Self-Assembly of Structures with Addressable Complexity

Design rules for controlling active topological defects

Topological defects play a central role in the physics of many materials, including magnets, superconductors, and liquid crystals. In active fluids, defects become autonomous particles that spontaneously propel from internal active stresses and drive chaotic flows stirring the fluid. The intimate connection between defect textures and active flow suggests that properties of active materials can be engineered by controlling defects, but design principles for their spatiotemporal control remain elusive. Here, we propose a symmetry-based additive strategy for using elementary activity patterns, as active topological tweezers, to create, move, and braid such defects. By combining theory and simulations, we demonstrate how, at the collective level, spatial activity gradients act like electric fields which, when strong enough, induce an inverted topological polarization of defects, akin to a negative susceptibility dielectric. We harness this feature in a dynamic setting to collectively pattern and transport interacting active defects. Our work establishes an additive framework to sculpt flows and manipulate active defects in both space and time, paving the way to design programmable active and living materials for transport, memory, and logic.

Inverse design of a pyrochlore lattice of DNA origami through model-driven experiments

Sophisticated statistical mechanics approaches and human intuition have demonstrated the possibility of self-assembling complex lattices or finite-size constructs. However, attempts so far have mostly only been successful in silico and often fail in experiment because of unpredicted traps associated with kinetic slowing down (gelation, glass transition) and competing ordered structures. Theoretical predictions also face the difficulty of encoding the desired interparticle interaction potential with the experimentally available nano- and micrometer-sized particles. To overcome these issues, we combine SAT assembly (a patchy-particle interaction design algorithm based on constrained optimization) with coarse-grained simulations of DNA nanotechnology to experimentally realize trap-free self-assembly pathways. We use this approach to assemble a pyrochlore three-dimensional lattice, coveted for its promise in the construction of optical metamaterials, and characterize it with small-angle x-ray scattering and scanning electron microscopy visualization.

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.

Pattern recognition in the nucleation kinetics of non-equilibrium self-assembly

Inspired by biology's most sophisticated computer, the brain, neural networks constitute a profound reformulation of computational principles1-3. Analogous high-dimensional, highly interconnected computational architectures also arise within information-processing molecular systems inside living cells, such as signal transduction cascades and genetic regulatory networks4-7. Might collective modes analogous to neural computation be found more broadly in other physical and chemical processes, even those that ostensibly play non-information-processing roles? Here we examine nucleation during self-assembly of multicomponent structures, showing that high-dimensional patterns of concentrations can be discriminated and classified in a manner similar to neural network computation. Specifically, we design a set of 917 DNA tiles that can self-assemble in three alternative ways such that competitive nucleation depends sensitively on the extent of colocalization of high-concentration tiles within the three structures. The system was trained in silico to classify a set of 18 grayscale 30 × 30 pixel images into three categories. Experimentally, fluorescence and atomic force microscopy measurements during and after a 150 hour anneal established that all trained images were correctly classified, whereas a test set of image variations probed the robustness of the results. Although slow compared to previous biochemical neural networks, our approach is compact, robust and scalable. Our findings suggest that ubiquitous physical phenomena, such as nucleation, may hold powerful information-processing capabilities when they occur within high-dimensional multicomponent systems.

Microelectronic Morphogenesis: Smart Materials with Electronics Assembling into Artificial Organisms

Microelectronic morphogenesis is the creation and maintenance of complex functional structures by microelectronic information within shape-changing materials. Only recently has in-built information technology begun to be used to reshape materials and their functions in three dimensions to form smart microdevices and microrobots. Electronic information that controls morphology is inheritable like its biological counterpart, genetic information, and is set to open new vistas of technology leading to artificial organisms when coupled with modular design and self-assembly that can make reversible microscopic electrical connections. Three core capabilities of cells in organisms, self-maintenance (homeostatic metabolism utilizing free energy), self-containment (distinguishing self from nonself), and self-reproduction (cell division with inherited properties), once well out of reach for technology, are now within the grasp of information-directed materials. Construction-aware electronics can be used to proof-read and initiate game-changing error correction in microelectronic self-assembly. Furthermore, noncontact communication and electronically supported learning enable one to implement guided self-assembly and enhance functionality. Here, the fundamental breakthroughs that have opened the pathway to this prospective path are reviewed, the extent and way in which the core properties of life can be addressed are analyzed, and the potential and indeed necessity of such technology for sustainable high technology in society is discussed.

