Thermodynamics of twisted DNA with solvent interaction

Force-induced unzipping of DNA in the presence of solvent molecules

The melting of double-stranded DNA (dsDNA) in the presence of solvent molecules is a fundamental process with significant implications for understanding the thermal and mechanical behavior of DNA and its interactions with the surrounding environment. The solvents play an essential role in the structural transformation of DNA subjected to a pulling force. In this study, we simulate the thermal and force induced denaturation of dsDNA and elucidate the solvent dependent melting behavior, identifying key factors that influence the stability of DNA melting in presence of solvent molecules. Using a statistical model, we first find the melting profile of short heterogeneous DNA molecules in the presence of solvent molecules in Force ensemble. We also investigate the effect of solvent's strengths on the melting profile of DNA. In the force ensemble, we consider two homogeneous DNA chains and apply the force on different locations along the chain in the presence of solvent molecules. Different pathways manifest the melting of the molecule in both ensembles, and we found several interesting features of melting DNA in a constant force ensemble, such as lower critical force when the chain is pulled from the base pair close to a solvent molecule. The results provide new insights into the force-induced unzipping of DNA and could be used to develop new methods for controlling the unzipping process. By providing a better understanding of melting and unzipping of dsDNA in the presence of solvent molecules, this study provides valuable guidelines for predicting DNA thermodynamic quantities and for designing DNA nanostructures.

Temperature dependence of DNA elasticity: An all-atom molecular dynamics simulation study

We used all-atom molecular dynamics simulation to investigate the elastic properties of double-stranded DNA (dsDNA). We focused on the influences of temperature on the stretch, bend, and twist elasticities, as well as the twist-stretch coupling, of the dsDNA over a wide range of temperature. The results showed that the bending and twist persistence lengths, together with the stretch and twist moduli, decrease linearly with temperature. However, the twist-stretch coupling behaves in a positive correction and enhances as the temperature increases. The potential mechanisms of how temperature affects dsDNA elasticity and coupling were investigated by using the trajectories from atomistic simulation, in which thermal fluctuations in structural parameters were analyzed in detail. We analyzed the simulation results by comparing them with previous simulation and experimental data, which are in good agreement. The prediction about the temperature dependence of dsDNA elastic properties provides a deeper understanding of DNA elasticities in biological environments and potentially helps in the further development of DNA nanotechnology.

Structure and Dynamics of dsDNA in Cell-like Environments

Deoxyribonucleic acid (DNA) is a fundamental biomolecule for correct cellular functioning and regulation of biological processes. DNA's structure is dynamic and has the ability to adopt a variety of structural conformations in addition to its most widely known double-stranded DNA (dsDNA) helix structure. Stability and structural dynamics of dsDNA play an important role in molecular biology. In vivo, DNA molecules are folded in a tightly confined space, such as a cell chamber or a channel, and are highly dense in solution; their conformational properties are restricted, which affects their thermodynamics and mechanical properties. There are also many technical medical purposes for which DNA is placed in a confined space, such as gene therapy, DNA encapsulation, DNA mapping, etc. Physiological conditions and the nature of confined spaces have a significant influence on the opening or denaturation of DNA base pairs. In this review, we summarize the progress of research on the stability and dynamics of dsDNA in cell-like environments and discuss current challenges and future directions. We include studies on various thermal and mechanical properties of dsDNA in ionic solutions, molecular crowded environments, and confined spaces. By providing a better understanding of melting and unzipping of dsDNA in different environments, this review provides valuable guidelines for predicting DNA thermodynamic quantities and for designing DNA/RNA nanostructures.

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.

Mechanical response to tension and torque of molecular chains via statistically interacting particles associated with extension, contraction, twist, and supercoiling

A methodology for the statistical mechanical analysis of polymeric chains under tension introduced previously is extended to include torque. The response of individual bonds between monomers or of entire groups of monomers to a combination of tension and torque involves, in the framework of this method of analysis, the (thermal or mechanical) activation of a specific mix of statistically interacting particles carrying quanta of extension or contraction and quanta of twist or supercoiling. The methodology, which is elucidated in applications of increasing complexity, is capable of describing the conversion between twist chirality and plectonemic chirality in quasistatic processes. The control variables are force or extension and torque or linkage (a combination of twist and writhe). The versatility of this approach is demonstrated in two applications relevant and promising for double-stranded DNA under controlled tension and torque. One application describes conformational transformations between (native) B-DNA, (underwound) S-DNA, and (overwound) P-DNA in accord with experimental data. The other application describes how the conversion between a twisted chain and a supercoiled chain accommodates variations of linkage and excess length in a buckling transition.

