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

Hydrogen-Bonded Fibrous Nanotubes Assembled from Trigonal Prismatic Building Blocks

In reticular chemistry, molecular building blocks are designed to create crystalline open frameworks. A key principle of reticular chemistry is that the most symmetrical networks are the likely outcomes of reactions, particularly when highly symmetrical building blocks are involved. The strategy of synthesizing low-dimensional networks aims to reduce explicitly the symmetry of the molecular building blocks. Here we report the spontaneous formation of hydrogen-bonded fibrous structures from trigonal prismatic building blocks, which were designed to form three-dimensional crystalline networks on account of their highly symmetrical structures. Utilizing different microscopic and spectroscopic techniques, we identify the structures at the early stages of the assembly process in order to and understand the growth mechanism. The symmetrical molecular building blocks are incorporated preferentially in the longitudinal direction, giving rise to anisotropic hydrogen-bonded porous organic nanotubes. Entropy-driven anisotropic growth provides micrometer-scale unidirectional nanotubes with high porosity. By combining experimental evidence and theoretical modeling, we have obtained a deep understanding of the nucleation and growth processes. Our findings offer fundamental insight into the molecular design of tubular structures. The nanotubes evolve further in the transverse directions to provide extended higher-order fibrous structures [nano- and microfibers], ultimately leading to large-scale interconnected hydrogen-bonded fiber-like structures with twists and turns. Our work provides fundamental understanding and paves the way for innovative molecular designs in low-dimensional networks.

Branching Crisscross Polymerization of Single-Stranded DNA Slats

Controlling where and when self-assembly happens is crucial in both biological and synthetic systems as it optimizes the utilization of available resources. We previously reported strictly seed-initiated linear crisscross polymerization with alternating recruitment of single-stranded DNA slats that are aligned in a parallel versus perpendicular orientation with respect to the double-helical axes. However, for some applications, it would be advantageous to produce growth that is faster than what a linear assembly can provide. Here, we implement crisscross polymerization with alternating sets of six parallel slats versus six perpendicular slats and use this framework to explore branching behavior. We present architectures that, respectively, are designed to exhibit primary, secondary, and hyperbranching growth. Thus, amplification via nonlinear crisscross polymerization can provide a route for applications such as low-cost, enzyme-free, and ultrasensitive detection.

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.

Simulations of DNA-Origami Self-Assembly Reveal Design-Dependent Nucleation Barriers

Nucleation is the rate-determining step in the kinetics of many self-assembly processes. However, the importance of nucleation in the kinetics of DNA-origami self-assembly, which involves both the binding of staple strands and the folding of the scaffold strand, is unclear. Here, using Monte Carlo simulations of a lattice model of DNA origami, we find that some, but not all, designs can have a nucleation barrier and that this barrier disappears at lower temperatures, rationalizing the success of isothermal assembly. We show that the height of the nucleation barrier depends primarily on the coaxial stacking of staples that are adjacent on the same helix, a parameter that can be modified with staple design. Creating a nucleation barrier to DNA-origami assembly could be useful in optimizing assembly times and yields, while eliminating the barrier may allow for fast molecular sensors that can assemble/disassemble without hysteresis in response to changes in the environment.

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."

Nonequilibrium self-assembly of multiple stored targets in a dimer-based system

Nonequilibrium self-assembly can be found in various biological processes where chemical potential gradients are exploited to steer the system to a desired organized structure with a particular function. Microtubules, for example, are composed of two globular protein subunits, α-tubulin and β-tubulin, which bind together to form polar dimers that self-assemble a hollow cylinder structure in a process driven by GTPase activity. Inspired by this process, we define a generic self-assembly lattice model containing particles of two subunits, which is driven out-of-equilibrium by a dimer-favoring local driving force. Using Monte Carlo simulations, we characterize the ability of this system to restore pre-encoded target structures as a function of the initial seed size, interaction energy, chemical potential, number of target structures, and strength of the nonequilibrium drive. We demonstrate some intriguing consequences of the drive, such as a smaller critical seed and an improved target assembly stability, compared to the equilibrium scenario. Our results can expand the theoretical basis of nonequilibrium self-assembly and provide deeper understanding of how nonequilibrium driving can overcome equilibrium constraints.

Data-driven coarse-grained modeling of non-equilibrium systems

Modeling a high-dimensional Hamiltonian system in reduced dimensions with respect to coarse-grained (CG) variables can greatly reduce computational cost and enable efficient bottom-up prediction of main features of the system for many applications. However, it usually experiences significantly altered dynamics due to loss of degrees of freedom upon coarse-graining. To establish CG models that can faithfully preserve dynamics, previous efforts mainly focused on equilibrium systems. In contrast, various soft matter systems are known to be out of equilibrium. Therefore, the present work concerns non-equilibrium systems and enables accurate and efficient CG modeling that preserves non-equilibrium dynamics and is generally applicable to any non-equilibrium process and any observable of interest. To this end, the dynamic equation of a CG variable is built in the form of the non-stationary generalized Langevin equation (nsGLE), where the two-time memory kernel is determined from the data of the auto-correlation function of the observable of interest. By embedding the nsGLE in an extended dynamics framework, the nsGLE can be solved efficiently to predict the non-equilibrium dynamics of the CG variable. To prove and exploit the equivalence of the nsGLE and extended dynamics, the memory kernel is parameterized in a two-time exponential expansion. A data-driven hybrid optimization process is proposed for the parameterization, which integrates the differential-evolution method with the Levenberg-Marquardt algorithm to efficiently tackle a non-convex and high-dimensional optimization problem.

Co-self-assembly of multiple DNA origami nanostructures in a single pot

Simultaneous self-assembly of two distinct DNA origami nanostructures folded with the same scaffold strand was achieved in a single pot. Relative yields were tuned by adjusting concentrations of the competing strands, correlating well with folding kinetics of individual structures. These results can faciliate efficient fabrication of multi-structure systems and materials.