Computational analysis of protein synthesis, diffusion, and binding in compartmental biochips

Protein complex assembly facilitates the combination of individual protein subunits into functional entities, and thus plays a crucial role in biology and biotechnology. Recently, we developed quasi-twodimensional, silicon-based compartmental biochips that are designed to study and administer the synthesis and assembly of protein complexes. At these biochips, individual protein subunits are synthesized from locally confined high-density DNA brushes and are captured on the chip surface by molecular traps. Here, we investigate single-gene versions of our quasi-twodimensional synthesis systems and introduce the trap-binding efficiency to characterize their performance. We show by mathematical and computational modeling how a finite trap density determines the dynamics of protein-trap binding and identify three distinct regimes of the trap-binding efficiency. We systematically study how protein-trap binding is governed by the system's three key parameters, which are the synthesis rate, the diffusion constant and the trap-binding affinity of the expressed protein. In addition, we describe how spatially differential patterns of traps modulate the protein-trap binding dynamics. In this way, we extend the theoretical knowledge base for synthesis, diffusion, and binding in compartmental systems, which helps to achieve better control of directed molecular self-assembly required for the fabrication of nanomachines for synthetic biology applications or nanotechnological purposes.

Creation of ordered 3D tubes out of DNA origami lattices

Hierarchical self-assembly of nanostructures with addressable complexity has been a promising route for realizing novel functional materials. Traditionally, the fabrication of such structures on a large scale has been achievable using top-down methods but with the cost of complexity of the fabrication equipment versus resolution and limitation mainly to 2D structures. More recently bottom-up methods using molecules like DNA have gained attention due to the advantages of low fabrication costs, high resolution and simplicity in an extension of the methods to the third dimension. One of the more promising bottom-up techniques is DNA origami due to the robust self-assembly of arbitrarily shaped nanostructures with feature sizes down to a few nanometers. Here, we show that under specific ionic conditions of the buffer, the employed plus-shaped, blunt-ended Seeman tile (ST) origami forms elongated, ordered 2D lattices, which are further rolled into 3D tubes in solution. Imaging structures on a surface by atomic force microscopy reveals ribbon-like structures, with single or double layers of the origami lattice. Further studies of the double-layered structures in a liquid state by confocal microscopy and cryo-TEM revealed elongated tube structures with a relatively uniform width but with a varying length. Through meticulous study, we concluded that the assembly process of these 3D DNA origami tubes is heavily dependent on the concentration of both mono- and divalent cations. In particular, nickel seems to act as a trigger for the formation of the tubular assemblies in liquid.

Tuning Nucleation Kinetics via Nonequilibrium Chemical Reactions

Unlike fluids at thermal equilibrium, biomolecular mixtures in living systems can sustain nonequilibrium steady states, in which active processes modify the conformational states of the constituent molecules. Despite qualitative similarities between liquid-liquid phase separation in these systems, the extent to which the phase-separation kinetics differ remains unclear. Here we show that inhomogeneous chemical reactions can alter the nucleation kinetics of liquid-liquid phase separation in a manner that is consistent with classical nucleation theory, but can only be rationalized by introducing a nonequilibrium interfacial tension. We identify conditions under which nucleation can be accelerated without changing the energetics or supersaturation, thus breaking the correlation between fast nucleation and strong driving forces that is typical of phase separation and self-assembly at thermal equilibrium.

Optimization of non-equilibrium self-assembly protocols using Markov state models

The promise of self-assembly to enable the bottom-up formation of materials with prescribed architectures and functions has driven intensive efforts to uncover rational design principles for maximizing the yield of a target structure. Yet, despite many successful examples of self-assembly, ensuring kinetic accessibility of the target structure remains an unsolved problem in many systems. In particular, long-lived kinetic traps can result in assembly times that vastly exceed experimentally accessible timescales. One proposed solution is to design non-equilibrium assembly protocols in which system parameters change over time to avoid such kinetic traps. Here, we develop a framework to combine Markov state model (MSM) analysis with optimal control theory to compute a time-dependent protocol that maximizes the yield of the target structure at a finite time. We present an adjoint-based gradient descent method that, in conjunction with MSMs for a system as a function of its control parameters, enables efficiently optimizing the assembly protocol. We also describe an interpolation approach to significantly reduce the number of simulations required to construct the MSMs. We demonstrate our approach with two examples; a simple semi-analytic model for the folding of a polymer of colloidal particles, and a more complex model for capsid assembly. Our results show that optimizing time-dependent protocols can achieve significant improvements in the yields of selected structures, including equilibrium free energy minima, long-lived metastable structures, and transient states.

