Designing the Self-Assembly of Arbitrary Shapes Using Minimal Complexity Building Blocks

Structural transitions of ionic microgel solutions driven by circularly polarized electric fields

In this work, a theoretical approach is developed to investigate the structural properties of ionic microgels induced by a circularly polarized (CP) electric field. Following a similar study on chain formation in the presence of linearly polarized fields [T. Colla et al., ACS Nano, 2018, 12, 4321-4337], we propose an effective potential between microgels which incorporates the field-induced interactions via a static, time averaged polarizing charge at the particle surface. In such a coarse-graining framework, the induced dipole interactions are controlled by external parameters such as the field strength and frequency, ionic strength, as well as microgel charge and concentration, thus providing a convenient route to induce different self-assembly scenarios through experimentally adjustable quantities. In contrast to the case of linearly polarized fields, dipole interactions in the case of CP light are purely repulsive in the direction perpendicular to the polarization plane, while featuring an in-plane attractive well. As a result, the CP field induces layering of planar sheets arranged perpendicularly to the field direction, in strong contrast to the chain formation observed in the case of linear polarizations. Depending on the field strength and particle concentration, in-plane crystallization can also take place. Combining molecular dynamics (MD) simulations and the liquid-state hypernetted-chain (HNC) formalism, we herein investigate the emergence of layering formation and in-plane crystal ordering as the dipole strength and microgel concentration are changed over a wide region of parameter space.

Accessing Semiaddressable Self-Assembly with Efficient Structure Enumeration

Modern experimental methods enable the creation of self-assembly building blocks with tunable interactions, but optimally exploiting this tunability for the self-assembly of desired structures remains an important challenge. Many studies of this inverse problem start with the so-called fully addressable limit, where every particle in a target structure is different. This leads to clear design principles that often result in high assembly yield, but it is not a scalable approach-at some point, one must grapple with "reusing" building blocks, which lowers the degree of addressability and may cause a multitude of off-target structures to form, complicating the design process. Here, we solve a key obstacle preventing robust inverse design in the "semiaddressable regime" by developing a highly efficient algorithm that enumerates all structures that can be formed from a given set of building blocks. By combining this with established partition-function-based yield calculations, we show that it is almost always possible to find economical semiaddressable designs where the entropic gain from reusing building blocks outweighs the presence of off-target structures and even increases the yield of the target. Thus, not only does our enumeration algorithm enable robust and scalable inverse design in the semiaddressable regime, our results demonstrate that it is possible to operate in this regime while maintaining the level of control often associated with full addressability.

Automating Blueprints for the Assembly of Colloidal Quasicrystal Clusters

One of the frontiers of nanotechnology is advancing beyond the periodic self-assembly of materials. Icosahedral quasicrystals, aperiodic in all directions, represent one of the most challenging targets that has yet to be experimentally realized at the colloidal scale. Previous attempts have required meticulous human-designed building blocks and often resulted in interactions beyond the current experimental capabilities. In this work, we introduce a framework for generating experimentally accessible designs that self-assemble into quasicrystalline arrangements. We present a design for icosahedral deoxyribonucleic acid (DNA) origami building blocks and demonstrate, through molecular simulations, their successful assembly into a target quasicrystalline structure. Our results highlight the feasibility of using automated design protocols to achieve complex quasicrystalline patterns, with applications in material science and nanotechnology.

Toward Precise Fabrication of Finite-Sized DNA Origami Superstructures

DNA origami enables the precise construction of 2D and 3D nanostructures with customizable shapes and the high-resolution organization of functional materials. However, the size of a single DNA origami is constrained by the length of the scaffold strand, and since its inception, scaling up the size and complexity has been a persistent pursuit. Hierarchical self-assembly of DNA origami units offers a feasible approach to overcome the limitation. Unlike periodic arrays, finite-sized DNA origami superstructures feature well-defined structural boundaries and uniform dimensions. In recent years, increasing attention has been directed toward precise control over the hierarchical self-assembly of DNA origami structures and their applications in fields such as nanophotonics, biophysics, and material science. This review summarizes the strategies for fabricating finite-sized DNA origami superstructures, including heterogeneous self-assembly, self-limited self-assembly, and templated self-assembly, along with a comparative analysis of the advantages and limitations of each approach. Subsequently, recent advancements in the application of these structures are discussed from a structure design perspective. Finally, an outlook on the current challenges and potential future directions is provided, highlighting opportunities for further research and development in this rapidly evolving field.