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.

Melting of DNA in confined geometries

The stability of DNA molecules during viral or biotechnological encapsulation is a topic of active current research. We studied the thermal stability of double-stranded DNA molecules of different lengths in a confined space. Using a statistical model, we evaluate the melting profile of DNA molecules in two geometries: conical and cylindrical. Our results show that not only the confinement, but also the geometry of the confined space plays a prominent role in the stability and opening of the DNA duplex. We find that for more confined spaces, cylindrical confinement stabilizes the DNA, but for less confined spaces conical geometry stabilizes the DNA overall. We also analyse the interaction between DNA sequence and stability, and the evenness with which strand separation occurs. Cylindrical and conical geometries enable a better controlled tuning of the stability of DNA encapsulation and the efficiency of its eventual release, compared to spherical or quasi-spherical geometries.

First-passage probability: a test for DNA Hamiltonian parameters

A method is developed to chose the set of input parameters for DNA mesoscopic Hamiltonian models.

Structural Flexibility of DNA-RNA Hybrid Duplex: Stretching and Twist-Stretch Coupling

DNA-RNA hybrid (DRH) duplexes play essential roles during the replication of DNA and the reverse transcription of RNA viruses, and their flexibility is important for their biological functions. Recent experiments indicated that A-form RNA and B-form DNA have a strikingly different flexibility in stretching and twist-stretch coupling, and the structural flexibility of DRH duplex is of great interest, especially in stretching and twist-stretch coupling. In this work, we performed microsecond all-atom molecular dynamics simulations with new AMBER force fields to characterize the structural flexibility of DRH duplex in stretching and twist-stretch coupling. We have calculated all the helical parameters, stretch modulus, and twist-stretch coupling parameters for the DRH duplex. First, our analyses on structure suggest that the DRH duplex exhibits an intermediate conformation between A- and B-forms and closer to A-form, which can be attributed to the stronger rigidity of the RNA strand than the DNA strand. Second, our calculations show that the DRH duplex has the stretch modulus of 834 ± 34 pN and a very weak twist-stretch coupling. Our quantitative analyses indicate that, compared with DNA and RNA duplexes, the different flexibility of the DRH duplex in stretching and twist-stretch coupling is mainly attributed to its apparently different basepair inclination in the helical structure.

DNA size in confined environments

For short DNA molecules in crowded environments, we evaluate macroscopic parameters such as the average end-to-end distance and the twist conformation by tuning the strength of the site specific confinement driven by the crowders.

Charge transport in a DNA model with solvent interaction

The charge transport in the modified DNA model is studied by taking into account the factor of solvent and the effect of coupling motions of nucleotides. We report on the presence of the modulational instability (MI) of a plane wave for charge migration in DNA and the generation of soliton-like excitations in DNA nucleotides. By applying the continuum approximation, we show that the original differential-difference equation for the DNA dynamics can be reduced to a set of three coupled nonlinear equations. The linear stability analysis of wave solutions of the coupled systems is performed and the growth rate of instability is found numerically. We also investigate the impact of solvent interaction. The solvent factor introduces a new behavior to the wave patterns, modifying also the intrinsic properties of localized structures. In the numerical simulations, we show that the solitons exists when taking into account the effect of solvent and confirms an highest propagation of localized structures in the systems. The effect of solvent forces introduces a robustness behavior to the formed patterns, reinforcing the idea that the information in the DNA model is confined and concentrated to specific regions for efficiency. We also show that the localized structures can be disappeared with the highest value of solvent factor and thereafter the information within the molecule is not perceptible or not transmitted to another sites.

