Nanocrystal Assemblies: Current Advances and Open Problems.

We explore the potential of nanocrystals (a term used equivalently to nanoparticles) as building blocks for nanomaterials, and the current advances and open challenges for fundamental science developments and applications. Nanocrystal assemblies are inherently multiscale, and the generation of revolutionary material properties requires a precise understanding of the relationship between structure and function, the former being determined by classical effects and the latter often by quantum effects. With an emphasis on theory and computation, we discuss challenges that hamper current assembly strategies and to what extent nanocrystal assemblies represent thermodynamic equilibrium or kinetically trapped metastable states. We also examine dynamic effects and optimization of assembly protocols. Finally, we discuss promising material functions and examples of their realization with nanocrystal assemblies.

Emergence of catalytic function in prebiotic information-coding polymers.

Life as we know it relies on the interplay between catalytic activity and information processing carried out by biological polymers. Here we present a plausible pathway by which a pool of prebiotic information-coding oligomers could acquire an early catalytic function, namely sequence-specific cleavage activity. Starting with a system capable of non-enzymatic templated replication, we demonstrate that even non-catalyzed spontaneous cleavage would promote proliferation by generating short fragments that act as primers. Furthermore, we show that catalytic cleavage function can naturally emerge and proliferate in this system. Specifically, a cooperative catalytic network with four subpopulations of oligomers is selected by the evolution in competition with chains lacking catalytic activity. The cooperative system emerges through the functional differentiation of oligomers into catalysts and their substrates. The model is inspired by the structure of the hammerhead RNA enzyme as well as other DNA- and RNA-based enzymes with cleavage activity that readily emerge through natural or artificial selection. We identify the conditions necessary for the emergence of the cooperative catalytic network. In particular, we show that it requires the catalytic rate enhancement over the spontaneous cleavage rate to be at least 102-103, a factor consistent with the existing experiments. The evolutionary pressure leads to a further increase in catalytic efficiency. The presented mechanism provides an escape route from a relatively simple pairwise replication of oligomers toward a more complex behavior involving catalytic function. This provides a bridge between the information-first origin of life scenarios and the paradigm of autocatalytic sets and hypercycles, albeit based on cleavage rather than synthesis of reactants.

Symmetry-specific characterization of bond orientation order in DNA-assembled nanoparticle lattices.

Bond-orientational order in DNA-assembled nanoparticles lattices is explored with the help of recently introduced Symmetry-specific Bond Order Parameters (SymBOPs). This approach provides a more sensitive analysis of local order than traditional scalar BOPs, facilitating the identification of coherent domains at the single bond level. The present study expands the method initially developed for assemblies of anisotropic particles to the isotropic ones or cases where particle orientation information is unavailable. The SymBOP analysis was applied to experiments on DNA-frame-based assembly of nanoparticle lattices. It proved highly sensitive in identifying coherent crystalline domains with different orientations, as well as detecting topological defects, such as dislocations. Furthermore, the analysis distinguishes individual sublattices within a single crystalline domain, such as pair of interpenetrating FCC lattices within a cubic diamond. The results underscore the versatility and robustness of SymBOPs in characterizing ordering phenomena, making them valuable tools for investigating structural properties in various systems.

Mitigation of SARS-CoV-2 transmission at a large public university.

In Fall 2020, universities saw extensive transmission of SARS-CoV-2 among their populations, threatening health of the university and surrounding communities, and viability of in-person instruction. Here we report a case study at the University of Illinois at Urbana-Champaign, where a multimodal "SHIELD: Target, Test, and Tell" program, with other non-pharmaceutical interventions, was employed to keep classrooms and laboratories open. The program included epidemiological modeling and surveillance, fast/frequent testing using a novel low-cost and scalable saliva-based RT-qPCR assay for SARS-CoV-2 that bypasses RNA extraction, called covidSHIELD, and digital tools for communication and compliance. In Fall 2020, we performed >1,000,000 covidSHIELD tests, positivity rates remained low, we had zero COVID-19-related hospitalizations or deaths amongst our university community, and mortality in the surrounding Champaign County was reduced more than 4-fold relative to expected. This case study shows that fast/frequent testing and other interventions mitigated transmission of SARS-CoV-2 at a large public university.