Symmetry-Guided Inverse Design of Self-Assembling Multiscale DNA Origami Tilings

Recent advances enable the creation of nanoscale building blocks with complex geometries and interaction specificities for self-assembly. This nearly boundless design space necessitates design principles for defining the mutual interactions between multiple particle species to target a user-specified complex structure or pattern. In this article, we develop a symmetry-based method to generate the interaction matrices that specify the assembly of two-dimensional tilings, which we illustrate using equilateral triangles. By exploiting the allowed 2D symmetries, we develop an algorithmic approach by which any periodic 2D tiling can be generated from an arbitrarily large number of subunit species, notably addressing an unmet challenge of engineering 2D crystals with periodicities that can be arbitrarily larger than the subunit size. To demonstrate the utility of our design approach, we encode specific interactions between triangular subunits synthesized by DNA origami and show that we can guide their self-assembly into tilings with a wide variety of symmetries, using up to 12 unique species of triangles. By conjugating specific triangles with gold nanoparticles, we fabricate gold-nanoparticle supracrystals whose lattice parameter spans up to 300 nm. Finally, to generate economical design rules, we compare the design economy of various tilings. In particular, we show that (1) higher symmetries allow assembly of larger unit cells with fewer subunits and (2) linear supracrystals can be designed more economically using linear primitive unit cells. This work provides a simple algorithmic approach to designing periodic assemblies, aiding in the multiscale assembly of supracrystals of nanostructured "meta-atoms" with engineered plasmonic functions.

Escaping Kinetic Traps Using Nonreciprocal Interactions

Kinetic traps are a notorious problem in equilibrium statistical mechanics, where temperature quenches ultimately fail to bring the system to low energy configurations. Using multifarious self-assembly as a model system, we introduce a mechanism to escape kinetic traps by utilizing nonreciprocal interactions between components. Introducing nonequilibrium effects offered by broken action-reaction symmetry in the system pushes the trajectory of the system out of arrested dynamics. The dynamics of the model is studied using tools from the physics of interfaces and defects. Our proposal can find applications in self-assembly, glassy systems, and systems with arrested dynamics to facilitate escape from local minima in rough energy landscapes.

Construction of Reconfigurable and Polymorphic DNA Origami Assemblies with Coiled-Coil Patches and Patterns

DNA origami nanodevices achieve programmable structure and tunable mechanical and dynamic properties by leveraging the sequence-specific interactions of nucleic acids. Previous advances have also established DNA origami as a useful building block to make well-defined micron-scale structures through hierarchical self-assembly, but these efforts have largely leveraged the structural features of DNA origami. The tunable dynamic and mechanical properties also provide an opportunity to make assemblies with adaptive structures and properties. Here the integration of DNA origami hinge nanodevices and coiled-coil peptides are reported into hybrid reconfigurable assemblies. With the same dynamic device and peptide interaction, it is made multiple higher-order assemblies (i.e., polymorphic assembly) by organizing clusters of peptides into patches or arranging single peptides into patterns on the surfaces of DNA origami to control the relative orientation of devices. The coiled-coil interactions are used to construct circular and linear assemblies whose structure and mechanical properties can be modulated with DNA-based reconfiguration. Reconfiguration of linear assemblies leads to micron scale motions and ≈2.5-10-fold increase in bending stiffness. The results provide a foundation for stimulus-responsive hybrid assemblies that can adapt their structure and properties in response to nucleic acid, peptide, protein, or other triggers.

Theory and simulation of ligand functionalized nanoparticles - a pedagogical overview

Synthesizing reconfigurable nanoscale synthons with predictive control over shape, size, and interparticle interactions is a holy grail of bottom-up self-assembly. Grand challenges in their rational design, however, lie in both the large space of experimental synthetic parameters and proper understanding of the molecular mechanisms governing their formation. As such, computational and theoretical tools for predicting and modeling building block interactions have grown to become integral in modern day self-assembly research. In this review, we provide an in-depth discussion of the current state-of-the-art strategies available for modeling ligand functionalized nanoparticles. We focus on the critical role of how ligand interactions and surface distributions impact the emergent, pre-programmed behaviors between neighboring particles. To help build insights into the underlying physics, we first define an "ideal" limit - the short ligand, "hard" sphere approximation - and discuss all experimental handles through the lens of perturbations about this reference point. Finally, we identify theories that are capable of bridging interparticle interactions to nanoscale self-assembly and conclude by discussing exciting new directions for this field.

