Twist-writhe partitioning in a coarse-grained DNA minicircle model

Torsion affects the calculation of DNA twisting number

The topological properties of DNA have long been a focal point in biophysics. In the 1970s, White proposed that the topology of closed DNA double helix follows White's formula: Lk=Wr+Tw. However, there has been controversy in the calculation of DNA twisting number, partly due to discrepancies in the definition of torsion in differential geometry. In this paper, we delved into a detailed study of torsion, revealing that the calculation of DNA twisting number should use the curve's geodesic torsion. Furthermore, we found that the discrepancy in DNA twisting numbers calculated using different torsion is N. This study elucidated the impact of torsion on the calculation of DNA twisting numbers, aiming to resolve controversies in the calculation of DNA topology and provided accurate computational methods and theoretical foundations for related research.

Applications and Advances in Machine Learning Force Fields

Force fields (FFs) form the basis of molecular simulations and have significant implications in diverse fields such as materials science, chemistry, physics, and biology. A suitable FF is required to accurately describe system properties. However, an off-the-shelf FF may not be suitable for certain specialized systems, and researchers often need to tailor the FF that fits specific requirements. Before applying machine learning (ML) techniques to construct FFs, the mainstream FFs were primarily based on first-principles force fields (FPFF) and empirical FFs. However, the drawbacks of FPFF and empirical FFs are high cost and low accuracy, respectively, so there is a growing interest in using ML as an effective and precise tool for reconciling this trade-off in developing FFs. In this review, we introduce the fundamental principles of ML and FFs in the context of machine learning force fields (MLFF). We also discuss the advantages and applications of MLFF compared to traditional FFs, as well as the MLFF toolkits widely employed in numerous applications.

spotter: a single-nucleotide resolution stochastic simulation model of supercoiling-mediated transcription and translation in prokaryotes

Stochastic simulation models have played an important role in efforts to understand the mechanistic basis of prokaryotic transcription and translation. Despite the fundamental linkage of these processes in bacterial cells, however, most simulation models have been limited to representations of either transcription or translation. In addition, the available simulation models typically either attempt to recapitulate data from single-molecule experiments without considering cellular-scale high-throughput sequencing data or, conversely, seek to reproduce cellular-scale data without paying close attention to many of the mechanistic details. To address these limitations, we here present spotter (Simulation of Prokaryotic Operon Transcription & Translation Elongation Reactions), a flexible, user-friendly simulation model that offers highly-detailed combined representations of prokaryotic transcription, translation, and DNA supercoiling. In incorporating nascent transcript and ribosomal profiling sequencing data, spotter provides a critical bridge between data collected in single-molecule experiments and data collected at the cellular scale. Importantly, in addition to rapidly generating output that can be aggregated for comparison with next-generation sequencing and proteomics data, spotter produces residue-level positional information that can be used to visualize individual simulation trajectories in detail. We anticipate that spotter will be a useful tool in exploring the interplay of processes that are crucially linked in prokaryotes.

Two Different Ways of Stress Release in Supercoiled DNA Minicircles under DNA Nick

It is generally believed that DNA nick is an effective way to release stress in supercoiled DNA, resulting from the twisting motion that individual strands rotate around the axis of the DNA helix. Here, we use MD simulations based on the oxDNA model to investigate the relaxation of 336 bp supercoiled minicircular DNA under DNA nick. Our simulations show that stress release, characterized by the abrupt decrease in linking number, may be induced by two types of DNA motion depending on the nick position. Except for the twisting motion, there is a writhing motion, that is, double strands collectively rotating with one plectoneme removal, which may occur in the process of DNA relaxation with the nick position in the loop region. Moreover, the writhing motion is more likely to occur in the DNA with relatively high hardness, such as C-G pairs. Our simulation results uncover the relationship between structural transformation, stress release, and DNA motion during the dynamic process under DNA nick, indicating the influence of nick position on the relaxation of the supercoiled DNA.

