A comparison between parallelization approaches in molecular dynamics simulations on GPUs

Modulating the DNA/Lipid Interface through Multivalent Hydrophobicity

Lipids and nucleic acids are two of the most abundant components of our cells, and both molecules are widely used as engineering materials for nanoparticles. Here, we present a systematic study of how hydrophobic modifications can be employed to modulate the DNA/lipid interface. Using a series of DNA anchors with increasing hydrophobicity, we quantified the capacity to immobilize double-stranded (ds) DNA to lipid membranes in the liquid phase. Contrary to electrostatic effects, hydrophobic anchors are shown to be phase-independent if sufficiently hydrophobic. For weak anchors, the overall hydrophobicity can be enhanced following the concept of multivalency. Finally, we demonstrate that structural flexibility and anchor orientation overrule the effect of multivalency, emphasizing the need for careful scaffold design if strong interfaces are desired. Together, our findings guide the design of tailored DNA/membrane interfaces, laying the groundwork for advancements in biomaterials, drug delivery vehicles, and synthetic membrane mimics for biomedical research and nanomedicine.

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/.

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.

Softness matters: effects of compression on the behavior of adsorbed microgels at interfaces

Deformable colloids and macromolecules adsorb at interfaces as they decrease the interfacial energy between the two media. The deformability, or softness, of these particles plays a pivotal role in the properties of the interface. In this study, we employ a comprehensive in situ approach, combining neutron reflectometry with molecular dynamics simulations, to thoroughly examine the profound influence of softness on the structure of microgel Langmuir monolayers under compression. Lateral compression of both hard and soft microgel particle monolayers induces substantial structural alterations, leading to an amplified protrusion of the microgels into the aqueous phase. However, a critical distinction emerges: hard microgels are pushed away from the interface, in stark contrast to the soft ones, which remain firmly anchored to it. Concurrently, on the air-exposed side of the monolayer, lateral compression induces a flattening of the surface of the hard monolayer. This phenomenon is not observed for the soft particles as the monolayer is already extremely flat even in the absence of compression. These findings significantly advance our understanding of the key role of softness on both the equilibrium phase behavior of the monolayer and its effect when soft colloids are used as stabilizers of responsive interfaces and emulsions.

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.

Auxetic polymer networks: The role of crosslinking, density, and disorder

Low-crosslinked polymer networks have recently been found to behave auxetically when subjected to small tensions, that is, their Poisson's ratio ν becomes negative. In addition, for specific state points, numerical simulations revealed that diamond-like networks reach the limit of mechanical stability, exhibiting values of ν = -1, a condition that we define as hyper-auxeticity. This behavior is interesting per se for its consequences in materials science but is also appealing for fundamental physics because the mechanical instability is accompanied by evidence of criticality. In this work, we deepen our understanding of this phenomenon by performing a large set of equilibrium and stress-strain simulations in combination with phenomenological elasticity theory. The two approaches are found to be in good agreement, confirming the above results. We also extend our investigations to disordered polymer networks and find that the hyper-auxetic behavior also holds in this case, still manifesting a similar critical-like behavior as in the diamond one. Finally, we highlight the role of the number density, which is found to be a relevant control parameter determining the elastic properties of the system. The validity of the results under disordered conditions paves the way for an experimental investigation of this phenomenon in real systems, such as hydrogels.

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.

Buckling and Interfacial Deformation of Fluorescent Poly(N-isopropylacrylamide) Microgel Capsules

Hollow microgels are fascinating model systems at the crossover between polymer vesicles, emulsions, and colloids as they deform, interpenetrate, and eventually shrink at higher volume fraction or when subjected to an external stress. Here, we introduce a system consisting of microgels with a micrometer-sized cavity enabling a straightforward characterization in situ using fluorescence microscopy techniques. Similarly to elastic capsules, these systems are found to reversibly buckle above a critical osmotic pressure, conversely to smaller hollow microgels, which were previously reported to deswell at high volume fraction. Simulations performed on monomer-resolved in silico hollow microgels confirm the buckling transition and show that the presented microgels can be described with a thin shell model theory. When brought to an interface, these microgels, that we define as microgel capsules, strongly deform and we thus propose to utilize them to locally probe interfacial properties within a theoretical framework adapted from the Johnson-Kendall-Roberts (JKR) theory. Besides their capability to sense their environment and to address fundamental questions on the elasticity and permeability of microgel systems, microgel capsules can be further envisioned as model systems mimicking anisotropic responsive biological systems such as red blood and epithelial cells thanks to the possibility offered by microgels to be synthesized with custom-designed properties.

