Sequence-dependent thermodynamics of a coarse-grained DNA model

Design and simulation of a wireframe DNA origami nanoactuator

This paper explores the use of deoxyribonucleic acid (DNA) origami structures as nanorobot components. Investigating the functional properties of DNA origami structures can facilitate the fabrication of DNA origami-based nanorobots. The wireframe structure stands out as one of the most interesting DNA origami structures. Hence, the present study aims to employ these structures to create DNA origami nanoactuators. The research delves into the design of DNA origami structures with the aim of opening under specific temperature conditions. Short DNA strands (staples) are one of the crucial parts of DNA origami structures, and the appropriate design of these strands can lead to the creation of structures with different properties. Thus, the components of the DNA origami nanoactuator are tailored to enable intentional opening at specific temperatures while maintaining stability at lower temperatures. This structural modification showcases the functional property of the DNA origami structure. The engineered DNA origami nanoactuator holds potential applications in medicine. By carrying drugs under specific temperature conditions and releasing them under different temperature conditions, it can serve as a platform for smart drug delivery purposes.

Weak-cooperative binding of a long single-stranded DNA chain on a surface

Binding gene-wide single-stranded nucleic acids to surface-immobilized complementary probes is an important but challenging process for biophysical studies and diagnostic applications. The challenge comes from the conformational dynamics of the long chain that affects its accessibility and weakens its hybridization to the probes. We investigated the binding of bacteriophage genome M13mp18 on several different 20-mer probes immobilized on the surface of a multi-spot, label-free biosensor, and observed that only a few of them display strong binding capability with dissociation constant as low as 10 pM. Comparing experimental data and computational analysis of the M13mp18 chain structural features, we found that the capturing performance of a specific probe is directly related to the multiplicity of binding sites on the genomic strand, and poorly connected with the predicted secondary and tertiary structure. We show that a model of weak cooperativity of transient bonds is compatible with the measured binding kinetics and accounts for the enhancement of probe capturing observed when more than 20 partial pairings with binding free energy lower than -10 kcal mol-1 are present. This mechanism provides a specific pattern of response of a genomic strand on a panel of properly selected oligomer probe sequences.

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

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

DNAforge: a design tool for nucleic acid wireframe nanostructures

DNAforge is an online tool that provides a unified, user-friendly interface to several recent design methods for DNA and RNA wireframe nanostructures, with the possibility of integrating additional methods into the same framework. Currently, DNAforge supports three design methods for DNA nanostructures and two for RNA nanostructures. The tool enables the design, visualisation and sequence generation for highly complex wireframe nanostructures with a simple fully automated process. DNAforge is freely accessible at https://dnaforge.org/.

De novo DNA-based catch bonds

All primary chemical interactions weaken under mechanical stress, which imposes fundamental mechanical limits on the materials constructed from them. Biological materials combine plasticity with strength, for which nature has evolved a unique solution-catch bonds, supramolecular interactions that strengthen under tension. Biological catch bonds use force-gated conformational switches to convert weak bonds into strong ones. So far, catch bonds remain exclusive to nature, leaving their potential as mechanoadaptive elements in synthetic systems untapped. Here we report the design and realization of artificial catch bonds. Starting from a minimal set of thermodynamic design requirements, we created a molecular motif capable of catch bonding. It consists of a DNA duplex featuring a cryptic domain that unfolds under tension to strengthen the interaction. We show that these catch bonds recreate force-enhanced rolling adhesion, a hallmark feature of biological catch bonds in bacteria and leukocytes. This Article introduces catch bonds into the synthetic domain, and could lead to the creation of artificial catch-bonded materials.

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

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

Inverse design of a pyrochlore lattice of DNA origami through model-driven experiments

Sophisticated statistical mechanics approaches and human intuition have demonstrated the possibility of self-assembling complex lattices or finite-size constructs. However, attempts so far have mostly only been successful in silico and often fail in experiment because of unpredicted traps associated with kinetic slowing down (gelation, glass transition) and competing ordered structures. Theoretical predictions also face the difficulty of encoding the desired interparticle interaction potential with the experimentally available nano- and micrometer-sized particles. To overcome these issues, we combine SAT assembly (a patchy-particle interaction design algorithm based on constrained optimization) with coarse-grained simulations of DNA nanotechnology to experimentally realize trap-free self-assembly pathways. We use this approach to assemble a pyrochlore three-dimensional lattice, coveted for its promise in the construction of optical metamaterials, and characterize it with small-angle x-ray scattering and scanning electron microscopy visualization.

Engineering Ultrasoft Interactions in Stiff All-DNA Dendrimers by Site-Specific Control of Scaffold Flexibility

A combined experimental and theoretical study of the structural correlations in moderately concentrated suspensions of all-DNA dendrimers of the second generation (G2) with controlled scaffold rigidity is reported here. Small-angle X-ray scattering experiments in concentrated aqueous saline solutions of stiff all-DNA G2 dendritic constructs reveal a novel anomalous liquid-like phase behavior which is reflected in the calculated structure factors as a two-step increase at low scattering wave vectors. By developing a new design strategy for adjusting the particle's internal flexibility based on site-selective incorporation of single-stranded DNA linkers into the dendritic scaffold, it is shown that this unconventional type of self-organization is strongly contingent on the dendrimer's stiffness. A comprehensive computer simulation study employing dendritic models with different levels of coarse-graining, and two theoretical approaches based on effective, pair-potential interactions, remarkably confirmed the origin of this unusual liquid-like behavior. The results demonstrate that the precise control of the internal structure of the dendritic scaffold conferred by the DNA can be potentially used to engineer a rich palette of novel ultrasoft interaction potentials that could offer a route for directed self-assembly of intriguing soft matter phases and experimental realizations of a host of unusual phenomena theoretically predicted for ultrasoft interacting systems.

