Multiscale simulation of DNA

The Avoidance of Purine Stretches by Cancer Mutations

Purine stretches, sequences of adenine (A) and guanine (G) in DNA, play critical roles in binding regulatory protein factors and influence gene expression by affecting DNA folding. This study investigates the relationship between purine stretches and cancer development, considering the aromaticity of purines, quantified by methods like Hückel's rule and NICS calculations, and the importance of the flanking sequence context. A pronounced avoidance of long purine stretches by typical cancer mutations was observed in public data on the intergenic regions of cancer patients, suggesting a role of intergenic sequences in chromatin reorganization and gene regulation. A statistically significant shortening of purine stretches in cancerous tumors (p value < 0.0001) was found. The insights into the aromatic nature of purines and their stacking energies explain the role of purine stretches in DNA structure, contributing to their role in cancer progression. This research lays the groundwork for understanding the nature of purine stretches, emphasizing their importance in gene regulation and chromatin restructuring, and offers potential avenues for novel cancer therapies and insights into cancer etiology.

Supercomputing in the biological sciences: Toward Zettascale and Yottascale simulations

Molecular simulations of biological systems tend to be significantly more compute-intensive than those in materials science and astrophysics, due to important contributions of long-range electrostatic forces and large numbers of time steps (>1E9) required. Simulations of biomolecular complexes of microseconds to milliseconds are considered state-of-the-art today. However, these time scales are miniscule in comparison to physiological time scales relevant to molecular machine activity, drug action, and elongation cycles for protein synthesis, RNA synthesis, and DNA synthesis (seconds to days). While an exascale supercomputer has simulated an entire virus for nanoseconds, this supercomputer would need to be 10 billion times faster to simulate that virus for 3 hours of physiological time, demonstrating the insatiable need for computing power. With growing interest in computational drug design from the pharmaceutical sector, the biological sciences are positioned to be an industry driver in computing.

Local volume concentration, packing domains, and scaling properties of chromatin

We propose the Self Returning Excluded Volume (SR-EV) model for the structure of chromatin based on stochastic rules and physical interactions. The SR-EV rules of return generate conformationally defined domains observed by single-cell imaging techniques. From nucleosome to chromosome scales, the model captures the overall chromatin organization as a corrugated system, with dense and dilute regions alternating in a manner that resembles the mixing of two disordered bi-continuous phases. This particular organizational topology is a consequence of the multiplicity of interactions and processes occurring in the nuclei, and mimicked by the proposed return rules. Single configuration properties and ensemble averages show a robust agreement between theoretical and experimental results including chromatin volume concentration, contact probability, packing domain identification and size characterization, and packing scaling behavior. Model and experimental results suggest that there is an inherent chromatin organization regardless of the cell character and resistant to an external forcing such as RAD21 degradation.

On the Power and Challenges of Atomistic Molecular Dynamics to Investigate RNA Molecules

RNA molecules play a vital role in biological processes within the cell, with significant implications for science and medicine. Notably, the biological functions exerted by specific RNA molecules are often linked to the RNA conformational ensemble. However, the experimental characterization of such three-dimensional RNA structures is challenged by the structural heterogeneity of RNA and by its multiple dynamic interactions with binding partners such as small molecules, proteins, and metal ions. Consequently, our current understanding of the structure-function relationship of RNA molecules is still limited. In this context, we highlight molecular dynamics (MD) simulations as a powerful tool to complement experimental efforts on RNAs. Despite the recognized limitations of current force fields for RNA MD simulations, examining the dynamics of selected RNAs has provided valuable functional insights into their structures.

CGeNArate: a sequence-dependent coarse-grained model of DNA for accurate atomistic MD simulations of kb-long duplexes

We present CGeNArate, a new model for molecular dynamics simulations of very long segments of B-DNA in the context of biotechnological or chromatin studies. The developed method uses a coarse-grained Hamiltonian with trajectories that are back-mapped to the atomistic resolution level with extreme accuracy by means of Machine Learning Approaches. The method is sequence-dependent and reproduces very well not only local, but also global physical properties of DNA. The efficiency of the method allows us to recover with a reduced computational effort high-quality atomic-resolution ensembles of segments containing many kilobases of DNA, entering into the gene range or even the entire DNA of certain cellular organelles.

Simulating the Lyotropic Phase Behavior of a Partially Self-Complementary DNA Tetramer

DNA oligomers in solution have been found to develop liquid crystal phases via a hierarchical process that involves Watson-Crick base pairing, supramolecular assembly into columns of duplexes, and long-range ordering. The multiscale nature of this phenomenon makes it difficult to quantitatively describe and assess the importance of the various contributions, particularly for very short strands. We performed molecular dynamics simulations based on the coarse-grained oxDNA model, aiming to depict all of the assembly processes involved and the phase behavior of solutions of the DNA GCCG tetramers. We find good quantitative matching to experimental data at both levels of molecular association (thermal melting) and collective ordering (phase diagram). We characterize the isotropic state and the low-density nematic and high-density columnar liquid crystal phases in terms of molecular order, size of aggregates, and structure, together with their effects on diffusivity processes. We observe a cooperative aggregation mechanism in which the formation of dimers is less thermodynamically favored than the formation of longer aggregates.

ANNaMo: Coarse-grained modeling for folding and assembly of RNA and DNA systems

The folding of RNA and DNA strands plays crucial roles in biological systems and bionanotechnology. However, studying these processes with high-resolution numerical models is beyond current computational capabilities due to the timescales and system sizes involved. In this article, we present a new coarse-grained model for investigating the folding dynamics of nucleic acids. Our model represents three nucleotides with a patchy particle and is parameterized using well-established nearest-neighbor models. Thanks to the reduction of degrees of freedom and to a bond-swapping mechanism, our model allows for simulations at timescales and length scales that are currently inaccessible to more detailed models. To validate the performance of our model, we conducted extensive simulations of various systems: We examined the thermodynamics of DNA hairpins, capturing their stability and structural transitions, the folding of an MMTV pseudoknot, which is a complex RNA structure involved in viral replication, and also explored the folding of an RNA tile containing a k-type pseudoknot. Finally, we evaluated the performance of the new model in reproducing the melting temperatures of oligomers and the dependence on the toehold length of the displacement rate in toehold-mediated displacement processes, a key reaction used in molecular computing. All in all, the successful reproduction of experimental data and favorable comparisons with existing coarse-grained models validate the effectiveness of the new model.