Design strategies for the self-assembly of polyhedral shells

The control over the self-assembly of complex structures is a long-standing challenge of material science, especially at the colloidal scale, as the desired assembly pathway is often kinetically derailed by the formation of amorphous aggregates. Here, we investigate in detail the problem of the self-assembly of the three Archimedean shells with five contact points per vertex, i.e., the icosahedron, the snub cube, and the snub dodecahedron. We use patchy particles with five interaction sites (or patches) as model for the building blocks and recast the assembly problem as a Boolean satisfiability problem (SAT) for the patch-patch interactions. This allows us to find effective designs for all targets and to selectively suppress unwanted structures. By tuning the geometrical arrangement and the specific interactions of the patches, we demonstrate that lowering the symmetry of the building blocks reduces the number of competing structures, which in turn can considerably increase the yield of the target structure. These results cement SAT-assembly as an invaluable tool to solve inverse design problems.

Computer-Aided Design of A-Trail Routed Wireframe DNA Nanostructures with Square Lattice Edges

In recent years, interest in wireframe DNA origami has increased, with different designs, software, and applications emerging at a fast pace. It is now possible to design a wide variety of shapes by starting with a 2D or 3D mesh and using different scaffold routing strategies. The design choices of the edges in wireframe structures can be important in some applications and have already been shown to influence the interactions between nanostructures and cells. In this work, we increase the alternatives for the design of A-trail routed wireframe DNA structures by using four-helix bundles (4HB). Our approach is based on the incorporation of additional helices to the edges of the wireframe structure to create a 4HB on a square lattice. We first developed the software for the design of these structures, followed by a demonstration of the successful design and folding of a library of structures, and then, finally, we investigated the higher mechanical rigidity of the reinforced structures. In addition, the routing of the scaffold allows us to easily incorporate these reinforced edges together with more flexible, single helix edges, thereby allowing the user to customize the desired stiffness of the structure. We demonstrated the successful folding of this type of hybrid structure and the different stiffnesses of the different parts of the nanostructures using a combination of computational and experimental techniques.

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.

Structure and elasticity of model disordered, polydisperse, and defect-free polymer networks

The elasticity of disordered and polydisperse polymer networks is a fundamental problem of soft matter physics that is still open. Here, we self-assemble polymer networks via simulations of a mixture of bivalent and tri- or tetravalent patchy particles, which result in an exponential strand length distribution analogous to that of experimental randomly cross-linked systems. After assembly, the network connectivity and topology are frozen and the resulting system is characterized. We find that the fractal structure of the network depends on the number density at which the assembly has been carried out, but that systems with the same mean valence and same assembly density have the same structural properties. Moreover, we compute the long-time limit of the mean-squared displacement, also known as the (squared) localization length, of the cross-links and of the middle monomers of the strands, showing that the dynamics of long strands is well described by the tube model. Finally, we find a relation connecting these two localization lengths at high density and connect the cross-link localization length to the shear modulus of the system.

Probing Temperature Responsivity of Microgels and Its Interplay with a Solid Surface by Super-Resolution Microscopy and Numerical Simulations

Super-resolution microscopy has become a powerful tool to investigate the internal structure of complex colloidal and polymeric systems, such as microgels, at the nanometer scale. An interesting feature of this method is the possibility of monitoring microgel response to temperature changes in situ. However, when performing advanced microscopy experiments, interactions between the particle and the environment can be important. Often microgels are deposited on a substrate, since they have to remain still for several minutes during the experiment. This study uses direct stochastic optical reconstruction microscopy (dSTORM) and advanced coarse-grained molecular dynamics simulations to investigate how individual microgels anchored on hydrophilic and hydrophobic surfaces undergo their volume phase transition with temperature. We find that, in the presence of a hydrophilic substrate, the structure of the microgel is unperturbed and the resulting density profiles quantitatively agree with simulations performed under bulk conditions. Instead, when a hydrophobic surface is used, the microgel spreads at the interface and an interesting competition between the two hydrophobic strengths,monomer-monomer vs monomer-surface,comes into play at high temperatures. The robust agreement between experiments and simulations makes the present study a fundamental step to establish this high-resolution monitoring technique as a platform for investigating more complex systems, these being either macromolecules with peculiar internal structure or nanocomplexes where molecules of interest can be encapsulated in the microgel network and controllably released with temperature.