The incipient denaturation mechanism of DNA

DNA denaturation is related to many important biological phenomena, such as its replication, transcription and the interaction with some specific proteins for single-stranded DNA. Dimethyl sulfoxide (DMSO) is a common chemical agent for DNA denaturation. In the present study, we investigate quantitatively the effects of different concentrations of DMSO on plasmid and linear DNA denaturation by atomic force microscopy (AFM) and UV spectrophotometry. We found that persistent length of DNA decreases significantly by adding a small amount of DMSO before ensemble DNA denaturation occurs; the persistence length of DNA in 3% DMSO solution decreases to 12 nm from about 50 nm without DMSO in solution. And local DNA denaturation occurs even at very low DMSO concentration (such as 0.1%), which can be directly observed in AFM imaging. Meanwhile, we observed the forming process of DNA contacts between different parts for plasmid DNA with increasing DMSO concentration. We suggest the initial mechanism of DNA denaturation as follows: DNA becomes more flexible due to the partial hydrogen bond braking in the presence of DMSO before local separation of the two complementary nucleotide chains.

The persistent length of DNA decreases significantly by adding small amount of DMSO. Local DNA denaturation occurs even at very low DMSO concentration, which can be observed by atomic force microscopy directly.

Chiral shape fluctuations and the origin of chirality in cholesteric phases of DNA origamis

Lyotropic cholesteric liquid crystal phases are ubiquitously observed in biological and synthetic polymer solutions, characterized by a complex interplay between thermal fluctuations and entropic and enthalpic forces. The elucidation of the link between microscopic features and macroscopic chiral structure, and of the relative roles of these competing contributions on phase organization, remains a topical issue. Here, we provide theoretical evidence of a previously unidentified mechanism of chirality amplification in lyotropic liquid crystals, whereby phase chirality is governed by fluctuation-stabilized helical deformations in the conformations of their constituent molecules. Our results compare favorably to recent experimental studies of DNA origami assemblies and demonstrate the influence of intramolecular mechanics on chiral supramolecular order, with potential implications for a broad class of experimentally relevant colloidal systems.

Braiding topology and the energy landscape of chromosome organization proteins

Assemblies of structural maintenance of chromosomes (SMC) proteins and kleisin subunits are essential to chromosome organization and segregation across all kingdoms of life. While structural data exist for parts of the SMC-kleisin complexes, complete structures of the entire complexes have yet to be determined, making mechanistic studies difficult. Using an integrative approach that combines crystallographic structural information about the globular subdomains, along with coevolutionary information and an energy landscape optimized force field (AWSEM), we predict atomic-scale structures for several tripartite SMC-kleisin complexes, including prokaryotic condensin, eukaryotic cohesin, and eukaryotic condensin. The molecular dynamics simulations of the SMC-kleisin protein complexes suggest that these complexes exist as a broad conformational ensemble that is made up of different topological isomers. The simulations suggest a critical role for the SMC coiled-coil regions, where the coils intertwine with various linking numbers. The twist and writhe of these braided coils are coupled with the motion of the SMC head domains, suggesting that the complexes may function as topological motors. Opening, closing, and translation along the DNA of the SMC-kleisin protein complexes would allow these motors to couple to the topology of DNA when DNA is entwined with the braided coils.

Dynamical control of denaturation bubble nucleation in supercoiled DNA minicircles

We examine the behavior of supercoiled DNA minicircles containing between 200 and 400 base-pairs, also named microDNA, in which supercoiling favors thermally assisted DNA denaturation bubbles of nanometer size and controls their lifetime. Mesoscopic modeling and accelerated dynamics simulations allow us to overcome the limitations of atomistic simulations encountered in such systems, and offer detailed insight into the thermodynamic and dynamical properties associated with the nucleation and closure mechanisms of long-lived thermally assisted denaturation bubbles which do not stem from bending- or torque-driven stress. Suitable tuning of the degree of supercoiling and size of specifically designed microDNA is observed to lead to the control of opening characteristic times in the millisecond range, and closure characteristic times ranging over well distinct timescales, from microseconds to several minutes. We discuss how our results can be seen as a dynamical bandwidth which might enhance selectivity for specific DNA binding proteins.

cgDNAweb: a web interface to the cgDNA sequence-dependent coarse-grain model of double-stranded DNA

The sequence-dependent statistical mechanical properties of fragments of double-stranded DNA is believed to be pertinent to its biological function at length scales from a few base pairs (or bp) to a few hundreds of bp, e.g. indirect read-out protein binding sites, nucleosome positioning sequences, phased A-tracts, etc. In turn, the equilibrium statistical mechanics behaviour of DNA depends upon its ground state configuration, or minimum free energy shape, as well as on its fluctuations as governed by its stiffness (in an appropriate sense). We here present cgDNAweb, which provides browser-based interactive visualization of the sequence-dependent ground states of double-stranded DNA molecules, as predicted by the underlying cgDNA coarse-grain rigid-base model of fragments with arbitrary sequence. The cgDNAweb interface is specifically designed to facilitate comparison between ground state shapes of different sequences. The server is freely available at cgDNAweb.epfl.ch with no login requirement.

