The field of complex self-assembly is moving toward the design of multi-particle structures consisting of thousands of distinct building blocks. To exploit the potential benefits of structures with such `addressable complexity,' we need to understand the factors that optimize the yield and the kinetics of self-assembly. Here we use a simple theoretical method to explain the key features responsible for the unexpected success of DNA-brick experiments, which are currently the only demonstration of reliable self-assembly with such a large number of components. Simulations confirm that our theory accurately predicts the narrow temperature window in which error-free assembly can occur. Even more strikingly, our theory predicts that correct assembly of the complete structure may require a time-dependent experimental protocol. Furthermore, we predict that low coordination numbers result in non-classical nucleation behavior, which we find to be essential for achieving optimal nucleation kinetics under mild growth conditions. We also show that, rather surprisingly, the use of heterogeneous bond energies improves the nucleation kinetics and in fact appears to be necessary for assembling certain intricate three-dimensional structures. This observation makes it possible to sculpt nucleation pathways by tuning the distribution of interaction strengths. These insights not only suggest how to improve the design of structures based on DNA bricks, but also point the way toward the creation of a much wider class of chemical or colloidal structures with addressable complexity.
Theories of phase change and self-assembly often invoke the idea of a `quasiequilibrium', a regime in which the nonequilibrium association of building blocks results nonetheless in a structure whose properties are determined solely by an underlying free energy landscape. Here we study a prototypical example of multicomponent self-assembly, a one-dimensional fiber grown from red and blue blocks. If the equilibrium structure possesses compositional correlations different from those characteristic of random mixing, then it cannot be generated without error at any finite growth rate: there is no q…
We use analytic theory and computer simulation to study patterns formed during the growth of two-component assemblies in 2D and 3D. We show that these patterns undergo a nonequilibrium phase transition, at a particular growth rate, between mixed and demixed arrangements of component types. This finding suggests that principles of nonequilibrium statistical mechanics can be used to predict the outcome of multicomponent self-assembly, and suggests an experimental route to the self-assembly of multicomponent structures of a qualitatively defined nature.
In order 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 occ…
We describe some of the important physical characteristics of the `pathways', i.e. dynamical processes, by which molecular, nanoscale and micron-scale self-assembly occurs. We highlight the fact that there exist features of self-assembly pathways that are common to a wide range of physical systems, even though those systems may be different in respect of their microscopic details. We summarize some existing theoretical descriptions of self-assembly pathways, and highlight areas -- notably, the description of self-assembly pathways that occur `far' from equilibrium -- that are likely to become …
Inverse design can be a useful strategy for discovering interactions that drive particles to spontaneously self-assemble into a desired structure. Here, we extend an inverse design methodology--relative entropy optimization--to determine isotropic interactions that promote assembly of targeted multicomponent phases, and we apply this extension to design interactions for a variety of binary crystals ranging from compact triangular and square architectures to highly open structures with dodecagonal and octadecagonal motifs. We compare the resulting optimized (self and cross) interactions for the…
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 repro…
Understanding the pathways by which viral capsid proteins assemble around their genomes could identify key intermediates as potential drug targets. In this work we use computer simulations to characterize assembly over a wide range of capsid protein-protein interaction strengths and solution ionic strengths. We find that assembly pathways can be categorized into two classes, in which intermediates are either predominantly ordered or disordered. Our results suggest that estimating the protein-protein and the protein-genome binding affinities may be sufficient to predict which pathway occurs. Fu…
Advances in synthetic methods have spawned an array of nanoparticles and bio-inspired molecules of diverse shapes and interaction geometries. Recent experiments indicate that such anisotropic particles exhibit a variety of 'nonclassical' self-assembly pathways, forming ordered assemblies via intermediates that do not share the architecture of the bulk material. Here we apply mean field theory to a prototypical model of interacting anisotropic particles, and find a clear thermodynamic impetus for nonclassical ordering in certain regimes of parameter space. In other parameter regimes, by contras…
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,…
The design space for a self-assembled multicomponent objects ranges from a solution in which every building block is unique to one with the minimum number of distinct building blocks that unambiguously define the target structure. Using a novel pipeline, we explore the design spaces for a set of structures of various sizes and complexities. To understand the implications of the different solutions, we analyse their assembly dynamics using patchy particle simulations and study the influence of the number of distinct building blocks and the angular and spatial tolerances on their interactions on…