Limits of economy and fidelity for programmable assembly of size-controlled triply periodic polyhedra

We propose and investigate an extension of the Caspar-Klug symmetry principles for viral capsid assembly to the programmable assembly of size-controlled triply periodic polyhedra, discrete variants of the Primitive, Diamond, and Gyroid cubic minimal surfaces. Inspired by a recent class of programmable DNA origami colloids, we demonstrate that the economy of design in these crystalline assemblies-in terms of the growth of the number of distinct particle species required with the increased size-scale (e.g., periodicity)-is comparable to viral shells. We further test the role of geometric specificity in these assemblies via dynamical assembly simulations, which show that conditions for simultaneously efficient and high-fidelity assembly require an intermediate degree of flexibility of local angles and lengths in programmed assembly. Off-target misassembly occurs via incorporation of a variant of disclination defects, generalized to the case of hyperbolic crystals. The possibility of these topological defects is a direct consequence of the very same symmetry principles that underlie the economical design, exposing a basic tradeoff between design economy and fidelity of programmable, size controlled assembly.

Inverse Design of Self-Folding 3D Shells

Self-folding is an emerging paradigm for the inverse design of three-dimensional structures. While most efforts have concentrated on the shape of the net, our approach introduces a new design dimension-bond specificity between the edges. We transform this design process into a Boolean satisfiability problem to derive solutions for various target structures. This method significantly enhances the yield of the folding process. Furthermore, by linearly combining independent solutions, we achieve designs for shape-shifting nets wherein the dominant structure evolves with varying external conditions. This approach is demonstrated through coarse-grained simulations on two examples of triangular and square nets capable of folding into multiple target shapes.

Blueprinting extendable nanomaterials with standardized protein blocks

A wooden house frame consists of many different lumber pieces, but because of the regularity of these building blocks, the structure can be designed using straightforward geometrical principles. The design of multicomponent protein assemblies, in comparison, has been much more complex, largely owing to the irregular shapes of protein structures1. Here we describe extendable linear, curved and angled protein building blocks, as well as inter-block interactions, that conform to specified geometric standards; assemblies designed using these blocks inherit their extendability and regular interaction surfaces, enabling them to be expanded or contracted by varying the number of modules, and reinforced with secondary struts. Using X-ray crystallography and electron microscopy, we validate nanomaterial designs ranging from simple polygonal and circular oligomers that can be concentrically nested, up to large polyhedral nanocages and unbounded straight 'train track' assemblies with reconfigurable sizes and geometries that can be readily blueprinted. Because of the complexity of protein structures and sequence-structure relationships, it has not previously been possible to build up large protein assemblies by deliberate placement of protein backbones onto a blank three-dimensional canvas; the simplicity and geometric regularity of our design platform now enables construction of protein nanomaterials according to 'back of an envelope' architectural blueprints.

Designing 3D multicomponent self-assembling systems with signal-passing building blocks

We introduce an allostery-mimetic building block model for the self-assembly of 3D structures. We represent the building blocks as patchy particles, where each binding site (patch) can be irreversibly activated or deactivated by binding of the particle's other controlling patches to another particle. We show that these allostery-mimetic systems can be designed to increase yields of target structures by disallowing misassembled states and can further decrease the smallest number of distinct species needed to assemble a target structure. Next, we show applications to design a programmable nanoparticle swarm for multifarious assembly: a system of particles that stores multiple possible target structures and a particular structure is recalled by presenting an external trigger signal. Finally, we outline a possible pathway for realization of such structures at nanoscale using DNA nanotechnology devices.

