Introducing improved structural properties and salt dependence into a coarse-grained model of DNA

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.

A multiscale analysis of DNA phase separation: from atomistic to mesoscale level

DNA condensation and phase separation is of utmost importance for DNA packing in vivo with important applications in medicine, biotechnology and polymer physics. The presence of hexagonally ordered DNA is observed in virus capsids, sperm heads and in dinoflagellates. Rigorous modelling of this process in all-atom MD simulations is presently difficult to achieve due to size and time scale limitations. We used a hierarchical approach for systematic multiscale coarse-grained (CG) simulations of DNA phase separation induced by the three-valent cobalt(III)-hexammine (CoHex³⁺). Solvent-mediated effective potentials for a CG model of DNA were extracted from all-atom MD simulations. Simulations of several hundred 100-bp-long CG DNA oligonucleotides in the presence of explicit CoHex³⁺ ions demonstrated aggregation to a liquid crystalline hexagonally ordered phase. Following further coarse-graining and extraction of effective potentials, we conducted modelling at mesoscale level. In agreement with electron microscopy observations, simulations of an 10.2-kb-long DNA molecule showed phase separation to either a toroid or a fibre with distinct hexagonal DNA packing. The mechanism of toroid formation is analysed in detail. The approach used here is based only on the underlying all-atom force field and uses no adjustable parameters and may be generalised to modelling chromatin up to chromosome size.

Building machines with DNA molecules

In nature, DNA molecules carry the hereditary information. But DNA has physical and chemical properties that make it attractive for uses beyond heredity. In this Review, we discuss the potential of DNA for creating machines that are both encoded by and built from DNA molecules. We review the main methods of DNA nanostructure assembly, describe recent advances in building increasingly complex molecular structures and discuss strategies for creating machine-like nanostructures that can be actuated and move. We highlight opportunities for applications of custom DNA nanostructures as scientific tools to address challenges across biology, chemistry and engineering.

Coarse-grained modelling of the structural properties of DNA origami

We use the oxDNA coarse-grained model to provide a detailed characterization of the fundamental structural properties of DNA origami, focussing on archetypal 2D and 3D origami. The model reproduces well the characteristic pattern of helix bending in a 2D origami, showing that it stems from the intrinsic tendency of anti-parallel four-way junctions to splay apart, a tendency that is enhanced both by less screened electrostatic interactions and by increased thermal motion. We also compare to the structure of a 3D origami whose structure has been determined by cryo-electron microscopy. The oxDNA average structure has a root-mean-square deviation from the experimental structure of 8.4 Å, which is of the order of the experimental resolution. These results illustrate that the oxDNA model is capable of providing detailed and accurate insights into the structure of DNA origami, and has the potential to be used to routinely pre-screen putative origami designs and to investigate the molecular mechanisms that regulate the properties of DNA origami.

Atomic structures of RNA nanotubes and their comparison with DNA nanotubes

We present a computational framework to model RNA based nanostructures and study their microscopic structures. We model hexagonal nanotubes made of 6 dsRNA (RNTs) connected by double crossover (DX) at different positions. Using several hundred nano-second (ns) long all-atom molecular dynamics simulations, we study the atomic structure, conformational change and elastic properties of RNTs in the presence of explicit water and ions. Based on several structural quantities such as root mean square deviation (RMSD) and root mean square fluctuation (RMSF), we find that the RNTs are almost as stable as DNA nanotubes (DNTs). Although the central portion of the RNTs maintain its cylindrical shape, both the terminal regions open up to give rise to a gating like behavior which can play a crucial role in drug delivery. From the bending angle distribution, we observe that the RNTs are more flexible than DNTs. The calculated persistence length of the RNTs is in the micron range which is an order of magnitude higher than that of a single dsRNA. The stretch modulus of the RNTs from the contour length distribution is in the range of 4-7 nN depending on the sequence. The calculated persistence length and stretch modulus are in the same range of values as in the case of DNTs. To understand the structural properties of RNTs at the individual base-pair level we have also calculated all the helicoidal parameters and analyzed the relative flexibility and rigidity of RNTs having a different sequence. These findings emphasized the fascinating properties of RNTs which will expedite further theoretical and experimental studies in this field.

Twist-bend coupling, twist waves, and the shape of DNA loops

By combining analytical and numerical calculations, we investigate the minimal-energy shape of short DNA loops of approximately 100 base pairs (bp). We show that in these loops the excess twist density oscillates as a response to an imposed bending stress, as recently found in DNA minicircles and observed in nucleosomal DNA. These twist oscillations, here referred to as twist waves, are due to the coupling between twist and bending deformations, which in turn originates from the asymmetry between DNA major and minor grooves. We introduce a simple analytical variational shape that reproduces the exact loop energy up to the fourth significant digit and is in very good agreement with shapes obtained from coarse-grained simulations. We, finally, analyze the loop dynamics at room temperature, and show that the twist waves are robust against thermal fluctuations. They perform a normal diffusive motion, whose origin is briefly discussed.

In-silico Design of DNA Oligonucleotides: Challenges and Approaches

DNA oligonucleotides are essential components of a high number of technologies in molecular biology. The key event of each oligonucleotide-based assay is the specific binding between oligonucleotides and their target DNA. However, single-stranded DNA molecules also tend to bind to unintended targets or themselves. The probability of such unspecific binding increases with the complexity of an assay. Therefore, accurate data management and design workflows are necessary to optimize the in-silico design of primers and probes. Important considerations concerning computational infrastructure and run time need to be made for both data management and the design process. Data retrieval, data updates, storage, filtering and analysis are the main parts of a sequence data management system. Each part needs to be well-implemented as the resulting sequences form the basis for the oligonucleotide design. Important key features, such as the oligonucleotide length, melting temperature, secondary structures and primer dimer formation, as well as the specificity, should be considered for the in-silico selection of oligonucleotides. The development of an efficient oligonucleotide design workflow demands the right balance between the precision of the applied computer models, the general expenditure of time, and computational workload. This paper gives an overview of important parameters during the design process, starting from the data retrieval, up to the design parameters for optimized oligonucleotide design.