Mechanism of DNA origami folding elucidated by mesoscopic simulations

Many experimental and computational efforts have sought to understand DNA origami folding, but the time and length scales of this process pose significant challenges. Here, we present a mesoscopic model that uses a switchable force field to capture the behavior of single- and double-stranded DNA motifs and transitions between them, allowing us to simulate the folding of DNA origami up to several kilobases in size. Brownian dynamics simulations of small structures reveal a hierarchical folding process involving zipping into a partially folded precursor followed by crystallization into the final structure. We elucidate the effects of various design choices on folding order and kinetics. Larger structures are found to exhibit heterogeneous staple incorporation kinetics and frequent trapping in metastable states, as opposed to more accessible structures which exhibit first-order kinetics and virtually defect-free folding. This model opens an avenue to better understand and design DNA nanostructures for improved yield and folding performance.

Coarse-grained modeling of DNA-RNA hybrids

We introduce oxNA, a new model for the simulation of DNA-RNA hybrids that is based on two previously developed coarse-grained models-oxDNA and oxRNA. The model naturally reproduces the physical properties of hybrid duplexes, including their structure, persistence length, and force-extension characteristics. By parameterizing the DNA-RNA hydrogen bonding interaction, we fit the model's thermodynamic properties to experimental data using both average-sequence and sequence-dependent parameters. To demonstrate the model's applicability, we provide three examples of its use-calculating the free energy profiles of hybrid strand displacement reactions, studying the resolution of a short R-loop, and simulating RNA-scaffolded wireframe origami.

Inverse Design of Self-Folding 3D Shells

Self-folding is an emerging paradigm for the inverse design of three-dimensional structures. While most efforts have concentrated on the shape of the net, our approach introduces a new design dimension-bond specificity between the edges. We transform this design process into a Boolean satisfiability problem to derive solutions for various target structures. This method significantly enhances the yield of the folding process. Furthermore, by linearly combining independent solutions, we achieve designs for shape-shifting nets wherein the dominant structure evolves with varying external conditions. This approach is demonstrated through coarse-grained simulations on two examples of triangular and square nets capable of folding into multiple target shapes.

Coarse-Grained Models to Study Protein-DNA Interactions and Liquid-Liquid Phase Separation

Recent advances in coarse-grained (CG) computational models for DNA have enabled molecular-level insights into the behavior of DNA in complex multiscale systems. However, most existing CG DNA models are not compatible with CG protein models, limiting their applications for emerging topics such as protein-nucleic acid assemblies. Here, we present a new computationally efficient CG DNA model. We first use experimental data to establish the model's ability to predict various aspects of DNA behavior, including melting thermodynamics and relevant local structural properties such as the major and minor grooves. We then employ an all-atom hydropathy scale to define nonbonded interactions between protein and DNA sites, to make our DNA model compatible with an existing CG protein model (HPS-Urry), which is extensively used to study protein phase separation, and show that our new model reasonably reproduces the experimental binding affinity for a prototypical protein-DNA system. To further demonstrate the capabilities of this new model, we simulate a full nucleosome with and without histone tails, on a microsecond time scale, generating conformational ensembles and provide molecular insights into the role of histone tails in influencing the liquid-liquid phase separation (LLPS) of HP1α proteins. We find that histone tails interact favorably with DNA, influencing the conformational ensemble of the DNA and antagonizing the contacts between HP1α and DNA, thus affecting the ability of DNA to promote LLPS of HP1α. These findings shed light on the complex molecular framework that fine-tunes the phase transition properties of heterochromatin proteins and contributes to heterochromatin regulation and function. Overall, the CG DNA model presented here is suitable to facilitate micrometer-scale studies with sub-nm resolution in many biological and engineering applications and can be used to investigate protein-DNA complexes, such as nucleosomes, or LLPS of proteins with DNA, enabling a mechanistic understanding of how molecular information may be propagated at the genome level.

Prediction and Control in DNA Nanotechnology

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

A rhythmically pulsing leaf-spring DNA-origami nanoengine that drives a passive follower

Molecular engineering seeks to create functional entities for modular use in the bottom-up design of nanoassemblies that can perform complex tasks. Such systems require fuel-consuming nanomotors that can actively drive downstream passive followers. Most artificial molecular motors are driven by Brownian motion, in which, with few exceptions, the generated forces are non-directed and insufficient for efficient transfer to passive second-level components. Consequently, efficient chemical-fuel-driven nanoscale driver-follower systems have not yet been realized. Here we present a DNA nanomachine (70 nm × 70 nm × 12 nm) driven by the chemical energy of DNA-templated RNA-transcription-consuming nucleoside triphosphates as fuel to generate a rhythmic pulsating motion of two rigid DNA-origami arms. Furthermore, we demonstrate actuation control and the simple coupling of the active nanomachine with a passive follower, to which it then transmits its motion, forming a true driver-follower pair.

Enzyme-Free Exponential Amplification via Growth and Scission of Crisscross Ribbons from Single-Stranded DNA Components

The self-assembly of DNA-based monomers into higher-order structures has significant potential for realizing various biomimetic behaviors including algorithmic assembly, ultrasensitive detection, and self-replication. For these behaviors, it is desirable to implement high energetic barriers to undesired spurious nucleation, where such barriers can be bypassed via seed-initiated assembly. Joint-neighbor capture is a mechanism enabling the construction of such barriers while allowing for algorithmic behaviors, such as bit-copying. Cycles of polymerization with division could accordingly be used for implementing exponential growth in self-replicating materials. Previously, we demonstrated crisscross polymerization, a strategy that attains robust seed-dependent self-assembly of single-stranded DNA and DNA-origami monomers via joint-neighbor capture. Here, we expand the crisscross assembly to achieve autonomous, isothermal exponential amplification of ribbons through their concurrent growth and scission via toehold-mediated strand displacement. We demonstrate how this crisscross chain reaction, or 3CR, can be used as a detection strategy through coupling to single- and double-stranded nucleic acid targets and introduce a rule-based stochastic modeling approach for simulating molecular self-assembly behaviors such as crisscross-ribbon scission.