We present a coarse-grained model of clathrin that is simple enough to be computationally tractable yet includes key observed qualitative features: a triskelion structure with excluded volume between legs; assembly of polymorphic cages in the bulk; formation of buds on a membrane. We investigate the assembly of our model using both Monte Carlo simulations and molecular dynamics with hydrodynamic interactions, in the latter employing a new membrane boundary condition. In the bulk, a range of known clathrin structures are assembled. A membrane budding pathway involving the coalescence of multipl…
A computational investigation was carried out to understand the aggregation of nanoscale graphene with two typical assembly pathways of stacking assembly and sliding assembly in water. The interfacial-organized monolayer water film (MWF) hindering the aggregation of nanographene in both stacking and sliding assembly pathways was reported for the first time. By means of potential mean forces (PMFs) calculation, no energy barrier was observed during the sliding assembly of two graphene nanosheets, while the PMF profiles could be impacted by the contact forms of nanographene and the MWF within th…
Understanding interactions between microparticles and lipid membranes is of increasing importance, especially for unraveling the influence of microplastics on our health and environment. Here, we study how a short-ranged adhesive force between microparticles and model lipid membranes causes membrane-mediated particle assembly. Using confocal microscopy, we observe the initial particle attachment to the membrane, then particle wrapping, and in rare cases spontaneous membrane tubulation. In the attached state, we measure that the particle mobility decreases by 26%. If multiple particles adhere t…
Although pathway-specific kinetic theories are fundamentally important to describe and under- stand reversible polymerisation kinetics, they come in principle at a cost of having a large number of system-specific parameters. Here, we construct a dynamical Landau theory to describe the kinetics of activated linear supramolecular self-assembly, which drastically reduces the number of parameters and still describes most of the interesting and generic behavior of the system in hand. This phenomenological approach hinges on the fact that if nucleated, the polymerisation transition resembles a phase…
Cyanobacteria sequester photosynthetic enzymes into microcompartments which facilitate the conversion of carbon dioxide into sugars. Geometric similarities between these structures and self-assembling viral capsids have inspired models that posit microcompartments as stable equilibrium arrangements of the constituent proteins. Here we describe a different mechanism for microcompartment assembly, one that is fundamentally nonequilibrium and yet highly reliable. This pathway is revealed by simulations of a molecular model resolving the size and shape of a cargo droplet, and the extent and topogr…
Hierarchically structured natural materials possess functionalities unattainable to the same components organized or mixed in simpler ways. For instance, the bones and teeth of mammals are far stronger and more durable than the mineral phases from which they are derived because their constituents are organized hierarchically from the molecular scale to the macroscale. Making similarly functional synthetic hierarchical materials will require an understanding of how to promote the self-assembly of structure on multiple lengthscales, without falling foul of numerous possible kinetic traps. Here w…
Protein aggregation is of great importance in biology, e.g., in amyloid fibrillation. The aggregation processes that occur at the cellular scale must be highly stochastic in nature because of the statistical number fluctuations that arise on account of the small system size at the cellular scale. We study the nucleated reversible self-assembly of monomeric building blocks into polymer-like aggregates using the method of kinetic Monte Carlo. Kinetic Monte Carlo, being inherently stochastic, allows us to study the impact of fluctuations on the polymerisation reactions. One of the most important …
From dumbbells to FCC crystals, we study the self-assembly pathway of amphiphatic, spherical colloidal particles as a function of the size of the hydrophobic region using molecular dynamics simulations. Specifically, we analyze how local inter-particle interactions correlate to the final self-assembled aggregate and how they affect the dynamical pathway of structure formation. We present a detailed diagram separating the many phases that we find for different sizes of the hydrophobic area, and uncover a narrow region where particles self-assemble into hollow, faceted cages that could potential…
We present a technique for calculating free-energy profiles for the nucleation of multicomponent structures that contain as many species as building blocks. We find that a key factor is the topology of the graph describing the connectivity of the target assembly. By considering the designed interactions separately from weaker, incidental interactions, our approach yields predictions for the equilibrium yield and nucleation barriers. These predictions are in good agreement with corresponding Monte Carlo simulations. We show that a few fundamental properties of the connectivity graph determine t…
Self-assembly is traditionally described as the process through which an initially disordered system relaxes towards an equilibrium ordered phase only driven by local interactions between its building blocks. However, This definition is too restrictive. Nature itself provides examples of amorphous, yet functional, materials assembled upon kinetically arresting the pathway towards the ground state. Kinetic self-assembly is intrinsically more flexible and reliable than its equilibrium counterpart, allowing control over the morphology of the final phase by tuning both the interactions and the the…