Identifying Physical Causes of Apparent Enhanced Cyclization of Short DNA Molecules with a Coarse-Grained Model

DNA cyclization is a powerful technique to gain insight into the nature of DNA bending. While the wormlike chain model provides a good description of small to moderate bending fluctuations, it is expected to break down for large bending. Recent cyclization experiments on strongly bent shorter molecules indeed suggest enhanced flexibility over and above that expected from the wormlike chain. Here, we use a coarse-grained model of DNA to investigate the subtle thermodynamics of DNA cyclization for molecules ranging from 30 to 210 base pairs. As the molecules get shorter, we find increasing deviations between our computed equilibrium j-factor and the classic wormlike chain predictions of Shimada and Yamakawa for a torsionally aligned looped molecule. These deviations are due to sharp kinking, first at nicks, and only subsequently in the body of the duplex. At the shortest lengths, substantial fraying at the ends of duplex domains is the dominant method of relaxation. We also estimate the dynamic j-factor measured in recent FRET experiments. We find that the dynamic j-factor is systematically larger than its equilibrium counterpart—with the deviation larger for shorter molecules—because not all the stress present in the fully cyclized state is present in the transition state. These observations are important for the interpretation of recent cyclization experiments, suggesting that measured anomalously high j-factors may not necessarily indicate non-WLC behavior in the body of duplexes.

Rolling circle amplification shows a sinusoidal template length-dependent amplification bias

Biophysical properties of DNA such as its longitudinal and torsional persistence length govern many processes and phenomena in biology, DNA nanotechnology and biotechnology. It has, for example, long been known that the circularization efficiency of short DNA fragments shows a periodic pattern where fragments with integer helical turns circularize much more efficiently than those with odd helical half turns due to stronger stacking of duplex ends. Small DNA circles can serve as templates for rolling circle amplification (RCA), which is a common and extremely robust amplification mechanism for nucleic acids. We discovered a strong template length-dependent amplification efficiency bias of RCA with the same periodicity as B-DNA. However, stacking cannot explain the mechanism behind this bias as the presence of the polymerase in the bifurcation fork inhibits base stacking of ends. Instead, coarse-grained molecular dynamics simulations imply that different amplification efficiencies come from a varying fraying probability of the last two downstream base pairs. We conclude that an increased strain-promoted fraying probability can increase the polymerization rate compared to a relaxed template.

DNA bipedal motor walking dynamics: an experimental and theoretical study of the dependency on step size

We present a detailed coarse-grained computer simulation and single molecule fluorescence study of the walking dynamics and mechanism of a DNA bipedal motor striding on a DNA origami. In particular, we study the dependency of the walking efficiency and stepping kinetics on step size. The simulations accurately capture and explain three different experimental observations. These include a description of the maximum possible step size, a decrease in the walking efficiency over short distances and a dependency of the efficiency on the walking direction with respect to the origami track. The former two observations were not expected and are non-trivial. Based on this study, we suggest three design modifications to improve future DNA walkers. Our study demonstrates the ability of the oxDNA model to resolve the dynamics of complex DNA machines, and its usefulness as an engineering tool for the design of DNA machines that operate in the three spatial dimensions.

Nucleic Acid Databases and Molecular-Scale Computing

DNA outperforms most conventional storage media in terms of information retention time, physical density, and volumetric coding capacity. Advances in synthesis and sequencing technologies have enabled implementations of large synthetic DNA databases with impressive storage capacity and reliable data recovery. Several robust DNA storage architectures featuring random access, error correction, and content rewritability have been constructed with the potential for scalability and cost reduction. We survey these recent achievements and discuss alternative routes for overcoming the hurdles of engineering practical DNA storage systems. We also review recent exciting work on in vivo DNA memory including intracellular recorders constructed by programmable genome editing tools. Besides information storage, DNA could serve as a versatile molecular computing substrate. We highlight several state-of-the-art DNA computing techniques such as strand displacement, localized hybridization chain reactions, and enzymatic reaction networks. We summarize how these simple primitives have facilitated rational designs and implementations of in vitro DNA reaction networks that emulate digital/analog circuits, artificial neural networks, or nonlinear dynamic systems. We envision these modular primitives could be strategically adapted for sophisticated database operations and massively parallel computations on DNA databases. We also highlight in vivo DNA computing modules such as CRISPR logic gates for building scalable genetic circuits in living cells. To conclude, we discuss various implications and challenges of DNA-based storage and computing, and we particularly encourage innovative work on bridging these two areas of research to further explore molecular parallelism and near-data processing. Such integrated molecular systems could lead to far-reaching applications in biocomputing, security, and medicine.

Twist-bend coupling and the statistical mechanics of the twistable wormlike-chain model of DNA: Perturbation theory and beyond

The simplest model of DNA mechanics describes the double helix as a continuous rod with twist and bend elasticity. Recent work has discussed the relevance of a little-studied coupling G between twisting and bending, known to arise from the groove asymmetry of the DNA double helix. Here the effect of G on the statistical mechanics of long DNA molecules subject to applied forces and torques is investigated. We present a perturbative calculation of the effective torsional stiffness C_{eff} for small twist-bend coupling. We find that the "bare" G is "screened" by thermal fluctuations, in the sense that the low-force, long-molecule effective free energy is that of a model with G=0 but with long-wavelength bending and twisting rigidities that are shifted by G-dependent amounts. Using results for torsional and bending rigidities for freely fluctuating DNA, we show how our perturbative results can be extended to a nonperturbative regime. These results are in excellent agreement with numerical calculations for Monte Carlo "triad" and molecular dynamics "oxDNA" models, characterized by different degrees of coarse graining, validating the perturbative and nonperturbative analyses. While our theory is in generally good quantitative agreement with experiment, the predicted torsional stiffness does systematically deviate from experimental data, suggesting that there are as-yet-uncharacterized aspects of DNA twisting-stretching mechanics relevant to low-force, long-molecule mechanical response, which are not captured by widely used coarse-grained models.