Correlated Hybrid DNA Structures Explored by the oxDNA Model

Thermodynamically, perfect DNA hybridization can be formed between probes and their corresponding targets due to the favorable energy. However, this is not the case dynamically. Here, we use molecular dynamics (MD) simulations based on the oxDNA model to investigate the process of DNA microarray hybridization. In general, correlated hybrid DNA structures are formed, including one probe associated with several targets as well as one target hybrid with multiple probes leading to the target-mediated hybridization. The formation of these two types of correlated structures largely depends on the surface coverage of the DNA microarray. Moreover, DNA sequence, DNA length, and spacer length have an impact on the structural formation. Our findings shed light on the dynamics of DNA hybridization, which is important for the application of DNA microarray.

Spatiotemporal Control over Polynucleotide Brush Growth on DNA Origami Nanostructures

DNA nanotechnology provides an approach to create precise, tunable, and biocompatible nanostructures for biomedical applications. However, the stability of these structures is severely compromised in biological milieu due to their fast degradation by nucleases. Recently, we showed how enzymatic polymerization could be harnessed to grow polynucleotide brushes of tunable length and location on the surface of DNA origami nanostructures, which greatly enhances their nuclease stability. Here, we report on strategies that allow for both spatial and temporal control over polymerization through activatable initiation, cleavage, and regeneration of polynucleotide brushes using restriction enzymes. The ability to site-specifically decorate DNA origami nanostructures with polynucleotide brushes in a spatiotemporally controlled way provides access to "smart" functionalized DNA architectures with potential applications in drug delivery and supramolecular assembly.

Ballistic Brownian Motion of Nanoconfined DNA

Theoretical treatments of polymer dynamics in liquid generally start with the basic assumption that motion at the smallest scale is heavily overdamped; therefore, inertia can be neglected. We report on the Brownian motion of tethered DNA under nanoconfinement, which was analyzed by molecular dynamics simulation and nanoelectrochemistry-based single-electron shuttle experiments. Our results show a transition into the ballistic Brownian motion regime for short DNA in sub-5 nm gaps, with quality coefficients as high as 2 for double-stranded DNA, an effect mainly attributed to a drastic increase in stiffness. The possibility for DNA to enter the underdamped regime could have profound implications on our understanding of the energetics of biomolecular engines such as the replication machinery, which operates in nanocavities that are a few nanometers wide.

Versatile computer-aided design of free-form DNA nanostructures and assemblies

Recent advances in structural DNA nanotechnology have been facilitated by design tools that continue to push the limits of structural complexity while simplifying an often-tedious design process. We recently introduced the software MagicDNA, which enables design of complex 3D DNA assemblies with many components; however, the design of structures with free-form features like vertices or curvature still required iterative design guided by simulation feedback and user intuition. Here, we present an updated design tool, MagicDNA 2.0, that automates the design of free-form 3D geometries, leveraging design models informed by coarse-grained molecular dynamics simulations. Our GUI-based, stepwise design approach integrates a high level of automation with versatile control over assembly and subcomponent design parameters. We experimentally validated this approach by fabricating a range of DNA origami assemblies with complex free-form geometries, including a 3D Nozzle, G-clef, and Hilbert and Trifolium curves, confirming excellent agreement between design input, simulation, and structure formation.

Leveraging Steric Moieties for Kinetic Control of DNA Strand Displacement Reactions

DNA strand displacement networks are a critical part of dynamic DNA nanotechnology and are proven primitives for implementing chemical reaction networks. Precise kinetic control of these networks is important for their use in a range of applications. Among the better understood and widely leveraged kinetic properties of these networks are toehold sequence, length, composition, and location. While steric hindrance has been recognized as an important factor in such systems, a clear understanding of its impact and role is lacking. Here, a systematic investigation of steric hindrance within a DNA toehold-mediated strand displacement network was performed through tracking kinetic reactions of reporter complexes with incremental concatenation of steric moieties near the toehold. Two subsets of steric moieties were tested with systematic variation of structures and reaction conditions to isolate sterics from electrostatics. Thermodynamic and coarse-grained computational modeling was performed to gain further insight into the impacts of steric hindrance. Steric factors yielded up to 3 orders of magnitude decrease in the reaction rate constant. This pronounced effect demonstrates that steric moieties can be a powerful tool for kinetic control in strand displacement networks while also being more broadly informative of DNA structural assembly in both DNA-based therapeutic and diagnostic applications that possess elements of steric hindrance through DNA functionalization with an assortment of chemistries.

Investigating the Hydrogen Bond-Induced Self-Assembly of Polysulfamides Using Molecular Simulations and Experiments

In this paper, we present a synergistic, experimental, and computational study of the self-assembly of N,N'-disubstituted polysulfamides driven by hydrogen bonds (H-bonds) between the H-bonding donor and acceptor groups present in repeating sulfamides as a function of the structural design of the polysulfamide backbone. We developed a coarse-grained (CG) polysulfamide model that captures the directionality of H-bonds between the sulfamide groups and used this model in molecular dynamics (MD) simulations to study the self-assembly of these polymers in implicit solvent. The CGMD approach was validated by reproducing experimentally observed trends in the extent of crystallinity for three polysulfamides synthesized with aliphatic and/or aromatic repeating units. After validation of our CGMD approach, we computationally predicted the effect of repeat unit bulkiness, length, and uniformity of segment lengths in the polymers on the extent of orientational and positional order among the self-assembled polysulfamide chains, providing key design principles for tuning the extent of crystallinity in polysulfamides in experiments. Those computational predictions were then experimentally tested through the synthesis and characterization of polysulfamide architectures.