DNA as a perfect quantum computer based on the quantum physics principles

DNA is a complex multi-resolution molecule whose theoretical study is a challenge. Its intrinsic multiscale nature requires chemistry and quantum physics to understand the structure and quantum informatics to explain its operation as a perfect quantum computer. Here, we present theoretical results of DNA that allow a better description of its structure and the operation process in the transmission, coding, and decoding of genetic information. Aromaticity is explained by the oscillatory resonant quantum state of correlated electron and hole pairs due to the quantized molecular vibrational energy acting as an attractive force. The correlated pairs form a supercurrent in the nitrogenous bases in a single band π -molecular orbital ( π -MO). The MO wave function ( Φ ) is assumed to be the linear combination of the n constituent atomic orbitals. The central Hydrogen bond between Adenine (A) and Thymine (T) or Guanine (G) and Cytosine (C) functions like an ideal Josephson Junction. The approach of a Josephson Effect between two superconductors is correctly described, as well as the condensation of the nitrogenous bases to obtain the two entangled quantum states that form the qubit. Combining the quantum state of the composite system with the classical information, RNA polymerase teleports one of the four Bell states. DNA is a perfect quantum computer.

From complex data to clear insights: visualizing molecular dynamics trajectories

Advances in simulations, combined with technological developments in high-performance computing, have made it possible to produce a physically accurate dynamic representation of complex biological systems involving millions to billions of atoms over increasingly long simulation times. The analysis of these computed simulations is crucial, involving the interpretation of structural and dynamic data to gain insights into the underlying biological processes. However, this analysis becomes increasingly challenging due to the complexity of the generated systems with a large number of individual runs, ranging from hundreds to thousands of trajectories. This massive increase in raw simulation data creates additional processing and visualization challenges. Effective visualization techniques play a vital role in facilitating the analysis and interpretation of molecular dynamics simulations. In this paper, we focus mainly on the techniques and tools that can be used for visualization of molecular dynamics simulations, among which we highlight the few approaches used specifically for this purpose, discussing their advantages and limitations, and addressing the future challenges of molecular dynamics visualization.

Prediction and Control in DNA Nanotechnology

DNA nanotechnology is a rapidly developing field that uses DNA as a building material for nanoscale structures. Key to the field's development has been the ability to accurately describe the behavior of DNA nanostructures using simulations and other modeling techniques. In this Review, we present various aspects of prediction and control in DNA nanotechnology, including the various scales of molecular simulation, statistical mechanics, kinetic modeling, continuum mechanics, and other prediction methods. We also address the current uses of artificial intelligence and machine learning in DNA nanotechnology. We discuss how experiments and modeling are synergistically combined to provide control over device behavior, allowing scientists to design molecular structures and dynamic devices with confidence that they will function as intended. Finally, we identify processes and scenarios where DNA nanotechnology lacks sufficient prediction ability and suggest possible solutions to these weak areas.

DNA supercoiling in bacteria: state of play and challenges from a viewpoint of physics based modeling

DNA supercoiling is central to many fundamental processes of living organisms. Its average level along the chromosome and over time reflects the dynamic equilibrium of opposite activities of topoisomerases, which are required to relax mechanical stresses that are inevitably produced during DNA replication and gene transcription. Supercoiling affects all scales of the spatio-temporal organization of bacterial DNA, from the base pair to the large scale chromosome conformation. Highlighted in vitro and in vivo in the 1960s and 1970s, respectively, the first physical models were proposed concomitantly in order to predict the deformation properties of the double helix. About fifteen years later, polymer physics models demonstrated on larger scales the plectonemic nature and the tree-like organization of supercoiled DNA. Since then, many works have tried to establish a better understanding of the multiple structuring and physiological properties of bacterial DNA in thermodynamic equilibrium and far from equilibrium. The purpose of this essay is to address upcoming challenges by thoroughly exploring the relevance, predictive capacity, and limitations of current physical models, with a specific focus on structural properties beyond the scale of the double helix. We discuss more particularly the problem of DNA conformations, the interplay between DNA supercoiling with gene transcription and DNA replication, its role on nucleoid formation and, finally, the problem of scaling up models. Our primary objective is to foster increased collaboration between physicists and biologists. To achieve this, we have reduced the respective jargon to a minimum and we provide some explanatory background material for the two communities.

Asymmetric Periodic Boundary Conditions for All-Atom Molecular Dynamics and Coarse-Grained Simulations of Nucleic Acids

Periodic boundary conditions are commonly applied in molecular dynamics simulations in the microcanonical (NVE), canonical (NVT), and isothermal-isobaric (NpT) ensembles. In their simplest application, a biological system of interest is placed in the middle of a solvation box, which is chosen 'sufficiently large' to minimize any numerical artifacts associated with the periodic boundary conditions. This practical approach brings limitations to the size of biological systems that can be simulated. Here, we study simulations of effectively infinitely long nucleic acids, which are solvated in the directions perpendicular to the polymer chain, while periodic boundary conditions are also applied along the polymer chain. We study the effects of these asymmetric periodic boundary conditions (APBC) on the simulated results, including the mechanical properties of biopolymers and the properties of the surrounding solvent. To get some further insights into the advantages of using the APBC, a coarse-grained worm-like chain model is first studied, illustrating how the persistence length can be extracted from the local properties of the polymer chain, which are less affected by the APBC than some global averages. This is followed by all-atom molecular dynamics simulations of DNA in ionic solutions, where we use the APBC to investigate sequence-dependent properties of DNA molecules and properties of the surrounding solvent.