Programming Structured DNA Assemblies to Probe Biophysical Processes

Structural DNA nanotechnology is beginning to emerge as a widely accessible research tool to mechanistically study diverse biophysical processes. Enabled by scaffolded DNA origami in which a long single strand of DNA is weaved throughout an entire target nucleic acid assembly to ensure its proper folding, assemblies of nearly any geometric shape can now be programmed in a fully automatic manner to interface with biology on the 1-100-nm scale. Here, we review the major design and synthesis principles that have enabled the fabrication of a specific subclass of scaffolded DNA origami objects called wireframe assemblies. These objects offer unprecedented control over the nanoscale organization of biomolecules, including biomolecular copy numbers, presentation on convex or concave geometries, and internal versus external functionalization, in addition to stability in physiological buffer. To highlight the power and versatility of this synthetic structural biology approach to probing molecular and cellular biophysics, we feature its application to three leading areas of investigation: light harvesting and nanoscale energy transport, RNA structural biology, and immune receptor signaling, with an outlook toward unique mechanistic insight that may be gained in these areas in the coming decade.

Triangulated Wireframe Structures Assembled Using Single-Stranded DNA Tiles

The field of structural DNA nanotechnology offers a wide range of design strategies with which to build structures with a desired aspect ratio, size, and shape. Compared with traditional close-packed DNA structures, triangulated wireframe structures require less material per surface or volume unit and improve the stability in biologically relevant conditions due to the reduced electrostatic repulsion. Herein, we expand the design space of the DNA single-stranded tile method to cover a range of anisotropic, finite, triangulated wireframe structures as well as a number of one-dimensional crystalline assemblies. These structures are composed of six-arm junctions with a single double helix as connecting edges that assemble in physiologically relevant salinities. For a reliable folding of the structures, single-stranded spacers 2-4 nucleotides long have to be introduced in the junction connecting neighboring arms. Coarse-grained molecular dynamics simulations using the oxDNA model suggests that the spacers prevent the stacking of DNA helices, thereby facilitating the assembly of planar geometries.

Flexibility defines structure in crystals of amphiphilic DNA nanostars

DNA nanostructures with programmable shape and interactions can be used as building blocks for the self-assembly of crystalline materials with prescribed nanoscale features, holding a vast technological potential. Structural rigidity and bond directionality have been recognised as key design features for DNA motifs to sustain long-range order in 3D, but the practical challenges associated with prescribing building-block geometry with sufficient accuracy have limited the variety of available designs. We have recently introduced a novel platform for the one-pot preparation of crystalline DNA frameworks supported by a combination of Watson-Crick base pairing and hydrophobic forces (Brady et al 2017 Nano Lett. 17 3276-81). Here we use small angle x-ray scattering and coarse-grained molecular simulations to demonstrate that, as opposed to available all-DNA approaches, amphiphilic motifs do not rely on structural rigidity to support long-range order. Instead, the flexibility of amphiphilic DNA building-blocks is a crucial feature for successful crystallisation.

Uncertainty quantification of a DNA origami mechanism using a coarse-grained model and kinematic variance analysis

Significant advances have been made towards the design, fabrication, and actuation of dynamic DNA nanorobots including the development of DNA origami mechanisms. These DNA origami mechanisms integrate relatively stiff links made of bundles of double-stranded DNA and relatively flexible joints made of single-stranded DNA to mimic the design of macroscopic machines and robots. Despite reproducing the complex configurations of macroscopic machines, these DNA origami mechanisms exhibit significant deviations from their intended motion behavior since nanoscale mechanisms are subject to significant thermal fluctuations that lead to variations in the geometry of the underlying DNA origami components. Understanding these fluctuations is critical to assess and improve the performance of DNA origami mechanisms and to enable precise nanoscale robotic functions. Here, we report a hybrid computational framework combining coarse-grained modeling with kinematic variance analysis to predict uncertainties in the motion pathway of a multi-component DNA origami mechanism. Coarse-grained modeling was used to evaluate the variation in geometry of individual components due to thermal fluctuations. This variation was incorporated in kinematic analyses to predict the motion pathway uncertainty of the entire mechanism, which agreed well with experimental characterization of motion. We further demonstrated the ability to predict the probability density of DNA origami mechanism conformations based on analysis of mechanical properties of individual joints. This integration of computational analysis, modeling tools, and experimental methods establish the foundation to predict and manage motion uncertainties of general DNA origami mechanisms to guide the design of DNA-based nanoscale machines and robots.

One-Step Photochemical Generation of Biofunctionalized Hydrogel Particles via Two-Phase Flow

Biofunctional hydrogel particles have become increasingly popular in medical diagnostics; however, their generation is time-consuming and typically requires several process steps. We report on a new method for the simple, fast, and reproducible one-step generation of monodisperse hydrogel particles equipped with biofunctional molecules such as proteins or DNA. Key to the approach is the simultaneous photo cross-linking of the polymer chains and covalent binding of proteins or DNA through a C,H insertion reaction inside aqueous plug compartments that are produced via microfluidics. The strong performance in biological binding assays of the functionalized particles is demonstrated.

