Unwinding Induced Melting of Double-Stranded DNA Studied by Free Energy Simulations

Melting and Bubble Formation in a Double-Stranded DNA: Microscopic Aspects of Early Base-Pair Opening Events and the Role of Water

Despite its rigid structure, DNA is a remarkably flexible molecule. Flexibility is essential for biological functions (such as transcription and gene repair), which require large-amplitude structural changes such as bubble formation. The bubbles thus formed are required to have a certain stability of their own and survive long on the time scale of molecular motions. A molecular understanding of fluctuations leading to quasi-stable structures is not available. Through extensive atomistic molecular dynamics simulations, we identify a sequence of microscopic events that culminate in local bubble formation, which is initiated by base-pair (BP) opening, resulting from the cleavage of native BP hydrogen bonds (HBs). This is followed by the formation of mismatched BPs with non-native contacts. These metastable structures can either revert to their original forms or undergo a flipping transition to form a local bubble that can span across 3-4 BPs. A substantial distortion of the DNA backbone and a disruption of BP stacking are observed because of the structural changes induced by these local perturbations. We also explored how water helps in the entire process. A small number of water molecules undergo rearrangement to stabilize the intermediate states by forming HBs with DNA bases. Water thus acts as a lubricant that counteracts the enthalpic penalty suffered from the loss of native BP contacts. Although the process of bubble formation is reversible, the sequence of steps involved poses an entropic barrier, preventing it from easily retracing the path to the native state.

The development of nucleic acids force fields: From an unchallenged past to a competitive future

Molecular dynamics simulations have strongly matured as a method to study biomolecular processes. Their validity, however, is determined by the accuracy of the underlying force fields that describe the forces between all atoms. In this article, we review the development of nucleic acids force fields. We describe the early attempts in the 1990s and emphasize their strong influence on recent force fields. State-of-the-art force fields still use the same Lennard-Jones parameters derived 25 years ago in spite of the fact that these parameters were in general not fitted for nucleic acids. In addition, electrostatic parameters also are deprecated, which may explain some of the current force field deficiencies. We compare different force fields for various systems and discuss new tests of the recently developed Tumuc1 force field. The OL-force fields and Tumuc1 are arguably the best force fields to describe the DNA double helix. However, no force field is flawless. In particular, the description of sugar-puckering remains a problem for nucleic acids force fields. Future refinements are required, so we review methods for force field refinement and give an outlook to the future of force fields.

Phase transition of DNA knotting in spherical space

Knots have been discovered in various biological systems, such as DNA. The knotting probability of DNA in free space depends non-monotonically on its bending rigidity and has a prominent peak. The current work aims to understand the underlying mechanism of the non-monotonic dependence of DNA knotting probability on bending rigidity. Monte Carlo simulations are performed on a closed DNA molecule confined in spherical space described by a worm-like chain model and a flexible kink model, respectively. The closed DNA's contour length and the spherical space radius both increase knotting probability, but also alter the unimodal dependence of knotting probability on bending rigidity. This is generalized using universal phase diagrams based on the two models. Under the flexible kink model, the total knotting probability of closed DNA is obviously increased at a relatively high excited energy. This supports the expectation that the entropy effect of knot size favours knot formation at a relatively low bending rigidity. In a given spherical space, the increasing contour length of closed DNA described by the worm-like chain model results in a visible shift in the knotting probability distribution. At the same time, the gyration radius of non-trivial closed DNA becomes comparable to that of trivial closed DNA, so that their ratio is not anti-correlated with average knot length. For closed DNA of various contour lengths, the relationship between average knot length and bending rigidity has a universal behaviour: the average knot length decreases to a local minimum at a bending rigidity of ∼5 and then gradually increases to a constant value. The existence of the local minimum is determined by the cut-off distance in repulsive Lennard-Jones potential. The bending rigidity corresponding to the beginning of the constant average knot length is consistent with that at the peak in the knotting distribution. At this point, the knot-size effect balances with the fragment free-energy effect and, at an even greater bending rigidity, knot length breathes around the average knot length value.

Twisting DNA by salt

The structure and properties of DNA depend on the environment, in particular the ion atmosphere. Here, we investigate how DNA twist -one of the central properties of DNA- changes with concentration and identity of the surrounding ions. To resolve how cations influence the twist, we combine single-molecule magnetic tweezer experiments and extensive all-atom molecular dynamics simulations. Two interconnected trends are observed for monovalent alkali and divalent alkaline earth cations. First, DNA twist increases monotonously with increasing concentration for all ions investigated. Second, for a given salt concentration, DNA twist strongly depends on cation identity. At 100 mM concentration, DNA twist increases as Na+ < K+ < Rb+ < Ba2+ < Li+ ≈ Cs+ < Sr2+ < Mg2+ < Ca2+. Our molecular dynamics simulations reveal that preferential binding of the cations to the DNA backbone or the nucleobases has opposing effects on DNA twist and provides the microscopic explanation of the observed ion specificity. However, the simulations also reveal shortcomings of existing force field parameters for Cs+ and Sr2+. The comprehensive view gained from our combined approach provides a foundation for understanding and predicting cation-induced structural changes both in nature and in DNA nanotechnology.