Quantification of macromolecule crowding at single-molecule level

Macromolecule crowding has a prominent impact on a series of biochemical processes in the cell. It is also expected to promote macromolecular complexation induced by excluded volume effects, which conflicts with recent advances in the thermodynamic interaction between inert, synthetic polymers, and nucleic acids. Along this line, a method combining high-resolution magnetic tweezers and extended crowder-oxDNA model was applied to resolve these discrepancies by systematically studying the kinetics and thermodynamics of the folding-unfolding transition for an individual DNA hairpin in a crowded environment. More specifically, from the magnetic tweezers-based experiments, the linear dependence of the critical force of the DNA hairpin on the polyethylene glycol (PEG) concentration was demonstrated, which is consistent with the results based on the crowder-oxDNA model in which the Lennard-Jones potential was adopted to express the interaction between the crowders and the DNA hairpin. These consistencies highlight that the excluded volume effects are mainly responsible for the interaction between PEG and the DNA hairpin, which is different from the interaction between dextran and the DNA hairpin. In the meantime, the dependence of the folding rate on the molecule weight of PEG, which was different from fluorescence resonance energy transfer-based results, was identified. The proposed method opens a path to detect the interaction between an inert, synthetic molecule, and the DNA hairpin, which is important to accurately mimic the cytosolic environments using mixtures of different inert molecules.

Toward a Molecular Mechanism of Complementary RNA Duplexes Denaturation

RNA duplexes are relatively rare but play very important biological roles. As an end-product of template-based RNA replication, they also have key implications for hypothetical primitive forms of life. Unless they are specifically separated by enzymes, these duplexes denature upon a temperature increase. However, mechanistic and kinetic aspects of RNA (and DNA) duplex thermal denaturation remain unclear at the microscopic level. We propose an in silico strategy that probes the thermal denaturation of RNA duplexes and allows for an extensive conformational space exploration along a wide temperature range with atomistic precision. We show that this approach first accounts for the strong sequence and length dependence of the duplexes melting temperature, reproducing the trends seen in the experiments and predicted by nearest-neighbor models. The simulations are then instrumental at providing a molecular picture of the temperature-induced strand separation. The textbook canonical "all-or-nothing" two-state model, very much inspired by the protein folding mechanism, can be nuanced. We demonstrate that a temperature increase leads to significantly distorted but stable structures with extensive base-fraying at the extremities, and that the fully formed duplexes typically do not form around melting. The duplex separation therefore appears as much more gradual than commonly thought.

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

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

A coarse-grained DNA model to study protein-DNA interactions and liquid-liquid phase separation

Recent advances in coarse-grained (CG) computational models for DNA have enabled molecular-level insights into the behavior of DNA in complex multiscale systems. However, most existing CG DNA models are not compatible with CG protein models, limiting their applications for emerging topics such as protein-nucleic acid assemblies. Here, we present a new computationally efficient CG DNA model. We first use experimental data to establish the model's ability to predict various aspects of DNA behavior, including melting thermodynamics and relevant local structural properties such as the major and minor grooves. We then employ an all-atom hydropathy scale to define non-bonded interactions between protein and DNA sites, to make our DNA model compatible with an existing CG protein model (HPS-Urry), that is extensively used to study protein phase separation, and show that our new model reasonably reproduces the experimental binding affinity for a prototypical protein-DNA system. To further demonstrate the capabilities of this new model, we simulate a full nucleosome with and without histone tails, on a microsecond timescale, generating conformational ensembles and provide molecular insights into the role of histone tails in influencing the liquid-liquid phase separation (LLPS) of HP1α proteins. We find that histone tails interact favorably with DNA, influencing the conformational ensemble of the DNA and antagonizing the contacts between HP1α and DNA, thus affecting the ability of DNA to promote LLPS of HP1α. These findings shed light on the complex molecular framework that fine-tunes the phase transition properties of heterochromatin proteins and contributes to heterochromatin regulation and function. Overall, the CG DNA model presented here is suitable to facilitate micron-scale studies with sub-nm resolution in many biological and engineering applications and can be used to investigate protein-DNA complexes, such as nucleosomes, or LLPS of proteins with DNA, enabling a mechanistic understanding of how molecular information may be propagated at the genome level.

Anomalous Diffusion of Polyelectrolyte Segments on Supported Charged Lipid Bilayers

This work provides mesoscale models for the anomalous diffusion of a polymer chain on a heterogeneous surface with rearranging randomly distributed adsorption sites. Both the "bead-spring" model and oxDNA model were simulated on supported lipid bilayer membranes with various molar fractions of charged lipids, using Brownian dynamics method. Our simulation results demonstrate that "bead-spring" chains exhibit sub-diffusion on charged lipid bilayers which agrees with previous experimental observations for short-time dynamics of DNA segments on membranes. In addition, the non-Gaussian diffusive behaviors of DNA segments have not been observed in our simulations. However, a simulated 17 base pairs double stranded DNA, using oxDNA model, performs normal diffusion on supported cationic lipid bilayers. Due to the number of positively charged lipids attracted by short DNA is small, the energy landscape that the short DNA experiences during diffusion is not as heterogeneous as that experienced by long DNA chains, which results in normal diffusion rather than sub-diffusion for short DNA.