Paper Origami-Inspired Design and Actuation of DNA Nanomachines with Complex Motions

Significant progress in DNA nanotechnology has accelerated the development of molecular machines with functions like macroscale machines. However, the mobility of DNA self-assembled nanorobots is still dramatically limited due to challenges with designing and controlling nanoscale systems with many degrees of freedom. Here, an origami-inspired method to design transformable DNA nanomachines is presented. This approach integrates stiff panels formed by bundles of double-stranded DNA connected with foldable creases formed by single-stranded DNA. To demonstrate the method, a DNA version of the paper origami mechanism called a waterbomb base (WBB) consisting of six panels connected by six joints is constructed. This nanoscale WBB can follow four distinct motion paths to transform between five distinct configurations including a flat square, two triangles, a rectangle, and a fully compacted trapezoidal shape. To achieve this, the sequence specificity of DNA base-pairing is leveraged for the selective actuation of joints and the ion-sensitivity of base-stacking interactions is employed for the flattening of joints. In addition, higher-order assembly of DNA WBBs into reconfigurable arrays is achieved. This work establishes a foundation for origami-inspired design for next generation synthetic molecular robots and reconfigurable nanomaterials enabling more complex and controllable motion.

Effects of Design Choices on the Stiffness of Wireframe DNA Origami Structures

DNA origami is a powerful method for the creation of 3D nanoscale objects, and in the past few years, interest in wireframe origami designs has increased due to their potential for biomedical applications. In DNA wireframe designs, the construction material is double-stranded DNA, which has a persistence length of around 50 nm. In this work, we study the effect of various design choices on the stiffness versus final size of nanoscale wireframe rods, given the constraints on origami designs set by the DNA origami scaffold size. An initial theoretical analysis predicts two competing mechanisms limiting rod stiffness, whose balancing results in an optimal edge length. For small edge lengths, the bending of the rod's overall frame geometry is the dominant factor, while the flexibility of individual DNA edges has a greater contribution at larger edge lengths. We evaluate our design choices through simulations and experiments and find that the stiffness of the structures increases with the number of sides in the cross-section polygon and that there are indications of an optimal member edge length. We also ascertain the effect of nicked DNA edges on the stiffness of the wireframe rods and demonstrate that ligation of the staple breakpoint nicks reduces the observed flexibility. Our simulations also indicate that the persistence length of wireframe DNA structures significantly decreases with increasing monovalent salt concentration.

Dynamics of supercoiled DNA with complex knots: large-scale rearrangements and persistent multi-strand interlocking

Knots and supercoiling are both introduced in bacterial plasmids by catalytic processes involving DNA strand passages. While the effects on plasmid organization has been extensively studied for knotting and supercoiling taken separately, much less is known about their concurrent action. Here, we use molecular dynamics simulations and oxDNA, an accurate mesoscopic DNA model, to study the kinetic and metric changes introduced by complex (five-crossing) knots and supercoiling in 2 kbp-long DNA rings. We find several unexpected results. First, the conformational ensemble is dominated by two distinct states, differing in branchedness and knot size. Secondly, fluctuations between these states are as fast as the metric relaxation of unknotted rings. In spite of this, certain boundaries of knotted and plectonemically-wound regions can persist over much longer timescales. These pinned regions involve multiple strands that are interlocked by the cooperative action of topological and supercoiling constraints. Their long-lived character may be relevant for the simplifying action of topoisomerases.

The temperature dependence of the helical twist of DNA

DNA is the carrier of all cellular genetic information and increasingly used in nanotechnology. Quantitative understanding and optimization of its functions requires precise experimental characterization and accurate modeling of DNA properties. A defining feature of DNA is its helicity. DNA unwinds with increasing temperature, even for temperatures well below the melting temperature. However, accurate quantitation of DNA unwinding under external forces and a microscopic understanding of the corresponding structural changes are currently lacking. Here we combine single-molecule magnetic tweezers measurements with atomistic molecular dynamics and coarse-grained simulations to obtain a comprehensive view of the temperature dependence of DNA twist. Experimentally, we find that DNA twist changes by ΔTw(T) = (-11.0 ± 1.2)°/(°C·kbp), independent of applied force, in the range of forces where torque-induced melting is negligible. Our atomistic simulations predict ΔTw(T) = (-11.1 ± 0.3)°/(°C·kbp), in quantitative agreement with experiments, and suggest that the untwisting of DNA with temperature is predominantly due to changes in DNA structure for defined backbone substates, while the effects of changes in substate populations are minor. Coarse-grained simulations using the oxDNA framework yield a value of ΔTw(T) = (-6.4 ± 0.2)°/(°C·kbp) in semi-quantitative agreement with experiments.

Bend-Induced Twist Waves and the Structure of Nucleosomal DNA

Recent work indicates that twist-bend coupling plays an important role in DNA micromechanics. Here we investigate its effect on bent DNA. We provide an analytical solution of the minimum-energy shape of circular DNA, showing that twist-bend coupling induces sinusoidal twist waves. This solution is in excellent agreement with both coarse-grained simulations of minicircles and nucleosomal DNA data, which is bent and wrapped around histone proteins in a superhelical conformation. Our analysis shows that the observed twist oscillation in nucleosomal DNA, so far attributed to the interaction with the histone proteins, is an intrinsic feature of free bent DNA, and should be observable in other protein-DNA complexes.

