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Self-closing assembly is prone to polymorphism due to thermally excited bending fluctuations, which permit the formation of off-target assemblies at the point of self-closure. One way to overcome this source of polymorphism is to use templated growth, a process in which assembly initiates from a precisely defined seed rather than by spontaneous nucleation. We explore this approach to quelling polymorphism in the self-closing assembly of cylindrical tubules assembled from DNA-origami subunits with user-specified inter-subunit binding angles and specific interactions. We develop two strategies to create seeds with precisely defined diameters and helicity: (1) using multicomponent assembly and (2) purifying a specific seed-type from a polymorphic mixture using gel electrophoresis and gel extraction. By tuning the seed and monomer concentrations and adjusting the assembly temperature, we determine the conditions under which tubules grow from the seed while avoiding spontaneous nucleation. We observe that templated tubules tend to follow the guidance of the seed, thereby increasing the selectivity of the target geometry. In addition, we find that by tuning the diameter of the seed, one can template the growth of monodisperse tubules over a range of target diameters, even while using a single monomer type with a single preferred local curvature. Our results demonstrate that employing precisely defined seeds to guide assembly can significantly decrease polymorphism in self-closing assembly in a controllable and economical way. 

Bottom-up self-assembly is a powerful approach to engineering at small scales. Special strategies are needed to formulate components that assemble into predetermined shapes with precise sizes. 

In equilibrium self-assembly, microscopic building blocks spontaneously self-organize into stable structures as dictated by their interaction potentials, which limits the accessible structural features to those that correspond to global minima in free energy landscapes; they are often ordered and periodic on length scales comparable to the building block size. Coupling the assembly process to an exergonic reaction drives the system out of equilibrium so that an assembly pathway can be engineered to target a specific kinetically stabilized state, which in principle opens up a vast design space with access to diverse complex structures with features on multiple length scales. However, the question of how such features might be specifically targeted remains unanswered. Here, we explore this design space using a DNA-encoded recipe consisting of multiple biomolecular reactions that dictate the time-dependent binding strength and specificity of each type of subunit in the sample independently, which makes it possible to program an assembly pathway that leads to a kinetically trapped final state. With this kinetic control, we show that the same set of building blocks can form clusters with different final structures. These structures, with tunable core-shell compositions, have feature sizes much larger than the building block size and are governed by the DNA-encoded assembly kinetics. Tuning the timing of individual biomolecular reactions using DNA-encoded recipes offers the opportunity to independently regulate how the many interactions of a large set of coassembling components evolve over time, opening up the potential of creating morphogenesis-like assembly processes involving engineered species. 

Coarsening, the growth of larger structures at the expense of smaller ones, is a fundamental process in multiphase systems. The cell cytoplasm is an example of an out-of-equilibrium multiphase system in which molecular phase-separated condensates nucleate and grow within an active fluid composed of biopolymers and energy-consuming enzymes. Here we uncover the mechanisms that govern the growth of condensates in a self-stirring active fluid. We study the coarsening of synthetic DNA-based condensates embedded within a three-dimensional reconstituted cytoskeleton composed of microtubules and molecular motors. By combining experiments and modelling, we explain the absence of self-similarity in active coarsening and the origin of the continuously varying coarsening exponents for condensates within either active or passive fluids. The coarsening dynamics are set by the statistics of binary collisions among droplets, which depend on their size-dependent motility, irrespective of their active or passive origins. We find that the scaling exponent of the collision kernel is a unifying control parameter for the coarsening and the size distribution of motile condensates. Our results expand our understanding of phase separation in far-from-equilibrium systems, with potential implications in materials science and biology. 

Abstract Modern experimental methods in programmable self-assembly make it possible to precisely design particle concentrations, shapes and interactions. However, more physical insight is needed before we can take full advantage of this vast design space to assemble nanostructures with complex form and function. Here we show how a substantial part of this design space can be quickly and comprehensively understood by identifying a class of thermodynamic constraints that act on it. These thermodynamic constraints form a high-dimensional convex polyhedron that determines which nanostructures can be assembled at high equilibrium yield and reveals limitations that govern the coexistence of structures. We validate our predictions through detailed, quantitative assembly experiments of nanoscale particles synthesized using DNA origami. Our results uncover physical relationships underpinning many-component programmable self-assembly in equilibrium and form the basis for robust inverse design, applicable to various systems from biological protein complexes to synthetic nanomachines. 

