa<0. We propose a statistical version of this model, based on bayesian segmentation methods of current use in bioinformatics; this leads to new algorithms with priors adapted to supercoiled DNA, taking into account the random nature of the free energies needed to denature base pairs.

The analysis of stress-induced duplex destabilization in long genomic DNA sequences

We present a method for calculating predicted locations and extents of stress-induced DNA duplex destabilization (SIDD) as functions of base sequence and stress level in long DNA molecules. The base pair denaturation energies are assigned individually, so the influences of near neighbors, methylated bases, adducts, or lesions can be included. Sample calculations indicate that copolymeric energetics give results that are close to those derived when full near-neighbor energetics are used; small but potentially informative differences occur only in the calculated SIDD properties of moderately destabilized regions. The method presented here for analyzing long sequences calculates the destabilization properties within windows of fixed length N, with successive windows displaced by an offset distance d(o). The final values of the relevant destabilization parameters for each base pair are calculated as weighted averages of the values computed for each window in which that base pair appears. This approach implicitly assumes that the strength of the direct coupling between remote base pairs that is induced by the imposed stress attenuates with their separation distance. This strategy enables calculations of the destabilization properties of DNA sequences of any length, up to and including complete chromosomes. We illustrate its utility by calculating the destabilization properties of the entire E. coli genomic DNA sequence. A preliminary analysis of the results shows that promoters are associated with SIDD regions in a highly statistically significant manner, suggesting that SIDD attributes may prove useful in the computational prediction of promoter locations in prokaryotes.

Single and multiple topologically driven structural transitions in DNA

We derive some exact general results concerning the behavior of topological absorbers (i.e., sequences undergoing topologically driven structural transitions) in closed circular DNA molecules. Starting from the formal physical framework that covers all known structural transitions, like those from standard B-DNA to nonstandard conformers Z-DNA, H-DNA, cruciform-DNA, melt-DNA or others, we develop a reduced state space description that leads to an analytically simplified "black box" view of absorbers. The latter contains only a single state variable-the total sequence unwinding u describing the topological state of the absorber. We show that the statistical mechanics of u is determined by the (one-dimensional) absorption free energy function G(abs) and find explicit expressions for G(abs) and for moments <u(n)> in terms of the standard experimental observable-the absorption function alpha:=<u>. The reduced state space method is then applied to systems consisting of several interacting topologically coupled absorbers and a formula predicting their collective behavior (superposition) in terms of their individual absorptions is derived. Using these results we formulate and discuss solution methods for two basic types of inverse problems that turn out to be fundamental for future absorber construction.

Isomorphism between cell and human languages: molecular biological, bioinformatic and linguistic implications

The concept of cell language has been defined in molecular terms. The molecule-based cell language is shown to be isomorphic with the sound- and visual signal-based human language with respect to ten out of the 13 design features of human language characterized by Hockett. Biocybernetics, a general molecular theory of living systems developed over the past two and a half decades, is found to provide a physical theory underlying the phenomenon of cell language. The concept of cell language integrates bioenergetics and bioinformatics on the one hand and reductionistic and holistic experimental data on the other to account for living processes on the molecular level. The isomorphism between cell and human languages suggests that the DNA of higher eucaryotes contains two classes of genes--structural genes corresponding to the lexicon and 'spatiotemporal genes' corresponding to the grammar of cell language. The former is located in coding regions of DNA and the latter is predicted to reside primarily in noncoding regions. The grammar of cell language is identified with the mapping of the nucleotide sequences of DNA onto its 4-dimensional folding patterns that control the spatiotemporal evolution of gene expression. Such a mapping has been referred to as the second genetic code, in contrast to the first genetic code which maps nucleotide triplets onto amino acids. The cell language theory introduces into biology the linguistic principle of 'rule-governed creativity,' leading to the formulation of the concept of 'rule-governed creative molecules' or 'creations.' This concept sheds new light on molecular biology, bioinformatics, protein folding, and developmental biology. In addition, the cell language theory suggests that human language is ultimately founded on cell language.