Coarse-Grained Double-Stranded RNA Model from Quantum-Mechanical Calculations

A coarse-grained model for simulating structural properties of double-stranded RNA is developed with parameters obtained from quantum-mechanical calculations. This model follows previous parametrization for double-stranded DNA, which is based on mapping the all-atom picture to a coarse-grained four-bead scheme. Chemical and structural differences between RNA and DNA have been taken into account for the model development. The parametrization is based on simulations using density functional theory (DFT) on separate units of the RNA molecule without implementing experimental data. The total energy is decomposed into four terms of physical significance: hydrogen bonding interaction, stacking interactions, backbone interactions, and electrostatic interactions. The first three interactions are treated within DFT, whereas the last one is included within a mean field approximation. Our double-stranded RNA coarse-grained model predicts stable helical structures for RNA. Other characteristics, such as structural or mechanical properties are reproduced with a very good accuracy. The development of the coarse-grained model for RNA allows extending the spatial and temporal length scales accessed by computer simulations and being able to model RNA-related biophysical processes, as well as novel RNA nanostructures.

Monte Carlo simulation algorithm for B-DNA

Understanding the structure-function relationship of biomolecules containing DNA has motivated experiments aimed at determining molecular structure using methods such as small-angle X-ray and neutron scattering (SAXS and SANS). SAXS and SANS are useful for determining macromolecular shape in solution, a process which benefits by using atomistic models that reproduce the scattering data. The variety of algorithms available for creating and modifying model DNA structures lack the ability to rapidly modify all-atom models to generate structure ensembles. This article describes a Monte Carlo algorithm for simulating DNA, not with the goal of predicting an equilibrium structure, but rather to generate an ensemble of plausible structures which can be filtered using experimental results to identify a sub-ensemble of conformations that reproduce the solution scattering of DNA macromolecules. The algorithm generates an ensemble of atomic structures through an iterative cycle in which B-DNA is represented using a wormlike bead-rod model, new configurations are generated by sampling bend and twist moves, then atomic detail is recovered by back mapping from the final coarse-grained configuration. Using this algorithm on commodity computing hardware, one can rapidly generate an ensemble of atomic level models, each model representing a physically realistic configuration that could be further studied using molecular dynamics. © 2016 Wiley Periodicals, Inc.

Multi-scale coarse-graining for the study of assembly pathways in DNA-brick self-assembly

Inspired by recent successes using single-stranded DNA tiles to produce complex structures, we develop a two-step coarse-graining approach that uses detailed thermodynamic calculations with oxDNA, a nucleotide-based model of DNA, to parametrize a coarser kinetic model that can reach the time and length scales needed to study the assembly mechanisms of these structures. We test the model by performing a detailed study of the assembly pathways for a two-dimensional target structure made up of 334 unique strands each of which are 42 nucleotides long. Without adjustable parameters, the model reproduces a critical temperature for the formation of the assembly that is close to the temperature at which assembly first occurs in experiments. Furthermore, the model allows us to investigate in detail the nucleation barriers and the distribution of critical nucleus shapes for the assembly of a single target structure. The assembly intermediates are compact and highly connected (although not maximally so), and classical nucleation theory provides a good fit to the height and shape of the nucleation barrier at temperatures close to where assembly first occurs.

Force-Induced Unravelling of DNA Origami

The mechanical properties of DNA nanostructures are of widespread interest as applications that exploit their stability under constant or intermittent external forces become increasingly common. We explore the force response of DNA origami in comprehensive detail by combining AFM single molecule force spectroscopy experiments with simulations using oxDNA, a coarse-grained model of DNA at the nucleotide level, to study the unravelling of an iconic origami system: the Rothemund tile. We contrast the force-induced melting of the tile with simulations of an origami 10-helix bundle. Finally, we simulate a recently proposed origami biosensor, whose function takes advantage of origami behavior under tension. We observe characteristic stick-slip unfolding dynamics in our force-extension curves for both the Rothemund tile and the helix bundle and reasonable agreement with experimentally observed rupture forces for these systems. Our results highlight the effect of design on force response: we observe regular, modular unfolding for the Rothemund tile that contrasts with strain-softening of the 10-helix bundle which leads to catastropic failure under monotonically increasing force. Further, unravelling occurs straightforwardly from the scaffold ends inward for the Rothemund tile, while the helix bundle unfolds more nonlinearly. The detailed visualization of the yielding events provided by simulation allows preferred pathways through the complex unfolding free-energy landscape to be mapped, as a key factor in determining relative barrier heights is the extensional release per base pair broken. We shed light on two important questions: how stable DNA nanostructures are under external forces and what design principles can be applied to enhance stability.

Sequence-Dependent Three Interaction Site Model for Single- and Double-Stranded DNA

We develop a robust coarse-grained model for single- and double-stranded DNA by representing each nucleotide by three interaction sites (TIS) located at the centers of mass of sugar, phosphate, and base. The resulting TIS model includes base-stacking, hydrogen bond, and electrostatic interactions as well as bond-stretching and bond angle potentials that account for the polymeric nature of DNA. The choices of force constants for stretching and the bending potentials were guided by a Boltzmann inversion procedure using a large representative set of DNA structures extracted from the Protein Data Bank. Some of the parameters in the stacking interactions were calculated using a learning procedure, which ensured that the experimentally measured melting temperatures of dimers are faithfully reproduced. Without any further adjustments, the calculations based on the TIS model reproduce the experimentally measured salt and sequence-dependence of the size of single-stranded DNA (ssDNA), as well as the persistence lengths of poly(dA) and poly(dT) chains. Interestingly, upon application of mechanical force, the extension of poly(dA) exhibits a plateau, which we trace to the formation of stacked helical domains. In contrast, the force-extension curve (FEC) of poly(dT) is entropic in origin and could be described by a standard polymer model. We also show that the persistence length of double-stranded DNA, formed from two complementary ssDNAs, is consistent with the prediction based on the worm-like chain. The persistence length, which decreases with increasing salt concentration, is in accord with the Odijk-Skolnick-Fixman theory intended for stiff polyelectrolyte chains near the rod limit. Our model predicts the melting temperatures of DNA hairpins with excellent accuracy, and we are able to recover the experimentally known sequence-specific trends. The range of applications, which did not require adjusting any parameter after the initial construction based solely on PDB structures and melting profiles of dimers, attests to the transferability and robustness of the TIS model for ssDNA and dsDNA.