Sequence-Dependent Properties of the RNA Duplex

Sequence-dependent properties of the DNA duplex have been accurately described using extensive molecular dynamics simulations. The RNA duplex meanwhile─which is typically represented as a sequence-averaged rigid rod─does not benefit from having equivalent molecular dynamics simulations. In this paper, we present a massive simulation effort using a set of ABC-optimized duplexes from which we derived tetramer-resolution properties of the RNA duplex and a simple mesoscopic model that can represent elastic properties of long RNA duplexes. Despite the extreme chemical similarity between DNA and RNA, the local and global elastic properties of the duplexes are very different. DNA duplexes show a complex and nonelastic pattern of flexibility, for instance, while RNA duplexes behave as an elastic system whose deformations can be represented by simple harmonic potentials. In RNA duplexes (RNA2), not only are intra- and interbase pair parameters (equilibrium and mechanical) different from those in the equivalent DNA duplex sequences (DNA2) but the correlations between movements also differ. Simple statements on the relative flexibility or stability of both polymers are meaningless and should be substituted by a more detailed description depending on the sequence and the type of deformation considered.

Kinetics of radiation-induced DNA double-strand breaks through coarse-grained simulations

Double-strand breaks (DSBs), i.e., the covalent cut of the DNA backbone over both strands, are a detrimental outcome of cell irradiation, bearing chromosomal aberrations and leading to cell apoptosis. In the early stages of the evolution of a DSB, the disruption of the residual interactions between the DNA moieties drives the fracture of the helical layout; in spite of its biological significance, the details of this process are still largely uncertain. Here, we address the mechanical rupture of DNA by DSBs via coarse-grained molecular dynamics simulations: the setup involves a 3855-bp DNA filament and diverse DSB motifs, i.e., within a range of distances between strand breaks (or DSB distance). By employing a coarse-grained model of DNA, we access the molecular details and characteristic timescales of the rupturing process. A sequence-nonspecific, linear correlation is observed between the DSB distance and the internal energy contribution to the disruption of the residual (Watson-Crick and stacking) contacts between DNA moieties, which is seemingly driven by an abrupt, cooperative process. Moreover, we infer an exponential dependence of the characteristic rupture times on the DSB distances, which we associate to an Arrhenius-like law of thermally-activated processes. This work lays the foundations of a detailed, mechanistic assessment of DSBs in silico as a benchmark to both numerical simulations and data from single-molecule experiments.

Brownian dynamics simulations of mesoscale chromatin fibers

The relationship between chromatin architecture and function defines a central problem in biology and medicine. Many computational chromatin models with atomic, coarse-grained, mesoscale, and polymer resolution have been used to shed light onto the mechanisms that dictate genome folding and regulation of gene expression. The associated simulation techniques range from Monte Carlo to molecular, Brownian, and Langevin dynamics. Here, we present an efficient Compute Unified Device Architecture (CUDA) implementation of Brownian dynamics (BD) to simulate chromatin fibers at the nucleosome resolution with our chromatin mesoscale model. With the CUDA implementation for computer architectures with graphic processing units (GPUs), we significantly accelerate compute-intensive hydrodynamic tensor calculations in the BD simulations by massive parallelization, boosting the performance a hundred-fold compared with central processing unit calculations. We validate our BD simulation approach by reproducing experimental trends on fiber diffusion and structure as a function of salt, linker histone binding, and histone-tail composition, as well as Monte Carlo equilibrium sampling results. Our approach proves to be physically accurate with performance that makes feasible the study of chromatin fibers in the range of kb or hundreds of nucleosomes (small gene). Such simulations are essential to advance the study of biological processes such as gene regulation and aberrant genome-structure related diseases.

Molecular dynamics modelling of the interaction of a synthetic zinc-finger miniprotein with DNA

We report the modelling of the DNA complex of an artificial miniprotein composed of two zinc finger modules and an AT-hook linking peptide. The computational study provides for the first time a structural view of these types of complexes, dissecting interactions that are key to modulate their stability. The relevance of these interactions was validated experimentally. These results confirm the potential of this type of computational approach for studying peptide-DNA complexes and suggest that they could be very useful for the rational design of non-natural, DNA binding miniproteins.

Computational Modeling of DNA 3D Structures: From Dynamics and Mechanics to Folding

DNA carries the genetic information required for the synthesis of RNA and proteins and plays an important role in many processes of biological development. Understanding the three-dimensional (3D) structures and dynamics of DNA is crucial for understanding their biological functions and guiding the development of novel materials. In this review, we discuss the recent advancements in computer methods for studying DNA 3D structures. This includes molecular dynamics simulations to analyze DNA dynamics, flexibility, and ion binding. We also explore various coarse-grained models used for DNA structure prediction or folding, along with fragment assembly methods for constructing DNA 3D structures. Furthermore, we also discuss the advantages and disadvantages of these methods and highlight their differences.

Controlled sulfur-based engineering confers mouldability to phosphorothioate antisense oligonucleotides

Phosphorothioates (PS) have proven their effectiveness in the area of therapeutic oligonucleotides with applications spanning from cancer treatment to neurodegenerative disorders. Initially, PS substitution was introduced for the antisense oligonucleotides (PS ASOs) because it confers an increased nuclease resistance meanwhile ameliorates cellular uptake and in-vivo bioavailability. Thus, PS oligonucleotides have been elevated to a fundamental asset in the realm of gene silencing therapeutic methodologies. But, despite their wide use, little is known on the possibly different structural changes PS-substitutions may provoke in DNA·RNA hybrids. Additionally, scarce information and significant controversy exists on the role of phosphorothioate chirality in modulating PS properties. Here, through comprehensive computational investigations and experimental measurements, we shed light on the impact of PS chirality in DNA-based antisense oligonucleotides; how the different phosphorothioate diastereomers impact DNA topology, stability and flexibility to ultimately disclose pro-Sp S and pro-Rp S roles at the catalytic core of DNA Exonuclease and Human Ribonuclease H; two major obstacles in ASOs-based therapies. Altogether, our results provide full-atom and mechanistic insights on the structural aberrations PS-substitutions provoke and explain the origin of nuclease resistance PS-linkages confer to DNA·RNA hybrids; crucial information to improve current ASOs-based therapies.

