Sequence-dependent thermodynamics of a coarse-grained DNA model

A review on nonlinear DNA physics

The study and the investigation of structural and dynamical properties of complex systems have attracted considerable interest among scientists in general and physicists and biologists in particular. The present review paper represents a broad overview of the research performed over the nonlinear dynamics of DNA, devoted to some different aspects of DNA physics and including analytical, quantum and computational tools to understand nonlinear DNA physics. We review in detail the semi-discrete approximation within helicoidal Peyrard-Bishop model and show that localized modulated solitary waves, usually called breathers, can emerge and move along the DNA. Since living processes occur at submolecular level, we then discuss a quantum treatment to address the problem of how charge and energy are transported on DNA and how they may play an important role for the functioning of living cells. While this problem has attracted the attention of researchers for a long time, it is still poorly understood how charge and energy transport can occur at distances comparable to the size of macromolecules. Here, we review a theory based on the mechanism of 'self-trapping' of electrons due to their interaction with mechanical (thermal) oscillation of the DNA structure. We also describe recent computational models that have been developed to capture nonlinear mechanics of DNA in vitro and in vivo, possibly under topological constraints. Finally, we provide some conjectures on potential future directions for this field.

SICOR: Subgraph Isomorphism Comparison of RNA Secondary Structures

RNA aptamer selection during SELEX experiments builds on secondary structural diversity. Advanced structural comparison methods can focus this diversity. We develop SICOR, which uses probabilistic subgraph isomorphisms for graph distances between RNA secondary structure graphs. SICOR outperforms other comparison methods and is applicable to many structural comparisons in experimental design.

Improving therapeutic potential of non-viral minimized DNA vectors

The tragic deaths of three patients in a recent AAV-based X-linked myotubular myopathy clinical trial highlight once again the pressing need for safe and reliable gene delivery vectors. Non-viral minimized DNA vectors offer one possible way to meet this need. Recent pre-clinical results with minimized DNA vectors have yielded promising outcomes in cancer therapy, stem cell therapy, stem cell reprograming, and other uses. Broad clinical use of these vectors, however, remains to be realized. Further advances in vector design and production are ongoing. An intriguing and promising potential development results from manipulation of the specific shape of non-viral minimized DNA vectors. By improving cellular uptake and biodistribution specificity, this approach could impact gene therapy, DNA nanotechnology, and personalized medicine.

MrDNA: a multi-resolution model for predicting the structure and dynamics of DNA systems

Although the field of structural DNA nanotechnology has been advancing with an astonishing pace, de novo design of complex 3D nanostructures and functional devices remains a laborious and time-consuming process. One reason for that is the need for multiple cycles of experimental characterization to elucidate the effect of design choices on the actual shape and function of the self-assembled objects. Here, we demonstrate a multi-resolution simulation framework, mrdna, that, in 30 min or less, can produce an atomistic-resolution structure of a self-assembled DNA nanosystem. We demonstrate fidelity of our mrdna framework through direct comparison of the simulation results with the results of cryo-electron microscopy (cryo-EM) reconstruction of multiple 3D DNA origami objects. Furthermore, we show that our approach can characterize an ensemble of conformations adopted by dynamic DNA nanostructures, the equilibrium structure and dynamics of DNA objects constructed using off-lattice self-assembly principles, i.e. wireframe DNA objects, and to study the properties of DNA objects under a variety of environmental conditions, such as applied electric field. Implemented as an open source Python package, our framework can be extended by the community and integrated with DNA design and molecular graphics tools.

Global and local mechanical properties control endonuclease reactivity of a DNA origami nanostructure

We used coarse-grained molecular dynamics simulations to characterize the global and local mechanical properties of a DNA origami triangle nanostructure. The structure presents two metastable conformations separated by a free energy barrier that is lowered upon omission of four specific DNA staples (defect). In contrast, only one stable conformation is present upon removing eight staples. The metastability is explained in terms of the intrinsic conformations of the three trapezoidal substructures. We computationally modeled the local accessibility to endonucleases, to predict the reactivity of twenty sites, and found good agreement with the experimental data. We showed that global fluctuations affect local reactivity: the removal of the DNA staples increased the computed accessibility to a restriction enzyme, at sites as distant as 40 nm, due to an increase in global fluctuation. These results raise the intriguing possibility of the rational engineering of allosterically modulated DNA origami.