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

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

Thermally reversible pattern formation in arrays of molecular rotors

Control over the mesoscale to microscale patterning of materials is of great interest to the soft matter community. Inspired by DNA origami rotors, we introduce a 2D nearest-neighbor lattice of spinning rotors that exhibit discrete orientational states and interactions with their neighbors. Monte Carlo simulations of rotor lattices reveal that they exhibit a variety of interesting ordering behaviors and morphologies that can be modulated through rotor design parameters. The rotor arrays exhibit diverse patterns including closed loops, radiating loops, and bricklayer structures in their ordered states. They exhibit specific heat peaks at very low temperatures for small system sizes, and some systems exhibit multiple order-disorder transitions depending on inter-rotor interaction design. We devise an energy-based order parameter and show via umbrella sampling and histogram reweighting that this order parameter captures well the order-disorder transitions occurring in these systems. We fabricate real DNA origami rotors which themselves can order via programmable DNA base-pairing interactions and demonstrate both ordered and disordered phases, illustrating how rotor lattices may be realized experimentally and used for responsive organization. This work establishes the feasibility of realizing structural nanomaterials that exhibit locally mediated microscale patterns which could have applications in sensing and precision surface patterning.

Stability of DNA and RNA hairpins: a comparative study based on ox-DNA

Advances in single-molecule experiments on macromolecular crowding urgently need an efficient simulation method to resolve their discrepancies quantitatively. Ox-DNA model has been since reworked to treat the thermodynamics and mechanical properties of DNA/RNA hairpin at a stretching force. In hopping experiments, the critical forces of RNA hairpins at different temperatures are greater than those of DNA hairpins, in addition, the Gibbs free energy at a fixed temperature required to convert an RNA hairpin into a single-stranded molecule at zero force is obviously greater than that of DNA hairpin and gradually decreases by increasing the temperature. As far as force-ramping experiments are concerned, the first-rupture forces of RNA/DNA hairpins corresponding to the maximum probability density linearly pertain to the force-loading rate, with those of RNA hairpins being greater. The extended ox-DNA model could potentially identify the interaction between biologically inert polymer and RNA/DNA hairpins in crowded environments.

Designing the Self-Assembly of Arbitrary Shapes Using Minimal Complexity Building Blocks

The design space for self-assembled multicomponent objects ranges from a solution in which every building block is unique to one with the minimum number of distinct building blocks that unambiguously define the target structure. We develop a pipeline to explore the design spaces for a set of structures of various sizes and complexities. To understand the implications of the different solutions, we analyze their assembly dynamics using patchy particle simulations and study the influence of the number of distinct building blocks, and the angular and spatial tolerances on their interactions, on the kinetics and yield of the target assembly. We show that the resource-saving solution with a minimum number of distinct blocks can often assemble just as well (or faster) than designs where each building block is unique. We further use our methods to design multifarious structures, where building blocks are shared between different target structures. Finally, we use coarse-grained DNA simulations to investigate the realization of multicomponent shapes using DNA nanostructures as building blocks.

Programming rigidity into size-defined wireframe DNA nanotubes

Nanotubes built from DNA hold promise for several biological and materials applications, due to their high aspect ratio and encapsulation potential. A particularly appealing goal is to control the size, shape, and dynamic behaviour of DNA nanotubes with minimal design alteration, as nanostructures of varying morphologies and lengths have been shown to exhibit distinct cellular uptake, encapsulation behaviour, and in vivo biodistribution. Herein, we report a systematic investigation, combining experimental and computational design, to modulate the length, flexibility, and longitudinal patterns of wireframe DNA nanotubes. Subtle design changes govern the structure and properties of our nanotubes, which are built from a custom-made, long, and size-defined template strand to which DNA rungs and linkers are attached. Unlike DNA origami, these custom-made strands possess regions with repeating sequences at strategic locations, thereby reducing the number of strands necessary for assembly. Through strand displacement, the nanotubes can be reversibly altered between extended and collapsed morphologies. These design concepts enable fine-tuning of the nanotube stiffness and may pave the way for the development of designer nanotubes for a variety of applications, including the study of cellular internalization, biodistribution, and uptake mechanisms for structures of varied shapes and sizes.

Mechanistic insight into the structure, thermodynamics and dynamics of equilibrium gels of multi-armed DNA nanostars

The unique sequence specificity rule of DNA makes it an ideal molecular building block for constructing periodic arrays and devices with nanoscale accuracy and precision. Here, we present the self-assembly of DNA nanostars having three, four and five arms into a gel phase using a simplistic coarse-grained bead-spring model developed by Z. Xing, C. Ness, D. Frenkel and E. Eiser (Macromolecules, 2019, 52, 504-512). Our simulations show that the DNA nanostars form a thermodynamically stable fully bonded gel phase from an unstructured liquid phase with the lowering of temperature. We characterize the phase transition by calculating several structural features such as the radial distribution function and structure factor. The thermodynamics of gelation is quantified by the potential energy and translational pair-entropy of the system. The phase transition from an arrested gel phase to an unstructured liquid phase has been modelled using a two-state theoretical model. We find that this transition is enthalpy driven, and loss of configuration and translational entropy is counterpoised by enthalpic interaction of the DNA sticky-ends, which gives rise to a gel phase at low temperature. The absolute rotational and translational entropy of the systems, measured using a two-phase thermodynamic model, also substantiates the gel transition. The slowing down of the dynamics upon approaching the transition temperature from a high temperature demonstrates the phase transition to a gel phase. A detailed numerical simulation study of the morphology, dynamics and thermodynamics of DNA gelation can provide guidance for future experiments, is easily extensible to other polymeric systems, and is expected to help in understanding the physics of self-assembly.