Stochastic paths controlling speed and dissipation

Natural processes occur in a finite amount of time and dissipate energy, entropy, and matter. Near equilibrium, thermodynamic intuition suggests that fast irreversible processes will dissipate more energy and entropy than slow quasistatic processes connecting the same initial and final states. For small systems, recently discovered thermodynamic speed limits suggest that faster processes will dissipate more than slower processes. Here, we test the hypothesis that this relationship between speed and dissipation holds for stochastic paths far from equilibrium. To analyze stochastic paths on finite timescales, we derive an exact expression for the path probabilities of continuous-time Markov chains from the path summation solution to the master equation. We present a minimal model for a driven system in which relative energies of the initial and target states control the speed, and the nonequilibrium currents of a cycle control the dissipation. Although the hypothesis holds near equilibrium, we find that faster processes can dissipate less under far-from-equilibrium conditions because of strong currents. This model serves as a minimal prototype for designing kinetics to sculpt the nonequilibrium path space so that faster paths produce less dissipation.

Time-Resolved Atomistic Imaging and Statistical Analysis of Daptomycin Oligomers with and without Calcium Ions

Daptomycin (DP) is effective against multiple drug-resistant Gram-positive pathogens because of its distinct mechanism of action. An accepted mechanism includes Ca²⁺-triggered aggregation of the DP molecule to form oligomers. DP and its oligomers have so far defied structural analysis at a molecular level. We studied the ability of DP molecule to aggregate by itself in water, the effects of Ca²⁺ ions to promote the aggregation, and the connectivity of the DP molecules in the oligomers by the combined use of dynamic light scattering in water and atomic-resolution cinematographic imaging of DP molecules captured on a carbon nanotube on which the DP molecule is installed as a fishhook. We found that the DP molecule aggregates weakly into dimers, trimers, and tetramers in water, and strongly in the presence of calcium ions, and that the tetramer is the largest oligomer in homogeneous aqueous solution. The dimer remains as the major species, and we propose a face-to-face stacked structure based on dynamic imaging using millisecond and angstrom resolution transmission electron microscopy. The tetramer in its cyclic form is the largest oligomer observed, while the trimer forms in its linear form. The study has shown that the DP molecule has an intrinsic property of forming tetramers in water, which is enhanced by the presence of calcium ions. Such experimental structural information will serve as a platform for future drug design. The data also illustrate the utility of cinematographic recording for the study of self-organization processes.

SAT-assembly: a new approach for designing self-assembling systems

We propose a general framework for solving inverse self-assembly problems, i.e. designing interactions between elementary units such that they assemble spontaneously into a predetermined structure. Our approach uses patchy particles as building blocks, where the different units bind at specific interaction sites (the patches), and we exploit the possibility of having mixtures with several components. The interaction rules between the patches is determined by transforming the combinatorial problem into a Boolean satisfiability problem (SAT) which searches for solutions where all bonds are formed in the target structure. Additional conditions, such as the non-satisfiability of competing structures (e.g. metastable states) can be imposed, allowing to effectively design the assembly path in order to avoid kinetic traps. We demonstrate this approach by designing and numerically simulating a cubic diamond structure from four particle species that assembles without competition from other polymorphs, including the hexagonal structure.

ATP-Induced Emergent Circularly Polarized Luminescence and Encryption

Biomimetic ATP-driven supramolecular assembly is important to understand various biological processes and dissipative systems. Here, we report an ATP-driven chiral assembly exhibiting circularly polarized luminescence (CPL) via the interaction of an achiral terpyridine-based Zn^II complex with nucleotides. It was found that while the metal complexes could co-assemble with the nucleotides to form fluorescent assemblies, only a combination of furan-substituted terpyridine complex and ATP showed an intense CPL with a dissymmetry factor (g_lum ) as high as 0.20. This means that the complex could recognize ATP using CPL as a readout signal, thus providing an example of ATP encryption. Interestingly, when ATP was transferred into ADP or AMP under enzymatic hydrolysis, the CPL decreases or disappears. Addition of ATP generates CPL again, thus producing an ATP-induced CPL system. This work presents the first example of ATP-induced CPL and encryption.