An associative memory Hamiltonian model for DNA and nucleosomes

A model for DNA and nucleosomes is introduced with the goal of studying chromosomes from a single base level all the way to higher-order chromatin structures. This model, dubbed the Widely Editable Chromatin Model (WEChroM), reproduces the complex mechanics of the double helix including its bending persistence length and twisting persistence length, and their respective temperature dependence. The WEChroM Hamiltonian is composed of chain connectivity, steric interactions, and associative memory terms representing all remaining interactions leading to the structure, dynamics, and mechanical characteristics of the B-DNA. Several applications of this model are discussed to demonstrate its applicability. WEChroM is used to investigate the behavior of circular DNA in the presence of positive and negative supercoiling. We show that it recapitulates the formation of plectonemes and of structural defects that relax mechanical stress. The model spontaneously manifests an asymmetric behavior with respect to positive or negative supercoiling, similar to what was previously observed in experiments. Additionally, we show that the associative memory Hamiltonian is also capable of reproducing the free energy of partial DNA unwrapping from nucleosomes. WEChroM is designed to emulate the continuously variable mechanical properties of the 10nm fiber and, by virtue of its simplicity, is ready to be scaled up to molecular systems large enough to investigate the structural ensembles of genes. WEChroM is implemented in the OpenMM simulation toolkits and is freely available for public use.

Ab initio predictions for 3D structure and stability of single- and double-stranded DNAs in ion solutions

The three-dimensional (3D) structure and stability of DNA are essential to understand/control their biological functions and aid the development of novel materials. In this work, we present a coarse-grained (CG) model for DNA based on the RNA CG model proposed by us, to predict 3D structures and stability for both dsDNA and ssDNA from the sequence. Combined with a Monte Carlo simulated annealing algorithm and CG force fields involving the sequence-dependent base-pairing/stacking interactions and an implicit electrostatic potential, the present model successfully folds 20 dsDNAs (≤52nt) and 20 ssDNAs (≤74nt) into the corresponding native-like structures just from their sequences, with an overall mean RMSD of 3.4Å from the experimental structures. For DNAs with various lengths and sequences, the present model can make reliable predictions on stability, e.g., for 27 dsDNAs with/without bulge/internal loops and 24 ssDNAs including pseudoknot, the mean deviation of predicted melting temperatures from the corresponding experimental data is only ~2.0°C. Furthermore, the model also quantificationally predicts the effects of monovalent or divalent ions on the structure stability of ssDNAs/dsDNAs.

To determine 3D structures and quantify stability of single- (ss) and double-stranded (ds) DNAs is essential to unveil the mechanisms of their functions and to further guide the production and development of novel materials. Although many DNA models have been proposed to reproduce the basic structural, mechanical, or thermodynamic properties of dsDNAs based on the secondary structure information or preset constraints, there are very few models can be used to investigate the ssDNA folding or dsDNA assembly from the sequence. Furthermore, due to the polyanionic nature of DNAs, metal ions (e.g., Na⁺ and Mg²⁺) in solutions can play an essential role in DNA folding and dynamics. Nevertheless, ab initio predictions for DNA folding in ion solutions are still an unresolved problem. In this work, we developed a novel coarse-grained model to predict 3D structures and thermodynamic stabilities for both ssDNAs and dsDNAs in monovalent/divalent ion solutions from their sequences. As compared with the extensive experimental data and available existing models, we showed that the present model can successfully fold simple DNAs into their native-like structures, and can also accurately reproduce the effects of sequence and monovalent/divalent ions on structure stability for ssDNAs including pseudoknot and dsDNAs with/without bulge/internal loops.

MiOS, an integrated imaging and computational strategy to model gene folding with nucleosome resolution

The linear sequence of DNA provides invaluable information about genes and their regulatory elements along chromosomes. However, to fully understand gene function and regulation, we need to dissect how genes physically fold in the three-dimensional nuclear space. Here we describe immuno-OligoSTORM, an imaging strategy that reveals the distribution of nucleosomes within specific genes in super-resolution, through the simultaneous visualization of DNA and histones. We combine immuno-OligoSTORM with restraint-based and coarse-grained modeling approaches to integrate super-resolution imaging data with Hi-C contact frequencies and deconvoluted micrococcal nuclease-sequencing information. The resulting method, called Modeling immuno-OligoSTORM, allows quantitative modeling of genes with nucleosome resolution and provides information about chromatin accessibility for regulatory factors, such as RNA polymerase II. With Modeling immuno-OligoSTORM, we explore intercellular variability, transcriptional-dependent gene conformation, and folding of housekeeping and pluripotency-related genes in human pluripotent and differentiated cells, thereby obtaining the highest degree of data integration achieved so far to our knowledge.

Carbon Nanodots from an In Silico Perspective

Carbon nanodots (CNDs) are the latest and most shining rising stars among photoluminescent (PL) nanomaterials. These carbon-based surface-passivated nanostructures compete with other related PL materials, including traditional semiconductor quantum dots and organic dyes, with a long list of benefits and emerging applications. Advantages of CNDs include tunable inherent optical properties and high photostability, rich possibilities for surface functionalization and doping, dispersibility, low toxicity, and viable synthesis (top-down and bottom-up) from organic materials. CNDs can be applied to biomedicine including imaging and sensing, drug-delivery, photodynamic therapy, photocatalysis but also to energy harvesting in solar cells and as LEDs. More applications are reported continuously, making this already a research field of its own. Understanding of the properties of CNDs requires one to go to the levels of electrons, atoms, molecules, and nanostructures at different scales using modern molecular modeling and to correlate it tightly with experiments. This review highlights different in silico techniques and studies, from quantum chemistry to the mesoscale, with particular reference to carbon nanodots, carbonaceous nanoparticles whose structural and photophysical properties are not fully elucidated. The role of experimental investigation is also presented. Hereby, we hope to encourage the reader to investigate CNDs and to apply virtual chemistry to obtain further insights needed to customize these amazing systems for novel prospective applications.

Importance of Sugar-Phosphate Backbone and Counterions to First-Principles Modeling of Nucleobases

DFT-based first-principles calculations were carried out to understand the electronic structure difference among a backbone-free nucleobase, a backbone-containing Na counterion nucleotide, and a backbone-containing H counterion nucleotide and their difference in the adsorption on graphene and on graphitic-carbon nitride. The study discovered that the inclusion of a sugar-phosphate backbone changes the electron affinity of most nucleobases from electron acceptors to electron donors. The methyl-terminated backbone-free model cannot replicate the steric effect induced by the sugar-phosphate backbone during the adsorption of nucleobases on 2D materials. Overall, we established that the sugar phosphate backbone should be included in the study of DNA nucleobase adsorption on 2D material. We also showed that when it comes to the adsorption on 2D materials, the backbone-containing H counterion model is superior to the Na counterion model because the Na counterion produces a LUMO near the Fermi energy, which may significantly affect the interaction with the 2D material.