Robotic DNA Nanostructures

Over the past decade, DNA nanotechnology has spawned a broad variety of functional nanostructures tailored toward the enabled state at which applications are coming increasingly in view. One of the branches of these applications is in synthetic biology, where the intrinsic programmability of the DNA nanostructures may pave the way for smart task-specific molecular robotics. In brief, the synthesis of the user-defined artificial DNA nano-objects is based on employing DNA molecules with custom lengths and sequences as building materials that predictably assemble together by obeying Watson-Crick base pairing rules. The general workflow of creating DNA nanoshapes is getting more and more straightforward, and some objects can be designed automatically from the top down. The versatile DNA nano-objects can serve as synthetic tools at the interface with biology, for example, in therapeutics and diagnostics as dynamic logic-gated nanopills, light-, pH-, and thermally driven devices. Such diverse apparatuses can also serve as optical polarizers, sensors and capsules, autonomous cargo-sorting robots, rotary machines, precision measurement tools, as well as electric and magnetic-field directed robotic arms. In this review, we summarize the recent progress in robotic DNA nanostructures, mechanics, and their various implementations.

Domain-Specific Programming Languages for Computational Nucleic Acid Systems

The construction of models of system behavior is of great importance throughout science and engineering. In bioengineering and bionanotechnology, these often take the form of dynamic models that specify the evolution of different species over time. To ensure that scientific observations and conclusions are consistent and that systems can be reliably engineered on the basis of model predictions, it is important that models of biomolecular systems can be constructed in a reliable, principled, and efficient manner. This review focuses on efforts to address this need by using domain-specific programming languages as the basis for custom design tools for researchers working on computational nucleic acid devices, where a domain-specific language is simply a programming language tailored to a particular application domain. The underlying thesis of our review is that there is a continuum of practical implementation strategies for computational nucleic acid systems, which can all benefit from appropriate domain-specific languages and software design tools. We emphasize the need for specialized yet flexible tools that can be realized using domain-specific languages that compile to more general-purpose representations.

Design, optimization and analysis of large DNA and RNA nanostructures through interactive visualization, editing and molecular simulation

This work seeks to remedy two deficiencies in the current nucleic acid nanotechnology software environment: the lack of both a fast and user-friendly visualization tool and a standard for structural analyses of simulated systems. We introduce here oxView, a web browser-based visualizer that can load structures with over 1 million nucleotides, create videos from simulation trajectories, and allow users to perform basic edits to DNA and RNA designs. We additionally introduce open-source software tools for extracting common structural parameters to characterize large DNA/RNA nanostructures simulated using the coarse-grained modeling tool, oxDNA, which has grown in popularity in recent years and is frequently used to prototype new nucleic acid nanostructural designs, model biophysics of DNA/RNA processes, and rationalize experimental results. The newly introduced software tools facilitate the computational characterization of DNA/RNA designs by providing multiple analysis scripts, including mean structures and structure flexibility characterization, hydrogen bond fraying, and interduplex angles. The output of these tools can be loaded into oxView, allowing users to interact with the simulated structure in a 3D graphical environment and modify the structures to achieve the required properties. We demonstrate these newly developed tools by applying them to design and analysis of a range of DNA/RNA nanostructures.

Design and synthesis of pleated DNA origami nanotubes with adjustable diameters

DNA origami allows for the synthesis of nanoscale structures and machines with nanometre precision and high yields. Tubular DNA origami nanostructures are particularly useful because their geometry facilitates a variety of applications including nanoparticle encapsulation, the construction of artificial membrane pores and as structural scaffolds that can uniquely spatially arrange nanoparticles in circular, linear and helical arrays. Here we report a system of parametrization for the design of radially symmetric DNA origami nanotubes with adjustable diameter, length, crossover density, pleat angle and chirality. The system is implemented into a computational algorithm that provides a practical means to navigate the complex geometry of DNA origami nanotube design. We apply this in the design, synthesis and characterization of novel DNA origami nanotubes. These include structures with pleated walls where the same number of duplexes can form nanotubes with different diameters, and to vary the diameter within the same structure. We also construct nanotubes that can be reconfigured into different chiral shapes. Finally, we explore the effect of strain on the local and global geometry of DNA origami nanotubes and demonstrate how pleated walls can provide a strategy to rigidify nanotubes and to construct closely packed parallel duplexes.