Characterizing the free-energy landscapes of DNA origamis

We show how coarse-grained modelling combined with umbrella sampling using distance-based order parameters can be applied to compute the free-energy landscapes associated with mechanical deformations of large DNA nanostructures. We illustrate this approach for the strong bending of DNA nanotubes and the potentially bistable landscape of twisted DNA origami sheets. The homogeneous bending of the DNA nanotubes is well described by the worm-like chain model; for more extreme bending the nanotubes reversibly buckle with the bending deformations localized at one or two "kinks". For a twisted one-layer DNA origami, the twist is coupled to the bending of the sheet giving rise to a free-energy landscape that has two nearly-degenerate minima that have opposite curvatures. By contrast, for a two-layer origami, the increased stiffness with respect to bending leads to a landscape with a single free-energy minimum that has a saddle-like geometry. The ability to compute such landscapes is likely to be particularly useful for DNA mechanotechnology and for understanding stress accumulation during the self-assembly of origamis into higher-order structures.

Homologous basic helix–loop–helix transcription factors induce distinct deformations of torsionally-stressed DNA: a potential transcription regulation mechanism

Changing torsional restraints on DNA is essential for the regulation of transcription. Torsional stress, introduced by RNA polymerase, can propagate along chromatin facilitating topological transitions and modulating the specific binding of transcription factors (TFs) to DNA. Despite the importance, the mechanistic details on how torsional stress impacts the TFs-DNA complexation remain scarce. Herein, we address the impact of torsional stress on DNA complexation with homologous human basic helix–loop–helix (BHLH) hetero- and homodimers: MycMax, MadMax and MaxMax. The three TF dimers exhibit specificity towards the same DNA consensus sequence, the E-box response element, while regulating different transcriptional pathways. Using microseconds-long atomistic molecular dynamics simulations together with the torsional restraint that controls DNA total helical twist, we gradually over- and underwind naked and complexed DNA to a maximum of ± 5°/bp step. We observe that the binding of the BHLH dimers results in a similar increase in DNA torsional rigidity. However, under torsional stress the BHLH dimers induce distinct DNA deformations, characterised by changes in DNA grooves geometry and a significant asymmetric DNA bending. Supported by bioinformatics analyses, our data suggest that torsional stress may contribute to the execution of differential transcriptional programs of the homologous TFs by modulating their collaborative interactions.

Orientation Dependence of DNA Blunt-End Stacking Studied by Free-Energy Simulations

DNA blunt ends can associate mediated by stacking interactions between the terminal base pairs that form blunt ends. The blunt end association plays a role in DNA repair and recombination processes and can also be of importance for the design of DNA-based nano-materials. Its function depends on the sequence and on the geometric arrangement that leads to stable interaction. For a stacked state, the relative orientation (twisting) of the base pairs is important. Molecular dynamics and advanced sampling simulations were used to calculate free energy change associated with twist changes of the stacked blunt-end base pairs. The calculations reproduce blunt stacking arrangements found in crystal structures of DNA oligonucleotides as free energy minima. To elucidate the physical origin of the stabilization of certain angular arrangements, the interactions between backbone atoms in the blunt-end stack were switched off in additional free energy calculations. It allows us to decipher the contributions to stacking stabilization due to the nucleobases and the backbone and to analyze the sequence dependence of the angular stacking preferences. Good qualitative agreement was also found for the comparison with quantum mechanical calculations. The results may help in the design of novel DNA-based materials.

