Self-Assembly of Structures with Addressable Complexity

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.

Transition from disordered aggregates to ordered lattices: kinetic control of the assembly of a computationally designed peptide

Natural biomolecular self-assembly typically occurs under a narrow range of solution conditions, and the design of sequences that can form prescribed structures under a range of such conditions would be valuable in the bottom-up assembly of predetermined nanostructures. We present a computationally designed peptide that robustly self-assembles into regular arrays under a wide range of solution pH and temperature conditions. Controling the solution conditions provides the opportunity to exploit a simple and reproducible approach for altering the pathway of peptide solution self-assembly. The computationally designed peptide forms a homotetrameric coiled-coil bundle that further self-assembles into 2-D plate structures with well-defined inter-bundle symmetry. Herein, we present how modulation of solution conditions, such as pH and temperature, can be used to control the kinetics of the inter-bundle assembly and manipulate the final morphology. Changes in solution pH primarily influence the inter-bundle assembly by affecting the charged state of ionizable residues on the bundle exterior while leaving the homotetrameric coiled-coil structure intact. At low pH, repulsive interactions prevent 2-D lattice nanostructure formation. Near the estimated isoelectric point of the peptide, bundle aggregation is rapid and yields disordered products, which subsequently transform into ordered nanostructures over days to weeks. At elevated temperatures (T = 40 °C or 50 °C), the formation of disordered, kinetically-trapped products largely can be eliminated, allowing the system to quickly assemble into plate-like nanostructured lattices. Moreover, subtle changes in pH and in the peptide charge state have a significant influence on the thickness of formed plates and on the hierarchical manner in which plates fuse into larger material structures with observable grain boundaries. These findings confirm the ability to finely tune the peptide assembly process to achieve a range of engineered structures with one simple 29-residue peptide building block.

Autocatalytic Time-Dependent Evolution of Metastable Two-Component Supramolecular Assemblies to Self-Sorted or Coassembled State

Despite substantial effort devoted in the history of supramolecular chemistry, synthetic supramolecular systems still lag behind biomolecular systems in terms of complexity and functionality. This is because biomolecular systems function in a multicomponent molecular network under out-of-equilibrium conditions. Here we report two-component supramolecular assemblies that are metastable and thus show time-dependent evolution. We found that the systems undergo either self-sorting or coassembly in time depending on the combination of components. Interestingly, this outcome, which had been previously achievable only under specific conditions, emerged from the two-component systems as a result of synergistic or reciprocal interplay between the coupled equilibria. We believe that this study sheds light on the similarity between synthetic and biomolecular systems and promotes better understanding of their intricate kinetic behaviors.

Kinetics-Controlled Amphiphile Self-Assembly Processes

Amphiphile self-assembly is an essential bottom-up approach of fabricating advanced functional materials. Self-assembled materials with desired structures are often obtained through thermodynamic control. Here, we demonstrate that the selection of kinetic pathways can lead to drastically different self-assembled structures, underlining the significance of kinetic control in self-assembly. By constructing kinetic network models from large-scale molecular dynamics simulations, we show that two largely similar amphiphiles, 1-[11-oxo-11-(pyren-1-ylmethoxy)-undecyl]pyridinium bromide (PYR) and 1-(11-((5a1,8a-dihydropyren-1-yl)methylamino)-11-oxoundecyl)pyridinium bromide (PYN), prefer distinct kinetic assembly pathways. While PYR prefers an incremental growth mechanism and forms a nanotube, PYN favors a hopping growth pathway leading to a vesicle. Such preference was found to originate from the subtle difference in the distributions of hydrophobic and hydrophilic groups in their chemical structures, which leads to different rates of the adhesion process among the aggregating micelles. Our results are in good agreement with experimental results, and accentuate the role of kinetics in the rational design of amphiphile self-assembly.

Free-energy predictions and absorption spectra calculations for supramolecular nanocarriers and their photoactive cargo

We reconstructed the free-energy landscape for supramolecular nanoparticles of amphiphilic methacrylated-based co-polymers. Their self-assembly in aqueous solution and encapsulation of borondipyrromethene (BODIPY) derivatives were enforced through atomistic free-energy simulations. The BODIPY binding modes detected in each of the free-energy basins were validated through a comparison of theoretical absorption spectra, calculated at the TD-DFT level, to their experimental counterparts. The nanoparticle distribution is controlled within a thermodynamic regime, with free-energy barriers approaching 8 kcal mol^-1, enabling the existence of different-sized nanoparticles in aqueous solution at room temperature. Two types of supramolecular morphologies were identified. One is compact and spherical in shape and the other is large and donut-like, with the former more stable than the latter by 4 kcal mol^-1. The morphology of the supramolecular host affects the binding mode of the BODIPY guests. Stacked BODIPY aggregates are encapsulated in the spherical nanocarriers, whereas isolated chromophores associate with the donut-shaped assemblies.