Mechanical properties of nucleic acids and the non-local twistable wormlike chain model

Mechanical properties of nucleic acids play an important role in many biological processes that often involve physical deformations of these molecules. At sufficiently long length scales (say, above ∼20-30 base pairs), the mechanics of DNA and RNA double helices is described by a homogeneous Twistable Wormlike Chain (TWLC), a semiflexible polymer model characterized by twist and bending stiffnesses. At shorter scales, this model breaks down for two reasons: the elastic properties become sequence-dependent and the mechanical deformations at distal sites get coupled. We discuss in this paper the origin of the latter effect using the framework of a non-local Twistable Wormlike Chain (nlTWLC). We show, by comparing all-atom simulations data for DNA and RNA double helices, that the non-local couplings are of very similar nature in these two molecules: couplings between distal sites are strong for tilt and twist degrees of freedom and weak for roll. We introduce and analyze a simple double-stranded polymer model that clarifies the origin of this universal distal couplings behavior. In this model, referred to as the ladder model, a nlTWLC description emerges from the coarsening of local (atomic) degrees of freedom into angular variables that describe the twist and bending of the molecule. Different from its local counterpart, the nlTWLC is characterized by a length-scale-dependent elasticity. Our analysis predicts that nucleic acids are mechanically softer at the scale of a few base pairs and are asymptotically stiffer at longer length scales, a behavior that matches experimental data.

Mechanism of reaction of RNA-dependent RNA polymerase from SARS-CoV-2

We combine molecular dynamics, statistical mechanics, and hybrid quantum mechanics/molecular mechanics simulations to describe mechanistically the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) RNA-dependent RNA polymerase (RdRp). Our study analyzes the binding mode of both natural triphosphate substrates as well as remdesivir triphosphate (the active form of drug), which is bound preferentially over ATP by RdRp while being poorly recognized by human RNA polymerase II (RNA Pol II). A comparison of incorporation rates between natural and antiviral nucleotides shows that remdesivir is incorporated more slowly into the nascent RNA compared with ATP, leading to an RNA duplex that is structurally very similar to an unmodified one, arguing against the hypothesis that remdesivir is a competitive inhibitor of ATP. We characterize the entire mechanism of reaction, finding that viral RdRp is highly processive and displays a higher catalytic rate of incorporation than human RNA Pol II. Overall, our study provides the first detailed explanation of the replication mechanism of RdRp.

Caging Polycations: Effect of Increasing Confinement on the Modes of Interaction of Spermidine3+ With DNA Double Helices

Polyamines have important roles in the modulation of the cellular function and are ubiquitous in cells. The polyamines putrescine²⁺, spermidine³⁺, and spermine⁴⁺ represent the most abundant organic counterions of the negatively charged DNA in the cellular nucleus. These polyamines are known to stabilize the DNA structure and, depending on their concentration and additional salt composition, to induce DNA aggregation, which is often referred to as condensation. However, the modes of interactions of these elongated polycations with DNA and how they promote condensation are still not clear. In the present work, atomistic molecular dynamics (MD) computer simulations of two DNA fragments surrounded by spermidine³⁺ (Spd³⁺) cations were performed to study the structuring of Spd³⁺ “caged” between DNA molecules. Microsecond time scale simulations, in which the parallel DNA fragments were constrained at three different separations, but allowed to rotate axially and move naturally, provided information on the conformations and relative orientations of surrounding Spm³⁺ cations as a function of DNA-DNA separation. Novel geometric criteria allowed for the classification of DNA-Spd³⁺ interaction modes, with special attention given to Spd³⁺ conformational changes in the space between the two DNA molecules (caged Spd³⁺). This work shows how changes in the accessible space, or confinement, around DNA affect DNA-Spd³⁺ interactions, information fundamental to understanding the interactions between DNA and its counterions in environments where DNA is compacted, e.g. in the cellular nucleus.

Two-phase dynamics of DNA supercoiling based on DNA polymer physics

DNA supercoils are generated in genome regulation processes such as transcription and replication and provide mechanical feedback to such processes. Under tension, a DNA supercoil can present a coexistence state of plectonemic and stretched phases. Experiments have revealed the dynamic behaviors of plectonemes, e.g., diffusion, nucleation, and hopping. To represent these dynamics with conformational changes, we demonstrated first the fast dynamics on the DNA to reach torque equilibrium within the plectonemic and stretched phases, and then identified the two-phase boundaries as collective slow variables to describe the essential dynamics. According to the timescale separation demonstrated here, we developed a two-phase model on the dynamics of DNA supercoiling, which can capture physiologically relevant events across timescales of several orders of magnitudes. In this model, we systematically characterized the slow dynamics between the two phases and compared the numerical results with those from the DNA polymer physics-based worm-like chain model. The supercoiling dynamics, including the nucleation, diffusion, and hopping of plectonemes, have been well represented and reproduced, using the two-phase dynamic model, at trivial computational costs. Our current developments, therefore, can be implemented to explore multiscale physical mechanisms of the DNA supercoiling-dependent physiological processes.

Searching for Low Probability Opening Events in a DNA Sliding Clamp

The β subunit of E. coli DNA polymererase III is a DNA sliding clamp associated with increasing the processivity of DNA synthesis. In its free form, it is a circular homodimer structure that can accomodate double-stranded DNA in a nonspecific manner. An open state of the clamp must be accessible before loading the DNA. The opening mechanism is still a matter of debate, as is the effect of bound DNA on opening/closing kinetics. We use a combination of atomistic, coarse-grained, and enhanced sampling strategies in both explicit and implicit solvents to identify opening events in the sliding clamp. Such simulations of large nucleic acid and their complexes are becoming available and are being driven by improvements in force fields and the creation of faster computers. Different models support alternative opening mechanisms, either through an in-plane or out-of-plane opening event. We further note some of the current limitations, despite advances, in modeling these highly charged systems with implicit solvent.