DNA origami tubes with reconfigurable cross-sections

Structural DNA nanotechnology has enabled the design and construction of complex nanoscale structures with precise geometry and programmable dynamic and mechanical properties. Recent efforts have led to major advances in the capacity to actuate shape changes of DNA origami devices and incorporate DNA origami into larger assemblies, which open the prospect of using DNA to design shape-morphing assemblies as components of micro-scale reconfigurable or sensing materials. Indeed, a few studies have constructed higher order assemblies with reconfigurable devices; however, these demonstrations have utilized structures with relatively simple motion, primarily hinges that open and close. To advance the shape changing capabilities of DNA origami assemblies, we developed a multi-component DNA origami 6-bar mechanism that can be reconfigured into various shapes and can be incorporated into larger assemblies while maintaining capabilities for a variety of shape transformations. We demonstrate the folding of the 6-bar mechanism into four different shapes and demonstrate multiple transitions between these shapes. We also studied the shape preferences of the 6-bar mechanism in competitive folding reactions to gain insight into the relative free energies of the shapes. Furthermore, we polymerized the 6-bar mechanism into tubes with various cross-sections, defined by the shape of the individual mechanism, and we demonstrate the ability to change the shape of the tube cross-section. This expansion of current single-device reconfiguration to higher order scales provides a foundation for nano to micron scale DNA nanotechnology applications such as biosensing or materials with tunable properties.

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.

RNA origami: design, simulation and application

Design strategies for DNA and RNA nanostructures have developed along parallel lines for the past 30 years, from small structural motifs derived from biology to large 'origami' structures with thousands to tens of thousands of bases. With the recent publication of numerous RNA origami structures and improved design methods-even permitting co-transcriptional folding of kilobase-sized structures - the RNA nanotechnolgy field is at an inflection point. Here, we review the key achievements which inspired and enabled RNA origami design and draw comparisons with the development and applications of DNA origami structures. We further present the available computational tools for the design and the simulation, which will be key to the growth of the RNA origami community. Finally, we portray the transition from RNA origami structure to function. Several functional RNA origami structures exist already, their expression in cells has been demonstrated and first applications in cell biology have already been realized. Overall, we foresee that the fast-paced RNA origami field will provide new molecular hardware for biophysics, synthetic biology and biomedicine, complementing the DNA origami toolbox.

Automated design of 3D DNA origami with non-rasterized 2D curvature

Improving the precision and function of encapsulating three-dimensional (3D) DNA nanostructures via curved geometries could have transformative impacts on areas such as molecular transport, drug delivery, and nanofabrication. However, the addition of non-rasterized curvature escalates design complexity without algorithmic regularity, and these challenges have limited the ad hoc development and usage of previously unknown shapes. In this work, we develop and automate the application of a set of previously unknown design principles that now includes a multilayer design for closed and curved DNA nanostructures to resolve past obstacles in shape selection, yield, mechanical rigidity, and accessibility. We design, analyze, and experimentally demonstrate a set of diverse 3D curved nanoarchitectures, showing planar asymmetry and examining partial multilayer designs. Our automated design tool implements a combined algorithmic and numerical approximation strategy for scaffold routing and crossover placement, which may enable wider applications of general DNA nanostructure design for nonregular or oblique shapes.

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.

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.

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.

SAT-assembly: a new approach for designing self-assembling systems

We propose a general framework for solving inverse self-assembly problems, i.e. designing interactions between elementary units such that they assemble spontaneously into a predetermined structure. Our approach uses patchy particles as building blocks, where the different units bind at specific interaction sites (the patches), and we exploit the possibility of having mixtures with several components. The interaction rules between the patches is determined by transforming the combinatorial problem into a Boolean satisfiability problem (SAT) which searches for solutions where all bonds are formed in the target structure. Additional conditions, such as the non-satisfiability of competing structures (e.g. metastable states) can be imposed, allowing to effectively design the assembly path in order to avoid kinetic traps. We demonstrate this approach by designing and numerically simulating a cubic diamond structure from four particle species that assembles without competition from other polymorphs, including the hexagonal structure.

In-situ study of the impact of temperature and architecture on the interfacial structure of microgels

The structural characterization of microgels at interfaces is fundamental to understand both their 2D phase behavior and their role as stabilizers that enable emulsions to be broken on demand. However, this characterization is usually limited by available experimental techniques, which do not allow a direct investigation at interfaces. To overcome this difficulty, here we employ neutron reflectometry, which allows us to probe the structure and responsiveness of the microgels in-situ at the air-water interface. We investigate two types of microgels with different cross-link density, thus having different softness and deformability, both below and above their volume phase transition temperature, by combining experiments with computer simulations of in silico synthesized microgels. We find that temperature only affects the portion of microgels in water, while the strongest effect of the microgels softness is observed in their ability to protrude into the air. In particular, standard microgels have an apparent contact angle of few degrees, while ultra-low cross-linked microgels form a flat polymeric layer with zero contact angle. Altogether, this study provides an in-depth microscopic description of how different microgel architectures affect their arrangements at interfaces, and will be the foundation for a better understanding of their phase behavior and assembly.