Design of hidden thermodynamic driving for non-equilibrium systems via mismatch elimination during DNA strand displacement

Recent years have seen great advances in the development of synthetic self-assembling molecular systems. Designing out-of-equilibrium architectures, however, requires a more subtle control over the thermodynamics and kinetics of reactions. We propose a mechanism for enhancing the thermodynamic drive of DNA strand-displacement reactions whilst barely perturbing forward reaction rates: the introduction of mismatches within the initial duplex. Through a combination of experiment and simulation, we demonstrate that displacement rates are strongly sensitive to mismatch location and can be tuned by rational design. By placing mismatches away from duplex ends, the thermodynamic drive for a strand-displacement reaction can be varied without significantly affecting the forward reaction rate. This hidden thermodynamic driving motif is ideal for the engineering of non-equilibrium systems that rely on catalytic control and must be robust to leak reactions.

100th Anniversary of Macromolecular Science Viewpoint: Modeling and Simulation of Macromolecules with Hydrogen Bonds: Challenges, Successes, and Opportunities

Macromolecular materials with directional interactions such as hydrogen bonds exhibit numerous attractive features in terms of structure, thermodynamics, and dynamics. Besides enabling precise tuning of desirable geometries in the assembled state (e.g., programmable coordination numbers depending on the valency of the directional interaction), mixing in a blend/composite through stabilization via hydrogen bonds between the various components, hydrogen bonds can also impart responsiveness to external stimuli (e.g., temperature, pH). In biomacromolecules (e.g., proteins, DNA, polysaccharides), hydrogen bonds play a key role in stabilizing secondary and tertiary structures, which in turn define the function of these macromolecules. In this Viewpoint, I present the challenges, successes, and opportunities for molecular modeling and simulations to conduct fundamental and application-focused research on macromolecular materials with hydrogen bonding interactions. The past successes and limitations of atomistic simulations are discussed first, followed by highlights from recent developments in coarse-grained modeling and their use in studies of (synthetic and biologically relevant) macromolecular materials. Model development focused on polynucleotides (e.g., DNA, RNA, etc.), polypeptides, polysaccharides, and synthetic polymers at experimentally relevant conditions are highlighted. This viewpoint ends with potential future directions for macromolecular modeling and simulations with other types of directional interactions beyond hydrogen bonding.

Computational design of probes to detect bacterial genomes by multivalent binding

Rapid methods for diagnosis of bacterial infections are urgently needed to reduce inappropriate use of antibiotics, which contributes to antimicrobial resistance. In many rapid diagnostic methods, DNA oligonucleotide probes, attached to a surface, bind to specific nucleotide sequences in the DNA of a target pathogen. Typically, each probe binds to a single target sequence; i.e., target-probe binding is monovalent. Here we show using computer simulations that the detection sensitivity and specificity can be improved by designing probes that bind multivalently to the entire length of the pathogen genomic DNA, such that a given probe binds to multiple sites along the target DNA. Our results suggest that multivalent targeting of long pieces of genomic DNA can allow highly sensitive and selective binding of the target DNA, even if competing DNA in the sample also contains binding sites for the same probe sequences. Our results are robust to mild fragmentation of the bacterial genome. Our conclusions may also be relevant for DNA detection in other fields, such as disease diagnostics more broadly, environmental management, and food safety.

Increasing Complexity in Wireframe DNA Nanostructures

Structural DNA nanotechnology has recently gained significant momentum, as diverse design tools for producing custom DNA shapes have become more and more accessible to numerous laboratories worldwide. Most commonly, researchers are employing a scaffolded DNA origami technique by "sculpting" a desired shape from a given lattice composed of packed adjacent DNA helices. Albeit relatively straightforward to implement, this approach contains its own apparent restrictions. First, the designs are limited to certain lattice types. Second, the long scaffold strand that runs through the entire structure has to be manually routed. Third, the technique does not support trouble-free fabrication of hollow single-layer structures that may have more favorable features and properties compared to objects with closely packed helices, especially in biological research such as drug delivery. In this focused review, we discuss the recent development of wireframe DNA nanostructures-methods relying on meshing and rendering DNA-that may overcome these obstacles. In addition, we describe each available technique and the possible shapes that can be generated. Overall, the remarkable evolution in wireframe DNA structure design methods has not only induced an increase in their complexity and thus expanded the prevalent shape space, but also already reached a state at which the whole design process of a chosen shape can be carried out automatically. We believe that by combining cost-effective biotechnological mass production of DNA strands with top-down processes that decrease human input in the design procedure to minimum, this progress will lead us to a new era of DNA nanotechnology with potential applications coming increasingly into view.