Molecular basis of Arginine and Lysine DNA sequence-dependent thermo-stability modulation

We have used a variety of theoretical and experimental techniques to study the role of four basic amino acids-Arginine, Lysine, Ornithine and L-2,4-Diaminobutyric acid-on the structure, flexibility and sequence-dependent stability of DNA. We found that the presence of organic ions stabilizes the duplexes and significantly reduces the difference in stability between AT- and GC-rich duplexes with respect to the control conditions. This suggests that these amino acids, ingredients of the primordial soup during abiogenesis, could have helped to equalize the stability of AT- and GC-rich DNA oligomers, facilitating a general non-catalysed self-replication of DNA. Experiments and simulations demonstrate that organic ions have an effect that goes beyond the general electrostatic screening, involving specific interactions along the grooves of the double helix. We conclude that organic ions, largely ignored in the DNA world, should be reconsidered as crucial structural elements far from mimics of small inorganic cations.

Predicting genome organisation and function with mechanistic modelling

Fitting-free mechanistic models based on polymer simulations predict chromatin folding in 3D by focussing on the underlying biophysical mechanisms. This class of models has been increasingly used in conjunction with experiments to study the spatial organisation of eukaryotic chromosomes. Feedback from experiments to models leads to successive model refinement and has previously led to the discovery of new principles for genome organisation. Here, we review the basis of mechanistic polymer simulations, explain some of the more recent approaches and the contexts in which they have been useful to explain chromosome biology, and speculate on how they might be used in the future.

The Impact of the HydroxyMethylCytosine epigenetic signature on DNA structure and function

We present a comprehensive, experimental and theoretical study of the impact of 5-hydroxymethylation of DNA cytosine. Using molecular dynamics, biophysical experiments and NMR spectroscopy, we found that Ten-Eleven translocation (TET) dioxygenases generate an epigenetic variant with structural and physical properties similar to those of 5-methylcytosine. Experiments and simulations demonstrate that 5-methylcytosine (mC) and 5-hydroxymethylcytosine (hmC) generally lead to stiffer DNA than normal cytosine, with poorer circularization efficiencies and lower ability to form nucleosomes. In particular, we can rule out the hypothesis that hydroxymethylation reverts to unmodified cytosine physical properties, as hmC is even more rigid than mC. Thus, we do not expect dramatic changes in the chromatin structure induced by differences in physical properties between d(mCpG) and d(hmCpG). Conversely, our simulations suggest that methylated-DNA binding domains (MBDs), associated with repression activities, are sensitive to the substitution d(mCpG) ➔ d(hmCpG), while MBD3 which has a dual activation/repression activity is not sensitive to the d(mCpG) d(hmCpG) change. Overall, while gene activity changes due to cytosine methylation are the result of the combination of stiffness-related chromatin reorganization and MBD binding, those associated to 5-hydroxylation of methylcytosine could be explained by a change in the balance of repression/activation pathways related to differential MBD binding.

In Eukaryotic cells, DNA epigenetic modifications play an important role in gene expression and regulation, and protein recognition. In this work we investigate the physical implications of cytosine 5-hydroxymethylation on DNA, its structural and flexibility differences with methylated and unmodified cytosine using molecular dynamics, biophysical experiments and NMR spectroscopy.

In particular the effect of hydroxyl group on free energy of nucleosome and Methyl binding Protein (MBD) binding, comparing in silico and experimental data to shed light on the effect of the reduced flexibility and the direct protein-DNA recognition.

Fluorescence lifetime imaging for studying DNA compaction and gene activities

Optical imaging is a most useful and widespread technique for the investigation of the structure and function of the cellular genomes. However, an analysis of immensely convoluted and irregularly compacted DNA polymer is highly challenging even by modern super-resolution microscopy approaches. Here we propose fluorescence lifetime imaging (FLIM) for the advancement of studies of genomic structure including DNA compaction, replication as well as monitoring of gene expression. The proposed FLIM assay employs two independent mechanisms for DNA compaction sensing. One mechanism relies on the inverse quadratic relation between the fluorescence lifetimes of fluorescence probes incorporated into DNA and their local refractive index, variable due to DNA compaction density. Another mechanism is based on the Förster resonance energy transfer (FRET) process between the donor and the acceptor fluorophores, both incorporated into DNA. Both these proposed mechanisms were validated in cultured cells. The obtained data unravel a significant difference in compaction of the gene-rich and gene-poor pools of genomic DNA. We show that the gene-rich DNA is loosely compacted compared to the dense DNA domains devoid of active genes.

Determining Sequence-Dependent DNA Oligonucleotide Hybridization and Dehybridization Mechanisms Using Coarse-Grained Molecular Simulation, Markov State Models, and Infrared Spectroscopy

A robust understanding of the sequence-dependent thermodynamics of DNA hybridization has enabled rapid advances in DNA nanotechnology. A fundamental understanding of the sequence-dependent kinetics and mechanisms of hybridization and dehybridization remains comparatively underdeveloped. In this work, we establish new understanding of the sequence-dependent hybridization/dehybridization kinetics and mechanism within a family of self-complementary pairs of 10-mer DNA oligomers by integrating coarse-grained molecular simulation, machine learning of the slow dynamical modes, data-driven inference of long-time kinetic models, and experimental temperature-jump infrared spectroscopy. For a repetitive ATATATATAT sequence, we resolve a rugged dynamical landscape comprising multiple metastable states, numerous competing hybridization/dehybridization pathways, and a spectrum of dynamical relaxations. Introduction of a G:C pair at the terminus (GATATATATC) or center (ATATGCATAT) of the sequence reduces the ruggedness of the dynamics landscape by eliminating a number of metastable states and reducing the number of competing dynamical pathways. Only by introducing a G:C pair midway between the terminus and the center to maximally disrupt the repetitive nature of the sequence (ATGATATCAT) do we recover a canonical "all-or-nothing" two-state model of hybridization/dehybridization with no intermediate metastable states. Our results establish new understanding of the dynamical richness of sequence-dependent kinetics and mechanisms of DNA hybridization/dehybridization by furnishing quantitative and predictive kinetic models of the dynamical transition network between metastable states, present a molecular basis with which to understand experimental temperature jump data, and furnish foundational design rules by which to rationally engineer the kinetics and pathways of DNA association and dissociation for DNA nanotechnology applications.