DNA elasticity from coarse-grained simulations: The effect of groove asymmetry

It is well established that many physical properties of DNA at sufficiently long length scales can be understood by means of simple polymer models. One of the most widely used elasticity models for DNA is the twistable worm-like chain (TWLC), which describes the double helix as a continuous elastic rod with bending and torsional stiffness. An extension of the TWLC, which has recently received some attention, is the model by Marko and Siggia, who introduced an additional twist-bend coupling, expected to arise from the groove asymmetry. By performing computer simulations of two available versions of oxDNA, a coarse-grained model of nucleic acids, we investigate the microscopic origin of twist-bend coupling. We show that this interaction is negligible in the oxDNA version with symmetric grooves, while it appears in the oxDNA version with asymmetric grooves. Our analysis is based on the calculation of the covariance matrix of equilibrium deformations, from which the stiffness parameters are obtained. The estimated twist-bend coupling coefficient from oxDNA simulations is G=30±1 nm. The groove asymmetry induces a novel twist length scale and an associated renormalized twist stiffness κ_t≈80 nm, which is different from the intrinsic torsional stiffness C≈110 nm. This naturally explains the large variations on experimental estimates of the intrinsic stiffness performed in the past.

Hierarchical bounding structures for efficient virial computations: Towards a realistic molecular description of cholesterics

We detail the application of bounding volume hierarchies to accelerate second-virial evaluations for arbitrary complex particles interacting through hard and soft finite-range potentials. This procedure, based on the construction of neighbour lists through the combined use of recursive atom-decomposition techniques and binary overlap search schemes, is shown to scale sub-logarithmically with particle resolution in the case of molecular systems with high aspect ratios. Its implementation within an efficient numerical and theoretical framework based on classical density functional theory enables us to investigate the cholesteric self-assembly of a wide range of experimentally relevant particle models. We illustrate the method through the determination of the cholesteric behavior of hard, structurally resolved twisted cuboids, and report quantitative evidence of the long-predicted phase handedness inversion with increasing particle thread angles near the phenomenological threshold value of 45°. Our results further highlight the complex relationship between microscopic structure and helical twisting power in such model systems, which may be attributed to subtle geometric variations of their chiral excluded-volume manifold.

Open-Boundary Molecular Dynamics of a DNA Molecule in a Hybrid Explicit/Implicit Salt Solution

The composition and electrolyte concentration of the aqueous bathing environment have important consequences for many biological processes and can profoundly affect the behavior of biomolecules. Nevertheless, because of computational limitations, many molecular simulations of biophysical systems can be performed only at specific ionic conditions: either at nominally zero salt concentration, i.e., including only counterions enforcing the system's electroneutrality, or at excessive salt concentrations. Here, we introduce an efficient molecular dynamics simulation approach for an atomistic DNA molecule at realistic physiological ionic conditions. The simulations are performed by employing the open-boundary molecular dynamics method that allows for simulation of open systems that can exchange mass and linear momentum with the environment. In our open-boundary molecular dynamics approach, the computational burden is drastically alleviated by embedding the DNA molecule in a mixed explicit/implicit salt-bathing solution. In the explicit domain, the water molecules and ions are both overtly present in the system, whereas in the implicit water domain, only the ions are explicitly present and the water is described as a continuous dielectric medium. Water molecules are inserted and deleted into/from the system in the intermediate buffer domain that acts as a water reservoir to the explicit domain, with both water molecules and ions free to enter or leave the explicit domain. Our approach is general and allows for efficient molecular simulations of biomolecules solvated in bathing salt solutions at any ionic strength condition.

Coarse-grained simulation of DNA using LAMMPS : An implementation of the oxDNA model and its applications

During the last decade coarse-grained nucleotide models have emerged that allow us to study DNA and RNA on unprecedented time and length scales. Among them is oxDNA, a coarse-grained, sequence-specific model that captures the hybridisation transition of DNA and many structural properties of single- and double-stranded DNA. oxDNA was previously only available as standalone software, but has now been implemented into the popular LAMMPS molecular dynamics code. This article describes the new implementation and analyses its parallel performance. Practical applications are presented that focus on single-stranded DNA, an area of research which has been so far under-investigated. The LAMMPS implementation of oxDNA lowers the entry barrier for using the oxDNA model significantly, facilitates future code development and interfacing with existing LAMMPS functionality as well as other coarse-grained and atomistic DNA models.

Selective layer-free blood serum ionogram based on ion-specific interactions with a nanotransistor

Despite being ubiquitous in the fields of chemistry and biology, the ion-specific effects of electrolytes pose major challenges for researchers. A lack of understanding about ion-specific surface interactions has hampered the development and application of materials for (bio-)chemical sensor applications. Here, we show that scaling a silicon nanotransistor sensor down to ~25 nm provides a unique opportunity to understand and exploit ion-specific surface interactions, yielding a surface that is highly sensitive to cations and inert to pH. The unprecedented sensitivity of these devices to Na⁺ and divalent ions can be attributed to an overscreening effect via molecular dynamics. The surface potential of multi-ion solutions is well described by the sum of the electrochemical potentials of each cation, enabling selective measurements of a target ion concentration without requiring a selective organic layer. We use these features to construct a blood serum ionogram for Na⁺, K⁺, Ca²⁺ and Mg²⁺, in an important step towards the development of a versatile, durable and mobile chemical or blood diagnostic tool.