Probing the Formation Kinetics and Thermodynamics with Rationally Designed Analytical Tools Enables One-Pot Synthesis and Purification of a Tetrahedral DNA Nanostructure

The development of robust analytical tools capable of probing the formation kinetics and thermodynamics of DNA nanostructures is a crucial step toward better understanding and manufacturing of diverse DNA-based materials. Herein, we introduce a real-time fluorescence anisotropy assay and rationally designed DNA reaction termination probes (DRTPs) as a set of new tools for exploring the formation mechanisms of DNA nanostructures. We deployed these tools for probing the formation of a classic tetrahedral DNA nanostructure (TDN) as a model system. Our tools revealed that the formation of TDN was dominated by simultaneous hybridization, whereas its undesired side products were caused mainly through step-wise hybridization. An optimal reaction temperature exists that favors the formation of TDN over side products. With insight into the TDN formation mechanism, we further engineered magnetic DRTPs to achieve single-step purification of TDN, enabling 10-fold improvement in the ratio between the targeted TDN and undesired side products without tedious procedures or bulky instruments. Combining the optimal reaction and purification conditions, we finally demonstrated the one-pot synthesis and purification of TDN. The analytical techniques offered in this work may hold potential to find wide applications and inspire new analytical methods for structural DNA nanotechnology.

The Art of Designing DNA Nanostructures with CAD Software

Since the arrival of DNA nanotechnology nearly 40 years ago, the field has progressed from its beginnings of envisioning rather simple DNA structures having a branched, multi-strand architecture into creating beautifully complex structures comprising hundreds or even thousands of unique strands, with the possibility to exactly control the positions down to the molecular level. While the earliest construction methodologies, such as simple Holliday junctions or tiles, could reasonably be designed on pen and paper in a short amount of time, the advent of complex techniques, such as DNA origami or DNA bricks, require software to reduce the time required and propensity for human error within the design process. Where available, readily accessible design software catalyzes our ability to bring techniques to researchers in diverse fields and it has helped to speed the penetration of methods, such as DNA origami, into a wide range of applications from biomedicine to photonics. Here, we review the historical and current state of CAD software to enable a variety of methods that are fundamental to using structural DNA technology. Beginning with the first tools for predicting sequence-based secondary structure of nucleotides, we trace the development and significance of different software packages to the current state-of-the-art, with a particular focus on programs that are open source.

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.

Computational design of probes to detect bacterial genomes by multivalent binding

Rapid methods for diagnosis of bacterial infections are urgently needed to reduce inappropriate use of antibiotics, which contributes to antimicrobial resistance. In many rapid diagnostic methods, DNA oligonucleotide probes, attached to a surface, bind to specific nucleotide sequences in the DNA of a target pathogen. Typically, each probe binds to a single target sequence; i.e., target-probe binding is monovalent. Here we show using computer simulations that the detection sensitivity and specificity can be improved by designing probes that bind multivalently to the entire length of the pathogen genomic DNA, such that a given probe binds to multiple sites along the target DNA. Our results suggest that multivalent targeting of long pieces of genomic DNA can allow highly sensitive and selective binding of the target DNA, even if competing DNA in the sample also contains binding sites for the same probe sequences. Our results are robust to mild fragmentation of the bacterial genome. Our conclusions may also be relevant for DNA detection in other fields, such as disease diagnostics more broadly, environmental management, and food safety.

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.

Spatial control of irreversible protein aggregation

Liquid cellular compartments form in the cyto- or nucleoplasm and can regulate aberrant protein aggregation. Yet, the mechanisms by which these compartments affect protein aggregation remain unknown. Here, we combine kinetic theory of protein aggregation and liquid-liquid phase separation to study the spatial control of irreversible protein aggregation in the presence of liquid compartments. We find that even for weak interactions aggregates strongly partition into the liquid compartment. Aggregate partitioning is caused by a positive feedback mechanism of aggregate nucleation and growth driven by a flux maintaining the phase equilibrium between the compartment and its surrounding. Our model establishes a link between specific aggregating systems and the physical conditions maximizing aggregate partitioning into the compartment. The underlying mechanism of aggregate partitioning could be used to confine cytotoxic protein aggregates inside droplet-like compartments but may also represent a common mechanism to spatially control irreversible chemical reactions in general.

Spatiotemporal control of coacervate formation within liposomes

Liquid-liquid phase separation (LLPS), especially coacervation, plays a crucial role in cell biology, as it forms numerous membraneless organelles in cells. Coacervates play an indispensable role in regulating intracellular biochemistry, and their dysfunction is associated with several diseases. Understanding of the LLPS dynamics would greatly benefit from controlled in vitro assays that mimic cells. Here, we use a microfluidics-based methodology to form coacervates inside cell-sized (~10 µm) liposomes, allowing control over the dynamics. Protein-pore-mediated permeation of small molecules into liposomes triggers LLPS passively or via active mechanisms like enzymatic polymerization of nucleic acids. We demonstrate sequestration of proteins (FtsZ) and supramolecular assemblies (lipid vesicles), as well as the possibility to host metabolic reactions (β-galactosidase activity) inside coacervates. This coacervate-in-liposome platform provides a versatile tool to understand intracellular phase behavior, and these hybrid systems will allow engineering complex pathways to reconstitute cellular functions and facilitate bottom-up creation of synthetic cells.

The understanding of liquid-liquid phase separation is crucial to cell biology and benefits from cell-mimicking in vitro assays. Here, the authors develop a microfluidic platform to study coacervate formation inside liposomes and show the potential of these hybrid systems to create synthetic cells.

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.