Zorana Zeravcic

Size limits of self-assembled colloidal structures made using specific interactions

Significance Nature uses hierarchical assembly to make complex structures such as biomolecules, virus shells, and microtubules with high fidelity. Today a key challenge is to translate this process to artificial systems, which hinges on understanding the fundamental questions of efficiency and scalability of self-assembly. Although self-assembly has been studied for decades, the principles behind it and its fundamental and practical limits are still largely unknown. In this paper we establish size limitations for assembling structures of controlled size and shape out of colloidal particles with specific interactions. Inspired by simulations of structures with highly variable shapes and sizes, we develop an understanding of yield through a general theory of excited states that compete with the desired structure in assembly. We establish size limitations for assembling structures of controlled size and shape out of colloidal particles with short-ranged interactions. Through simulations we show that structures with highly variable shapes made out of dozens of particles can form with high yield, as long as each particle in the structure binds only to the particles in their local environment. To understand this, we identify the excited states that compete with the ground-state structure and demonstrate that these excited states have a completely topological characterization, valid when the interparticle interactions are short-ranged. This allows complete enumeration of the energy landscape and gives bounds on how large a colloidal structure can assemble with high yield. For large structures the yield can be significant, even with hundreds of particles.

Self-replicating colloidal clusters

Significance One of the hallmarks of living systems is self-replication. Mimicking nature’s ability to self-replicate would not only give more insight into biological mechanisms of self-replication but also could potentially revolutionize material science and nanotechnology. Over the past 60 y, much research, both theoretical and experimental, has been focused on understanding and realizing self-replicating systems. However, artificial systems that efficiently self-replicate remained elusive. In this paper, we construct schemes for self-replication of small clusters of isotropic particles. By manipulating the energy landscape of the process, we show how exponential replication can be achieved. As a proof of principle, we show exponential self-replication of an octahedral cluster using finite-temperature computer simulations. We construct schemes for self-replicating clusters of spherical particles, validated with computer simulations in a finite-temperature heat bath. Each particle has stickers uniformly distributed over its surface, and the rules for self-replication are encoded into the specificity and strength of interactions. Geometrical constraints imply that a compact cluster can copy itself only with help of a catalyst, a smaller cluster that increases the surface area to form a template. Replication efficiency requires optimizing interaction energies to destabilize all kinetic traps along the reaction pathway, as well as initiating a trigger event that specifies when the new cluster disassociates from its parent. Although there is a reasonably wide parameter range for self-replication, there is a subtle balance between the speed of the reaction, and the error rate. As a proof of principle, we construct interactions that self-replicate an octahedron, requiring a two-particle dimer for a catalyst. The resulting self-replication scheme is a hypercycle, and computer simulations confirm the exponential growth of both octahedron and catalyst replicas.

Contact changes near jamming

We probe the onset and effect of contact changes in soft harmonic particle packings which are sheared quasistatically. We find that the first contact changes are the creation or breaking of contacts on a single particle. We characterize the critical strain, statistics of breaking versus making a contact, and ratio of shear modulus before and after such events, and explain their finite size scaling relations. For large systems at finite pressure, the critical strain vanishes but the ratio of shear modulus before and after a contact change approaches one: linear response remains relevant in large systems. For finite systems close to jamming the critical strain also vanishes, but here linear response already breaks down after a single contact change.

Multifarious assembly mixtures: Systems allowing retrieval of diverse stored structures

Significance Self-assembly has recently emerged as a powerful technique for synthesizing structures on the nano- and microscales. The basis of this development is the use of biopolymers, like DNA, to design specific interactions between multiple species of components, allowing the spontaneous assembly of complex structures. Our work addresses a fundamental limitation of the existing approaches to self-assembly: Namely, every target structure must have its own dedicated set of components, which are programmed to assemble only that very structure. In contrast, in biological systems, the same set of components can assemble many different complexes. Inspired by this, we extend the self-assembly framework to mixtures of shared components capable of assembling distinct structures on demand. Self-assembly materials are traditionally designed so that molecular or mesoscale components form a single kind of large structure. Here, we propose a scheme to create “multifarious assembly mixtures,” which self-assemble many different large structures from a set of shared components. We show that the number of multifarious structures stored in the solution of components increases rapidly with the number of different types of components. However, each stored structure can be retrieved by tuning only a few parameters, the number of which is only weakly dependent on the size of the assembled structure. Implications for artificial and biological self-assembly are discussed.

Spontaneous emergence of catalytic cycles with colloidal spheres.

Significance Biological systems inspire a new paradigm for material synthesis, aiming to design materials that emulate living systems, providing both functionality and self-replication. Colloidal particles endowed with specific interactions provide a particularly promising approach for realizing this vision. Here, we consider a set of colloidal spheres with specific, time-dependent interactions and demonstrate that the interactions can be designed so that clusters of particles create other clusters through templating reactions. Surprisingly, simple templating rules generically give rise to the production of a sea of clusters of various sizes. The sea of clusters grows exponentially in a catalytic cycle. This is a specific realization of Dyson’s notion of an exponentially growing metabolism, emerging naturally from a simple scheme. Colloidal particles endowed with specific time-dependent interactions are a promising route for realizing artificial materials that have the properties of living ones. Previous work has demonstrated how this system can give rise to self-replication. Here, we introduce the process of colloidal catalysis, in which clusters of particles catalyze the creation of other clusters through templating reactions. Surprisingly, we find that simple templating rules generically lead to the production of huge numbers of clusters. The templating reactions among this sea of clusters give rise to an exponentially growing catalytic cycle, a specific realization of Dyson’s notion of an exponentially growing metabolism. We demonstrate this behavior with a fixed set of interactions between particles chosen to allow a catalysis of a specific six-particle cluster from a specific seven-particle cluster, yet giving rise to the catalytic production of a sea of clusters of sizes between 2 and 11 particles. The fact that an exponentially growing cycle emerges naturally from such a simple scheme demonstrates that the emergence of exponentially growing metabolisms could be simpler than previously imagined.