Geometric and topological entropies of sphere packing.

We present a statistical mechanical description of randomly packed spherical particles, where the average coordination number is treated as a macroscopic thermodynamic variable. The overall packing entropy is shown to have two contributions: geometric, reflecting statistical weights of individual configurations, and topological, which corresponds to the number of topologically distinct states. Both of them are computed in the thermodynamic limit for isostatic and weakly underconstrained packings in 2D and 3D. The theory generalizes concepts of granular and glassy configurational entropies for the case of nonjammed systems. It is directly applicable to sticky colloids and predicts an asymptotic phase behavior of sticky spheres in the limit of strong binding.

Symmetry-specific orientational order parameters for complex structures.

A comprehensive framework of characterizing complex self-assembled structures with a set of orientational order parameters is presented. It is especially relevant in the context of using anisotropic building blocks with various symmetries. Two classes of tensor order parameters are associated with polyhedral nematic and bond orientational order. For the latter, a variation of classical bond order parameters (BOPs) is introduced, which takes advantage of the symmetry of constituent particles and/or expected crystalline phases. These symmetrized BOPs can be averaged over an entire system or assigned locally to an individual bond. By combining that with the bond percolation procedure, one is able to identify coherent domains within a self-assembled structure. As a demonstration of the proposed framework, we apply it to a simulated hybrid system that combines isotropic and patchy particles with octahedral symmetry. Not only does the methodology allow one to identify individual crystalline domains but also it detects coherent clusters of a peculiar compact amorphous structure that is not space-filling and lacks any long-range order.

Controlling morphology in hybrid isotropic/patchy particle assemblies.

Brownian dynamics is used to study self-assembly in a hybrid system of isotropic particles (IPs), combined with anisotropic building blocks that represent special "designer particles." Those are modeled as spherical patchy particles (PPs) with binding only allowed between their patches and IPs. In this study, two types of PPs are considered: Octahedral PPs (Oh-PPs) and Square PPs (Sq-PPs), with octahedral and square arrangements of patches, respectively. The self-assembly is additionally facilitated by the simulated annealing procedure. The resultant structures are characterized by a combination of local correlations in cubatic ordering and a symmetry-specific variation of bond orientation order parameters (SymBOPs). By varying the PP/IP size ratio, we detected a sharp crossover between two distinct morphologies in both types of systems. High symmetry phases, NaCl crystal for Oh-PP and square lattice for Sq-PP, are observed for larger size ratios. For the smaller ones, the dominant morphologies are significantly different, e.g., Oh-PPs form a compact amorphous structure with predominantly face-to-face orientation of neighboring PPs. Unusually, for a morphology without a long-range order, it is still possible to identify well organized coherent clusters of this structure, thanks to the adoption of our SymBOP-based characterization.

Stochastic social behavior coupled to COVID-19 dynamics leads to waves, plateaus, and an endemic state.

It is well recognized that population heterogeneity plays an important role in the spread of epidemics. While individual variations in social activity are often assumed to be persistent, that is, constant in time, here we discuss the consequences of dynamic heterogeneity. By integrating the stochastic dynamics of social activity into traditional epidemiological models, we demonstrate the emergence of a new long timescale governing the epidemic, in broad agreement with empirical data. Our stochastic social activity model captures multiple features of real-life epidemics such as COVID-19, including prolonged plateaus and multiple waves, which are transiently suppressed due to the dynamic nature of social activity. The existence of a long timescale due to the interplay between epidemic and social dynamics provides a unifying picture of how a fast-paced epidemic typically will transition to an endemic state.

Time-dependent heterogeneity leads to transient suppression of the COVID-19 epidemic, not herd immunity.