Probing the Mechanical Properties of DNA Nanostructures with Metadynamics

Molecular dynamics simulations are often used to provide feedback in the design workflow of DNA nanostructures. However, even with coarse-grained models, the convergence of distributions from unbiased simulation is slow, limiting applications to equilibrium structural properties. Given the increasing interest in dynamic, reconfigurable, and deformable devices, methods that enable efficient quantification of large ranges of motion, conformational transitions, and mechanical deformation are critically needed. Metadynamics is an automated biasing technique that enables the rapid acquisition of molecular conformational distributions by flattening free energy landscapes. Here we leveraged this approach to sample the free energy landscapes of DNA nanostructures whose unbiased dynamics are nonergodic, including bistable Holliday junctions and part of a bistable DNA origami structure. Taking a DNA origami-compliant joint as a case study, we further demonstrate that metadynamics can predict the mechanical response of a full DNA origami device to an applied force, showing good agreement with experiments. Our results exemplify the efficient computation of free energy landscapes and force response in DNA nanodevices, which could be applied for rapid feedback in iterative design workflows and generally facilitate the integration of simulation and experiments. Metadynamics will be particularly useful to guide the design of dynamic devices for nanorobotics, biosensing, or nanomanufacturing applications.

Probing the Mechanical Properties of DNA Nanostructures with Metadynamics

Molecular dynamics simulations are often used to provide feedback in the design workflow of DNA nanostructures. However, even with coarse-grained models, the convergence of distributions from unbiased simulation is slow, limiting applications to equilibrium structural properties. Given the increasing interest in dynamic, reconfigurable, and deformable devices, methods that enable efficient quantification of large ranges of motion, conformational transitions, and mechanical deformation are critically needed. Metadynamics is an automated biasing technique that enables the rapid acquisition of molecular conformational distributions by flattening free energy landscapes. Here we leveraged this approach to sample the free energy landscapes of DNA nanostructures whose unbiased dynamics are nonergodic, including bistable Holliday junctions and part of a bistable DNA origami structure. Taking a DNA origami-compliant joint as a case study, we further demonstrate that metadynamics can predict the mechanical response of a full DNA origami device to an applied force, showing good agreement with experiments. Our results exemplify the efficient computation of free energy landscapes and force response in DNA nanodevices, which could be applied for rapid feedback in iterative design workflows and generally facilitate the integration of simulation and experiments. Metadynamics will be particularly useful to guide the design of dynamic devices for nanorobotics, biosensing, or nanomanufacturing applications.

The Free-Energy Landscape of a Mechanically Bistable DNA Origami

Molecular simulations using coarse-grained models allow the structure, dynamics and mechanics of DNA origamis to be comprehensively characterized. Here, we focus on the free-energy landscape of a jointed DNA origami that has been designed to exhibit two mechanically stable states and for which a bistable landscape has been inferred from ensembles of structures visualized by electron microscopy. Surprisingly, simulations using the oxDNA model predict that the defect-free origami has a single free-energy minimum. The expected second state is not stable because the hinge joints do not simply allow free angular motion but instead lead to increasing free-energetic penalties as the joint angles relevant to the second state are approached. This raises interesting questions about the cause of this difference between simulations and experiment, such as how assembly defects might affect the ensemble of structures observed experimentally.

Design and simulation of DNA, RNA and hybrid protein-nucleic acid nanostructures with oxView

Molecular simulation has become an integral part of the DNA/RNA nanotechnology research pipeline. In particular, understanding the dynamics of structures and single-molecule events has improved the precision of nanoscaffolds and diagnostic tools. Here we present oxView, a design tool for visualization, design, editing and analysis of simulations of DNA, RNA and nucleic acid-protein nanostructures. oxView provides an accessible software platform for designing novel structures, tweaking existing designs, preparing them for simulation in the oxDNA/RNA molecular simulation engine and creating visualizations of simulation results. In several examples, we present procedures for using the tool, including its advanced features that couple the design capabilities with a coarse-grained simulation engine and scripting interface that can programmatically edit structures and facilitate design of complex structures from multiple substructures. These procedures provide a practical basis from which researchers, including experimentalists with limited computational experience, can integrate simulation and 3D visualization into their existing research programs.

OxDNA to Study Species Interactions

Molecular ecology uses molecular genetic data to answer traditional ecological questions in biogeography and biodiversity, among others. Several ecological principles, such as the niche hypothesis and the competitive exclusions, are based on the fact that species compete for resources. More in generally, it is now recognized that species interactions play a crucial role in determining the coexistence and abundance of species. However, experimentally controllable platforms, which allow us to study and measure competitions among species, are rare and difficult to implement. In this work, we suggest exploiting a Molecular Dynamics coarse-grained model to study interactions among single strands of DNA, representing individuals of different species, which compete for binding to other oligomers considered as resources. In particular, the well-established knowledge of DNA–DNA interactions at the nanoscale allows us to test the hypothesis that the maximum consecutive overlap between pairs of oligomers measure the species’ competitive advantages. However, we suggest that a more complex structure also plays a role in the ability of the species to successfully bind to the target resource oligomer. We complement the simulations with experiments on populations of DNA strands which qualitatively confirm our hypotheses. These tools constitute a promising starting point for further developments concerning the study of controlled, DNA-based, artificial ecosystems.