Temperature protocols to guide selective self-assembly of competing structures

Multicomponent self-assembly mixtures offer the possibility of encoding multiple target structures with the same set of interacting components. Selective retrieval of one of the stored structures has been attempted by preparing an initial state that favors the assembly of the required target, through seeding, concentration patterning, or specific choices of interaction strengths. This may not be possible in an experiment where on-the-fly reconfiguration of the building blocks to switch functionality may be required. In this paper, we explore principles of inverse design of a multicomponent, self-assembly mixture capable of encoding two competing structures that can be selected through simple temperature protocols. We design the target structures to realize the generic situation in which one of the targets has the lower nucleation barrier, while the other is globally more stable. We observe that, to avoid the formation of spurious or chimeric aggregates, the number of neighboring component pairs that occur in both structures should be minimal. Our design also requires the inclusion of components that are part of only one of the target structures. We observe, however, that to maximize the selectivity of retrieval, the component library itself should be maximally shared by the two targets, within such a constraint. We demonstrate that temperature protocols can be designed that lead to the formation of either one of the target structures with high selectivity. We discuss the important role played by secondary aggregation products in improving selectivity, which we term "vestigial aggregates."

The time complexity of self-assembly

Time efficiency of self-assembly is crucial for many biological processes. Moreover, with the advances of nanotechnology, time efficiency in artificial self-assembly becomes ever more important. While structural determinants and the final assembly yield are increasingly well understood, kinetic aspects concerning the time efficiency, however, remain much more elusive. In computer science, the concept of time complexity is used to characterize the efficiency of an algorithm and describes how the algorithm's runtime depends on the size of the input data. Here we characterize the time complexity of nonequilibrium self-assembly processes by exploring how the time required to realize a certain, substantial yield of a given target structure scales with its size. We identify distinct classes of assembly scenarios, i.e., "algorithms" to accomplish this task, and show that they exhibit drastically different degrees of complexity. Our analysis enables us to identify optimal control strategies for nonequilibrium self-assembly processes. Furthermore, we suggest an efficient irreversible scheme for the artificial self-assembly of nanostructures, which complements the state-of-the-art approach using reversible binding reactions and requires no fine-tuning of binding energies.

Self-assembly of photonic crystals by controlling the nucleation and growth of DNA-coated colloids

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.

Multifarious colloidal structures: new insight into ternary and quadripartite ordered assemblies

DNA-mediated assembly of colloidal particles can be utilized to produce a variety of structures which may have desirable phononic, photonic, or electronic transport properties. Recent developments in linker-mediated assembly processes allow for interactions to be coordinated between many different types of colloidal particles more easily and with fewer unique sequences than direct hybridization. However, the dynamics of colloidal self-assembly becomes increasingly more complex when coordinating interactions between three or more distinct interacting elements. In such cases particle pairs with similar binding energies are allowed to interact unpredictably, and enthalpically degenerate binding sites will be noticeably more present while numerous secondary phases may also result from the self-assembly process. Therefore, it is necessary to develop procedures for predicting feasible superstructure geometries for these systems before they can be implemented in material design. Here we investigate the formation of multifarious ordered structures through self-assembly of multiple types of spherically symmetrical colloidal particles with a variety of interaction matrices. We utilize Molecular Dynamics (MD) simulations to study the growth behavior of systems with different types of interacting elements and different particle sizes, and also predict the formation and stability of the target structures. We also study the phononic spectra of various ternary structures in order to identify the influence of key structural parameters on phonon bandgap frequencies and ranges. Our results provide direct guidelines for designing ternary and quadripartite multifarious colloidal structures, and motivate new directions for future experimental work to target formation of multi-component colloidal superstructures beyond the well-established binary symmetries studied in the past.

Symmetry-derived structure directing agents for two-dimensional crystals of arbitrary colloids

We derive properties of self-assembling rings which can template the organization of an arbitrary colloid into any periodic symmetry in two Euclidean dimensions. By viewing this as a tiling problem, we illustrate how the shape and chemical patterning of these rings are derivable, and are explicitly reflected by the symmetry group's orbifold symbol. We performed molecular dynamics simulations to observe their self-assembly and found 5 different characteristics which could be easily rationalized on the basis of this symbol. These include systems which undergo chiral phase separation, are addressably complex, exhibit self-limiting growth into clusters, form ordered "rods" in only one-dimension akin to a smectic phase, and those from symmetry groups which are pluripotent and allow one to select rings which exhibit different behaviors. We discuss how the curvature of the ring's edges plays an integral role in achieving correct self-assembly, and illustrate how to obtain these shapes. This provides a method for patterning colloidal systems at interfaces without explicitly programming this information onto the colloid itself.