Epidemics generally spread through a succession of waves that reflect factors on multiple timescales. On short timescales, superspreading events lead to burstiness and overdispersion, whereas long-term persistent heterogeneity in susceptibility is expected to lead to a reduction in both the infection peak and the herd immunity threshold (HIT). Here, we develop a general approach to encompass both timescales, including time variations in individual social activity, and demonstrate how to incorporate them phenomenologically into a wide class of epidemiological models through reparameterization. We derive a nonlinear dependence of the effective reproduction number [Formula: see text] on the susceptible population fraction S. We show that a state of transient collective immunity (TCI) emerges well below the HIT during early, high-paced stages of the epidemic. However, this is a fragile state that wanes over time due to changing levels of social activity, and so the infection peak is not an indication of long-lasting herd immunity: Subsequent waves may emerge due to behavioral changes in the population, driven by, for example, seasonal factors. Transient and long-term levels of heterogeneity are estimated using empirical data from the COVID-19 epidemic and from real-life face-to-face contact networks. These results suggest that the hardest hit areas, such as New York City, have achieved TCI following the first wave of the epidemic, but likely remain below the long-term HIT. Thus, in contrast to some previous claims, these regions can still experience subsequent waves.

Structured sequences emerge from random pool when replicated by templated ligation.

The central question in the origin of life is to understand how structure can emerge from randomness. The Eigen theory of replication states, for sequences that are copied one base at a time, that the replication fidelity has to surpass an error threshold to avoid that replicated specific sequences become random because of the incorporated replication errors [M. Eigen, Naturwissenschaften 58 (10), 465-523 (1971)]. Here, we showed that linking short oligomers from a random sequence pool in a templated ligation reaction reduced the sequence space of product strands. We started from 12-mer oligonucleotides with two bases in all possible combinations and triggered enzymatic ligation under temperature cycles. Surprisingly, we found the robust creation of long, highly structured sequences with low entropy. At the ligation site, complementary and alternating sequence patterns developed. However, between the ligation sites, we found either an A-rich or a T-rich sequence within a single oligonucleotide. Our modeling suggests that avoidance of hairpins was the likely cause for these two complementary sequence pools. What emerged was a network of complementary sequences that acted both as templates and substrates of the reaction. This self-selecting ligation reaction could be restarted by only a few majority sequences. The findings showed that replication by random templated ligation from a random sequence input will lead to a highly structured, long, and nonrandom sequence pool. This is a favorable starting point for a subsequent Darwinian evolution searching for higher catalytic functions in an RNA world scenario.

Entropic elasticity and negative thermal expansion in a simple cubic crystal.

While most solids expand when heated, some materials show the opposite behavior: negative thermal expansion (NTE). In polymers and biomolecules, NTE originates from the entropic elasticity of an ideal, freely jointed chain. The origin of NTE in solids has been widely believed to be different. Our neutron scattering study of a simple cubic NTE material, ScF3, overturns this consensus. We observe that the correlation in the positions of the neighboring fluorine atoms rapidly fades on warming, indicating an uncorrelated thermal motion constrained by the rigid Sc-F bonds. This leads us to a quantitative theory of NTE in terms of entropic elasticity of a floppy network crystal, which is in remarkable agreement with experimental results. We thus reveal the formidable universality of the NTE phenomenon in soft and hard matter.

Onset of natural selection in populations of autocatalytic heteropolymers.

Reduction of information entropy along with ever-increasing complexity is among the key signatures of life. Understanding the onset of such behavior in the early prebiotic world is essential for solving the problem of the origin of life. Here we study a general problem of heteropolymers capable of template-assisted ligation based on Watson-Crick-like hybridization. The system is driven off-equilibrium by cyclic changes in the environment. We model the dynamics of 2-mers, i.e., sequential pairs of specific monomers within the heteropolymer population. While the possible number of them is Z 2 (where Z is the number of monomer types), we observe that most of the 2-mers get extinct, leaving no more than 2Z survivors. This leads to a dramatic reduction of the information entropy in the sequence space. Our numerical results are supported by a general mathematical analysis of the competition of growing polymers for constituent monomers. This natural-selection-like process ultimately results in a limited subset of polymer sequences. Importantly, the set of surviving sequences depends on initial concentrations of monomers and remains exponentially large (2 L down from Z L for length L) in each of realizations. Thus, an inhomogeneity in initial conditions allows for a massively parallel search of the sequence space for biologically functional polymers, such as ribozymes. We also propose potential experimental implementations of our model in the contexts of either biopolymers or artificial nano-structures.

