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.

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.

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.

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.