Features of genomic organization in a nucleotide-resolution molecular model of the Escherichia coli chromosome

We describe structural models of the Escherichia coli chromosome in which the positions of all 4.6 million nucleotides of each DNA strand are resolved. Models consistent with two basic chromosomal orientations, differing in their positioning of the origin of replication, have been constructed. In both types of model, the chromosome is partitioned into plectoneme-abundant and plectoneme-free regions, with plectoneme lengths and branching patterns matching experimental distributions, and with spatial distributions of highly-transcribed chromosomal regions matching recent experimental measurements of the distribution of RNA polymerases. Physical analysis of the models indicates that the effective persistence length of the DNA and relative contributions of twist and writhe to the chromosome's negative supercoiling are in good correspondence with experimental estimates. The models exhibit characteristics similar to those of ‘fractal globules,’ and even the most genomically-distant parts of the chromosome can be physically connected, through paths combining linear diffusion and inter-segmental transfer, by an average of only ∼10 000 bp. Finally, macrodomain structures and the spatial distributions of co-expressed genes are analyzed: the latter are shown to depend strongly on the overall orientation of the chromosome. We anticipate that the models will prove useful in exploring other static and dynamic features of the bacterial chromosome.

A Solvent-Mediated Coarse-Grained Model of DNA Derived with the Systematic Newton Inversion Method

We present a new class of coarse-grained (CG) force fields (FFs) for B-DNA with explicit ions suited for large-scale mesoscale simulations at microsecond-micrometer scale using a wide spectrum of particle simulation methods from molecular dynamics to dissipative particle dynamics. The effective solvent-mediated pairwise interactions making up the FFs are obtained by inverting radial distribution functions and other particle-particle distributions obtained from all-atom simulations of numbers of octadecamer DNA fragments from the Ascona B-DNA library. The inverse Monte Carlo (IMC) method, later known as Newton inversion (NI) (Lyubartsev, A. P.; Laaksonen, A. Phys. Rev. E, 1995, 52, 3730-3737), was used together with the iterative Boltzmann inversion (IBI) scheme to compute the effective CG potentials. We show that this systematic structure-based approach is capable of providing converged potentials that accurately reproduce the structural features of the underlying atomistic system within a few percents of relative difference. We also show that a simple one-site-per-nucleotide model with 10 intramolecular pair interaction potentials is able to reproduce key features of DNA, for example, the persistence length and its dependence on the ionic concentration, experimentally determined around 50 nm at physiological salt concentration.

DNA denaturation bubbles: free-energy landscape and nucleation/closure rates

The issue of the nucleation and slow closure mechanisms of non-superhelical stress-induced denaturation bubbles in DNA is tackled using coarse-grained MetaDynamics and Brownian simulations. A minimal mesoscopic model is used where the double helix is made of two interacting bead-spring rotating strands with a prescribed torsional modulus in the duplex state. We demonstrate that timescales for the nucleation (respectively, closure) of an approximately 10 base-pair bubble, in agreement with experiments, are associated with the crossing of a free-energy barrier of 22 kBT (respectively, 13 kBT) at room temperature T. MetaDynamics allows us to reconstruct accurately the free-energy landscape, to show that the free-energy barriers come from the difference in torsional energy between the bubble and duplex states, and thus to highlight the limiting step, a collective twisting, that controls the nucleation/closure mechanism, and to access opening time scales on the millisecond range. Contrary to small breathing bubbles, those more than 4 base-pair bubbles are of biological relevance, for example, when a pre-existing state of denaturation is required by specific DNA-binding proteins.

