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.

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.

Simulation of reversible molecular mechanical logic gates and circuits.

Landauer's principle places a fundamental lower limit on the work required to perform a logically irreversible operation. Logically reversible gates provide a way to avoid these work costs and also simplify the task of making the computation as a whole thermodynamically reversible. The inherent reversibility of mechanical logic gates would make them good candidates for the design of practical logically reversible computing systems if not for the relatively large size and mass of such systems. In this paper we outline the design and simulation of reversible molecular mechanical logic gates that come close to the limits of thermodynamic reversibility even under the effects of thermal noise, and outline associated circuit components from which arbitrary combinatorial reversible circuits can be constructed and simulated. We demonstrate that isolated components can be operated in a thermodynamically reversible manner, and explore the complexities of combining components to implement more complex computations. Finally, we demonstrate a method to construct arbitrarily large reversible combinatorial circuits using multiple external controls and signal boosters with a working half-adder circuit.

Planar 2D wireframe DNA origami.

Two-dimensional (2D) DNA origami is widely used for applications ranging from excitonics to single-molecule biophysics. Conventional, single-layer 2D DNA origami exhibits flexibility and curvature in solution; however, that may limit its suitability as a 2D structural template. In contrast, 2D wireframe DNA origami rendered with six-helix bundle edges offers local control over duplex orientations with enhanced in-plane rigidity. Here, we investigate the 3D structure of these assemblies using cryo-electron microscopy (cryo-EM). 3D reconstructions reveal a high degree of planarity and homogeneity in solution for polygonal objects with and without internal mesh, enabling 10-Å resolution for a triangle. Coarse-grained simulations were in agreement with cryo-EM data, offering molecular structural insight into this class of 2D DNA origami. Our results suggest that these assemblies may be valuable for 2D material applications and geometries that require high structural fidelity together with local control over duplex orientations, rather than parallel duplex assembly.

Symmetry and simplicity spontaneously emerge from the algorithmic nature of evolution.

SignificanceWhy does evolution favor symmetric structures when they only represent a minute subset of all possible forms? Just as monkeys randomly typing into a computer language will preferentially produce outputs that can be generated by shorter algorithms, so the coding theorem from algorithmic information theory predicts that random mutations, when decoded by the process of development, preferentially produce phenotypes with shorter algorithmic descriptions. Since symmetric structures need less information to encode, they are much more likely to appear as potential variation. Combined with an arrival-of-the-frequent mechanism, this algorithmic bias predicts a much higher prevalence of low-complexity (high-symmetry) phenotypes than follows from natural selection alone and also explains patterns observed in protein complexes, RNA secondary structures, and a gene regulatory network.

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.

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.

Massively Parallelized Molecular Force Manipulation with On-Demand Thermal and Optical Control.

In single-molecule force spectroscopy (SMFS), a tethered molecule is stretched using a specialized instrument to study how macromolecules extend under force. One problem in SMFS is the serial and slow nature of the measurements, performed one molecule at a time. To address this long-standing challenge, we report on the origami polymer force clamp (OPFC) which enables parallelized manipulation of the mechanical forces experienced by molecules without the need for dedicated SMFS instruments or surface tethering. The OPFC positions target molecules between a rigid nanoscale DNA origami beam and a responsive polymer particle that shrinks on demand. As a proof-of-concept, we record the steady state and time-resolved mechanical unfolding dynamics of DNA hairpins using the fluorescence signal from ensembles of molecules and confirm our conclusion using modeling.

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 systems3-5. 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.

Programming patchy particles to form three-dimensional dodecagonal quasicrystals.

Model patchy particles have been shown to be able to form a wide variety of structures, including symmetric clusters, complex crystals, and even two-dimensional quasicrystals. Here, we investigate whether we can design patchy particles that form three-dimensional quasicrystals, in particular targeting a quasicrystal with dodecagonal symmetry that is made up of stacks of two-dimensional quasicrystalline layers. We obtain two designs that are able to form such a dodecagonal quasicrystal in annealing simulations. The first is a one-component system of seven-patch particles but with wide patches that allow them to adopt both seven- and eight-coordinated environments. The second is a ternary system that contains a mixture of seven- and eight-patch particles and is likely to be more realizable in experiments, for example, using DNA origami. One interesting feature of the first system is that the resulting quasicrystals very often contain a screw dislocation.

Computing the Elastic Mechanical Properties of Rodlike DNA Nanostructures.

To study the elastic properties of rodlike DNA nanostructures, we perform long simulations of these structures using the oxDNA coarse-grained model. By analyzing the fluctuations in these trajectories, we obtain estimates of the bend and twist persistence lengths and the underlying bend and twist elastic moduli and couplings between them. Only on length scales beyond those associated with the spacings between the interhelix crossovers do the bending fluctuations behave like those of a wormlike chain. The obtained bending persistence lengths are much larger than that for double-stranded DNA and increase nonlinearly with the number of helices, whereas the twist moduli increase approximately linearly. To within the numerical error in our data, the twist-bend coupling constants are of order zero. That the bending persistence lengths that we obtain are generally somewhat higher than in experiment probably reflects both that the simulated origamis have no assembly defects and that the oxDNA extensional modulus for double-stranded DNA is too large.