Nearly thirty years after its inception, the field of DNA-programmed colloidal self-assembly has begun to realize its initial promise. In this review, we summarize recent developments in designing effective interactions and understanding the dynamic self-assembly pathways of DNA-coated nanoparticles and microparticles, as well as how these advances have propelled tremendous progress in crystal engineering. We also highlight exciting new directions showing that new classes of subunits combining nanoparticles with DNA origami can be used to engineer novel multicomponent assemblies, including structures with self-limiting, finite sizes. We conclude by providing an outlook on how recent theoretical advances focusing on the kinetics of self-assembly could usher in new materials-design opportunities, like the possibility of retrieving multiple distinct target structures from a single suspension or accessing new classes of materials that are stabilized by energy dissipation, mimicking self-assembly in living systems. 

Programmable self-assembly has recently enabled the creation of complex structures through precise control of the interparticle interactions and the particle geometries. Targeting ever more structurally complex, dynamic, and functional assemblies necessitates going beyond the design of the structure itself, to the measurement and control of the local flexibility of the intersubunit connections and its impact on the collective mechanics of the entire assembly. In this study, we demonstrate a method to infer the mechanical properties of multisubunit assemblies using cryogenic electron microscopy (cryo-EM) and RELION’s multi-body refinement. Specifically, we analyze the fluctuations of pairs of DNA-origami subunits that self-assemble into tubules. By measuring the fluctuations of dimers using cryo-EM, we extract mechanical properties such as the bending modulus and interparticle spring constant. These properties are then applied to elastic models to predict assembly outcomes, which align well with experimental observations. This approach not only provides a deeper understanding of nanoparticle mechanics but also opens pathways to refining subunit designs to achieve precise assembly behavior. This methodology could have broader applications in the study of nanomaterials, including protein assemblies, where understanding the interplay of mechanical properties and subunit geometry is essential for controlling complex self-assembled structures. 

Biology is teeming with intricate molecular structures whose geometries are inextricably linked to their function. A prototypical example is the helical bacterial flagellum, a complex curved crystalline assembly of proteins that the bacterium uses to swim. Because synthetic analogues of these and other curved crystalline assemblies could be valuable platforms for nanotechnologies, including drug delivery and plasmonics, controllable synthesis of variable-curvature structures of diverse material systems, from fullerenes to supramolecular assemblies, has been a long-standing goal. Here, we develop and implement a design strategy to program the self-assembly of a complex spectrum of two-periodic curved crystals with variable periodicity, spatial dimension, and topology, spanning from toroids to achiral serpentine tubules to both left- and right-handed helical tubules. Notably, our design strategy exploits a kirigami-based mapping of a modular class of 2D planar tilings to 3D curved crystals that preserves the periodicity, twofold rotational symmetries, and subunit dimensions by modulating the arrangement of disclination defects. We survey the modular geometry of these curved crystals and infer the addressable interactions required to assemble them from triangular subunits. To demonstrate this design strategy in practice, we program the self-assembly of toroids, helical, and serpentine tubules from DNA origami subunits, deriving the distinct kirigami foldings of a single two-periodic planar tiling. A simulation model of the assembly pathways reveals physical considerations for programming the geometric specificity of the intersubunit angles in the curved crystal required to avoid defect-mediated misassembly. 

Nonspecific interactions between DNA-coated colloidal particles play a critical role in determining the stabilities of competing crystal polymorphs. 

We describe a modular design approach for creating versatile DNA origami subunits that can target diverse self-assembled structures. The subunit consists of a constant “core module” with variable “bond modules” and “angle modules” added to its exterior, controlling interaction specificity, strength, and structural geometry. The design features flexible joints between subunits, implemented by using single-stranded angle modules, whose mechanical properties and possible conformations are characterized by cryogenic electron microscopy and coarse-grained molecular modeling. We demonstrate the design’s versatility through the assembly of structures with different Gaussian curvature, including sheets, spherical shells, and tubes. Our findings suggest that incorporating a judicious amount of flexibility in the bonds provides error tolerance in design and fabrication while maintaining target fidelity. Furthermore, off-target assemblies potentially introduced by flexibility can be counterbalanced by increasing the number of distinct bonds. This approach enables precise targeting of specific structural binding angles across a broad range of configurations by eliminating unfavorable interactions.