Torsional stress can regulate the unwrapping of two outer half superhelical turns of nucleosomal DNA

Torsional stress has a significant impact on the structure and stability of the nucleosome. RNA polymerase imposes torsional stress on the DNA in chromatin and unwraps the DNA from the nucleosome to access the genetic information encoded in the DNA. To understand how the torsional stress affects the stability of the nucleosome, we examined the unwrapping of two half superhelical turns of nucleosomal DNA from either end of the DNA under torsional stress with all-atom molecular dynamics simulations. The free energies for unwrapping the DNA indicate that positive stress that overtwists DNA facilitates a large-scale asymmetric unwrapping of the DNA without a large extension of the DNA. During the unwrapping, one end of the DNA was dissociated from H3 and H2A-H2B, while the other end of the DNA stably remained wrapped. The detailed analysis indicates that this asymmetric dissociation is facilitated by the geometry and bendability of the DNA under positive stress. The geometry stabilized the interaction between the major groove of the twisted DNA and the H3 αN-helix, and the straightened DNA destabilized the interaction with H2A-H2B. Under negative stress, the DNA became more bendable and flexible, which facilitated the binding of the unwrapped DNA to the octamer in a stable state. Consequently, we conclude that the torsional stress has a significant impact on the affinity of the DNA and the octamer through the inherent nature of the DNA and can change the accessibility of regulatory proteins.

Accurate modeling of DNA conformational flexibility by a multivariate Ising model

The sequence-dependent structure and deformability of DNA play a major role for binding of proteins and regulation of gene expression. So far, most efforts to model DNA flexibility are based on unimodal harmonic stiffness models at base-pair resolution. However, multimodal behavior due to distinct conformational substates also contributes significantly to the conformational flexibility of DNA. Moreover, these local substates are correlated to their nearest-neighbor substates. A description for DNA elasticity which includes both multimodality and nearest-neighbor coupling has remained a challenge, which we solve by combining our multivariate harmonic approximation with an Ising model for the substates. In a series of applications to DNA fluctuations and protein-DNA complexes, we demonstrate substantial improvements over the unimodal stiffness model. Furthermore, our multivariate Ising model reveals a mechanical destabilization for adenine (A)-tracts to undergo nucleosome formation. Our approach offers a wide range of applications to determine sequence-dependent deformation energies of DNA and to investigate indirect readout contributions to protein-DNA recognition.

Specifically bound BZIP transcription factors modulate DNA supercoiling transitions

Torsional stress on DNA, introduced by molecular motors, constitutes an important regulatory mechanism of transcriptional control. Torsional stress can modulate specific binding of transcription factors to DNA and introduce local conformational changes that facilitate the opening of promoters and nucleosome remodelling. Using all-atom microsecond scale molecular dynamics simulations together with a torsional restraint that controls the total twist of a DNA fragment, we address the impact of torsional stress on DNA complexation with a human BZIP transcription factor, MafB. We gradually over- and underwind DNA alone and in complex with MafB by 0.5° per dinucleotide step, starting from the relaxed state to a maximum of 5° per dinucleotide step, monitoring the evolution of the protein-DNA contacts at different degrees of torsional strain. Our computations show that MafB changes the DNA sequence-specific response to torsional stress. The dinucleotide steps that are susceptible to absorbing most of the torsional stress become more torsionally rigid, as they are involved in protein-DNA contacts. Also, the protein undergoes substantial conformational changes to follow the stress-induced DNA deformation, but mostly maintains the specific contacts with DNA. This results in a significant asymmetric increase of free energy of DNA twisting transitions, relative to free DNA, where overtwisting is more energetically unfavourable. Our data suggest that specifically bound BZIP factors could act as torsional stress insulators, modulating the propagation of torsional stress along the chromatin fibre, which might promote cooperative binding of collaborative DNA-binding factors.

How global DNA unwinding causes non-uniform stress distribution and melting of DNA

DNA unwinding is an important process that controls binding of proteins, gene expression and melting of double-stranded DNA. In a series of all-atom MD simulations on two DNA molecules containing a transcription start TATA-box sequence we demonstrate that application of a global restraint on the DNA twisting dramatically changes the coupling between helical parameters and the distribution of deformation energy along the sequence. Whereas only short range nearest-neighbor coupling is observed in the relaxed case, long-range coupling is induced in the globally restrained case. With increased overall unwinding the elastic deformation energy is strongly non-uniformly distributed resulting ultimately in a local melting transition of only the TATA box segment during the simulations. The deformation energy tends to be stored more in cytidine/guanine rich regions associated with a change in conformational substate distribution. Upon TATA box melting the deformation energy is largely absorbed by the melting bubble with the rest of the sequences relaxing back to near B-form. The simulations allow us to characterize the structural changes and the propagation of the elastic energy but also to calculate the associated free energy change upon DNA unwinding up to DNA melting. Finally, we design an Ising model for predicting the local melting transition based on empirical parameters. The direct comparison with the atomistic MD simulations indicates a remarkably good agreement for the predicted necessary torsional stress to induce a melting transition, for the position and length of the melted region and for the calculated associated free energy change between both approaches.