A localized DNA finite-state machine with temporal resolution

The identity and timing of environmental stimulus play a pivotal role in living organisms in programming their signaling networks and developing specific phenotypes. The ability to unveil history-dependent signals will advance our understanding of temporally regulated biological processes. Here, we have developed a two-input, five-state DNA finite-state machine (FSM) to sense and record the temporally ordered inputs. The spatial organization of the processing units on DNA origami enables facile modulation of the energy landscape of DNA strand displacement reactions, allowing precise control of the reactions along predefined paths for different input orders. The use of spatial constraints brings about a simple, modular design for the FSM with a minimum set of orthogonal components and confers minimized leaky reactions and fast kinetics. The FSM demonstrates the capability of sensing the temporal orders of two microRNAs, highlighting its potential for temporally resolved biosensing and smart therapeutics.

Predicting the Free-Form Shape of Structured DNA Assemblies from Their Lattice-Based Design Blueprint

Structured DNA assemblies have been designed primarily on a three-dimensional lattice because it is easy to arrange and cross-link the helices there. However, when we design free-form structures including wireframes and topologically closed circular objects on a lattice, artificially stretched bonds connecting bases are inevitably and arbitrarily formed. They often lead to nonconvergence or convergence to a wrong configuration in computational analysis to predict the equilibrium shape of the structure when started from its lattice-based configuration, which hinders the design process of free-form structures. Here, we present a computational procedure enabling the shape prediction of free-form structures from their lattice-based design blueprint without any convergence issue. It automatically partitions the structure into substructures and relocates them into a new configuration. When the analysis for calculating the equilibrium shape begins from this configuration, no convergence issue occurs because substructures and stretched bonds connecting them do not overlap and intertwine each other during analysis. Using the proposed approach, we could obtain the free-form shape of a comprehensive set of wireframe and circular structures accurately and quickly. We further demonstrated that it also facilitated a design of wireframe structures with nonstraight edges.

The interplay of supercoiling and thymine dimers in DNA

Thymine dimers are a major mutagenic photoproduct induced by UV radiation. While they have been the subject of extensive theoretical and experimental investigations, questions of how DNA supercoiling affects local defect properties, or, conversely, how the presence of such defects changes global supercoiled structure, are largely unexplored. Here, we introduce a model of thymine dimers in the oxDNA forcefield, parametrized by comparison to melting experiments and structural measurements of the thymine dimer induced bend angle. We performed extensive molecular dynamics simulations of double-stranded DNA as a function of external twist and force. Compared to undamaged DNA, the presence of a thymine dimer lowers the supercoiling densities at which plectonemes and bubbles occur. For biologically relevant supercoiling densities and forces, thymine dimers can preferentially segregate to the tips of the plectonemes, where they enhance the probability of a localized tip-bubble. This mechanism increases the probability of highly bent and denatured states at the thymine dimer site, which may facilitate repair enzyme binding. Thymine dimer-induced tip-bubbles also pin plectonemes, which may help repair enzymes to locate damage. We hypothesize that the interplay of supercoiling and local defects plays an important role for a wider set of DNA damage repair systems.

Characterizing the free-energy landscapes of DNA origamis

We show how coarse-grained modelling combined with umbrella sampling using distance-based order parameters can be applied to compute the free-energy landscapes associated with mechanical deformations of large DNA nanostructures. We illustrate this approach for the strong bending of DNA nanotubes and the potentially bistable landscape of twisted DNA origami sheets. The homogeneous bending of the DNA nanotubes is well described by the worm-like chain model; for more extreme bending the nanotubes reversibly buckle with the bending deformations localized at one or two "kinks". For a twisted one-layer DNA origami, the twist is coupled to the bending of the sheet giving rise to a free-energy landscape that has two nearly-degenerate minima that have opposite curvatures. By contrast, for a two-layer origami, the increased stiffness with respect to bending leads to a landscape with a single free-energy minimum that has a saddle-like geometry. The ability to compute such landscapes is likely to be particularly useful for DNA mechanotechnology and for understanding stress accumulation during the self-assembly of origamis into higher-order structures.