DNA structure and function

The proposal of a double-helical structure for DNA over 60 years ago provided an eminently satisfying explanation for the heritability of genetic information. But why is DNA, and not RNA, now the dominant biological information store? We argue that, in addition to its coding function, the ability of DNA, unlike RNA, to adopt a B-DNA structure confers advantages both for information accessibility and for packaging. The information encoded by DNA is both digital - the precise base specifying, for example, amino acid sequences - and analogue. The latter determines the sequence-dependent physicochemical properties of DNA, for example, its stiffness and susceptibility to strand separation. Most importantly, DNA chirality enables the formation of supercoiling under torsional stress. We review recent evidence suggesting that DNA supercoiling, particularly that generated by DNA translocases, is a major driver of gene regulation and patterns of chromosomal gene organization, and in its guise as a promoter of DNA packaging enables DNA to act as an energy store to facilitate the passage of translocating enzymes such as RNA polymerase.

Surface charge effects on the 2D conformation of supercoiled DNA

We have adsorbed plasmid pUc19 DNA on a supported bilayer. By varying the fraction of cationic lipids in the membrane, we have tuned the surface charge. Plasmid conformations were imaged by Atomic Force Microscopy (AFM). We performed two sets of experiments: deposition from salt free solution on charged bilayers and deposition from salty solutions on neutral bilayers. Both sets show similar trends: at low surface charge density or low bulk salt concentration, the internal electrostatic repulsion forces plasmids to adopt completely opened structures, while at high surface charge density or higher bulk salt concentration, usual supercoiled plectonemes are observed. We experimentally demonstrate the equivalence of surface screening by mobile interfacial charges and bulk screening from salt ions. At low to medium screening, the electrostatic repulsion at plasmid crossings is predominant, leading to a number of crossovers decreasing linearly with the characteristic screening length. We compare our data with an analytical 2D-equilibrated model developed recently for the system and extract the DNA effective charge density when strands are adsorbed at the surface.

Perspective: Coarse-grained models for biomolecular systems

By focusing on essential features, while averaging over less important details, coarse-grained (CG) models provide significant computational and conceptual advantages with respect to more detailed models. Consequently, despite dramatic advances in computational methodologies and resources, CG models enjoy surging popularity and are becoming increasingly equal partners to atomically detailed models. This perspective surveys the rapidly developing landscape of CG models for biomolecular systems. In particular, this review seeks to provide a balanced, coherent, and unified presentation of several distinct approaches for developing CG models, including top-down, network-based, native-centric, knowledge-based, and bottom-up modeling strategies. The review summarizes their basic philosophies, theoretical foundations, typical applications, and recent developments. Additionally, the review identifies fundamental inter-relationships among the diverse approaches and discusses outstanding challenges in the field. When carefully applied and assessed, current CG models provide highly efficient means for investigating the biological consequences of basic physicochemical principles. Moreover, rigorous bottom-up approaches hold great promise for further improving the accuracy and scope of CG models for biomolecular systems.

Hydrophobic organic linkers in the self-assembly of small molecule-DNA hybrid dimers: a computational-experimental study of the role of linkage direction in product distributions and stabilities

Detailed computational and experimental studies reveal the crucial role that hydrophobic interactions play in the self-assembly of small molecule-DNA hybrids (SMDHs) into cyclic nanostructures. In aqueous environments, the distribution of the cyclic structures (dimers or higher-order structures) greatly depends on how well the hydrophobic surfaces of the organic cores in these nanostructures are minimized. Specifically, when the cores are attached to the 3'-ends of the DNA component strands, they can insert into the minor groove of the duplex that forms upon self-assembly, favoring the formation of cyclic dimers. However, when the cores are attached to the 5'-ends of the DNA component strands, such insertion is hindered, leading to the formation of higher-order cyclic structures. These computational insights are supported by experimental results that show clear differences in product distributions and stabilities for a broad range of organic core-linked DNA hybrids with different linkage directions and flexibilities.