Equilibrium mechanisms of self-limiting assembly

Self-assembly is a ubiquitous process in synthetic and biological systems, broadly defined as the spontaneous organization of multiple subunits (e.g. macromolecules, particles) into ordered multi-unit structures. The vast majority of equilibrium assembly processes give rise to two states: one consisting of dispersed disassociated subunits, and the other, a bulk-condensed state of unlimited size. This review focuses on the more specialized class of self-limiting assembly, which describes equilibrium assembly processes resulting in finite-size structures. These systems pose a generic and basic question, how do thermodynamic processes involving non-covalent interactions between identical subunits "measure" and select the size of assembled structures? In this review, we begin with an introduction to the basic statistical mechanical framework for assembly thermodynamics, and use this to highlight the key physical ingredients that ensure equilibrium assembly will terminate at finite dimensions. Then, we introduce examples of self-limiting assembly systems, and classify them within this framework based on two broad categories: self-closing assemblies and open-boundary assemblies. These include well-known cases in biology and synthetic soft matter - micellization of amphiphiles and shell/tubule formation of tapered subunits - as well as less widely known classes of assemblies, such as short-range attractive/long-range repulsive systems and geometrically-frustrated assemblies. For each of these self-limiting mechanisms, we describe the physical mechanisms that select equilibrium assembly size, as well as potential limitations of finite-size selection. Finally, we discuss alternative mechanisms for finite-size assemblies, and draw contrasts with the size-control that these can achieve relative to self-limitation in equilibrium, single-species assemblies.

Hierarchical self-assembly of miktoarm star copolymers with pathway complexity

The self-assembly of amphiphilic miktoarm star copolymers shows hierarchical pathway complexity from molecular building blocks to miktoarm stars to micellar nano-objects to complex hierarchical assemblies.

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.

Linker-mediated self-assembly of mobile DNA-coated colloids

Developing construction methods of materials tailored for given applications with absolute control over building block placement poses an immense challenge. DNA-coated colloids offer the possibility of realising programmable self-assembly, which, in principle, can assemble almost any structure in equilibrium, but remains challenging experimentally. Here, we propose an innovative system of linker-mediated mobile DNA-coated colloids (mDNACCs), in which mDNACCs are bridged by the free DNA linkers in solution, whose two single-stranded DNA tails can bind with specific single-stranded DNA receptors of complementary sequence coated on colloids. We formulate a mean-field theory efficiently calculating the effective interaction between mDNACCs, where the entropy of DNA linkers plays a nontrivial role. Particularly, when the binding between free DNA linkers in solution and the corresponding receptors on mDNACCs is strong, the linker-mediated colloidal interaction is determined by the linker entropy depending on the linker concentration.

Grand canonical inverse design of multicomponent colloidal crystals

Inverse design methods are powerful computational approaches for creating colloidal systems which self-assemble into a target morphology by reverse engineering the Hamiltonian of the system. Despite this, these optimization procedures tend to yield Hamiltonians which are too complex to be experimentally realized. An alternative route to complex structures involves the use of several different components, however, conventional inverse design methods do not explicitly account for the possibility of phase separation into compositionally distinct structures. Here, we present an inverse design scheme for multicomponent colloidal systems by combining active learning with a method to directly compute their ground state phase diagrams. This explicitly accounts for phase separation and can locate stable regions of Hamiltonian parameter space which grid-based surveys are prone to miss. Using this we design low-density, binary structures with Lennard-Jones-like pairwise interactions that are simpler than in the single component case and potentially realizable in an experimental setting. This reinforces the concept that ground states of simple, multicomponent systems might be rich with previously unappreciated diversity, enabling the assembly of non-trivial structures with only few simple components instead of a single complex one.

Programming the Nucleation of DNA Brick Self-Assembly with a Seeding Strand

Recently, the DNA brick strategy has provided a highly modular and scalable approach for the construction of complex structures, which can be used as nanoscale pegboards for the precise organization of molecules and nanoparticles for many applications. Despite the dramatic increase of structural complexity provided by the DNA brick method, the assembly pathways are still poorly understood. Herein, we introduce a "seed" strand to control the crucial nucleation and assembly pathway in DNA brick assembly. Through experimental studies and computer simulations, we successfully demonstrate that the regulation of the assembly pathways through seeded growth can accelerate the assembly kinetics and increase the optimal temperature by circa 4-7 °C for isothermal assembly. By improving our understanding of the assembly pathways, we provide new guidelines for the design of programmable pathways to improve the self-assembly of DNA nanostructures.