Free energy landscape of salt-actuated reconfigurable DNA nanodevices

Achieving rapid, noninvasive actuation of DNA structures is critical to expanding the functionality of DNA nanotechnology. A promising actuation approach involves introducing multiple, short pairs of single-stranded DNA overhangs to components of the structure and triggering hybridization or dissociation of the overhangs via changes in solution ionic conditions to drive structural transitions. Here, we reveal the underlying basis of this new approach by computing via molecular simulations the free energy landscape of DNA origami hinges actuated between open and closed states. Our results reveal how the overhangs collectively introduce a sharp free-energy minimum at the closed state and a broad energy barrier between open and closed states and how changes in ionic conditions modulate these features of the landscape to drive actuation towards the open or closed state. We demonstrate the critical role played by hinge confinement in stabilizing the hybridized state of the overhangs and magnifying the energy barrier to dissociation. By analyzing how the distribution of overhangs and their length and sequence modulate the energy landscape, we obtain design rules for tuning the actuation behavior. The molecular insights obtained here should be applicable to a broad range of systems involving DNA hybridization within confined systems.

Small RNA Biosensor Design Strategy To Mitigate Off-Analyte Response

Several bottlenecks in the design of current sensor technologies for small noncoding RNA must be addressed. The small size of the sensors and the large number of other nucleotides that may have sequence similarity makes selectivity a real concern. Many of the current sensors have one strand with an exposed region called a toehold. The toehold serves as a place for the analyte nucleic acid strand to bind and initiate competitive displacement of sensors' secondary strands. Since the toehold region is not protected, any endogenous oligonucleotide sequences that are similar or only different by a few nucleic acids will interact with the toehold and cause false signals. To address sensor selectivity, we investigated how the toehold location in the sensor impacts the sensitivity and selectivity for the analyte of interest. We will discuss the differences in sensitivity and selectivity for a miR-146a-5p biosensor in the presence of different naturally occurring mismatch sequences. We found that altering the toehold location lowered the rate of the false signal from off-analyte microRNA by upward of 20 percentage points. Detection limits as low as 56 pM were observed when the sensor concentration was 5 nM. The findings herein are broadly applicable to other small and large RNAs as well as other types of sensing platforms.

Conformational enhancement of fidelity in toehold-sequestered DNA nanodevices

Simple design principles improve conformational stability and decrease strand leakage by two orders of magnitude.

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.

Recent Progress towards Chemically-Specific Coarse-Grained Simulation Models with Consistent Dynamical Properties

Coarse-grained (CG) models can provide computationally efficient and conceptually simple characterizations of soft matter systems. While generic models probe the underlying physics governing an entire family of free-energy landscapes, bottom-up CG models are systematically constructed from a higher-resolution model to retain a high level of chemical specificity. The removal of degrees of freedom from the system modifies the relationship between the relative time scales of distinct dynamical processes through both a loss of friction and a “smoothing” of the free-energy landscape. While these effects typically result in faster dynamics, decreasing the computational expense of the model, they also obscure the connection to the true dynamics of the system. The lack of consistent dynamics is a serious limitation for CG models, which not only prevents quantitatively accurate predictions of dynamical observables but can also lead to qualitatively incorrect descriptions of the characteristic dynamical processes. With many methods available for optimizing the structural and thermodynamic properties of chemically-specific CG models, recent years have seen a stark increase in investigations addressing the accurate description of dynamical properties generated from CG simulations. In this review, we present an overview of these efforts, ranging from bottom-up parameterizations of generalized Langevin equations to refinements of the CG force field based on a Markov state modeling framework. We aim to make connections between seemingly disparate approaches, while laying out some of the major challenges as well as potential directions for future efforts.

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.

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.

TacoxDNA: A user-friendly web server for simulations of complex DNA structures, from single strands to origami

Simulations of nucleic acids at different levels of structural details are increasingly used to complement and interpret experiments in different fields, from biophysics to medicine and materials science. However, the various structural models currently available for DNA and RNA and their accompanying suites of computational tools can be very rarely used in a synergistic fashion. The tacoxDNA webserver and standalone software package presented here are a step toward a long-sought interoperability of nucleic acids models. The webserver offers a simple interface for converting various common input formats of DNA structures and setting up molecular dynamics (MD) simulations. Users can, for instance, design DNA rings with different topologies, such as knots, with and without supercoiling, by simply providing an XYZ coordinate file of the DNA centre-line. More complex DNA geometries, as designable in the cadnano, CanDo and Tiamat tools, can also be converted to all-atom or oxDNA representations, which can then be used to run MD simulations. Though the latter are currently geared toward the native and LAMMPS oxDNA representations, the open-source package is designed to be further expandable. TacoxDNA is available at http://tacoxdna.sissa.it. © 2019 Wiley Periodicals, Inc.