Self-Limiting Polymerization of DNA Origami Subunits with Strain Accumulation.

Biology demonstrates how a near infinite array of complex systems and structures at many scales can originate from the self-assembly of component parts on the nanoscale. But to fully exploit the benefits of self-assembly for nanotechnology, a crucial challenge remains: How do we rationally encode well-defined global architectures in subunits that are much smaller than their assemblies? Strain accumulation via geometric frustration is one mechanism that has been used to explain the self-assembly of global architectures in diverse and complex systems a posteriori. Here we take the next step and use strain accumulation as a rational design principle to control the length distributions of self-assembling polymers. We use the DNA origami method to design and synthesize a molecular subunit known as the PolyBrick, which perturbs its shape in response to local interactions via flexible allosteric blocking domains. These perturbations accumulate at the ends of polymers during growth, until the deformation becomes incompatible with further extension. We demonstrate that the key thermodynamic factors for controlling length distributions are the intersubunit binding free energy and the fundamental strain free energy, both which can be rationally encoded in a PolyBrick subunit. While passive polymerization yields geometrical distributions, which have the highest statistical length uncertainty for a given mean, the PolyBrick yields polymers that approach Gaussian length distributions whose variance is entirely determined by the strain free energy. We also show how strain accumulation can in principle yield length distributions that become tighter with increasing subunit affinity and approach distributions with uniform polymer lengths. Finally, coarse-grained molecular dynamics and Monte Carlo simulations delineate and quantify the dominant forces influencing strain accumulation in a molecular system. This study constitutes a fundamental investigation of the use of strain accumulation as a rational design principle in molecular self-assembly.

Measuring Internal Forces in Single-Stranded DNA: Application to a DNA Force Clamp.

We present a new method for calculating internal forces in DNA structures using coarse-grained models and demonstrate its utility with the oxDNA model. The instantaneous forces on individual nucleotides are explored and related to model potentials, and using our framework, internal forces are calculated for two simple DNA systems and for a recently published nanoscopic force clamp. Our results highlight some pitfalls associated with conventional methods for estimating internal forces, which are based on elastic polymer models, and emphasize the importance of carefully considering secondary structure and ionic conditions when modeling the elastic behavior of single-stranded DNA. Beyond its relevance to the DNA nanotechnological community, we expect our approach to be broadly applicable to calculations of internal force in a variety of structures-from DNA to protein-and across other coarse-grained simulation models.

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

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

Designer protein assemblies with tunable phase diagrams in living cells.

Protein self-organization is a hallmark of biological systems. Although the physicochemical principles governing protein-protein interactions have long been known, the principles by which such nanoscale interactions generate diverse phenotypes of mesoscale assemblies, including phase-separated compartments, remain challenging to characterize. To illuminate such principles, we create a system of two proteins designed to interact and form mesh-like assemblies. We devise a new strategy to map high-resolution phase diagrams in living cells, which provide self-assembly signatures of this system. The structural modularity of the two protein components allows straightforward modification of their molecular properties, enabling us to characterize how interaction affinity impacts the phase diagram and material state of the assemblies in vivo. The phase diagrams and their dependence on interaction affinity were captured by theory and simulations, including out-of-equilibrium effects seen in growing cells. Finally, we find that cotranslational protein binding suffices to recruit a messenger RNA to the designed micron-scale structures.

Reconfigurable T-junction DNA Origami.

DNA self-assembly allows the construction of nanometre-scale structures and devices. Structures with thousands of unique components are routinely assembled in good yield. Experimental progress has been rapid, based largely on empirical design rules. Herein, we demonstrate a DNA origami technique designed as a model system with which to explore the mechanism of assembly. The origami fold is controlled through single-stranded loops embedded in a double-stranded DNA template and is programmed by a set of double-stranded linkers that specify pairwise interactions between loop sequences. Assembly is via T-junctions formed by hybridization of single-stranded overhangs on the linkers with the loops. The sequence of loops on the template and the set of interaction rules embodied in the linkers can be reconfigured with ease. We show that a set of just two interaction rules can be used to assemble simple T-junction origami motifs and that assembly can be performed at room temperature.

Programming patchy particles to form complex periodic structures.

We introduce a scheme to design patchy particles so that a given target crystal is the global free-energy minimum at sufficiently low temperature. A key feature is a torsional component to the potential that only allows binding when particles have the correct relative orientations. In all examples studied, the target crystal structures readily assembled on annealing from a low-density fluid phase, albeit with the simpler target structures assembling more rapidly. The most complex example was a clathrate with 46 particles in its primitive unit cell. We also explored whether the structural information encoded in the particle interactions could be further reduced. For example, removing the torsional restrictions led to the assembly of an alternative crystal structure for the BC8-forming design, but the more complex clathrate design was still able to assemble because of the greater remaining specificity.

Design and synthesis of pleated DNA origami nanotubes with adjustable diameters.

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