Neutralization-Induced Self-Assembly of Cellulose Oligomers into Antibiofouling Crystalline Nanoribbon Networks in Complex Mixtures

Molecular self-assembly in solutions is a powerful strategy for fabricating functional architectures. Various bio(macro)molecules have been used as self-assembly components. However, structural polysaccharides, such as cellulose and chitin, have rarely been a research focus for molecular self-assembly, even though their crystalline assemblies potentially have robust physicochemical properties. Herein, we demonstrated the neutralization-induced self-assembly of cellulose oligomers into antibiofouling crystalline nanoribbon networks to produce physically cross-linked hydrogels. The self-assembly proceeded even in versatile complex mixtures, such as serum-containing cell culture media, in a controlled manner for 3D cell culture. The cultured cells grew into cell aggregates (spheroids), which were simply collected through natural filtration due to the mechanically crushable property of the crystalline nanoribbons through water flow by pipetting. We will show the potential of cellulose oligomers for biocompatible, crystalline soft materials.

Selective Metal-Phenolic Assembly from Complex Multicomponent Mixtures

Selective self-assembly in multicomponent mixtures offers a method for isolating desired components from complex systems for the rapid production of functional materials. Developing approaches capable of selective assembly of "target" components into intended three-dimensional structures is challenging because of the intrinsically high complexity of multicomponent systems. Herein, we report the selective coordination-driven self-assembly of metal-phenolic networks (MPNs) from a series of complex multicomponent systems (including crude plant extracts) into thin films via metal chelation with phenolic ligands. The metal (Fe^III) selectively assembles low abundant phenolic components (e.g., myricetrin and quercetrin) from plant extracts into thin films. This selective metal-phenolic assembly is independent of the substrate properties (e.g., size, surface charge, and shape). Moreover, the high selectivity is consistent across different target phenolic ligands in model mixtures, even though each individual component can form thin films from single-component systems. A computational simulation of film formation suggests that the driving force for the selective behavior stems from differences in the number of chelating sites in the phenolic structures. The MPN films are shown to demonstrate improved antioxidant properties compared with the corresponding phenolic compounds in their free form, therefore exhibiting potential as free-standing antioxidant films.

Designing Superlattice Structure via Self-Assembly of One-Component Polymer-Grafted Nanoparticles

The control of the self-assembly of the nanocrystals into ordered structures has been extensively investigated, but fewer efforts have been devoted to studying one-component polymer-grafted nanoparticles (OPNPs). Herein, through coarse-grained molecular dynamics simulation, we design a novel nanoparticle (NP) grafted with polymer chains, focusing on its self-assembled structures. First, we examine the effects of length and density of grafted polymer chains by calculating the radial distribution function between NPs, as well as through direct visualization. We observe a monotonic change of the arranged morphology of grafted-NPs as a function of the density of grafted polymer chains, which indicates that the increase of the grafting density contributes to the order of the morphology. Meanwhile, we find that much longer grafted polymer chains worsen the regularity of the morphology. Then, we probe the influence of the stiffness of grafted polymer chains (denoted by K ranging from 0 to 500) on the order of grafted-NPs, finding that the order of the structure exhibits a nonmonotonic behavior as a function of K at moderate grafting density. For high grafting density, the order of the morphology is initially enhanced and becomes saturated as a function of K. For the effect of K on the stress-strain behavior, the system with the lowest order demonstrates the most remarkable reinforced mechanical behavior for both low and high grafting density. Last, we establish the phase diagram by varying the stiffness and density of the grafted polymer chains, which contains the amorphous, ordered, and superlattice structures, respectively. In general, our simulated results provide guidelines to tailor the self-assembly of the OPNPs by taking advantage of the length, density, and stiffness of grafted polymer chains.

The role of the side chain in the conformational and self-assembly patterns of C2-symmetric Val and Phe pseudopeptidic derivatives

Side chain as the main conformational and self-assembly structural factor for C₂-pseudopeptides.