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.

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.

Computational Simulation of Adapter Length-Dependent LASSO Probe Capture Efficiency

Multiplexed cloning of long DNA sequences is a valuable technique in many biotechnology applications, such as long-read genome sequencing and the creation of open reading frame (ORF) libraries. Long-adapter single-stranded oligonucleotide (LASSO) probes have shown promise as a tool to clone long DNA fragments. LASSO probes are molecular inversion probes (MIP) engineered with an adapter region of user-defined length, flanked between template-specific probe sequences. Herein, we demonstrate that the adapter length is a key feature of LASSO that influences the efficiency of gene capture and cloning. Furthermore, we applied a model based on Monte Carlo molecular simulation in order to study the relationship between the long-adapter length of LASSO and capture enrichment. Our results suggest that the adapter length is a factor that contributes to the free energy of target-probe interaction, thereby determining the efficiency of capture. The results indicate that LASSOs with extremely long adapters cannot capture the targets well. They also suggest that targets of different lengths may prefer adapters of different lengths.

Track-walking molecular motors: a new generation beyond bridge-burning designs

Track-walking molecular motors are the core bottom-up mechanism for nanometre-resolved translational movements - a fundamental technological capability at the root of numerous applications ranging from nanoscale assembly lines and chemical synthesis to molecular robots and shape-changing materials. Over the last 10 years, artificial molecular walkers (or nanowalkers) have evolved from the 1st generation of bridge-burning designs to the 2nd generation capable of truly sustainable movements. Invention of non-bridge-burning nanowalkers was slow at first, but has picked up speed since 2012, and is now close to breaking major barriers for wide-spread development. Here we review the 2nd generation of artificial nanowalkers, which are mostly made of DNA molecules and draw energy from light illumination or from chemical fuels for entirely autonomous operation. They are typically symmetric dimeric motors walking on entirely periodic tracks, yet the motors possess an inherent direction for large-scale amplification of the action of many motor copies. These translational motors encompass the function of rotational molecular motors on circular or linear tracks, and may involve molecular shuttles as 'engine' motifs. Some rules of thumb are provided to help readers design similar motors from DNA or other molecular building blocks. Opportunities and challenges for future development are discussed, especially in the areas of molecular robotics and active materials based on the advanced motors.

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.

Overtwisting induces polygonal shapes in bent DNA

By combining analytical results and simulations of various coarse-grained models, we investigate the minimal energy shape of DNA minicircles which are torsionally constrained by an imposed over or undertwist. We show that twist-bend coupling, a cross interaction term discussed in the recent DNA literature, induces minimal energy shapes with a periodic alternation of parts with high and low curvature resembling rounded polygons. We briefly discuss the possible experimental relevance of these findings. We finally show that the twist and bending energies of minicircles are governed by renormalized stiffness constants, rather than the bare ones. This has important consequences for the analysis of experiments involving circular DNA meant to determine DNA elastic constants.

Structure, stability and specificity of the binding of ssDNA and ssRNA with proteins

Recognition of single-stranded DNA (ssDNA) or single-stranded RNA (ssRNA) is important for many fundamental cellular functions. A variety of single-stranded DNA-binding proteins (ssDBPs) and single-stranded RNA-binding proteins (ssRBPs) have evolved that bind ssDNA and ssRNA, respectively, with varying degree of affinities and specificities to form complexes. Structural studies of these complexes provide key insights into their recognition mechanism. However, computational modeling of the specific recognition process and to predict the structure of the complex is challenging, primarily due to the heterogeneity of their binding energy landscape and the greater flexibility of ssDNA or ssRNA compared with double-stranded nucleic acids. Consequently, considerably fewer computational studies have explored interactions between proteins and single-stranded nucleic acids compared with protein interactions with double-stranded nucleic acids. Here, we report a newly developed energy-based coarse-grained model to predict the structure of ssDNA–ssDBP and ssRNA–ssRBP complexes and to assess their sequence-specific interactions and stabilities. We tuned two factors that can modulate specific recognition: base–aromatic stacking strength and the flexibility of the single-stranded nucleic acid. The model was successfully applied to predict the binding conformations of 12 distinct ssDBP and ssRBP structures with their cognate ssDNA and ssRNA partners having various sequences. Estimated binding energies agreed well with the corresponding experimental binding affinities. Bound conformations from the simulation showed a funnel-shaped binding energy distribution where the native-like conformations corresponded to the energy minima. The various ssDNA–protein and ssRNA–protein complexes differed in the balance of electrostatic and aromatic energies. The lower affinity of the ssRNA–ssRBP complexes compared with the ssDNA–ssDBP complexes stems from lower flexibility of ssRNA compared to ssDNA, which results in higher rate constants for the dissociation of the complex (k_off) for complexes involving the former.