Nanobase.org: a repository for DNA and RNA nanostructures

We introduce a new online database of nucleic acid nanostructures for the field of DNA and RNA nanotechnology. The database implements an upload interface, searching and database browsing. Each deposited nanostructures includes an image of the nanostructure, design file, an optional 3D view, and additional metadata such as experimental data, protocol or literature reference. The database accepts nanostructures in any preferred format used by the uploader for the nanostructure design. We further provide a set of conversion tools that encourage design file conversion into common formats (oxDNA and PDB) that can be used for setting up simulations, interactive editing or 3D visualization. The aim of the repository is to provide to the DNA/RNA nanotechnology community a resource for sharing their designs for further reuse in other systems and also to function as an archive of the designs that have been achieved in the field so far. Nanobase.org is available at https://nanobase.org/.

Molecular Dynamics of Heterogeneous Systems on GPUs and Their Application to Nucleation in Gas Expanding to a Vacuum

Expansion of water vapor through a small orifice to a vacuum produces liquid or frozen clusters which in the experiment serve as model particles for atmospheric aerosols. Yet, there are controversies about the shape of these clusters, suggesting that the nucleation process is not fully understood. Such questions can be answered by molecular dynamics simulations; however, they require microsecond-scale runs with thousands of molecules and accurate energy conservation. The available highly parallel codes typically utilize domain decomposition and are inefficient for heterogeneous systems as clusters in a dilute gas. In this work, we present an implementation of molecular dynamics on graphics processing units based on the Verlet list and apply it to several systems for which experimental data are available. We reproduce sufficiently sized clusters but not the experimentally observed clusters of irregular shape.

Rapid prototyping of arbitrary 2D and 3D wireframe DNA origami

Wireframe DNA origami assemblies can now be programmed automatically from the top-down using simple wireframe target geometries, or meshes, in 2D and 3D, using either rigid, six-helix bundle (6HB) or more compliant, two-helix bundle (DX) edges. While these assemblies have numerous applications in nanoscale materials fabrication due to their nanoscale spatial addressability and high degree of customization, no easy-to-use graphical user interface software yet exists to deploy these algorithmic approaches within a single, standalone interface. Further, top-down sequence design of 3D DX-based objects previously enabled by DAEDALUS was limited to discrete edge lengths and uniform vertex angles, limiting the scope of objects that can be designed. Here, we introduce the open-source software package ATHENA with a graphical user interface that automatically renders single-stranded DNA scaffold routing and staple strand sequences for any target wireframe DNA origami using DX or 6HB edges, including irregular, asymmetric DX-based polyhedra with variable edge lengths and vertices demonstrated experimentally, which significantly expands the set of possible 3D DNA-based assemblies that can be designed. ATHENA also enables external editing of sequences using caDNAno, demonstrated using asymmetric nanoscale positioning of gold nanoparticles, as well as providing atomic-level models for molecular dynamics, coarse-grained dynamics with oxDNA, and other computational chemistry simulation approaches.

Effect of Internal Architecture on the Assembly of Soft Particles at Fluid Interfaces

Monolayers of soft colloidal particles confined at fluid interfaces are at the core of a broad range of technological processes, from the stabilization of responsive foams and emulsions to advanced lithographic techniques. However, establishing a fundamental relation between their internal architecture, which is controlled during synthesis, and their structural and mechanical properties upon interfacial confinement remains an elusive task. To address this open issue, which defines the monolayer's properties, we synthesize core-shell microgels, whose soft core can be chemically degraded in a controlled fashion. This strategy allows us to obtain a series of particles ranging from analogues of standard batch-synthesized microgels to completely hollow ones after total core removal. Combined experimental and numerical results show that our hollow particles have a thin and deformable shell, leading to a temperature-responsive collapse of the internal cavity and a complete flattening after adsorption at a fluid interface. Mechanical characterization shows that a critical degree of core removal is required to obtain soft disk-like particles at an oil-water interface, which present a distinct response to compression. At low packing fractions, the mechanical response of the monolayer is dominated by the outer polymer chains forming a corona surrounding the particles within the interfacial plane, regardless of the presence of a core. By contrast, at high compression, the absence of a core enables the particles to deform in the direction orthogonal to the interface and to be continuously compressed without altering the monolayer structure. These findings show how fine, single-particle architectural control during synthesis can be engineered to determine the interfacial behavior of microgels, enabling one to link particle conformation with the resulting material properties.