Communication: Programmable self-assembly of thin-shell mesostructures.

We study numerically the possibility of programmable self-assembly of various thin-shell architectures. They include clusters isomorphic to fullerenes C20 and C60, finite and infinite sheets, tube-shaped and toroidal mesostructures. Our approach is based on the recently introduced directionally functionalized nanoparticle platform, for which we employ a hybrid technique of Brownian dynamics with stochastic bond formation. By combining a number of strategies, we were able to achieve a near-perfect yield of the desired structures with a reduced "alphabet" of building blocks. Among those strategies are the following: the use of bending rigidity of the interparticle bond as a control parameter, programming the morphology with a seed architecture, use of chirality-preserving symmetries for reduction of the particle alphabet, and the hierarchic approach.

Layer-by-layer assembly of patchy particles as a route to nontrivial structures.

We propose a strategy for robust high-quality self-assembly of nontrivial periodic structures out of patchy particles and investigate it with Brownian dynamics simulations. Its first element is the use of specific patch-patch and shell-shell interactions between the particles, which can be implemented through differential functionalization of patched and shell regions with specific DNA strands. The other key element of our approach is the use of a layer-by-layer protocol that allows one to avoid the formation of undesired random aggregates. As an example, we design and self-assemble in silico a version of a double diamond lattice in which four particle types are arranged into bcc crystal made of four fcc sublattices. The lattice can be further converted to cubic diamond by selective removal of the particles of certain types. Our results demonstrate that by combining the directionality, selectivity of interactions, and the layer-by-layer protocol, a high-quality robust self-assembly can be achieved.

Self-organized architectures from assorted DNA-framed nanoparticles.

The science of self-assembly has undergone a radical shift from asking questions about why individual components self-organize into ordered structures, to manipulating the resultant order. However, the quest for far-reaching nanomanufacturing requires addressing an even more challenging question: how to form nanoparticle (NP) structures with designed architectures without explicitly prescribing particle positions. Here we report an assembly concept in which building instructions are embedded into NPs via DNA frames. The integration of NPs and DNA origami frames enables the fabrication of NPs with designed anisotropic and selective interactions. Using a pre-defined set of different DNA-framed NPs, we show it is possible to design diverse planar architectures, which include periodic structures and shaped meso-objects that spontaneously emerge on mixing of the different topological types of NP. Even objects of non-trivial shapes, such as a nanoscale model of Leonardo da Vinci's Vitruvian Man, can be self-assembled successfully.

Generic phase diagram of binary superlattices.

Emergence of a large variety of self-assembled superlattices is a dramatic recent trend in the fields of nanoparticle and colloidal sciences. Motivated by this development, we propose a model that combines simplicity with a remarkably rich phase behavior applicable to a wide range of such self-assembled systems. Those systems include nanoparticle and colloidal assemblies driven by DNA-mediated interactions, electrostatics, and possibly, controlled drying. In our model, a binary system of large and small hard spheres (L and S, respectively) interacts via selective short-range ("sticky") attraction. In its simplest version, this binary sticky sphere model features attraction only between S and L particles. We show that, in the limit when this attraction is sufficiently strong compared with [Formula: see text], the problem becomes purely geometrical: the thermodynamically preferred state should maximize the number of [Formula: see text] contacts. A general procedure for constructing the phase diagram as a function of system composition f and particle size ratio r is outlined. In this way, the global phase behavior can be calculated very efficiently for a given set of plausible candidate phases. Furthermore, the geometric nature of the problem enables us to generate those candidate phases through a well-defined and intuitive construction. We calculate the phase diagrams for both 2D and 3D systems and compare the results with existing experiments. Most of the 3D superlattices observed to date are featured in our phase diagram, whereas several more are predicted for future discovery.