Quantifying bimolecular self-assembly is pivotal to understanding cellular function. In recent years, a large progress has been made in understanding the structure and biophysics of protein-protein interactions. Particularly, various computational tools are available for predicting these structures and to estimate their stability and the driving forces of their formation. The understating of the interactions between proteins and nucleic acids, however, is still limited, presumably due to the involvement of non-specific interactions as well as the high conformational plasticity that may demand an induced-fit mechanism. In particular, the interactions between proteins and single-stranded nucleic acids (i.e., single-stranded DNA and RNA) is very challenging due to their high flexibility. Furthermore, the interface between proteins and single-stranded nucleic acids is often chemically more heterogeneous than the interface between proteins and double-stranded DNA. In this study, we developed a coarse-grained computational model to predict the structure of complexes between proteins and single-stranded nucleic acids. The model was applied to estimate binding affinities and the estimated binding energies agreed well with the corresponding experimental binding affinities. The kinetics of association as well as the specificity of the complexes between proteins and ssDNA are different than those with ssRNA, mostly due to differences in their conformational flexibility.

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.

Nanomechanics of Diaminopurine-Substituted DNA

2,6-diaminopurine (DAP) is a nucleobase analog of adenine. When incorporated into double-stranded DNA (dsDNA), it forms three hydrogen bonds with thymine. Rare in nature, DAP substitution alters the physical characteristics of a DNA molecule without sacrificing sequence specificity. Here, we show that in addition to stabilizing double-strand hybridization, DAP substitution also changes the mechanical and conformational properties of dsDNA. Thermal melting experiments reveal that DAP substitution raises melting temperatures without diminishing sequence-dependent effects. Using a combination of atomic force microscopy (AFM), magnetic tweezer (MT) nanomechanical assays, and circular dichroism spectroscopy, we demonstrate that DAP substitution increases the flexural rigidity of dsDNA yet also facilitates conformational shifts, which manifest as changes in molecule length. DAP substitution increases both the static and dynamic persistence length of DNA (measured by AFM and MT, respectively). In the static case (AFM), in which tension is not applied to the molecule, the contour length of DAP-DNA appears shorter than wild-type (WT)-DNA; under tension (MT), they have similar dynamic contour lengths. At tensions above 60 pN, WT-DNA undergoes characteristic overstretching because of strand separation (tension-induced melting) and spontaneous adoption of a conformation termed S-DNA. Cyclic overstretching and relaxation of WT-DNA at near-zero loading rates typically yields hysteresis, indicative of tension-induced melting; conversely, cyclic stretching of DAP-DNA showed little or no hysteresis, consistent with the adoption of the S-form, similar to what has been reported for GC-rich sequences. However, DAP-DNA overstretching is distinct from GC-rich overstretching in that it happens at a significantly lower tension. In physiological salt conditions, evenly mixed AT/GC DNA typically overstretches around 60 pN. GC-rich sequences overstretch at similar if not slightly higher tensions. Here, we show that DAP-DNA overstretches at 52 pN. In summary, DAP substitution decreases the overall stability of the B-form double helix, biasing toward non-B-form DNA helix conformations at zero tension and facilitating the B-to-S transition at high tension.

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.

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.

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.

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.

Tethered multifluorophore motion reveals equilibrium transition kinetics of single DNA double helices

Understanding cellular functions and dysfunctions often begins with quantifying the interactions between the binding partners involved in the processes. Learning about the kinetics of the interactions is of particular importance to understand the dynamics of cellular processes. We created a tethered multifluorophore motion assay using DNA origami that enables over 1-hour-long recordings of the statistical binding and unbinding of single pairs of biomolecules directly in equilibrium. The experimental concept is simple and the data interpretation is very direct, which makes the system easy to use for a wide variety of researchers. Due to the modularity and addressability of the DNA origami-based assay, our system may be readily adapted to study various other molecular interactions.

