Self-Assembly of Arbitrary Shapes Using RNAse Enzymes: Meeting the Kolmogorov Bound with Small Scale Factor (extended abstract)

We consider a model of algorithmic self-assembly of geometric shapes out of square Wang tiles studied in SODA 2010, in which there are two types of tiles (e.g., constructed out of DNA and RNA material) and one operation that destroys all tiles of a particular type (e.g., an RNAse enzyme destroys all RNA tiles). We show that a single use of this destruction operation enables much more efficient construction of arbitrary shapes. In particular, an arbitrary shape can be constructed using an asymptotically optimal number of distinct tile types (related to the shape's Kolmogorov complexity), after scaling the shape by only a logarithmic factor. By contrast, without the destruction operation, the best such result has a scale factor at least linear in the size of the shape, and is connected only by a spanning tree of the scaled tiles. We also characterize a large collection of shapes that can be constructed efficiently without any scaling

Self-Replication via Tile Self-Assembly (Extended Abstract)

In this paper we present a model containing modifications to the Signal-passing Tile Assembly Model (STAM), a tile-based self-assembly model whose tiles are capable of activating and deactivating glues based on the binding of other glues. These modifications consist of an extension to 3D, the ability of tiles to form "flexible" bonds that allow bound tiles to rotate relative to each other, and allowing tiles of multiple shapes within the same system. We call this new model the STAM*, and we present a series of constructions within it that are capable of self-replicating behavior. Namely, the input seed assemblies to our STAM* systems can encode either "genomes" specifying the instructions for building a target shape, or can be copies of the target shape with instructions built in. A universal tile set exists for any target shape (at scale factor 2), and from a genome assembly creates infinite copies of the genome as well as the target shape. An input target structure, on the other hand, can be "deconstructed" by the universal tile set to form a genome encoding it, which will then replicate and also initiate the growth of copies of assemblies of the target shape. Since the lengths of the genomes for these constructions are proportional to the number of points in the target shape, we also present a replicator which utilizes hierarchical self-assembly to greatly reduce the size of the genomes required. The main goals of this work are to examine minimal requirements of self-assembling systems capable of self-replicating behavior, with the aim of better understanding self-replication in nature as well as understanding the complexity of mimicking it

Engineering Molecular Self-assembly and Reconfiguration in DNA Nanostructures

Smart electronics have developed ubiquitously to assist people in everything from navigation to health monitoring. The rise of complex electronics relied on rational design of platforms to build ever larger and more complex circuit networks and for frameworks to test those electronics. Biochemical circuits have also seen dramatic advancement in the last two decades within the field of DNA nanotechnology. As with electronics, DNA nanotechnology applied rational design to DNA molecules to build ever more complex biochemical networks that, beyond current electronics, also retain a significant measure of biological compatibility and plasticity akin to many networks of biological origin. Well situated for promising applications in diagnostics and therapeutics, advancing DNA nanotechnology devices will also rely upon larger platforms and testing frameworks. In roughly the last decade, researchers have been building upon the invention of DNA origami, a technique allowing the robust construction of biomolecular nano-structures capable of precise nanometer positioning of proteins, nanoparticles, and other molecules. DNA circuits have computed on the nanostructures; DNA robots have moved nanoparticles, made choices, and have even sorted cargo on the surface of a nanostructure. The complexity of circuits and devices continues to rise. In this thesis, we will discuss our contributions to the field of DNA nanotechnology by developing design rules and systematic approaches to controlling nanostructure complex assembly. These rules and approaches allow for the construction of molecular structures with a tunable diversity, large systems approaching the size of bacteria yet retaining nanometer precision, and biological plasticity inspired dynamic systems for arbitrary reconfiguration. Using a DNA origami tile tailored for array formation with a high continuous surface area, we create a framework inspired from molecular stochasticity for programming DNA array formation and gaining control over diversity of global properties through simple local rules. Three general forms of planar networks, random loops, mazes, and trees, were manipulated on the micron scale upon the self-assembled DNA arrays. We demonstrate control of several properties of the networks, such as branching rules, growth directions, the proximity between adjacent networks, and size distributions. The large diversity, in principle, allows for a wide, but tunable, testing environment for molecular circuits. By further applying these principles to subunits of finite assemblies, variable components may be mixed with fixed components potentially opening additional applications in high throughput device or drug screening. Next we turned to expanding the platform size biochemical circuits may be built upon. While DNA origami allows nanometer precise placement, the size remains roughly below 0.05 um2. Toward making large arbitrarily complex structures with only a set of simple tiles, multi-stage self-assembly has been explored in theory and for small DNA tiles. None were successful experimentally with DNA origami. We developed a strategy for DNA origami: a simple rule set applied recursively in each stage of a hierarchical self-assembly process, and to significantly reduce costs, a constant set of unique DNA strands regardless of size. We also developed a software tool to automatically compile a designed surface pattern into experimental protocols. We experimentally demonstrated DNA origami arrays approaching the size of small bacteria, 0.5 um2, with several arbitrary patterns, each consisting of 8,704 specifically chosen pixel locations with nanometer precision, including a bacteria sized portrait of a bacteria. The large platform opens the door to more advanced molecular circuits for applications such as diagnostics. Finally we demonstrated control over the dynamics of DNA origami reconfiguration in tile arrays. In an approach we call DNA tile displacement, we showed that a DNA origami array may have tiles arbitrarily replaced by another tile, including tiles of another shape or surface pattern. We also demonstrated control over the kinetics of tile displacement and performed several general purpose reconfigurations of DNA nanostructures. Examples include sequential reconfiguration, competitive reconfiguration, cooperative reconfiguration, and finally the scalability of multi-step reconfiguration as demonstrated through a fully playable nano-scale biomolecular tic-tac-toe game. The major ramifications are a plasticity more common to biology than to electronics—molecular platforms with arbitrary patterning that can reconfigure an arbitrary part of the nanostructure in an arbitrary order based on environmental signals. In principle, such reconfiguration can allow advanced circuits with the capacity to adapt to environmental needs or heal damaged components.</p