Design Approaches and Computational Tools for DNA Nanostructures

Designing a structure in nanoscale with desired shape and properties has been enabled by structural DNA nanotechnology. Design strategies in this research field have evolved to interpret various aspects of increasingly more complex nanoscale assembly and to realize molecular-level functionality by exploring static to dynamic characteristics of the target structure. Computational tools have naturally been of significant interest as they are essential to achieve a fine control over both shape and physicochemical properties of the structure. Here, we review the basic design principles of structural DNA nanotechnology together with its computational analysis and design tools.

Coarse-grained simulations of phase separation driven by DNA and its sensor protein cGAS

The enzyme cGAS functions as a sensor that recognizes the cytosolic DNA from foreign pathogen. The activation of the protein triggers the transcription of inflammatory genes, leading into the establishment of an antipathogen state. An interesting new discovery is that the detection of DNA by cGAS induced the formation of liquid-like droplets. However how cells regulate the formation of these droplets is still not fully understood. In order to unravel the molecular mechanism beneath the DNA-mediated phase separation of cGAS, we developed a polymer-based coarse-grained model which takes into accounts the basic structural organization in DNA and cGAS, as well as the binding properties between these biomolecules. This model was further integrated into a hybrid simulation algorithm. With this computational method, a multi-step kinetic process of aggregation between cGAS and DNA was observed. Moreover, we systematically tested the model under different concentrations and binding parameters. Our simulation results show that phase separation requires both cGAS dimerization and protein-DNA interactions, whereas polymers can be kinetically trapped in small aggregates under strong binding affinities. Additionally, we demonstrated that supramolecular assembly can be facilitated by increasing the number of functional modules in protein or DNA polymers, suggesting that multivalency and intrinsic disordered regions play positive roles in regulating phase separation. This is consistent to previous experimental evidences. Taken together, this is, to the best of our knowledge, the first computational model to study condensation of cGAS-DNA complexes. While the method can reach the timescale beyond the capability of atomic-level MD simulations, it still includes information about spatial arrangement of functional modules in biopolymers that is missing in the mean-field theory. Our work thereby adds a useful dimension to a suite of existing experimental and computational techniques to study the dynamics of phase separation in biological systems.

A Primer on the oxDNA Model of DNA: When to Use it, How to Simulate it and How to Interpret the Results

The oxDNA model of Deoxyribonucleic acid has been applied widely to systems in biology, biophysics and nanotechnology. It is currently available via two independent open source packages. Here we present a set of clearly documented exemplar simulations that simultaneously provide both an introduction to simulating the model, and a review of the model's fundamental properties. We outline how simulation results can be interpreted in terms of-and feed into our understanding of-less detailed models that operate at larger length scales, and provide guidance on whether simulating a system with oxDNA is worthwhile.

Biomolecular modeling thrives in the age of technology

The biomolecular modeling field has flourished since its early days in the 1970s due to the rapid adaptation and tailoring of state-of-the-art technology. The resulting dramatic increase in size and timespan of biomolecular simulations has outpaced Moore's law. Here, we discuss the role of knowledge-based versus physics-based methods and hardware versus software advances in propelling the field forward. This rapid adaptation and outreach suggests a bright future for modeling, where theory, experimentation and simulation define three pillars needed to address future scientific and biomedical challenges.

Interactions Between Nucleosomes: From Atomistic Simulation to Polymer Model

The organization of genomes in space and time dimension plays an important role in gene expression and regulation. Chromatin folding occurs in a dynamic, structured way that is subject to biophysical rules and biological processes. Nucleosomes are the basic unit of chromatin in living cells, and here we report on the effective interactions between two nucleosomes in physiological conditions using explicit-solvent all-atom simulations. Free energy landscapes derived from umbrella sampling simulations agree well with recent experimental and simulation results. Our simulations reveal the atomistic details of the interactions between nucleosomes in solution and can be used for constructing the coarse-grained model for chromatin in a bottom-up manner.

DFFR: A New Method for High-Throughput Recalibration of Automatic Force-Fields for Drugs

We present drug force-field recalibration (DFFR), a new method for refining of automatic force-fields used to represent small drugs in docking and molecular dynamics simulations. The method is based on fine-tuning of torsional terms to obtain ensembles that reproduce observables derived from reference data. DFFR is fast and flexible and can be easily automatized for a high-throughput regime, making it useful in drug-design projects. We tested the performance of the method in a few model systems and also in a variety of druglike molecules using reference data derived from: (i) density functional theory coupled to a self-consistent reaction field (DFT/SCRF) calculations on highly populated conformers and (ii) enhanced sampling quantum mechanical/molecular mechanics (QM/MM) where the drug is reproduced at the QM level, while the solvent is represented by classical force-fields. Extension of the method to include other sources of reference data is discussed.

Computing 3D Chromatin Configurations from Contact Probability Maps by Inverse Brownian Dynamics

The three-dimensional (3D) organization of chromatin, on the length scale of a few genes, is crucial in determining the functional state-accessibility and amount of gene expression-of the chromatin. Recent advances in chromosome conformation capture experiments provide partial information on the chromatin organization in a cell population, namely the contact count between any segment pairs, but not on the interaction strength that leads to these contact counts. However, given the contact matrix, determining the complete 3D organization of the whole chromatin polymer is an inverse problem. In this work, a novel inverse Brownian dynamics method based on a coarse-grained bead-spring chain model has been proposed to compute the optimal interaction strengths between different segments of chromatin such that the experimentally measured contact count probability constraints are satisfied. Applying this method to the α-globin gene locus in two different cell types, we predict the 3D organizations corresponding to active and repressed states of chromatin at the locus. We show that the average distance between any two segments of the region has a broad distribution and cannot be computed as a simple inverse relation based on the contact probability alone. The results presented for multiple normalization methods suggest that all measurable quantities may crucially depend on the nature of normalization. We argue that by experimentally measuring predicted quantities, one may infer the appropriate form of normalization.