Hierarchical assembly is more robust than egalitarian assembly in synthetic capsids

Self-assembly of complex and functional materials remains a grand challenge in soft material science. Efficient assembly depends on a delicate balance between thermodynamic and kinetic effects, requiring fine-tuning affinities and concentrations of subunits. By contrast, we introduce an assembly paradigm that allows large error-tolerance in the subunit affinity and helps avoid kinetic traps. Our combined experimental and computational approach uses a model system of triangular subunits programmed to assemble into T = 3 icosahedral capsids comprising 60 units. The experimental platform uses DNA origami to create monodisperse colloids whose three-dimensional geometry is controlled to nanometer precision, with two distinct bonds whose affinities are controlled to kBT precision, quantified in situ by static light scattering. The computational model uses a coarse-grained representation of subunits, short-ranged potentials, and Langevin dynamics. Experimental observations and modeling reveal that when the bond affinities are unequal, two distinct hierarchical assembly pathways occur, in which the subunits first form dimers in one case and pentamers in another. These hierarchical pathways produce complete capsids faster and are more robust against affinity variation than egalitarian pathways, in which all binding sites have equal strengths. This finding suggests that hierarchical assembly may be a general engineering principle for optimizing self-assembly of complex target structures.

Construction and reconfiguration of dynamic DNA origami assemblies with coiled-coil patches and patterns

DNA origami nanodevices achieve programmable structure and tunable mechanical and dynamic properties by leveraging the sequence specific interactions of nucleic acids. Previous advances have also established DNA origami as a useful building block to make well-defined micron-scale structures through hierarchical self-assembly, but these efforts have largely leveraged the structural features of DNA origami. The tunable dynamic and mechanical properties also provide an opportunity to make assemblies with adaptive structure and properties. Here we report the integration of DNA origami hinge nanodevices and coiled-coil peptides into hybrid reconfigurable assemblies. With the same dynamic device and peptide interaction, we make multiple higher order assemblies by organizing clusters of peptides (i.e. patches) or arranging single peptides (i.e. patterns) on the surfaces of DNA origami to control the relative orientation of devices. We use coiled-coil interactions to construct circular and linear assemblies whose structure and mechanical properties can be modulated with DNA-based actuation. Actuation of linear assemblies leads to micron scale motions and ~2.5-10-fold increase in bending stiffness. Our results provide a foundation for stimulus responsive hybrid assemblies that can adapt their structure and properties in response to nucleic acid, peptide, protein, or other triggers.

Blueprinting expandable nanomaterials with standardized protein building blocks

A wooden house frame consists of many different lumber pieces, but because of the regularity of these building blocks, the structure can be designed using straightforward geometrical principles. The design of multicomponent protein assemblies in comparison has been much more complex, largely due to the irregular shapes of protein structures 1 . Here we describe extendable linear, curved, and angled protein building blocks, as well as inter-block interactions that conform to specified geometric standards; assemblies designed using these blocks inherit their extendability and regular interaction surfaces, enabling them to be expanded or contracted by varying the number of modules, and reinforced with secondary struts. Using X-ray crystallography and electron microscopy, we validate nanomaterial designs ranging from simple polygonal and circular oligomers that can be concentrically nested, up to large polyhedral nanocages and unbounded straight "train track" assemblies with reconfigurable sizes and geometries that can be readily blueprinted. Because of the complexity of protein structures and sequence-structure relationships, it has not been previously possible to build up large protein assemblies by deliberate placement of protein backbones onto a blank 3D canvas; the simplicity and geometric regularity of our design platform now enables construction of protein nanomaterials according to "back of an envelope" architectural blueprints.

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.

Designing the Self-Assembly of Arbitrary Shapes Using Minimal Complexity Building Blocks

The design space for self-assembled multicomponent objects ranges from a solution in which every building block is unique to one with the minimum number of distinct building blocks that unambiguously define the target structure. We develop a pipeline to explore the design spaces for a set of structures of various sizes and complexities. To understand the implications of the different solutions, we analyze their assembly dynamics using patchy particle simulations and study the influence of the number of distinct building blocks, and the angular and spatial tolerances on their interactions, on the kinetics and yield of the target assembly. We show that the resource-saving solution with a minimum number of distinct blocks can often assemble just as well (or faster) than designs where each building block is unique. We further use our methods to design multifarious structures, where building blocks are shared between different target structures. Finally, we use coarse-grained DNA simulations to investigate the realization of multicomponent shapes using DNA nanostructures as building blocks.