Self-Assembly of Any Shape with Constant Tile Types using High Temperature

Inspired by nature and motivated by a lack of top-down tools for precise nanoscale manufacture, self-assembly is a bottom-up process where simple, unorganized components autonomously combine to form larger more complex structures. Such systems hide rich algorithmic properties - notably, Turing universality - and a self-assembly system can be seen as both the object to be manufactured as well as the machine controlling the manufacturing process. Thus, a benchmark problem in self-assembly is the unique assembly of shapes: to design a set of simple agents which, based on aggregation rules and random movement, self-assemble into a particular shape and nothing else. We use a popular model of self-assembly, the 2-handed or hierarchical tile assembly model, and allow the existence of repulsive forces, which is a well-studied variant. The technique utilizes a finely-tuned temperature (the minimum required affinity required for aggregation of separate complexes). We show that calibrating the temperature and the strength of the aggregation between the tiles, one can encode the shape to be assembled without increasing the number of distinct tile types. Precisely, we show one tile set for which the following holds: for any finite connected shape S, there exists a setting of binding strengths between tiles and a temperature under which the system uniquely assembles S at some scale factor. Our tile system only uses one repulsive glue type and the system is growth-only (it produces no unstable assemblies). The best previous unique shape assembly results in tile assembly models use O(K(S)/(log K(S))) distinct tile types, where K(S) is the Kolmogorov (descriptional) complexity of the shape S

DNA-BASED SELF-ASSEMBLY AND NANOROBOTICS: THEORY AND EXPERIMENTS

We study the following fundamental questions in DNA-based self-assembly and nanorobotics: How to control errors in self-assembly? How to construct complex nanoscale objects in simpler ways? How to transport nanoscale objects in programmable manner? Fault tolerance in self-assembly: Fault tolerant self-assembly is important for nanofab-rication and nanocomputing applications. It is desirable to design compact error-resilient schemes that do not result in the increase in the original size of the assemblies. We present a comprehensive theory of compact error-resilient schemes for algorithmic self-assembly in two and three dimensions, and discuss the limitations and capabilities of redundancy based compact error correction schemes. New and powerful self-assembly model: We develop a reversible self-assembly model in which the glue strength between two juxtaposed tiles is a function of the time they have been in neighboring positions. Under our time-dependent glue model, we can rigorously study and demonstrate catalysis and self-replication in the tile assembly. We can assemble thin rectangles of size k × N using O

Designing the self-assembly of arbitrary shapes using minimal complexity building blocks

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 the kinetics and yield of the target assembly. We show that the resource-saving solution with minimum number of distinct blocks can often assemble just as well (or faster) than designs where each building block is unique. We further use our methods to design multifarious structures, where building blocks are shared between different target structures. Finally, we use coarse-grained DNA simulations to investigate the realisation of multicomponent shapes using DNA nanostructures as building blocks.Comment: 12 page

Randomness, information encoding, and shape replication in various models of DNA-inspired self-assembly

Self-assembly is the process by which simple, unorganized components autonomously combine to form larger, more complex structures. Researchers are turning to self-assembly technology for the design of ever smaller, more complex, and precise nanoscale devices, and as an emerging fundamental tool for nanotechnology. We introduce the robust random number generation problem, the problem of encoding a target string of bits in the form of a bit string pad, and the problem of shape replication in various models of tile-based self-assembly. Also included are preliminary results in each of these directions with discussion of possible future work directions

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

Program Size and Temperature in Self-Assembly

Winfree’s abstract Tile Assembly Model is a model of molecular self-assembly of DNA complexes known as tiles, which float freely in solution and attach one at a time to a growing “seed” assembly based on specific binding sites on their four sides. We show that there is a polynomial-time algorithm that, given an n×n square, finds the minimal tile system (i.e., the system with the smallest number of distinct tile types) that uniquely self-assembles the square, answering an open question of Adleman et al. (Combinatorial optimization problems in self-assembly, STOC 2002). Our investigation leading to this algorithm reveals other positive and negative results about the relationship between the size of a tile system and its “temperature” (the binding strength threshold required for a tile to attach)