A multi-modal coarse grained model of DNA flexibility mappable to the atomistic level

We present a new coarse grained method for the simulation of duplex DNA. The algorithm uses a generalized multi-harmonic model that can represent any multi-normal distribution of helical parameters, thus avoiding caveats of current mesoscopic models for DNA simulation and representing a breakthrough in the field. The method has been parameterized from accurate parmbsc1 atomistic molecular dynamics simulations of all unique tetranucleotide sequences of DNA embedded in long duplexes and takes advantage of the correlation between helical states and backbone configurations to derive atomistic representations of DNA. The algorithm, which is implemented in a simple web interface and in a standalone package reproduces with high computational efficiency the structural landscape of long segments of DNA untreatable by atomistic molecular dynamics simulations.

Chromatin Compaction Multiscale Modeling: A Complex Synergy Between Theory, Simulation, and Experiment

Understanding the mechanisms that trigger chromatin compaction, its patterns, and the factors they depend on, is a fundamental and still open question in Biology. Chromatin compacts and reinforces DNA and is a stable but dynamic structure, to make DNA accessible to proteins. In recent years, computational advances have provided larger amounts of data and have made large-scale simulations more viable. Experimental techniques for the extraction and reconstitution of chromatin fibers have improved, reinvigorating theoretical and experimental interest in the topic and stimulating debate on points previously considered as certainties regarding chromatin. A great assortment of approaches has emerged, from all-atom single-nucleosome or oligonucleosome simulations to various degrees of coarse graining, to polymer models, to fractal-like structures and purely topological models. Different fiber-start patterns have been studied in theory and experiment, as well as different linker DNA lengths. DNA is a highly charged macromolecule, making ionic and electrostatic interactions extremely important for chromatin topology and dynamics. Indeed, the repercussions of varying ionic concentration have been extensively examined at the computational level, using all-atom, coarse-grained, and continuum techniques. The presence of high-curvature AT-rich segments in DNA can cause conformational variations, attesting to the fact that the role of DNA is both structural and electrostatic. There have been some tentative attempts to describe the force fields governing chromatin conformational changes and the energy landscapes of these transitions, but the intricacy of the system has hampered reaching a consensus. The study of chromatin conformations is an intrinsically multiscale topic, influenced by a wide range of biological and physical interactions, spanning from the atomic to the chromosome level. Therefore, powerful modeling techniques and carefully planned experiments are required for an overview of the most relevant phenomena and interactions. The topic provides fertile ground for interdisciplinary studies featuring a synergy between theoretical and experimental scientists from different fields and the cross-validation of respective results, with a multi-scale perspective. Here, we summarize some of the most representative approaches, and focus on the importance of electrostatics and solvation, often overlooked aspects of chromatin modeling.

Pattern preferences of DNA nucleotide motifs by polyamines putrescine2+, spermidine3+ and spermine4

The interactions of natural polyamines (putrescine2+, spermidine3+ and spermine4+) with DNA double helix are studied to characterize their nucleotide sequence pattern preference. Atomistic Molecular Dynamics simulations have been carried out for three systems consisting of the same DNA fragment d(CGCGAATTCGCGAATTCGCG) with different polyamines. The results show that polyamine molecules are localized with well-recognized patterns along the double helix with different residence times. We observed a clear hierarchy in the residence times of the polyamines, with the longest residence time (ca 100ns) in the minor groove. The analysis of the sequence dependence shows that polyamine molecules prefer the A-tract regions of the minor groove - in its narrowest part. The preferable localization of putrescine2+, spermidine3+ and spermine4+ in the minor groove with A-tract motifs is correlated with modulation of the groove width by a specific nucleotide sequences. We did develop a theoretical model pointing to the electrostatic interactions as the main driving force in this phenomenon, making it even more prominent for polyamines with higher charges. The results of the study explain the specificity of polyamine interactions with A-tract region of the DNA double helix which is also observed in experiments.

The static and dynamic structural heterogeneities of B-DNA: extending Calladine-Dickerson rules

We present a multi-laboratory effort to describe the structural and dynamical properties of duplex B-DNA under physiological conditions. By processing a large amount of atomistic molecular dynamics simulations, we determine the sequence-dependent structural properties of DNA as expressed in the equilibrium distribution of its stochastic dynamics. Our analysis includes a study of first and second moments of the equilibrium distribution, which can be accurately captured by a harmonic model, but with nonlocal sequence-dependence. We characterize the sequence-dependent choreography of backbone and base movements modulating the non-Gaussian or anharmonic effects manifested in the higher moments of the dynamics of the duplex when sampling the equilibrium distribution. Contrary to prior assumptions, such anharmonic deformations are not rare in DNA and can play a significant role in determining DNA conformation within complexes. Polymorphisms in helical geometries are particularly prevalent for certain tetranucleotide sequence contexts and are always coupled to a complex network of coordinated changes in the backbone. The analysis of our simulations, which contain instances of all tetranucleotide sequences, allow us to extend Calladine-Dickerson rules used for decades to interpret the average geometry of DNA, leading to a set of rules with quantitative predictive power that encompass nonlocal sequence-dependence and anharmonic fluctuations.

Evolutionary Refinement of DNA Nanostructures Using Coarse-Grained Molecular Dynamics Simulations

In the past decade, DNA nanostructures have made the leap from small assemblies of a handful of oligonucleotides to megadalton objects assembled from hundreds or thousands of component DNA strands. Most DNA designs today are either lattice based with simple and reliable design tools or lattice free with a larger shape space but more challenging design and lower rigidity. In parallel with the development of DNA nanostructures, software packages for the simulation of nucleic acids have seen rapid development allowing for the simulation of the dynamics of full DNA nanostructure assemblies. Here, we implement an unsupervised software based on the coarse-grained molecular dynamics package oxDNA to simulate DNA origami structures and evaluate their rigidity. From this, the software autonomously produces mutant structures by adding or removing base pairs or modifying the positions of internal supports. These mutant structures are iteratively generated and evaluated by simulation to create an in silico evolution toward more rigid DNA nanostructures.