Communication: Free energy of ligand-receptor systems forming multimeric complexes

Ligand-receptor interactions are ubiquitous in biology and have become popular in materials in view of their applications to programmable self-assembly. Although complex functionalities often emerge from the simultaneous interaction of more than just two linker molecules, state of the art theoretical frameworks enable the calculation of the free energy only in systems featuring one-to-one ligand/receptor binding. In this Communication, we derive a general formula to calculate the free energy of systems featuring simultaneous direct interaction between an arbitrary number of linkers. To exemplify the potential and generality of our approach, we apply it to the systems recently introduced by Parolini et al. [ACS Nano 10, 2392 (2016)] and Halverson and Tkachenko [J. Chem. Phys. 144, 094903 (2016)], both featuring functionalized Brownian particles interacting via three-linker complexes.

Investigating the role of boundary bricks in DNA brick self-assembly

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 of DNA bricks to investigate the role of boundary bricks in the self-assembly of complex multicomponent target structures. We demonstrate that boundary bricks lower the free-energy barrier to nucleation and that boundary bricks on edges stabilize the final structure. However, boundary bricks are also more prone to aggregation, as they can stabilize partially assembled intermediates. We explore some design strategies that permit us to benefit from the stabilizing role of boundary bricks whilst minimizing their ability to hinder assembly; in particular, we show that maximizing the total number of boundary bricks is not an optimal strategy.

Supracolloidal reconfigurable polyhedra via hierarchical self-assembly

Enclosed three-dimensional structures with hollow interiors have been attractive targets for the self-assembly of building blocks across different length scales. Colloidal self-assembly, in particular, has enormous potential as a bottom-up means of structure fabrication exploiting a priori designed building blocks because of the scope for tuning interparticle interactions. Here we use computer simulation study to demonstrate the self-assembly of designer charge-stabilised colloidal magnetic particles into a series of supracolloidal polyhedra, each displaying a remarkable two-level structural hierarchy. The parameter space for design supports thermodynamically stable polyhedra of very different morphologies, namely tubular and hollow spheroidal structures, involving the formation of subunits of four-fold and three-fold rotational symmetry, respectively. The spheroidal polyhedra are chiral, despite having a high degree of rotational symmetry. The dominant pathways for self-assembly into these polyhedra reveal two distinct mechanisms - a growth mechanism via sequential attachment of the subunits for a tubular structure and a staged or hierarchical pathway for a spheroidal polyhedron. These supracolloidal architectures open up in response to an external magnetic field. Our results suggest design rules for synthetic reconfigurable containers at the microscale exploiting a hierarchical self-assembly scheme.

Nanoparticle assembly: from fundamentals to applications: concluding remarks

Nanoparticles, due to their broadly tunable functions, are major building blocks for generating new materials. However, building such materials for practical applications by self-assembly is quite challenging. Following the Faraday Discussion on "Nanoparticle Assembly: from Fundamentals to Applications" we discuss here the current trends in the field of self-assembly, including: understanding the unique interplay of molecular and nanoscale effects, a development of novel approaches for the creation of targeted nanoparticle architectures, advances in controlling dynamic behavior of systems and enabling new functions through specifically formed structures.

Optimal Self-Assembly of Linked Constructs and Catenanes via Spatial Confinement

How to direct the self-assembly of simple templates toward constructs with complex shape and topology is still an open problem. Recent advancements have made it possible to self-assemble various types of knotted constructs, but targeting general multicomponent topologies, that is, links and catenanes, has proved much harder. Here, we study how the yield and complexity of self-assembled links depends on both intrinsic and extrinsic system properties and, particularly, template shape and spatial confinement. We show that slit confinement does not necessarily suppress linking but can rather enhance it significantly thanks to entropic effects. We also found that only a limited set of binary links are recurrent for different template shapes. These privileged topologies include all those experimentally realized so far plus a few additional ones, such as the 7₇² and 7₈² links that, hence, ought to be ideal candidates for broadening the current class of constructs with addressable topology.

DNA brick self-assembly with an off-lattice potential

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 that our off-lattice model for DNA bricks results in robust self-assembly into a variety of target structures.

A variational approach to nucleation simulation

We study by computer simulation the nucleation of a supersaturated Lennard-Jones vapor into the liquid phase. The large free energy barriers to transition make the time scale of this process impossible to study by ordinary molecular dynamics simulations. Therefore we use a recently developed enhanced sampling method [Valsson and Parrinello, Phys. Rev. Lett.113, 090601 (2014)] based on the variational determination of a bias potential. We differ from previous applications of this method in that the bias is constructed on the basis of the physical model provided by the classical theory of nucleation. We examine the technical problems associated with this approach. Our results are very satisfactory and will pave the way for calculating the nucleation rates in many systems.