Techniques for the Generation of Arbitrary Three-Dimensional Shapes in Tile-Based Self-Assembly Systems

A big challenge in nanorobotics is the construction of nanoscale objects. DNA is a bio-compatible tool to reliably and constructively create objects at the nanoscale. A possible tool to build nano-sized structures are tile-based self-assembly systems on the basis of DNA. It is challenging and time-consuming to efficiently design blueprints for the desired objects. This paper presents basic algorithms for the creation of tilesets for nxnxn-cubes in the aTAM model. Only few publications focus on three-dimensional DNA crystals. Three-dimensional shapes are likely to be of more use in nanorobotics. We present three variations: hollow cubes, cube-grids and filled cubes. The paper also presents a basic algorithm to create arbitrary, finite, connected, three-dimensional and predefined shapes at temperature 1, as well as ideas for more efficient algorithms. Among those are algorithms for spheres, ellipsoids, red blood cells and other promising designs. The algorithms and tilesets are tested/verified using a software that has been developed for the purpose of verifying three-dimensional sets of tiletypes and was influenced by the tool ISU TAS. Others can use the simulator and the algorithms to quickly create sets of tiletypes for their desired nanostructures. A long learning process may thus be omitted

Active Self-Assembly of Algorithmic Shapes and Patterns in Polylogarithmic Time

We describe a computational model for studying the complexity of self-assembled structures with active molecular components. Our model captures notions of growth and movement ubiquitous in biological systems. The model is inspired by biology's fantastic ability to assemble biomolecules that form systems with complicated structure and dynamics, from molecular motors that walk on rigid tracks and proteins that dynamically alter the structure of the cell during mitosis, to embryonic development where large-scale complicated organisms efficiently grow from a single cell. Using this active self-assembly model, we show how to efficiently self-assemble shapes and patterns from simple monomers. For example, we show how to grow a line of monomers in time and number of monomer states that is merely logarithmic in the length of the line. Our main results show how to grow arbitrary connected two-dimensional geometric shapes and patterns in expected time that is polylogarithmic in the size of the shape, plus roughly the time required to run a Turing machine deciding whether or not a given pixel is in the shape. We do this while keeping the number of monomer types logarithmic in shape size, plus those monomers required by the Kolmogorov complexity of the shape or pattern. This work thus highlights the efficiency advantages of active self-assembly over passive self-assembly and motivates experimental effort to construct general-purpose active molecular self-assembly systems

Optimization of supply diversity for the self-assembly of simple objects in two and three dimensions

The field of algorithmic self-assembly is concerned with the design and analysis of self-assembly systems from a computational perspective, that is, from the perspective of mathematical problems whose study may give insight into the natural processes through which elementary objects self-assemble into more complex ones. One of the main problems of algorithmic self-assembly is the minimum tile set problem (MTSP), which asks for a collection of types of elementary objects (called tiles) to be found for the self-assembly of an object having a pre-established shape. Such a collection is to be as concise as possible, thus minimizing supply diversity, while satisfying a set of stringent constraints having to do with the termination and other properties of the self-assembly process from its tile types. We present a study of what we think is the first practical approach to MTSP. Our study starts with the introduction of an evolutionary heuristic to tackle MTSP and includes results from extensive experimentation with the heuristic on the self-assembly of simple objects in two and three dimensions. The heuristic we introduce combines classic elements from the field of evolutionary computation with a problem-specific variant of Pareto dominance into a multi-objective approach to MTSP.Comment: Minor typos correcte

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

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

Nanometrology and super-resolution imaging with DNA

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