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DNA-coated colloids can crystallize into a multitude of lattices, ranging from face-centered cubic to diamond, opening avenues to producing structures with useful photonic properties. The potential design space of DNA-coated colloids is large, but its exploration is hampered by a reliance on chemically modified DNA that is slow and expensive to commercially synthesize. Here we introduce a method to controllably tailor the sequences of DNA-coated particles by covalently appending new sequence domains onto the DNA grafted to colloidal particles. The tailored particles crystallize as readily and at the same temperature as those produced via direct chemical synthesis, making them suitable for self-assembly. Moreover, we show that particles coated with a single sequence can be converted into a variety of building blocks with differing specificities by appending different DNA sequences to them. This method will make it practical to identify optimal and complex particle sequence designs and paves the way to programming the assembly kinetics of DNA-coated colloids. 

Photonic crystals—a class of materials whose optical properties derive from their structure in addition to their composition—can be created by self-assembling particles whose sizes are comparable to the wavelengths of visible light. Proof-of-principle studies have shown that DNA can be used to guide the self-assembly of micrometer-sized colloidal particles into fully programmable crystal structures with photonic properties in the visible spectrum. However, the extremely temperature-sensitive kinetics of micrometer-sized DNA-functionalized particles has frustrated attempts to grow large, monodisperse crystals that are required for photonic metamaterial applications. Here we describe a robust two-step protocol for self-assembling single-domain crystals that contain millions of optical-scale DNA-functionalized particles: Monodisperse crystals are initially assembled in monodisperse droplets made by microfluidics, after which they are grown to macroscopic dimensions via seeded diffusion-limited growth. We demonstrate the generality of our approach by assembling different macroscopic single-domain photonic crystals with metamaterial properties, like structural coloration, that depend on the underlying crystal structure. By circumventing the fundamental kinetic traps intrinsic to crystallization of optical-scale DNA-coated colloids, we eliminate a key barrier to engineering photonic devices from DNA-programmed materials.

 

In contrast to most self-assembling synthetic materials, which undergo unbounded growth, many biological self-assembly processes are self-limited. That is, the assembled structures have one or more finite dimensions that are much larger than the size scale of the individual monomers. In many such cases, the finite dimension is selected by a preferred curvature of the monomers, which leads to self-closure of the assembly. In this article, we study an example class of self-closing assemblies: cylindrical tubules that assemble from triangular monomers. By combining kinetic Monte Carlo simulations, free energy calculations, and simple theoretical models, we show that a range of programmable size scales can be targeted by controlling the intricate balance between the preferred curvature of the monomers and their interaction strengths. However, their assembly is kinetically controlled—the tubule morphology is essentially fixed shortly after closure, resulting in a distribution of tubule widths that is significantly broader than the equilibrium distribution. We develop a simple kinetic model based on this observation and the underlying free-energy landscape of assembling tubules that quantitatively describes the distributions. Our results are consistent with recent experimental observations of tubule assembly from triangular DNA origami monomers. The modeling framework elucidates design principles for assembling self-limited structures from synthetic components, such as artificial microtubules that have a desired width and chirality. 

Self-assembly is one of the most promising strategies for making functional materials at the nanoscale, yet new design principles for making self-limiting architectures, rather than spatially unlimited periodic lattice structures, are needed. To address this challenge, we explore the tradeoffs between addressable assembly and self-closing assembly of a specific class of self-limiting structures: cylindrical tubules. We make triangular subunits using DNA origami that have specific, valence-limited interactions and designed binding angles, and we study their assembly into tubules that have a self-limited width that is much larger than the size of an individual subunit. In the simplest case, the tubules are assembled from a single component by geometrically programming the dihedral angles between neighboring subunits. We show that the tubules can reach many micrometers in length and that their average width can be prescribed through the dihedral angles. We find that there is a distribution in the width and the chirality of the tubules, which we rationalize by developing a model that considers the finite bending rigidity of the assembled structure as well as the mechanism of self-closure. Finally, we demonstrate that the distributions of tubules can be further sculpted by increasing the number of subunit species, thereby increasing the assembly complexity, and demonstrate that using two subunit species successfully reduces the number of available end states by half. These results help to shed light on the roles of assembly complexity and geometry in self-limited assembly and could be extended to other self-limiting architectures, such as shells, toroids, or triply periodic frameworks. 

DNA-coated colloids can self-assemble into an incredible diversity of crystal structures, but their applications have been limited by poor understanding and control over the crystallization dynamics. To address this challenge, we use microfluidics to quantify the kinetics of DNA-programmed self-assembly along the entire crystallization pathway, from thermally activated nucleation through reaction-limited and diffusion-limited phases of crystal growth. Our detailed measurements of the temperature and concentration dependence of the kinetics at all stages of crystallization provide a stringent test of classical theories of nucleation and growth. After accounting for the finite rolling and sliding rates of micrometer-sized DNA-coated colloids, we show that modified versions of these classical theories predict the absolute nucleation and growth rates with quantitative accuracy. We conclude by applying our model to design and demonstrate protocols for assembling large single crystals with pronounced structural coloration, an essential step in creating next-generation optical metamaterials from colloids. 

Targeted drug delivery relies on two physical processes: the selective binding of a therapeutic particle to receptors on a specific cell membrane, followed by transport of the particle across the membrane. In this article, we address some of the challenges in controlling the thermodynamics and dynamics of these two processes by combining a simple experimental system with a statistical mechanical model. Specifically, we characterize and model multivalent ligand–receptor binding between colloidal particles and fluid lipid bilayers, as well as the surface mobility of membrane-bound particles. We show that the mobility of the receptors within the fluid membrane is key to both the thermodynamics and dynamics of binding. First, we find that the particle-membrane binding free energy—or avidity—is a strongly nonlinear function of the ligand–receptor affinity. We attribute the nonlinearity to a combination of multivalency and recruitment of fluid receptors to the binding site. Our results also suggest that partial wrapping of the bound particles by the membrane enhances avidity further. Second, we demonstrate that the lateral mobility of membrane-bound particles is also strongly influenced by the recruitment of receptors. Specifically, we find that the lateral diffusion coefficient of a membrane-bound particle is dominated by the hydrodynamic drag against the aggregate of receptors within the membrane. These results provide one of the first direct validations of the working theoretical framework for multivalent interactions. They also highlight that the fluidity and elasticity of the membrane are as important as the ligand–receptor affinity in determining the binding and transport of small particles attached to membranes. 

The ability to design and synthesize ever more complicated colloidal particles opens the possibility of self-assembling a zoo of complex structures, including those with one or more self-limited length scales. An undesirable feature of systems with self-limited length scales is that thermal fluctuations can lead to the assembly of nearby, off-target states. We investigate strategies for limiting off-target assembly by using multiple types of subunits. Using simulations and energetics calculations, we explore this concept by considering the assembly of tubules built from triangular subunits that bind edge to edge. While in principle, a single type of triangle can assemble into tubules with a monodisperse width distribution, in practice, the finite bending rigidity of the binding sites leads to the formation of off-target structures. To increase the assembly specificity, we introduce tiling rules for assembling tubules from multiple species of triangles. We show that the selectivity of the target structure can be dramatically improved by using multiple species of subunits, and provide a prescription for choosing the minimum number of subunit species required for near-perfect yield. Our approach of increasing the system’s complexity to reduce the accessibility of neighboring structures should be generalizable to other systems beyond the self-assembly of tubules.