Predicting DNA kinetics with a truncated continuous-time Markov chain method

Predicting the kinetics of reactions involving nucleic acid strands is a fundamental task in biology and biotechnology. Reaction kinetics can be modeled as an elementary step continuous-time Markov chain, where states correspond to secondary structures and transitions correspond to base pair formation and breakage. Since the number of states in the Markov chain could be large, rates are determined by estimating the mean first passage time from sampled trajectories. As a result, the cost of kinetic predictions becomes prohibitively expensive for rare events with extremely long trajectories. Also problematic are scenarios where multiple predictions are needed for the same reaction, e.g., under different environmental conditions, or when calibrating model parameters, because a new set of trajectories is needed multiple times. We propose a new method, called pathway elaboration, to handle these scenarios. Pathway elaboration builds a truncated continuous-time Markov chain through both biased and unbiased sampling. The resulting Markov chain has moderate state space size, so matrix methods can efficiently compute reaction rates, even for rare events. Also the transition rates of the truncated Markov chain can easily be adapted when model or environmental parameters are perturbed, making model calibration feasible. We illustrate the utility of pathway elaboration on toehold-mediated strand displacement reactions, show that it well-approximates trajectory-based predictions of unbiased elementary step models on a wide range of reaction types for which such predictions are feasible, and demonstrate that it performs better than alternative truncation-based approaches that are applicable for mean first passage time estimation. Finally, in a small study, we use pathway elaboration to optimize the Metropolis kinetic model of Multistrand, an elementary step simulator, showing that the optimized parameters greatly improve reaction rate predictions. Our framework and dataset are available at https://github.com/DNA-and-Natural-Algorithms-Group/PathwayElaboration.

Interplay of the mechanical and structural properties of DNA nanostructures determines their electrostatic interactions with lipid membranes

Nucleic acids and lipids function in close proximity in biological processes, as well as in nanoengineered constructs for therapeutic applications. As both molecules carry a rich charge profile, and frequently coexist in complex ionic solutions, the electrostatics surely play a pivotal role in interactions between them. Here we discuss how each component of a DNA/ion/lipid system determines its electrostatic attachment. We examine membrane binding of a library of DNA molecules varying from nanoengineered DNA origami through plasmids to short DNA domains, demonstrating the interplay between the molecular structure of the nucleic acid and the phase of lipid bilayers. Furthermore, the magnitude of DNA/lipid interactions is tuned by varying the concentration of magnesium ions in the physiologically relevant range. Notably, we observe that the structural and mechanical properties of DNA are critical in determining its attachment to lipid bilayers and demonstrate that binding is correlated positively with the size, and negatively with the flexibility of the nucleic acid. The findings are utilized in a proof-of-concept comparison of membrane interactions of two DNA origami designs - potential nanotherapeutic platforms - showing how the results can have a direct impact on the choice of DNA geometry for biotechnological applications.

Toehold-Mediated Strand Displacement in Random Sequence Pools

Toehold-mediated strand displacement (TMSD) has been used extensively for molecular sensing and computing in DNA-based molecular circuits. As these circuits grow in complexity, sequence similarity between components can lead to cross-talk, causing leak, altered kinetics, or even circuit failure. For small non-biological circuits, such unwanted interactions can be designed against. In environments containing a huge number of sequences, taking all possible interactions into account becomes infeasible. Therefore, a general understanding of the impact of sequence backgrounds on TMSD reactions is of great interest. Here, we investigate the impact of random DNA sequences on TMSD circuits. We begin by studying individual interfering strands and use the obtained data to build machine learning models that estimate kinetics. We then investigate the influence of pools of random strands and find that the kinetics are determined by only a small subpopulation of strongly interacting strands. Consequently, their behavior can be mimicked by a small collection of such strands. The equilibration of the circuit with the background sequences strongly influences this behavior, leading to up to 1 order of magnitude difference in reaction speed. Finally, we compare two established and one novel technique that speed up TMSD reactions in random sequence pools: a three-letter alphabet, protection of toeholds by intramolecular secondary structure, or by an additional blocking strand. While all of these techniques were useful, only the latter can be used without sequence constraints. We expect that our insights will be useful for the construction of TMSD circuits that are robust to molecular noise.

The oxDNA Coarse-Grained Model as a Tool to Simulate DNA Origami

This chapter introduces how to run molecular dynamics simulations for DNA origami using the oxDNA coarse-grained model.

The wending rhombus: Self-assembling 3D DNA crystals

In this perspective, we provide a summary of recent developments in self-assembling three-dimensional (3D) DNA crystals. Starting from the inception of this subfield, we describe the various advancements in structure that have led to an increase in the diversity of macromolecular crystal motifs formed through self-assembly, and we further comment on the future directions of the field, which exploit noncanonical base pairing interactions beyond Watson-Crick. We then survey the current applications of self-assembling 3D DNA crystals in reversibly active nanodevices and materials engineering and provide an outlook on the direction researchers are taking these structures. Finally, we compare 3D DNA crystals with DNA origami and suggest how these distinct subfields might work together to enhance biomolecule structure solution, nanotechnological motifs, and their applications.

Energy landscapes of rotary DNA origami devices determined by fluorescence particle tracking

Biomolecular nanomechanical devices are of great interest as tools for the processing and manipulation of molecules, thereby mimicking the function of nature's enzymes. DNA nanotechnology provides the capability to build molecular analogs of mechanical machine elements such as joints and hinges via sequence-programmable self-assembly, which are otherwise known from traditional mechanical engineering. Relative to their size, these molecular machine elements typically do not reach the same relative precision and reproducibility that we know from their macroscopic counterparts; however, as they are scaled down to molecular sizes, physical effects typically not considered by mechanical engineers such as Brownian motion, intramolecular forces, and the molecular roughness of the devices begin to dominate their behavior. In order to investigate the effect of different design choices on the roughness of the mechanical energy landscapes of DNA nanodevices in greater detail, we here study an exemplary DNA origami-based structure, a modularly designed rotor-stator arrangement, which resembles a rotatable nanorobotic arm. Using fluorescence tracking microscopy, we follow the motion of individual rotors and record their corresponding energy landscapes. We then utilize the modular construction of the device to exchange its constituent parts individually and systematically test the effect of different design variants on the movement patterns. This allows us to identify the design parameters that most strongly affect the shape of the energy landscapes of the systems. Taking into account these insights, we are able to create devices with significantly flatter energy landscapes, which translates to mechanical nanodevices with improved performance and behaviors more closely resembling those of their macroscopic counterparts.