An Accurate Estimate of the Free Energy and Phase Diagram of All-DNA Bulk Fluids

We present a numerical study in which large-scale bulk simulations of self-assembled DNA constructs have been carried out with a realistic coarse-grained model. The investigation aims at obtaining a precise, albeit numerically demanding, estimate of the free energy for such systems. We then, in turn, use these accurate results to validate a recently proposed theoretical approach that builds on a liquid-state theory, the Wertheim theory, to compute the phase diagram of all-DNA fluids. This hybrid theoretical/numerical approach, based on the lowest-order virial expansion and on a nearest-neighbor DNA model, can provide, in an undemanding way, a parameter-free thermodynamic description of DNA associating fluids that is in semi-quantitative agreement with experiments. We show that the predictions of the scheme are as accurate as those obtained with more sophisticated methods. We also demonstrate the flexibility of the approach by incorporating non-trivial additional contributions that go beyond the nearest-neighbor model to compute the DNA hybridization free energy.

How Well Can DNA Rupture DNA? Shearing and Unzipping Forces inside DNA Nanostructures

A purely DNA nanomachine must support internal stresses across short DNA segments with finite rigidity, producing effects that can be qualitatively very different from experimental observations of isolated DNA in fixed-force ensembles. In this article, computational simulations are used to study how well the rigidity of a driving DNA duplex can rupture a double-stranded DNA target into single-stranded segments and how well this stress can discriminate between unzipping or shearing geometries. This discrimination is found to be maximized at an optimal length but deteriorates as the driving duplex is either lengthened or shortened. This differs markedly from a fixed-force ensemble and has implications for the design parameters and limitations of dynamic DNA nanomachines.

Characterizing the Motion of Jointed DNA Nanostructures Using a Coarse-Grained Model

As detailed structural characterizations of large complex DNA nanostructures are hard to obtain experimentally, particularly if they have substantial flexibility, coarse-grained modeling can potentially provide an important complementary role. Such modeling can provide a detailed view of both the average structure and the structural fluctuations, as well as providing insight into how the nanostructure's design determines its structural properties. Here, we present a case study of jointed DNA nanostructures using the oxDNA model. In particular, we consider archetypal hinge and sliding joints, as well as more complex structures involving a number of such coupled joints. Our results highlight how the nature of the motion in these structures can sensitively depend on the precise details of the joints. Furthermore, the generally good agreement with experiments illustrates the power of this approach and suggests the use of such modeling to prescreen the properties of putative designs.

Structure and conformational dynamics of scaffolded DNA origami nanoparticles

Synthetic DNA is a highly programmable nanoscale material that can be designed to self-assemble into 3D structures that are fully determined by underlying Watson–Crick base pairing. The double crossover (DX) design motif has demonstrated versatility in synthesizing arbitrary DNA nanoparticles on the 5–100 nm scale for diverse applications in biotechnology. Prior computational investigations of these assemblies include all-atom and coarse-grained modeling, but modeling their conformational dynamics remains challenging due to their long relaxation times and associated computational cost. We apply all-atom molecular dynamics and coarse-grained finite element modeling to DX-based nanoparticles to elucidate their fine-scale and global conformational structure and dynamics. We use our coarse-grained model with a set of secondary structural motifs to predict the equilibrium solution structures of 45 DX-based DNA origami nanoparticles including a tetrahedron, octahedron, icosahedron, cuboctahedron and reinforced cube. Coarse-grained models are compared with 3D cryo-electron microscopy density maps for these five DNA nanoparticles and with all-atom molecular dynamics simulations for the tetrahedron and octahedron. Our results elucidate non-intuitive atomic-level structural details of DX-based DNA nanoparticles, and offer a general framework for efficient computational prediction of global and local structural and mechanical properties of DX-based assemblies that are inaccessible to all-atom based models alone.

Adaptive resolution simulations of biomolecular systems

In this review article, we discuss and analyze some recently developed hybrid atomistic-mesoscopic solvent models for multiscale biomolecular simulations. We focus on the biomolecular applications of the adaptive resolution scheme (AdResS), which allows solvent molecules to change their resolution back and forth between atomistic and coarse-grained representations according to their positions in the system. First, we discuss coupling of atomistic and coarse-grained models of salt solution using a 1-to-1 molecular mapping-i.e., one coarse-grained bead represents one water molecule-for development of a multiscale salt solution model. In order to make use of coarse-grained molecular models that are compatible with the MARTINI force field, one has to resort to a supramolecular mapping, in particular to a 4-to-1 mapping, where four water molecules are represented with one coarse-grained bead. To this end, bundled atomistic water models are employed, i.e., the relative movement of water molecules that are mapped to the same coarse-grained bead is restricted by employing harmonic springs. Supramolecular coupling has recently also been extended to polarizable coarse-grained water models with explicit charges. Since these coarse-grained models consist of several interaction sites, orientational degrees of freedom of the atomistic and coarse-grained representations are coupled via a harmonic energy penalty term. The latter aligns the dipole moments of both representations. The reviewed multiscale solvent models are ready to be used in biomolecular simulations, as illustrated in a few examples.

A coarse-grained model for assisting the investigation of structure and dynamics of large nucleic acids by ion mobility spectrometry-mass spectrometry

Ion Mobility Spectrometry-Mass Spectrometry (IMS-MS) is a rapidly emerging tool for the investigation of nucleic acid structure and dynamics. IMS-MS determinations can provide valuable information regarding alternative topologies, folding intermediates, and conformational heterogeneities, which are not readily accessible to other analytical techniques. The leading strategies for data interpretation rely on computational and experimental approaches to correctly assign experimental observations to putative structures. A very effective strategy involves the application of molecular dynamics (MD) simulations to predict the structure of the analyte molecule, calculate its collision cross section (CCS), and then compare this computational value with the corresponding experimental data. While this approach works well for small nucleic acid species, analyzing larger nucleic acids of biological interest is hampered by the computational cost associated with capturing their extensive structure and dynamics in all-atom detail. In this report, we describe the implementation of a coarse graining (CG) approach to reduce the cost of the computational methods employed in the data interpretation workflow. Our framework employs a five-bead model to accurately represent each nucleotide in the nucleic acid structure. The beads are appropriately parameterized to enable the direct calculation of CCS values from CG models, thus affording the ability to pursue the analysis of larger, highly dynamic constructs. The validity of this approach was successfully confirmed by the excellent correlation between the CCS values obtained in parallel by all-atom and CG workflows.