Here, we describe a method for the enhanced self-assembly of triblock Janus colloids targeted to form a kagome lattice. Using computer simulations, we demonstrate that the formation of this elusive structure can be significantly improved by self-propelling or activating the colloids along the axis connecting their hydrophobic hemispheres. The process by which metastable aggregates are destabilized and transformed into the favored kagome lattice is quite general, and we argue this active approach provides a systematic pathway to improving the self-assembly of a large number of colloidal structu…
Co-assembly of inorganic nanoparticles (NPs) and nanostructured polymer matrix represents an intricate interplay of enthalpic or entropic forces. Particle size largely affects the phase behavior of the nanocomposite. Theoretical studies indicate that new morphologies would emerge when the particles become comparable to the soft matrix's size, but this has rarely been supported experimentally. By designing a multicomponent blend composed of NPs, block copolymer-based supramolecules, and small molecules, a 3-D ordered lattice beyond the native BCP's morphology was recently reported when the part…
Although pathway-specific kinetic theories are fundamentally important to describe and understand reversible polymerisation kinetics, they come in principle at a cost of having a large number of system-specific parameters. Here, we construct a dynamical Landau theory to describe the kinetics of activated linear supramolecular self-assembly, which drastically reduces the number of parameters and still describes most of the interesting and generic behavior of the system in hand. This phenomenological approach hinges on the fact that if nucleated, the polymerisation transition resembles a phase t…
Bacterial microcompartments are large, roughly icosahedral shells that assemble around enzymes and reactants involved in certain metabolic pathways in bacteria. Motivated by microcompartment assembly, we use coarse-grained computational and theoretical modeling to study the factors that control the size and morphology of a protein shell assembling around hundreds to thousands of molecules. We perform dynamical simulations of shell assembly in the presence and absence of cargo over a range of interaction strengths, subunit and cargo stoichiometries, and the shell spontaneous curvature. Dependin…
The formation of a viral capsid -- the highly-ordered protein shell that surrounds the genome of a virus -- is the canonical example of self-assembly. The capsids of many positive-sense RNA viruses spontaneously assemble from in vitro mixtures of the coat protein and RNA. The high yield of proper capsids that assemble is remarkable, given their structural complexity: 180 identical proteins must arrange into three distinct local configurations to form an icosahedral capsid with a triangulation number of 3 (T = 3). Despite a wealth of data from structural studies and simulations, even the most f…
We systematically study the design of simple patchy sphere models that reversibly self-assemble into monodisperse icosahedral clusters. We find that the optimal patch width is a compromise between structural specificity (the patches must be narrow enough to energetically select the desired clusters) and kinetic accessibility (they must be sufficiently wide to avoid kinetic traps). Similarly, for good yields the temperature must be low enough for the clusters to be thermodynamically stable, but the clusters must also have enough thermal energy to allow incorrectly formed bonds to be broken. Ord…
A series of simulations aimed at elucidating the self-assembly dynamics of spherical virus capsids is described. This little-understood phenomenon is a fascinating example of the complex processes that occur in the simplest of organisms. The fact that different viruses adopt similar structural forms is an indication of a common underlying design, motivating the use of simplified, low-resolution models in exploring the assembly process. Several versions of a molecular dynamics approach are described. Polyhedral shells of different sizes are involved, the assembly pathways are either irreversibl…
We report the synthesis of complex salts made from the cationic surfactant dodecyltrimethyl-ammonium and diblock copolymers poly(acrylic acid)-block-poly(acrylamide) of different molecular weights. In water, the complex salts self-assemble into stable hierarchical aggregates with a dense core and a diffuse shell. In contrast to earlier reports, the surfactant/polymer aggregates exhibit a liquid crystalline structure of Pm3n cubic symmetry. The crystal structure is analogous to that obtained with homopolymer. Size and aggregation numbers were estimated from a combination of light and small-angl…
Multi-step pathways, constituted of a sequence of reconfigurations, are central to a wide variety of natural and man-made systems. Such pathways autonomously execute in self-guided processes such as protein folding and self-assembly, but require external control in macroscopic mechanical systems, provided by, e.g., actuators in robotics or manual folding in origami. Here we introduce shape-changing mechanical metamaterials, that exhibit self-guided multi-step pathways in response to global uniform compression. Their design combines strongly nonlinear mechanical elements with a multimodal archi…
Self-assembly at submicroscopic scales is an important but little understood phenomenon. A prominent example is virus capsid growth, whose underlying behavior can be modeled using simple particles that assemble into polyhedral shells. Molecular dynamics simulation of shell formation in the presence of an atomistic solvent provides new insight into the self-assembly mechanism, notably that growth proceeds via a cascade of strongly reversible steps and, despite the large variety of possible intermediates, only a small fraction of highly bonded forms appear on the pathway.
