Distributions of bubble lifetimes and bubble lengths in DNA

Large bubble drives circular DNA melting

We investigate the melting transition of non-supercoiled circular DNA of different lengths, employing Brownian dynamics simulations. In the absence of supercoiling, we find that melting of circular DNA is driven by a large bubble, which agrees with the previous predictions of circular DNA melting in the presence of supercoiling. By analyzing sector-wise changes in average base-pair distance, our study reveals that the melting behavior of circular DNA closely resembles that of linear DNA. Additionally, we find a marked difference in the thermal stability of circular DNA over linear DNA at very short length scales, an effect that diminishes as the length of circular DNA increases. The stability of smaller circular DNA is linked to the occurrence of transient small bubbles, characterized by a lower probability of growth.

Twist-stretch relations in nucleic acids

Nucleic acids are highly deformable helical molecules constantly stretched, twisted and bent in their biological functioning. Single molecule experiments have shown that double stranded (ds)-RNA and standard ds-DNA have opposite twist-stretch patterns and stretching properties when overwound under a constant applied load. The key structural features of the A-form RNA and B-form DNA helices are here incorporated in a three-dimensional mesoscopic Hamiltonian model which accounts for the radial, bending and twisting fluctuations of the base pairs. Using path integral techniques which sum over the ensemble of the base pair fluctuations, I compute the average helical repeat of the molecules as a function of the load. The obtained twist-stretch relations and stretching properties, for short A- and B-helical fragments, are consistent with the opposite behaviors observed in kilo-base long molecules.

Examining DNA breathing with pyDNA-EPBD

MOTIVATION

The two strands of the DNA double helix locally and spontaneously separate and recombine in living cells due to the inherent thermal DNA motion. This dynamics results in transient openings in the double helix and is referred to as "DNA breathing" or "DNA bubbles." The propensity to form local transient openings is important in a wide range of biological processes, such as transcription, replication, and transcription factors binding. However, the modeling and computer simulation of these phenomena, have remained a challenge due to the complex interplay of numerous factors, such as, temperature, salt content, DNA sequence, hydrogen bonding, base stacking, and others.

RESULTS

We present pyDNA-EPBD, a parallel software implementation of the Extended Peyrard-Bishop-Dauxois (EPBD) nonlinear DNA model that allows us to describe some features of DNA dynamics in detail. The pyDNA-EPBD generates genomic scale profiles of average base-pair openings, base flipping probability, DNA bubble probability, and calculations of the characteristically dynamic length indicating the number of base pairs statistically significantly affected by a single point mutation using the Markov Chain Monte Carlo algorithm.

AVAILABILITY AND IMPLEMENTATION

pyDNA-EPBD is supported across most operating systems and is freely available at https://github.com/lanl/pyDNA_EPBD. Extensive documentation can be found at https://lanl.github.io/pyDNA_EPBD/.

Equilibrium melting probabilities of a DNA molecule with a defect: An exact solution of the Poland-Scheraga model

In this study we derive analytically the equilibrium melting probabilities for basepairs of a DNA molecule with a defect site. We assume that the defect is characterized by a change in the Watson-Crick basepair energy of the defect basepair, and in the associated two stacking energies for the defect, as compared to the remaining parts of the DNA. The defect site could, for instance, occur due to DNA basepair mismatching, cross-linking, or by the chemical modifications when attaching fluorescent labels, such as fluorescent-quencher pairs, to DNA. Our exact solution of the Poland-Scheraga model for DNA melting provides the probability that the labeled basepair, and its neighbors, are open at different temperatures. Our work is of direct importance, for instance, for studies where fluorophore-quencher pairs are used for studying single basepair fluctuations of designed DNA molecules.

Influence of a Single Deuterium Substitution for Protium on the Frequency Generation of Different-Size Bubbles in IFNA17

The influence of a single 2H/1H replacement on the frequency generation of different-size bubbles in the human interferon alpha-17 gene (IFNA17) under various energies was studied by a developed algorithm and mathematical modeling without simplifications or averaging. This new approach showed the efficacy of researching DNA bubbles and open states both when all hydrogen bonds in nitrogenous base pairs are protium and after an 2H-substitution. After a single deuterium substitution under specific energies, it was demonstrated that the non-coding region of IFNA17 had a more significant regulatory role in bubble generation in the whole gene than the promoter had. It was revealed that a single deuterium substitution for protium has an influence on the frequency generation of DNA bubbles, which also depends on their size and is always higher for the smaller bubbles under the largest number of the studied energies. Wherein, compared to the natural condition under the same critical value of energy, the bigger raises of the bubble frequency occurrence (maximums) were found for 11-30 base pair (bp) bubbles (higher by 319%), 2-4 bp bubbles (higher by 300%), and 31 bp and over ones (higher by 220%); whereas the most significant reductions of the indicators (minimums) were observed for 11-30 bp bubbles (lower by 43%) and bubbles size over 30 bp (lower by 82%). In this study, we also analyzed the impact of several circumstances on the AT/GC ratio in the formation of DNA bubbles, both under natural conditions and after a single hydrogen isotope exchange. Moreover, based on the obtained data, substantial positive and inverse correlations were revealed between the AT/GC ratio and some factors (energy values, size of DNA bubbles). So, this modeling and variant of the modified algorithm, adapted for researching DNA bubbles, can be useful to study the regulation of replication and transcription in the genes under different isotopic substitutions in the nucleobases.