A dsDNA model optimized for electrokinetic applications

We present a coarse-grained (CG) model of a charged double-stranded DNA immersed in an electrolyte solution that can be used for a variety of electrokinetic applications. The model is based on an earlier rigid and immobile model of Weik et al. and includes now semi-flexibility and mobility, so that DNA dynamics can be sufficiently captured to simulate a full nanopore translocation process. To this end we couple the DNA hydrodynamically via a raspberry approach to a lattice-Boltzmann fluid and parametrize the counterions with a distant dependent friction. The electrokinetic properties of the CG DNA model inside an infinite cylinder is fitted against experimental data from Smeets et al. and all-atom simulation data from Kesselheim et al. The stiffness of our CG DNA is modeled via a harmonic angle potential fitted against experimental data of Brunet et al. Finally, the quality of our tuned parameters is tested by measuring the electrophoretic mobility of our DNA model for various numbers of base pairs and salt concentrations. Our results compare excellently with the experimental data sets of Stellwagen et al. and Hoagland et al.

Conformational Dynamics of Mechanically Compliant DNA Nanostructures from Coarse-Grained Molecular Dynamics Simulations

Structural DNA nanotechnology, the assembly of rigid 3D structures of complex yet precise geometries, has recently been used to design dynamic, mechanically compliant nanostructures with tunable equilibrium conformations and conformational distributions. Here we use coarse-grained molecular dynamics simulations to provide insights into the conformational dynamics of a set of mechanically compliant DNA nanostructures-DNA hinges that use single-stranded DNA "springs" to tune the equilibrium conformation of a layered double-stranded DNA "joint" connecting two stiff "arms" constructed from DNA helix bundles. The simulations reproduce the experimentally measured equilibrium angles between hinge arms for a range of hinge designs. The hinges are found to be structurally stable, except for some fraying of the open ends of the DNA helices comprising the hinge arms and some loss of base-pairing interactions in the joint regions coinciding with the crossover junctions, especially in hinges designed to exhibit a small bending angle that exhibit large local stresses resulting in strong kinks in their joints. Principal component analysis reveals that while the hinge dynamics are dominated by bending motion, some twisting and sliding of hinge arms relative to each other also exists. Forced deformation of the hinges reveals distinct bending mechanisms for hinges with short, inextensible springs versus those with longer, more extensible springs. Lastly, we introduce an approach for rapidly predicting equilibrium hinge angles from individual force-deformation behaviors of its single- and double-stranded DNA components. Taken together, these results demonstrate that coarse-grained modeling is a promising approach for designing, predicting, and studying the dynamics of compliant DNA nanostructures, where conformational fluctuations become important, multiple deformation mechanisms exist, and continuum approaches may not yield accurate properties.

Pore translocation of knotted DNA rings

We use an accurate coarse-grained model for DNA and stochastic molecular dynamics simulations to study the pore translocation of 10-kbp-long DNA rings that are knotted. By monitoring various topological and physical observables we find that there is not one, as previously assumed, but rather two qualitatively different modes of knot translocation. For both modes the pore obstruction caused by knot passage has a brief duration and typically occurs at a late translocation stage. Both effects are well in agreement with experiments and can be rationalized with a transparent model based on the concurrent tensioning and sliding of the translocating knotted chains. We also observed that the duration of the pore obstruction event is more controlled by the knot translocation velocity than the knot size. These features should advance the interpretation and design of future experiments aimed at probing the spontaneous knotting of biopolymers.

The 1-Particle-per-k-Nucleotides (1PkN) Elastic Network Model of DNA Dynamics with Sequence-Dependent Geometry

Coarse-grained models of DNA have made important contributions to the determination of the physical properties of genomic DNA, working as a molecular machine for gene regulation. In this study, to analyze the global dynamics of long DNA sequences with consideration of sequence-dependent geometry, we propose elastic network models of DNA where each particle represents k nucleotides (1-particle-per-k-nucleotides, 1PkN). The models were adjusted according to profiles of the anisotropic fluctuations obtained from our previous 1-particle-per-1-nucleotide (1P1N) model, which was proven to reproduce such profiles of all-atom models. We confirmed that the 1P3N and 1P4N models are suitable for the analysis of detailed dynamics such as local twisting motion. The models are intended for the analysis of large structures, e.g., 10-nm fibers in the nucleus, and nucleoids of mitochondrial or phage DNA at low computational costs. As an example, we surveyed the physical characteristics of the whole mitochondrial human and Plasmodium falciparum genomes.

Condensation and Demixing in Solutions of DNA Nanostars and Their Mixtures

We present a numerical/theoretical approach to efficiently evaluate the phase diagram of self-assembling DNA nanostars. Combining input information based on a realistic coarse-grained DNA potential with the Wertheim association theory, we derive a parameter-free thermodynamic description of these systems. We apply this method to investigate the phase behavior of single components and mixtures of DNA nanostars with different numbers of sticky arms, elucidating the role of the system functionality and of salt concentration. Specifically, we evaluate the propensity to demix, the gas-liquid phase boundaries and the location of the critical points. The predicted critical parameters compare very well with existing experimental results for the available compositions. The approach developed here is very general, easily extensible to other all-DNA systems, and provides guidance for future experiments.