In the standard DNA brick set-up, distinct 32-nucleotide strands of single-stranded DNA are each designed to bind specifically to four other such molecules. Experimentally, it has been demonstrated that the overall yield is increased if certain bricks which occur on the outer faces of target structures are merged with adjacent bricks. However, it is not well understood by what mechanism such `boundary bricks' increase the yield, as they likely influence both the nucleation process and the final stability of the target structure. Here, we use Monte Carlo simulations with a patchy particle model…
We explore the use of templated self-assembly to facilitate the formation of complex target structures made from patchy particles. First, we consider the templating of high-symmetry shell structures around a spherical core particle. We find that nucleation around the core particle can inhibit aggregate formation, a process which often hinders self-assembly. In particular, this new assembly pathway allows dodecahedral shells to form readily, whereas these structures never form in the absence of the template. Secondly, we consider the self-assembly of multi-shell structures, where the central ic…
The self-assembly of functionalized (patchy) particles with directional interactions into target structures is still a challenge, despite the significant experimental advances on their synthesis. The self-assembly pathways are typically characterized by high energy barriers that hinder the access to stable (equilibrium) structures. A possible strategy to tackle this challenge is to perform annealing cycles. By periodically switching on and off the inter-particle bonds, one expects to smooth-out the kinetic pathways and favor the assembly of targeted structures. Preliminary results have shown t…
Steering Active-Colloid Assembly by Biasing Dissipation
University of Science and Technology of China（中国科学技术大学）；Rice University（莱斯大学）；Hefei National Research Center for Physical Sciences at the Microscale（合肥微尺度物质科学国家研究中心）
The desire to create cell-like models for fundamental science and applications has spurred extensive effort towards creating giant unilamellar vesicles (GUVs). However, a route to selectively self-assemble GUVs in bulk has remained elusive. In bulk solution, membrane-forming molecules such as phospholipids, single-tailed surfactants, and block copolymers typically self-assemble into multilamellar, onion-like structures. So although self-assembly processes can form nanoscale unilamellar vesicles, scaffolding by droplets or surfaces is required to create GUVs. Here we show that surprisingly, it …
We report Monte Carlo simulations of a simple off-lattice patchy-particle model for DNA `bricks'. We relate the parameters that characterise this model with the binding free energy of pairs of single-stranded DNA molecules. We verify that an off-lattice potential parameterised in this way reproduces much of the behaviour seen with a simpler lattice model we introduced previously, although the relaxation of the geometric constraints leads to a more error-prone self-assembly pathway. We investigate the self-assembly process as a function of the strength of the non-specific interactions. We show …
Polypeptides can self-assemble into hierarchically organized fibrils consisting of a stack of individually folded polypeptides driven together by hydrophobic interaction. Using a coarse grained model, we systematically studied this self-assembly as a function of temperature and hydrophobicity of the residues on the outside of the building block. We find the self-assembly can occur via two different pathways - a random aggregation-folding route, and a templated-folding process - thus indicating a strong coupling between folding and assembly. The simulation results can explain experimental evide…
The optimal design of DNA origami systems that assemble rapidly and robustly is hampered by the lack of a model for self-assembly that is sufficiently detailed yet computationally tractable. Here, we propose a model for DNA origami that strikes a balance between these two criteria by representing these systems on a lattice at the level of binding domains. The free energy of hybridization between individual binding domains is estimated with a nearest-neighbour model. Double helical segments are treated as rigid rods, but we allow flexibility at points where the backbone of one of the strands is…