Bubble Relaxation Dynamics in Homopolymer DNA Sequences

Understanding the inherent timescales of large bubbles in DNA is critical to a thorough comprehension of its physicochemical characteristics, as well as their potential role on helix opening and biological function. In this work, we employ the coarse-grained Peyrard-Bishop-Dauxois model of DNA to study relaxation dynamics of large bubbles in homopolymer DNA, using simulations up to the microsecond time scale. By studying energy autocorrelation functions of relatively large bubbles inserted into thermalised DNA molecules, we extract characteristic relaxation times from the equilibration process for both adenine-thymine (AT) and guanine-cytosine (GC) homopolymers. Bubbles of different amplitudes and widths are investigated through extensive statistics and appropriate fittings of their relaxation. Characteristic relaxation times increase with bubble amplitude and width. We show that, within the model, relaxation times are two orders of magnitude longer in GC sequences than in AT sequences. Overall, our results confirm that large bubbles leave a lasting impact on the molecule's dynamics, for times between 0.5-500 ns depending on the homopolymer type and bubble shape, thus clearly affecting long-time evolutions of the molecule.

Non-linear Hamiltonian models for DNA

Nucleic acids' physical properties have been investigated by theoretical methods based both on fully atomistic representations and on coarse-grained models, e.g., the worm-like-chain, taken from polymer physics. In this review article, I discuss an intermediate (mesoscopic) approach and show how to build a three-dimensional Hamiltonian model which accounts for the main interactions responsible for the stability of the helical molecules. While the 3D mesoscopic model yields a sufficiently detailed description of the helix at the level of the base pair, it also allows one to predict the thermodynamical and structural properties of molecules in solution. Relying on the idea that the base pair fluctuations can be conceived as trajectories, I have built over the past years a computational method based on the time-dependent path integral formalism to derive the partition function. While the main features of the method are presented, I focus here in particular on a newly developed statistical method to set the maximum amplitude of the base pair fluctuations, a key parameter of the theory. Some applications to the calculation of DNA flexibility properties are discussed together with the available experimental data.

Melting of confined DNA: static and dynamic properties

We study dsDNA (double strand DNA) melting in detail within varying strip-like confinement in a two-dimensional lattice model. The interplay between reduced configurational entropy and attractive base-pairing energy results in a non-monotonic melting profile of DNA. Structural transitions associated with confined DNA melting reveal a stretched or extended state for very strong confinement. By using the exact enumeration method, we investigate the emergence of a local denatured zone e.g. bubbles during DNA melting. The survival time of a single bubble within varying strip width is studied from the Fokker-Planck formalism by considering the bubble size as a reaction co-ordinate. We show that a simple lattice model can capture the sequence heterogeneity effect on DNA melting and bubble dynamics within the strip. Different time scales of bubble zipping for different DNA sequences are found, which may have potential applications in denaturation mapping.

Bubble lifetimes in DNA gene promoters and their mutations affecting transcription

Relative lifetimes of inherent double stranded DNA openings with lengths up to ten base pairs are presented for different gene promoters and corresponding mutants that either increase or decrease transcriptional activity in the framework of the Peyrard-Bishop-Dauxois model. Extensive microcanonical simulations are used with energies corresponding to physiological temperature. The bubble lifetime profiles along the DNA sequences demonstrate a significant reduction of the average lifetime at the mutation sites when the mutated promoter decreases transcription, while a corresponding enhancement of the bubble lifetime is observed in the case of mutations leading to increased transcription. The relative difference in bubble lifetimes between the mutated and wild type promoters at the position of mutation varies from 20% to more than 30% as the bubble length decreases.

Base pair fluctuations in helical models for nucleic acids

A statistical method is developed to estimate the maximum amplitude of the base pair fluctuations in a three dimensional mesoscopic model for nucleic acids. The base pair thermal vibrations around the helix diameter are viewed as a Brownian motion for a particle embedded in a stable helical structure. The probability to return to the initial position is computed, as a function of time, by integrating over the particle paths consistent with the physical properties of the model potential. The zero time condition for the first-passage probability defines the constraint to select the integral cutoff for various macroscopic helical conformations, obtained by tuning the twist, bending, and slide motion between adjacent base pairs along the molecule stack. Applying the method to a short homogeneous chain at room temperature, we obtain meaningful estimates for the maximum fluctuations in the twist conformation with ∼10.5 base pairs per helix turn, typical of double stranded DNA helices. Untwisting the double helix, the base pair fluctuations broaden and the integral cutoff increases. The cutoff is found to increase also in the presence of a sliding motion, which shortens the helix contour length, a situation peculiar of dsRNA molecules.