Controlling Fragment Competition on Pathways to Addressable Self-Assembly

Addressable self-assembly is the formation of a target structure from a set of unique molecular or colloidal building blocks, each of which occupies a defined location in the target. The requirement that each type of building block appears exactly once in each copy of the target introduces severe restrictions on the combinations of particles and on the pathways that lead to successful self-assembly. These restrictions can limit the efficiency of self-assembly and the final yield of the product. In particular, partially formed fragments may compete with each other if their compositions overlap, since they cannot be combined. Here, we introduce a "completability" algorithm to quantify competition between self-assembling fragments and use it to deduce general principles for suppressing the effects of fragment incompatibility in the self-assembly of small addressable clusters. Competition originates from loops in the bonding network of the target structure, but loops may be needed to provide structural rigidity and thermodynamic stability. An optimal compromise can be achieved by careful choice of bonding networks and by promoting semihierarchical pathways that rule out competition between early fragments. These concepts are illustrated in simulations of self-assembly in two contrasting addressable targets of 20 unique components each.

Formation and Growth of Mesoglobules in Aqueous Poly(N-isopropylacrylamide) Solutions Revealed with Kinetic Small-Angle Neutron Scattering and Fast Pressure Jumps

The phase transition from swollen chains to polymer mesoglobules of an aqueous solution of poly(N-isopropylacrylamide) is investigated with kinetic small-angle neutron scattering with 50 ms time resolution in conjunction with millisecond pressure jumps across the coexistence line. The time-resolved study evidenced three distinct regimes: fractal clusters form during the first second and transform into compact mesoglobules. During the following ∼20 s, these grow by diffusion-limited coalescence. The final step consists of a slow growth characterized by an energy barrier of several k_BT. The method opens opportunities for kinetic structural studies of multicomponent systems over wide length and time scales and gives a structural picture spanning from the chain collapse to mesoscopic phase separation.

Multi-scale coarse-graining for the study of assembly pathways in DNA-brick self-assembly

Inspired by recent successes using single-stranded DNA tiles to produce complex structures, we develop a two-step coarse-graining approach that uses detailed thermodynamic calculations with oxDNA, a nucleotide-based model of DNA, to parametrize a coarser kinetic model that can reach the time and length scales needed to study the assembly mechanisms of these structures. We test the model by performing a detailed study of the assembly pathways for a two-dimensional target structure made up of 334 unique strands each of which are 42 nucleotides long. Without adjustable parameters, the model reproduces a critical temperature for the formation of the assembly that is close to the temperature at which assembly first occurs in experiments. Furthermore, the model allows us to investigate in detail the nucleation barriers and the distribution of critical nucleus shapes for the assembly of a single target structure. The assembly intermediates are compact and highly connected (although not maximally so), and classical nucleation theory provides a good fit to the height and shape of the nucleation barrier at temperatures close to where assembly first occurs.

Nonisotropic Self-Assembly of Nanoparticles: From Compact Packing to Functional Aggregates

Quantum strongly correlated systems that exhibit interesting features in condensed matter physics often need an unachievable temperature or pressure range in classical materials. One solution is to introduce a scaling factor, namely, the lattice parameter. Synthetic heterostructures named superlattices or supracrystals are synthesized by the assembling of colloidal atoms. These include semiconductors, metals, and insulators for the exploitation of their unique properties. Most of them are currently limited to dense packing. However, some of desired properties need to adjust the colloidal atoms neighboring number. Here, the current state of research in nondense packing is summarized, discussing the benefits, outlining possible scenarios and methodologies, describing examples reported in the literature, briefly discussing the challenges, and offering preliminary conclusions. Penetrating such new and intriguing research fields demands a multidisciplinary approach accounting for the coupling of statistic physics, solid state and quantum physics, chemistry, computational science, and mathematics. Standard interactions between colloidal atoms and emerging fields, such as the use of Casimir forces, are reported. In particular, the focus is on the novelty of patchy colloidal atoms to meet this challenge.

Direct observation and rational design of nucleation behavior in addressable self-assembly

Current efforts aimed at constructing complex supramolecular structures often suffer from low yields or require long assembly protocols. We address these problems by demonstrating a facile strategy for optimizing the nucleation step of a multicomponent self-assembly reaction. By tracking the formation of multisubunit clusters in situ, our experiments show that modifying the critical nucleus required to initiate structure growth can broaden the range of conditions over which self-assembly occurs and, consequently, can dramatically improve the final yield of correctly formed structures. Since varying the design of only a small portion of the target structure optimizes its yield, this strategy provides a practical route to improve the speed and accuracy of self-assembly in biomolecular, colloidal, and nanoparticle systems.