We describe a tethered multifluorophore motion assay based on DNA origami for revealing bimolecular reaction kinetics on the single-molecule level. Molecular binding partners may be placed at user-defined positions and in user-defined stoichiometry; and binding states are read out by tracking the motion of quickly diffusing fluorescent reporter units. Multiple dyes per reporter unit enable singe-particle observation for more than 1 hour. We applied the system to study in equilibrium reversible hybridization and dissociation of complementary DNA single strands as a function of tether length, cation concentration, and sequence. We observed up to hundreds of hybridization and dissociation events per single reactant pair and could produce cumulative statistics with tens of thousands of binding and unbinding events. Because the binding partners per particle do not exchange, we could also detect subtle heterogeneity from molecule to molecule, which enabled separating data reflecting the actual target strand pair binding kinetics from falsifying influences stemming from chemically truncated oligonucleotides. Our data reflected that mainly DNA strand hybridization, but not strand dissociation, is affected by cation concentration, in agreement with previous results from different assays. We studied 8-bp-long DNA duplexes with virtually identical thermodynamic stability, but different sequences, and observed strongly differing hybridization kinetics. Complementary full-atom molecular-dynamics simulations indicated two opposing sequence-dependent phenomena: helical templating in purine-rich single strands and secondary structures. These two effects can increase or decrease, respectively, the fraction of strand collisions leading to successful nucleation events for duplex formation.

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.

Oli2go: an automated multiplex oligonucleotide design tool

The success of widely used oligonucleotide-based experiments, ranging from PCR to microarray, strongly depends on an accurate design. The design process involves a number of steps, which use specific parameters to produce high quality oligonucleotides. Oli2go is an efficient, user friendly, fully automated multiplex oligonucleotide design tool, which performs primer and different hybridization probe designs as well as specificity and cross dimer checks in a single run. The main improvement to existing oligonucleotide design web-tools is that oli2go combines multiple steps in an all-in-one solution, where other web applications only accomplish parts of the whole design workflow. Especially, the oli2go specificity check is not only performed against a single species (e.g. mouse), but against bacteria, viruses, fungi, invertebrates, plants, protozoa, archaea and sequences from whole genome shotgun sequence projects and environmental samples, at once. This allows the design of highly specific oligonucleotides in multiplex applications, which is further assured by performing dimer checks not only on the primers themselves, but in an all-against-all fashion. The software is freely accessible to all users at http://oli2go.ait.ac.at/.

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.

How to simulate patchy particles⋆

Patchy particles is the name given to a large class of systems of mesoscopic particles characterized by a repulsive core and a discrete number of short-range and highly directional interaction sites. Numerical simulations have contributed significantly to our understanding of the behaviour of patchy particles, but, although simple in principle, advanced simulation techniques are often required to sample the low temperatures and long time-scales associated with their self-assembly behaviour. In this work we review the most popular simulation techniques that have been used to study patchy particles, with a special focus on Monte Carlo methods. We cover many of the tools required to simulate patchy systems, from interaction potentials to biased moves, cluster moves, and free-energy methods. The review is complemented by an educationally oriented Monte Carlo computer code that implements all the techniques described in the text to simulate a well-known tetrahedral patchy particle model.

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.

A coarse-grained model for DNA origami

Modeling tools provide a valuable support for DNA origami design. However, current solutions have limited application for conformational analysis of the designs. In this work we present a tool for a thorough study of DNA origami structure and dynamics. The tool is based on a novel coarse-grained model dedicated to geometry optimization and conformational analysis of DNA origami. We explored the ability of the model to predict dynamic behavior, global shapes, and fine details of two single-layer systems designed in hexagonal and square lattices using atomic force microscopy, Förster resonance energy transfer spectroscopy, and all-atom molecular dynamic simulations for validation of the results. We also examined the performance of the model for multilayer systems by simulation of DNA origami with published cryo-electron microscopy and atomic force microscopy structures. A good agreement between the simulated and experimental data makes the model suitable for conformational analysis of DNA origami objects. The tool is available at http://vsb.fbb.msu.ru/cosm as a web-service and as a standalone version.

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.