A Self-Regulating DNA Rotaxane Linear Actuator Driven by Chemical Energy

Nature-inspired molecular machines can exert mechanical forces by controlling and varying the distance between two molecular subunits in response to different inputs. Here, we present an automated molecular linear actuator composed of T7 RNA polymerase (T7RNAP) and a DNA [2]rotaxane. A T7 promoter region and terminator sequences are introduced into the rotaxane axle to achieve automated and iterative binding and detachment of T7RNAP in a self-controlled fashion. Transcription by T7RNAP is exploited to control the release of the macrocycle from a single-stranded (ss) region in the T7 promoter to switch back and forth from a static state (hybridized macrocycle) to a dynamic state (movable macrocycle). During transcription, the T7RNAP keeps restricting the movement range on the axle available for the interlocked macrocycle and prevents its return to the promotor region. Since this range is continuously depleted as T7RNAP moves along, a directional and active movement of the macrocycle occurs. When it reaches the transcription terminator, the polymerase detaches, and the system can reset as the macrocycle moves back to hybridize again to the ss-promoter docking site. The hybridization is required for the initiation of a new transcription cycle. The rotaxane actuator runs autonomously and repeats these self-controlled cycles of transcription and movement as long as NTP-fuel is available.

How to design an icosahedral quasicrystal through directional bonding

Icosahedral quasicrystals (IQCs) are materials that exhibit long-range order but lack periodicity in any direction. Although IQCs were the first reported quasicrystals¹, they have been experimentally observed only in metallic alloys², not in other materials. By contrast, quasicrystals with other symmetries (particularly dodecagonal) have now been found in several soft-matter systems^3-5. Here we introduce a class of IQCs built from model patchy colloids that could be realized experimentally using DNA origami particles. Our rational design strategy leads to systems that robustly assemble in simulations into a target IQC through directional bonding. This is illustrated for both body-centred and primitive IQCs, with the simplest systems involving just two particle types. The key design feature is the geometry of the interparticle interactions favouring the propagation of an icosahedral network of bonds, despite this leading to many particles not being fully bonded. As well as furnishing model systems in which to explore the fundamental physics of IQCs, our approach provides a potential route towards functional quasicrystalline materials.

Programmable site-specific functionalization of DNA origami with polynucleotide brushes

Combining surface-initiated, TdT (terminal deoxynucleotidyl transferase) catalyzed enzymatic polymerization (SI-TcEP) with precisely engineered DNA origami nanostructures (DONs) presents an innovative pathway for the generation of stable, polynucleotide brush-functionalized origami nanostructures. We demonstrate that SI-TcEP can site-specifically pattern DONs with brushes containing both natural and non-natural nucleotides. The brush functionalization can be precisely controlled in terms of the location of initiation sites on the origami core and the brush height and composition. Coarse-grained simulations predict the conformation of the brush-functionalized DONs that agree well with the experimentally observed morphologies. We find that polynucleotide brush-functionalization increases the nuclease resistance of DONs significantly, and that this stability can be spatially programmed through the site-specific growth of polynucleotide brushes. The ability to site-specifically decorate DONs with brushes of natural and non-natural nucleotides provides access to a large range of functionalized DON architectures that would allow for further supramolecular assembly, and for potential applications in smart nanoscale delivery systems.

SBMOpenMM: A Builder of Structure-Based Models for OpenMM

Molecular dynamics (MD) simulations have become a standard tool to correlate the structure and function of biomolecules and significant advances have been made in the study of proteins and their complexes. A major drawback of conventional MD simulations is the difficulty and cost of obtaining converged results, especially when exploring potential energy surfaces containing considerable energy barriers. This limits the wide use of MD calculations to determine the thermodynamic properties of biomolecular processes. Indeed, this is true when considering the conformational entropy of such processes, which is ultimately critical in assessing the simulations' convergence. Alternatively, a wide range of structure-based models (SBMs) has been used in the literature to unravel the basic mechanisms of biomolecular dynamics. These models introduce simplifications that focus on the relevant aspects of the physical process under study. Because of this, SBMs incorporate the need to modify the force field definition and parameters to target specific biophysical simulations. Here we introduce SBMOpenMM, a Python library to build force fields for SBMs, that uses the OpenMM framework to create and run SBM simulations. The code is flexible and user-friendly and profits from the high customizability and performance provided by the OpenMM platform.

OxDNA.org: a public webserver for coarse-grained simulations of DNA and RNA nanostructures

OxDNA and oxRNA are popular coarse-grained models used by the DNA/RNA nanotechnology community to prototype, analyze and rationalize designed DNA and RNA nanostructures. Here, we present oxDNA.org, a graphical web interface for running, visualizing and analyzing oxDNA and oxRNA molecular dynamics simulations on a GPU-enabled high performance computing server. OxDNA.org automatically generates simulation files, including a multi-step relaxation protocol for structures exported in non-physical states from DNA/RNA design tools. Once the simulation is complete, oxDNA.org provides an interactive visualization and analysis interface using the browser-based visualizer oxView to facilitate the understanding of simulation results for a user's specific structure. This online tool significantly lowers the entry barrier of integrating simulations in the nanostructure design pipeline for users who are not experts in the technical aspects of molecular simulation. The webserver is freely available at oxdna.org.