To optimize a self-assembly reaction, it is essential to understand the factors that govern its pathway. Here, we examine the influence of nucleation pathways in a model system for addressable, multicomponent self-assembly based on a prototypical “DNA-brick” structure. By combining temperature-dependent dynamic light scattering and atomic force microscopy with coarse-grained simulations, we show how subtle changes in the nucleation pathway profoundly affect the yield of the correctly formed structures. In particular, we can increase the range of conditions over which self-assembly occurs by using stable multisubunit clusters that lower the nucleation barrier for assembling subunits in the interior of the structure. Consequently, modifying only a small portion of a structure is sufficient to optimize its assembly. Due to the generality of our coarse-grained model and the excellent agreement that we find with our experimental results, the design principles reported here are likely to apply generically to addressable, multicomponent self-assembly.

Programmable and Multifunctional DNA-Based Materials for Biomedical Applications

DNA encodes the genetic information; recently, it has also become a key player in material science. Given the specific Watson-Crick base-pairing interactions between only four types of nucleotides, well-designed DNA self-assembly can be programmable and predictable. Stem-loops, sticky ends, Holliday junctions, DNA tiles, and lattices are typical motifs for forming DNA-based structures. The oligonucleotides experience thermal annealing in a near-neutral buffer containing a divalent cation (usually Mg²⁺ ) to produce a variety of DNA nanostructures. These structures not only show beautiful landscape, but can also be endowed with multifaceted functionalities. This Review begins with the fundamental characterization and evolutionary trajectory of DNA-based artificial structures, but concentrates on their biomedical applications. The coverage spans from controlled drug delivery to high therapeutic profile and accurate diagnosis. A variety of DNA-based materials, including aptamers, hydrogels, origamis, and tetrahedrons, are widely utilized in different biomedical fields. In addition, to achieve better performance and functionality, material hybridization is widely witnessed, and DNA nanostructure modification is also discussed. Although there are impressive advances and high expectations, the development of DNA-based structures/technologies is still hindered by several commonly recognized challenges, such as nuclease instability, lack of pharmacokinetics data, and relatively high synthesis cost.

Finding the Optimal Nets for Self-Folding Kirigami

Three-dimensional shells can be synthesized from the spontaneous self-folding of two-dimensional templates of interconnected panels, called nets. However, some nets are more likely to self-fold into the desired shell under random movements. The optimal nets are the ones that maximize the number of vertex connections, i.e., vertices that have only two of its faces cut away from each other in the net. Previous methods for finding such nets are based on random search, and thus, they do not guarantee the optimal solution. Here, we propose a deterministic procedure. We map the connectivity of the shell into a shell graph, where the nodes and links of the graph represent the vertices and edges of the shell, respectively. Identifying the nets that maximize the number of vertex connections corresponds to finding the set of maximum leaf spanning trees of the shell graph. This method allows us not only to design the self-assembly of much larger shell structures but also to apply additional design criteria, as a complete catalog of the maximum leaf spanning trees is obtained.

Biomimetic temporal self-assembly via fuel-driven controlled supramolecular polymerization

Temporal control of supramolecular assemblies to modulate the structural and transient characteristics of synthetic nanostructures is an active field of research within supramolecular chemistry. Molecular designs to attain temporal control have often taken inspiration from biological assemblies. One such assembly in Nature which has been studied extensively, for its well-defined structure and programmable self-assembly, is the ATP-driven seeded self-assembly of actin. Here we show, in a synthetic manifestation of actin self-assembly, an ATP-selective and ATP-fuelled, controlled supramolecular polymerization of a phosphate receptor functionalised monomer. It undergoes fuel-driven nucleation and seeded growth that provide length control and narrow dispersity of the resultant assemblies. Furthermore, coupling via ATP-hydrolysing enzymes yielded its transient characteristics. These results will usher investigations into synthetic analogues of important biological self-assembly motifs and will prove to be a significant advancement toward biomimetic temporally programmed materials.

Optimising minimal building blocks for addressable self-assembly

Addressable structures are characterised by the set of unique components from which they are built and by the specific location that each component occupies. For an addressable structure to self-assemble, its constituent building blocks must be encoded with sufficient information to define their positions with respect to each other and to enable them to navigate to those positions. DNA, with its vast scope for encoding specific interactions, has been successfully used to synthesise addressable systems of several hundred components. In this work we examine the complementary question of the minimal requirements for building blocks to undergo addressable self-assembly driven by a controlled temperature quench. Our testbed is an idealised model of cubic particles patterned with attractive interactions. We introduce a scheme for optimising the interactions using a variant of basin-hopping and a negative design principle. The designed building blocks are tested dynamically in simple target structures to establish how their complexity affects the limits of reliable self-assembly.