Vivern-A Virtual Environment for Multiscale Visualization and Modeling of DNA Nanostructures

DNA nanostructures offer promising applications, particularly in the biomedical domain, as they can be used for targeted drug delivery, construction of nanorobots, or as a basis for molecular motors. One of the most prominent techniques for assembling these structures is DNA origami. Nowadays, desktop applications are used for the in silico design of such structures. However, as such structures are often spatially complex, their assembly and analysis are complicated. Since virtual reality (VR) was proven to be advantageous for such spatial-related tasks and there are no existing VR solutions focused on this domain, we propose Vivern, a VR application that allows domain experts to design and visually examine DNA origami nanostructures. Our approach presents different abstracted visual representations of the nanostructures, various color schemes, and an ability to place several DNA nanostructures and proteins in one environment, thus allowing for the detailed analysis of complex assemblies. We also present two novel examination tools, the Magic Scale Lens and the DNA Untwister, that allow the experts to visually embed different representations into local regions to preserve the context and support detailed investigation. To showcase the capabilities of our solution, prototypes of novel nanodevices conceptualized by our collaborating experts, such as DNA-protein hybrid structures and DNA origami superstructures, are presented. Finally, the results of two rounds of evaluations are summarized. They demonstrate the advantages of our solution, especially for scenarios where current desktop tools are very limited, while also presenting possible future research directions.

A bistable and reconfigurable molecular system with encodable bonds

Molecular systems with ability to controllably transform between different conformations play pivotal roles in regulating biochemical functions. Here, we report the design of a bistable DNA origami four-way junction (DOJ) molecular system that adopts two distinct stable conformations with controllable reconfigurability by using conformation-controlled base stacking. Exquisite control over DOJ's conformation and transformation is realized by programming the stacking bonds (quasi-blunt-ends) within the junction to induce prescribed coaxial stacking of neighboring junction arms. A specific DOJ conformation may be achieved by encoding the stacking bonds with binary stacking sequences based on thermodynamic calculations. Dynamic transformations of DOJ between various conformations are achieved by using specific environmental and molecular stimulations to reprogram the stacking codes. This work provides a useful platform for constructing self-assembled DNA nanostructures and nanomachines and insights for future design of artificial molecular systems with increasing complexity and reconfigurability.

Mechanical deformation behaviors and structural properties of ligated DNA crystals

DNA self-assembly has emerged as a powerful strategy for constructing complex nanostructures. While the mechanics of individual DNA strands have been studied extensively, the deformation behaviors and structural properties of self-assembled architectures are not well understood. This is partly due to the small dimensions and limited experimental methods available. DNA crystals are macroscopic crystalline structures assembled from nanoscale motifs via sticky-end association. The large DNA constructs may thus be an ideal platform to study structural mechanics. Here, we investigate the fundamental mechanical properties and behaviors of ligated DNA crystals made of tensegrity triangular motifs. We perform coarse-grained molecular dynamics simulations and confirm the results with nanoindentation experiments using atomic force microscopy. We observe various deformation modes, including untension, linear elasticity, duplex dissociation, and single-stranded component stretch. We find that the mechanical properties of a DNA architecture are correlated with those of its components. However, the structure shows complex behaviors which may not be predicted by components alone and the architectural design must be considered.

An overview of structural approaches to study therapeutic RNAs

RNAs provide considerable opportunities as therapeutic agent to expand the plethora of classical therapeutic targets, from extracellular and surface proteins to intracellular nucleic acids and its regulators, in a wide range of diseases. RNA versatility can be exploited to recognize cell types, perform cell therapy, and develop new vaccine classes. Therapeutic RNAs (aptamers, antisense nucleotides, siRNA, miRNA, mRNA and CRISPR-Cas9) can modulate or induce protein expression, inhibit molecular interactions, achieve genome editing as well as exon-skipping. A common RNA thread, which makes it very promising for therapeutic applications, is its structure, flexibility, and binding specificity. Moreover, RNA displays peculiar structural plasticity compared to proteins as well as to DNA. Here we summarize the recent advances and applications of therapeutic RNAs, and the experimental and computational methods to analyze their structure, by biophysical techniques (liquid-state NMR, scattering, reactivity, and computational simulations), with a focus on dynamic and flexibility aspects and to binding analysis. This will provide insights on the currently available RNA therapeutic applications and on the best techniques to evaluate its dynamics and reactivity.

Algorithmic Design of 3D Wireframe RNA Polyhedra

We address the problem of de novo design and synthesis of nucleic acid nanostructures, a challenge that has been considered in the area of DNA nanotechnology since the 1980s and more recently in the area of RNA nanotechnology. Toward this goal, we introduce a general algorithmic design process and software pipeline for rendering 3D wireframe polyhedral nanostructures in single-stranded RNA. To initiate the pipeline, the user creates a model of the desired polyhedron using standard 3D graphic design software. As its output, the pipeline produces an RNA nucleotide sequence whose corresponding RNA primary structure can be transcribed from a DNA template and folded in the laboratory. As case examples, we design and characterize experimentally three 3D RNA nanostructures: a tetrahedron, a triangular bipyramid, and a triangular prism. The design software is openly available and also provides an export of the targeted 3D structure into the oxDNA molecular dynamics simulator for easy simulation and visualization.

A simple solution to the problem of self-assembling cubic diamond crystals

The self-assembly of colloidal diamond (CD) crystals is considered as one of the most coveted goals of nanotechnology, both from the technological and fundamental points of view. For applications, colloidal diamond is a photonic crystal which can open new possibilities of manipulating light for information processing. From a fundamental point of view, its unique symmetry exacerbates a series of problems that are commonly faced during the self-assembly of target structures, such as the presence of kinetic traps and the formation of crystalline defects and alternative structures (polymorphs). Here we demonstrate that all these problems can be systematically addressed via SAT-assembly, a design framework that converts self-assembly into a Boolean satisfiability problem (SAT). Contrary to previous solutions (requiring four or more components), we prove that the assembly of the CD crystal only requires a binary mixture. Moreover, we use molecular dynamics simulations of a system composed by nearly a million nucleotides to test a DNA nanotechnology design that constitutes a promising candidate for experimental realization.