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

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

Coarse-grained nucleic acid-protein model for hybrid nanotechnology

The emerging field of hybrid DNA-protein nanotechnology brings with it the potential for many novel materials which combine the addressability of DNA nanotechnology with the versatility of protein interactions. However, the design and computational study of these hybrid structures is difficult due to the system sizes involved. To aid in the design and in silico analysis process, we introduce here a coarse-grained DNA/RNA-protein model that extends the oxDNA/oxRNA models of DNA/RNA with a coarse-grained model of proteins based on an anisotropic network model representation. Fully equipped with analysis scripts and visualization, our model aims to facilitate hybrid nanomaterial design towards eventual experimental realization, as well as enabling study of biological complexes. We further demonstrate its usage by simulating DNA-protein nanocage, DNA wrapped around histones, and a nascent RNA in polymerase.

Effects of Model Shape, Volume, and Softness of the Capsid for DNA Packaging of phi29

Double-stranded DNA is under extreme confinement when packed in phage phi29 with osmotic pressures approaching 60 atm and densities near liquid crystalline. The shape of the capsid determined from experiment is elongated. We consider the effects of the capsid shape and volume on the DNA distribution. We propose simple models for the capsid of phage phi29 to capture volume, shape, and wall flexibility, leading to an accurate DNA density profile. The effect of the packaging motor twisting the DNA on the resulting density distribution has been explored. We find packing motor induced twisting leads to a greater numbers of defects formed. The emergence of defects such as bubbles or large roll angles along the DNA shows a sequence dependence, and the resulting flexibility leads to an inhomogeneous distribution of defects occurring more often at TpA steps and AT-rich regions. In conjunction with capsid elongation, this has effects on the global DNA packing structures.

Accelerating the Finite-Element Method for Reaction-Diffusion Simulations on GPUs with CUDA

DNA nanotechnology offers a fine control over biochemistry by programming chemical reactions in DNA templates. Coupled to microfluidics, it has enabled DNA-based reaction-diffusion microsystems with advanced spatio-temporal dynamics such as traveling waves. The Finite Element Method (FEM) is a standard tool to simulate the physics of such systems where boundary conditions play a crucial role. However, a fine discretization in time and space is required for complex geometries (like sharp corners) and highly nonlinear chemistry. Graphical Processing Units (GPUs) are increasingly used to speed up scientific computing, but their application to accelerate simulations of reaction-diffusion in DNA nanotechnology has been little investigated. Here we study reaction-diffusion equations (a DNA-based predator-prey system) in a tortuous geometry (a maze), which was shown experimentally to generate subtle geometric effects. We solve the partial differential equations on a GPU, demonstrating a speedup of ∼100 over the same resolution on a 20 cores CPU.

Designing Patchy Interactions to Self-Assemble Arbitrary Structures

One of the fundamental goals of nanotechnology is to exploit selective and directional interactions between molecules to design particles that self-assemble into desired structures, from capsids, to nanoclusters, to fully formed crystals with target properties (e.g., optical, mechanical, etc.). Here, we provide a general framework which transforms the inverse problem of self-assembly of colloidal crystals into a Boolean satisfiability problem for which solutions can be found numerically. Given a reference structure and the desired number of components, our approach produces designs for which the target structure is an energy minimum, and also allows us to exclude solutions that correspond to competing structures. We demonstrate the effectiveness of our approach by designing model particles that spontaneously nucleate milestone structures such as the cubic diamond, the pyrochlore, and the clathrate lattices.

Structure and the role of filling rate on model dsDNA packed in a phage capsid

The conformation of DNA inside bacteriophages is of paramount importance for understanding packaging and ejection mechanisms. Models describing the structure of the confined macromolecule have depicted highly ordered conformations, such as spooled or toroidal arrangements that focus on reproducing experimental results obtained by averaging over thousands of configurations. However, it has been seen that more disordered states, including DNA kinking and the presence of domains with different DNA orientation can also accurately reproduce many of the structural experiments. In this work we have compared the results obtained through different simulated filling rates. We find a rate dependence for the resulting constrained states showing different anisotropic configurations. We present a quantitative analysis of the density distribution and the DNA orientation across the capsid showing excellent agreement with structural experiments. Second, we have analyzed the correlations within the capsid, finding evidence of the presence of domains characterized by aligned segments of DNA characterized by the structure factor. Finally, we have measured the number and distribution of DNA defects such as the emergence of bubbles and kinks as function of the filling rate. We find the slower the rate the fewer kink defects that appear and they would be unlikely at experimental filling rates with our model parameters. DNA domains of various orientation get larger with slower rates.

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

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