The emergence of sequence-dependent structural motifs in stretched, torsionally constrained DNA

The double-helical structure of DNA results from canonical base pairing and stacking interactions. However, variations from steady-state conformations resulting from mechanical perturbations in cells have physiological relevance but their dependence on sequence remains unclear. Here, we use molecular dynamics simulations showing sequence differences result in markedly different structural motifs upon physiological twisting and stretching. We simulate overextension on different sequences of DNA ((AA)12, (AT)12, (CC)12 and (CG)12) with supercoiling densities at 200 and 50 mM salt concentrations. We find that DNA denatures in the majority of stretching simulations, surprisingly including those with over-twisted DNA. GC-rich sequences are observed to be more stable than AT-rich ones, with the specific response dependent on the base pair order. Furthermore, we find that (AT)12 forms stable periodic structures with non-canonical hydrogen bonds in some regions and non-canonical stacking in others, whereas (CG)12 forms a stacking motif of four base pairs independent of supercoiling density. Our results demonstrate that 20-30% DNA extension is sufficient for breaking B-DNA around and significantly above cellular supercoiling, and that the DNA sequence is crucial for understanding structural changes under mechanical stress. Our findings have important implications for the activities of protein machinery interacting with DNA in all cells.

SerraNA: a program to determine nucleic acids elasticity from simulation data

AT-rich motifs can generate extreme mechanical properties, which are critical for creating strong global bends when phased properly.

How methyl-sugar interactions determine DNA structure and flexibility

The sequence dependent structure and flexibility of the DNA double helix is of key importance for gene expression and DNA packing and it can be modulated by DNA modifications. The presence of a C5′-methyl group in thymine or the frequent C5′-methylated-cytosine affects the DNA fine structure, however, the underlying mechanism and steric origins have remained largely unexplained. Employing Molecular Dynamics free energy simulations that allow switching on or off interactions with the methyl groups in several DNA sequences, we systematically identified the physical origin of the coupling between methyl groups and DNA backbone fine structure. Whereas methyl-solvent and methyl–nucleobase interactions were found to be of minor importance, the methyl group interaction with the 5′ neighboring sugar was identified as main cause for influencing the population of backbone substates. The sterical methyl sugar clash prevents the formation of unconventional stabilizing hydrogen bonds between nucleobase and backbone. The technique was also used to study the contribution of methyl groups to DNA flexibility and served to explain why the presence of methyl sugar clashes in thymine and methyl-cytosine can result in an overall local increase of DNA flexibility.

Maximum Entropy (Most Likely) Double Helical and Double Logarithmic Spiral Trajectories in Space-Time

The ubiquity of double helical and logarithmic spirals in nature is well observed, but no explanation is ever offered for their prevalence. DNA and the Milky Way galaxy are examples of such structures, whose geometric entropy we study using an information-theoretic (Shannon entropy) complex-vector analysis to calculate, respectively, the Gibbs free energy difference between B-DNA and P-DNA, and the galactic virial mass. Both of these analytic calculations (without any free parameters) are consistent with observation to within the experimental uncertainties. We define conjugate hyperbolic space and entropic momentum co-ordinates to describe these spiral structures in Minkowski space-time, enabling a consistent and holographic Hamiltonian-Lagrangian system that is completely isomorphic and complementary to that of conventional kinematics. Such double spirals therefore obey a maximum-entropy path-integral variational calculus (“the principle of least exertion”, entirely comparable to the principle of least action), thereby making them the most likely geometry (also with maximal structural stability) to be adopted by any such system in space-time. These simple analytical calculations are quantitative examples of the application of the Second Law of Thermodynamics as expressed in geometric entropy terms. They are underpinned by a comprehensive entropic action (“exertion”) principle based upon Boltzmann’s constant as the quantum of exertion.

Molecular Mechanisms of DNA Replication and Repair Machinery: Insights from Microscopic Simulations

Reproduction, the hallmark of biological activity, requires making an accurate copy of the genetic material to allow the progeny to inherit parental traits. In all living cells, the process of DNA replication is carried out by a concerted action of multiple protein species forming a loose protein-nucleic acid complex, the replisome. Proofreading and error correction generally accompany replication but also occur independently, safeguarding genetic information through all phases of the cell cycle. Advances in biochemical characterization of intracellular processes, proteomics and the advent of single-molecule biophysics have brought about a treasure trove of information awaiting to be assembled into an accurate mechanistic model of the DNA replication process. In this review, we describe recent efforts to model elements of DNA replication and repair processes using computer simulations, an approach that has gained immense popularity in many areas of molecular biophysics but has yet to become mainstream in the DNA metabolism community. We highlight the use of diverse computational methods to address specific problems of the fields and discuss unexplored possibilities that lie ahead for the computational approaches in these areas.