Slow closure of denaturation bubbles in DNA: twist matters

The closure of long equilibrated denaturation bubbles in DNA is studied using Brownian dynamics simulations. A minimal mesoscopic model is used where the double helix is made of two interacting bead-spring freely rotating strands, with a nonzero torsional modulus in the duplex state, κ(φ)=200 to 300k(B)T. For DNAs of lengths N=40 to 100 base pairs (bps) with a large initial bubble in their middle, long closure times of 0.1 to 100μs are found. The bubble starts winding from both ends until it reaches a ≈10 bp metastable state due to the large elastic energy stored in the bubble. The final closure is limited by three competing mechanisms depending on κ(φ) and N: arms diffusion until their alignment, bubble diffusion along the DNA until one end is reached, or local Kramers process (crossing over a torsional energy barrier). For clamped ends or long DNAs, the closure occurs via this last temperature-activated mechanism, yielding a good quantitative agreement with the experiments.

Coarse-grained model DNA: structure, sequences, stems, circles, hairpins

A coarse-grained model for DNA that is intended to function realistically at the level of individual bases is reported. The model is composed of residues with up to eight coarse-grained beads each, which is sufficient for DNA-like base stacking and base-base recognition by hydrogen bonding. The beads interact by means of short-ranged pair potentials and a simple implicit solvent model. Movement is simulated by Brownian dynamics without hydrodynamic coupling. The main stabilizing forces are base stacking and hydrogen bonding, as modified by the effects of solvation. Complementary double-stranded chains of such residues form stable double helices over long runs (~10 μs) at or near room temperature, with structural parameters close to those of B-form DNA. Most mismatched chains or mismatched regions within a complementary molecule melt and become disordered. Long-range fluctuations and elastic properties, as measured by bending and twisting persistence lengths, are close to experimental values. Single-stranded chains are flexible, with transient stretches of free bases in equilibrium with globules stabilized by intrastrand stacking and hydrogen bonding. Model DNAs in covalently closed loops form right- or left-handed supercoils, depending on the sign of overtwist or undertwist. Short stem-loop structures melt at elevated temperatures and reanneal when the temperature is carefully lowered. Overall, most qualitative properties of real DNA arise naturally in the model from local interactions at the base-pair level.

Nematic disclinations as twisted ribbons

The disclination loops entangling colloidal structures in nematics are geometrically stabilized and restricted according to topological rules. We focus on colloidal dimers and show how the writhe and twist, which are constrained to sum to a constant value, are affected by changing the intercolloidal spacing, the twist angle of the cell, and the cholesteric pitch. We analyze the geometric properties of disclination loops using finite difference numerical simulations of colloidal dimers. The observed trends are explained and correlated to the symmetry properties and effects of liquid crystal elasticity.

Denaturation of circular DNA: supercoil mechanism

The denaturation transition which takes place in circular DNA is analyzed by extending the Poland-Scheraga (PS) model to include the winding degrees of freedom. We consider the case of a homopolymer whereby the winding number of the double-stranded helix, released by a loop denaturation, is absorbed by supercoils. We find that as in the case of linear DNA, the order of the transition is determined by the loop exponent c. However the first-order transition displayed by the PS model for c>2 in linear DNA is replaced by a continuous transition with arbitrarily high order as c approaches 2, while the second-order transition found in the linear case in the regime 1<c≤2 disappears. In addition, our analysis reveals that melting under fixed linking number is a condensation transition, where the condensate is a macroscopic loop which appears above the critical temperature.

Structural, mechanical, and thermodynamic properties of a coarse-grained DNA model

We explore in detail the structural, mechanical, and thermodynamic properties of a coarse-grained model of DNA similar to that recently introduced in a study of DNA nanotweezers [T. E. Ouldridge, A. A. Louis, and J. P. K. Doye, Phys. Rev. Lett. 134, 178101 (2010)]. Effective interactions are used to represent chain connectivity, excluded volume, base stacking, and hydrogen bonding, naturally reproducing a range of DNA behavior. The model incorporates the specificity of Watson-Crick base pairing, but otherwise neglects sequence dependence of interaction strengths, resulting in an "average base" description of DNA. We quantify the relation to experiment of the thermodynamics of single-stranded stacking, duplex hybridization, and hairpin formation, as well as structural properties such as the persistence length of single strands and duplexes, and the elastic torsional and stretching moduli of double helices. We also explore the model's representation of more complex motifs involving dangling ends, bulged bases and internal loops, and the effect of stacking and fraying on the thermodynamics of the duplex formation transition.