Twist-stretch profiles of DNA chains

Helical molecules change their twist number under the effect of a mechanical load. We study the twist-stretch relation for a set of short DNA molecules modeled by a mesoscopic Hamiltonian. Finite temperature path integral techniques are applied to generate a large ensemble of possible configurations for the base pairs of the sequence. The model also accounts for the bending and twisting fluctuations between adjacent base pairs along the molecules stack. Simulating a broad range of twisting conformation, we compute the helix structural parameters by averaging over the ensemble of base pairs configurations. The method selects, for any applied force, the average twist angle which minimizes the molecule's free energy. It is found that the chains generally over-twist under an applied stretching and the over-twisting is physically associated to the contraction of the average helix diameter, i.e. to the damping of the base pair fluctuations. Instead, assuming that the maximum amplitude of the bending fluctuations may decrease against the external load, the DNA molecule first over-twists for weak applied forces and then untwists above a characteristic force value. Our results are discussed in relation to available experimental information albeit for kilo-base long molecules.

DNA melting in the presence of molecular crowders

We study the opening of double stranded DNA (dsDNA) in the presence of molecular crowders using the Peyrard–Bishop–Dauxois (PBD) model.

Computational 3D Assembling Methods for DNA: A Survey

DNA encodes the genetic information of most living beings, except viruses that use RNA. Unlike other types of molecules, DNA is not usually described by its atomic structure being instead usually described by its base-pair sequence, i.e., the textual sequence of its subsidiary molecules known as nucleotides ( adenine (A), cytosine (C), guanine (G), and thymine (T)). The three-dimensional assembling of DNA molecules based on its base-pair sequence has been, for decades, a topic of interest for many research groups all over the world. In this paper, we survey the major methods found in the literature to assemble and visualize DNA molecules from their base-pair sequences. We divided these methods into three categories: predictive methods, adaptive methods, and thermodynamic methods . Predictive methods aim to predict a conformation of the DNA from its base pair sequence, while the goal of adaptive methods is to assemble DNA base-pairs sequences along previously known conformations, as needed in scenarios such as DNA Monte Carlo simulations. Unlike these two geometric methods, thermodynamic methods are energy-based and aim to predict secondary structural motifs of DNA in cases where hydrogen bonds between base pairs might be broken because of temperature changes. We also present the major software tools that implements predictive, adaptive, and thermodynamic methods.

Flexibility of short DNA helices under mechanical stretching

The flexibility of short DNA fragments is studied by a Hamiltonian model which treats the inter-strand and intra-strand forces at the level of the base pair.

Twisting and bending stress in DNA minicircles

The interplay between bending of the molecule axis and appearance of disruptions in circular DNA molecules, with ∼100 base pairs, is addressed. Three minicircles with different radii and almost equal contents of AT and GC pairs are investigated. The DNA sequences are modeled by a mesoscopic Hamiltonian which describes the essential interactions in the helix at the level of the base pair and incorporates twisting and bending degrees of freedom. Helix unwinding and bubble formation patterns are consistently computed by a path integral method that sums over a large number of molecule configurations compatible with the model potential. The path ensembles are determined, as a function of temperature, by minimizing the free energy of the system. Fluctuational openings appear along the helix to release the stress due to the bending of the molecule backbone. In agreement with the experimental findings, base pair disruptions are found with larger probability in the smallest minicircle of 66 bps whose bending angle is ∼6°. For this minicircle, a sizeable untwisting is obtained with the helical repeat showing a step-like increase at T = 315 K. The method can be generalized to determine the bubble probability profiles of open ends linear sequences.

Anharmonic stacking in supercoiled DNA

Multistep denaturation in a short circular DNA molecule is analyzed by a mesoscopic Hamiltonian model which accounts for the helicoidal geometry. Computation of melting profiles by the path integral method suggests that stacking anharmonicity stabilizes the double helix against thermal disruption of the hydrogen bonds. Twisting is essential in the model to capture the importance of nonlinear effects on the thermodynamical properties. In a ladder model with zero twist, anharmonic stacking scarcely affects the thermodynamics. Moderately untwisted helices, with respect to the equilibrium conformation, show an energetic advantage against the overtwisted ones. Accordingly moderately untwisted helices better sustain local fluctuational openings and make more unlikely the thermally driven complete strand separation.