Coarse-Grained Simulations for the Characterization and Optimization of Hybrid Protein-DNA Nanostructures

We present here the combination of experimental and computational modeling tools for the design and characterization of protein-DNA hybrid nanostructures. Our work incorporates several features in the design of these nanostructures: (1) modeling of the protein-DNA linker identity and length; (2) optimizing the design of protein-DNA cages to account for mechanical stresses; (3) probing the incorporation efficiency of protein-DNA conjugates into DNA nanostructures. The modeling tools were experimentally validated using structural characterization methods like cryo-TEM and AFM. Our method can be used for fitting low-resolution electron density maps when structural insights cannot be deciphered from experiments, as well as enable in-silico validation of nanostructured systems before their experimental realization. These tools will facilitate the design of complex hybrid protein-DNA nanostructures that seamlessly integrate the two different biomolecules.

Leakless end-to-end transport of small molecules through micron-length DNA nanochannels

Designed and engineered protein and DNA nanopores can be used to sense and characterize single molecules and control transmembrane transport of molecular species. However, designed biomolecular pores are less than 100 nm in length and are used primarily for transport across lipid membranes. Nanochannels that span longer distances could be used as conduits for molecules between nonadjacent compartments or cells. Here, we design micrometer-long, 7-nm-diameter DNA nanochannels that small molecules can traverse according to the laws of continuum diffusion. Binding DNA origami caps to channel ends eliminates transport and demonstrates that molecules diffuse from one channel end to the other rather than permeating through channel walls. These micrometer-length nanochannels can also grow, form interconnects, and interface with living cells. This work thus shows how to construct multifunctional, dynamic agents that control molecular transport, opening ways of studying intercellular signaling and modulating molecular transport between synthetic and living cells.

Mutual effects between single-stranded DNA conformation and Na+-Mg2+ ion competition in mixed salt solutions

The ion-dependence of single-stranded DNA (ssDNA) conformational changes has attracted growing attention because of its biological and technological importance. Although single-species ion effects have been extensively explored, it is challenging to study the ssDNA conformational properties under mixed monovalent/divalent ion conditions due to the complications of ssDNA flexibility and ion-ion competition. In this study, we apply Langevin dynamics simulations to investigate mixed Na⁺/Mg²⁺ ion-dependent ssDNA conformations. The ssDNA structure is described using a coarse-grained model, in which the phosphate, base, and sugar of each nucleotide are represented by three different beads. A novel improvement in our simulation model is that mixed-salt-related electrostatic interactions are computed via combining Manning counterion condensation (MCC) theory with the Monte Carlo tightly bound ion (MCTBI) model. Based on this MCC-MCTBI combination, we report new empirical functions to describe the ion-concentration-dependent and ssDNA conformation/structure-dependent electrostatic effects. The calculation results relating to the ion binding properties and the simulation results relating to the ssDNA conformational properties are validated against experimental results. In addition, our simulation results suggest a quantitative relationship between the ssDNA conformation and Na⁺-Mg²⁺ competition; this in turn reveals their mutual impact in the ion atmosphere.

Selective Integrin α5β1 Targeting through Spatially Constrained Multivalent DNA-Based Nanoparticles

Targeting cells specifically based on receptor expression levels remains an area of active research to date. Selective binding of receptors cannot be achieved by increasing the individual binding strength, as this does not account for differing distributions of receptor density across healthy and diseased cells. Engaging receptors above a threshold concentration would be desirable in devising selective diagnostics. Integrins are prime target candidates as they are readily available on the cell surface and have been reported to be overexpressed in diseases. Insights into their spatial organization would therefore be advantageous to design selective targeting agents. Here, we investigated the effect of activation method on integrin α₅β₁ clustering by immunofluorescence and modeled the global neighbor distances with input from an immuno-staining assay and image processing of microscopy images. This data was used to engineer spatially-controlled DNA-scaffolded bivalent ligands, which we used to compare trends in spatial-selective binding observed across HUVEC, CHO and HeLa in resting versus activated conditions in confocal microscopy images. For HUVEC and CHO, the data demonstrated an improved selectivity and localisation of binding for smaller spacings ~7 nm and ~24 nm, in good agreement with the model. A deviation from the mode predictions for HeLa was observed, indicative of a clustered, instead of homogeneous, integrin organization. Our findings demonstrate how low-technology imaging methods can guide the design of spatially controlled ligands to selectively differentiate between cell type and integrin activation state.

Tuning curved DNA origami structures through mechanical design and chemical adducts

The bending and twisting of DNA origami structures are important features for controlling the physical properties of DNA nanodevices. It has not been fully explored yet how to finely tune the bending and twisting of curved DNA structures. Traditional tuning of the curved DNA structures was limited to controlling the in-plane-bending angle through varying the numbers of base pairs of deletions and insertions. Here, we developed two tuning strategies of curved DNA origami structures fromin silicoandin vitroaspects.In silico, the out-of-plane bending and twisting angles of curved structures were introduced, and were tuned through varying the patterns of base pair deletions and insertions.In vitro, a chemical adduct (ethidium bromide) was applied to dynamically tune a curved spiral. The 3D structural conformations, like chirality, of the curved DNA structures were finely tuned through these two strategies. The simulation and TEM results demonstrated that the patterns of base pair insertions and deletions and chemical adducts could effectively tune the bending and twisting of curved DNA origami structures. These strategies expand the programmable accuracy of curved DNA origami structures and have potential in building efficient dynamic functional nanodevices.