In situ microscopy of the self-assembly of branched nanocrystals in solution.

Solution-phase self-assembly of nanocrystals into mesoscale structures is a promising strategy for constructing functional materials from nanoscale components. Liquid environments are key to self-assembly since they allow suspended nanocrystals to diffuse and interact freely, but they also complicate experiments. Real-time observations with single-particle resolution could have transformative impact on our understanding of nanocrystal self-assembly. Here we use real-time in situ imaging by liquid-cell electron microscopy to elucidate the nucleation and growth mechanism and properties of linear chains of octapod-shaped nanocrystals in their native solution environment. Statistical mechanics modelling based on these observations and using the measured chain-length distribution clarifies the relative importance of dipolar and entropic forces in the assembly process and gives direct access to the interparticle interaction. Our results suggest that monomer-resolved in situ imaging combined with modelling can provide unprecedented quantitative insight into the microscopic processes and interactions that govern nanocrystal self-assembly in solution.

Sequential programmable self-assembly: Role of cooperative interactions.

We propose a general strategy of "sequential programmable self-assembly" that enables a bottom-up design of arbitrary multi-particle architectures on nano- and microscales. We show that a naive realization of this scheme, based on the pairwise additive interactions between particles, has fundamental limitations that lead to a relatively high error rate. This can be overcome by using cooperative interparticle binding. The cooperativity is a well known feature of many biochemical processes, responsible, e.g., for signaling and regulations in living systems. Here we propose to utilize a similar strategy for high precision self-assembly, and show that DNA-mediated interactions provide a convenient platform for its implementation. In particular, we outline a specific design of a DNA-based complex which we call "DNA spider," that acts as a smart interparticle linker and provides a built-in cooperativity of binding. We demonstrate versatility of the sequential self-assembly based on spider-functionalized particles by designing several mesostructures of increasing complexity and simulating their assembly process. This includes a number of finite and repeating structures, in particular, the so-called tetrahelix and its several derivatives. Due to its generality, this approach allows one to design and successfully self-assemble virtually any structure made of a "GEOMAG" magnetic construction toy, out of nanoparticles. According to our results, once the binding cooperativity is strong enough, the sequential self-assembly becomes essentially error-free.

Diamond family of nanoparticle superlattices.

Diamond lattices formed by atomic or colloidal elements exhibit remarkable functional properties. However, building such structures via self-assembly has proven to be challenging because of the low packing fraction, sensitivity to bond orientation, and local heterogeneity. We report a strategy for creating a diamond superlattice of nano-objects via self-assembly and demonstrate its experimental realization by assembling two variant diamond lattices, one with and one without atomic analogs. Our approach relies on the association between anisotropic particles with well-defined tetravalent binding topology and isotropic particles. The constrained packing of triangular binding footprints of truncated tetrahedra on a sphere defines a unique three-dimensional lattice. Hence, the diamond self-assembly problem is solved via its mapping onto two-dimensional triangular packing on the surface of isotropic spherical particles.

Chromatic patchy particles: Effects of specific interactions on liquid structure.

We study the structural and thermodynamic properties of patchy particle liquids, with a special focus on the role of "color," i.e., specific interactions between individual patches. A possible experimental realization of such "chromatic" interactions is by decorating the particle patches with single-stranded DNA linkers. The complementarity of the linkers can promote selective bond formation between predetermined pairs of patches. By using MD simulations, we compare the local connectivity, the bond orientation order, and other structural properties of the aggregates formed by the "colored" and "colorless" systems. The analysis is done for spherical particles with two different patch arrangements (tetrahedral and cubic). It is found that the aggregated (liquid) phase of the "colorless" patchy particles is better connected, denser and typically has stronger local order than the corresponding "colored" one. This, in turn, makes the colored liquid less stable thermodynamically. Specifically, we predict that in a typical case the chromatic interactions should increase the relative stability of the crystalline phase with respect to the disordered liquid, thus expanding its region in the phase diagram.