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

Fractals, Randomization, Optimal Constructions, and Replication in Algorithmic Self-Assembly

The problem of the strict self-assembly of infinite fractals within tile self-assembly is considered. In particular, tile assembly algorithms are provided for the assembly of the discrete Sierpinski triangle and the discrete Sierpinski carpet. The robust random number generation problem in the abstract tile assembly model is introduced. First, it is shown this is possible for a robust fair coin flip within the aTAM, and that such systems guarantee a worst case O(1) space usage. This primary construction is accompanied with variants that show trade-offs in space complexity, initial seed size, temperature, tile complexity, bias, and extensibility. This work analyzes the number of tile types t, bins b, and stages necessary and sufficient to assemble n × n squares and scaled shapes in the staged tile assembly model. Further, this work shows how to design a universal shape replicator in a 2-HAM self-assembly system with both attractive and repulsive forces

Self-Assembly of Tiles: Theoretical Models, the Power of Signals, and Local Computing

DNA-based self-assembly is an autonomous process whereby a disordered system of DNA sequences forms an organized structure or pattern as a consequence of Watson-Crick complementarity of DNA sequences, without external direction. Here, we propose self-assembly (SA) hypergraph automata as an automata-theoretic model for patterned self-assembly. We investigate the computational power of SA-hypergraph automata and show that for every recognizable picture language, there exists an SA-hypergraph automaton that accepts this language. Conversely, we prove that for any restricted SA-hypergraph automaton, there exists a Wang Tile System, a model for recognizable picture languages, that accepts the same language. Moreover, we investigate the computational power of some variants of the Signal-passing Tile Assembly Model (STAM), as well as propose the concept of {\it Smart Tiles}, i.e., tiles with glues that can be activated or deactivated by signals, and which possess a limited amount of local computing capability. We demonstrate the potential of smart tiles to perform some robotic tasks such as replicating complex shapes

Beyond DNA origami: the unfolding prospects of nucleic acid nanotechnology

Nucleic acid nanotechnology exploits the programmable molecular recognition properties of natural and synthetic nucleic acids to assemble structures with nanometer‐scale precision. In 2006, DNA origami transformed the field by providing a versatile platform for self‐assembly of arbitrary shapes from one long DNA strand held in place by hundreds of short, site‐specific (spatially addressable) DNA ‘staples’. This revolutionary approach has led to the creation of a multitude of two‐dimensional and three‐dimensional scaffolds that form the basis for functional nanodevices. Not limited to nucleic acids, these nanodevices can incorporate other structural and functional materials, such as proteins and nanoparticles, making them broadly useful for current and future applications in emerging fields such as nanomedicine, nanoelectronics, and alternative energy. WIREs Nanomed Nanobiotechnol 2012, 4:139–152. doi: 10.1002/wnan.170 For further resources related to this article, please visit the WIREs website .Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/90282/1/170_ftp.pd

Automated evolutionary design of self-assembly and self-organising systems

Self-assembly and self-organisation are natural construction processes where the spontaneous formation of aggregates emerges throughout the progressive interplay of local interactions among its constituents. Made upon cooperative self-reliant components, self-assembly and self-organising systems are seen as distributed, not necessarily synchronous, autopoietic mechanisms for the bottom-up fabrication of supra-structures. The systematic understanding of how nature endows these autonomous components with sufficient ''intelligence'' to combine themselves to form useful aggregates brings challenging questions to science, answers to which have many potential applications in matters of life and technological advances. It is for this reason that the investigation to be presented along this thesis focuses on the automated design of self-assembly and self-organising systems by means of artificial evolution. Towards this goal, this dissertation embodies research on evolutionary algorithms applied to the parameters design of a computational model of self-organisation and the components design of a computational model of self-assembly. In addition, an analytical assessment combining correlation metrics and clustering, as well as the exploration of emergent patterns of cooperativity and the measurement of activity across evolution, is made. The results support the research hypothesis that an adaptive process such as artificial evolution is indeed a suitable strategy for the automated design of self-assembly and self-organising systems where local interactions, homogeneity and both stochastic and discrete models of execution play a crucial role in emergent complex structures

Foundations of coverage algorithms in autonomic mobile sensor networks

Drones are poised to become a prominent focus of advances in the near future as hardware platforms manufactured via mass production become accessible to consumers in higher quantities at lower costs than ever before. As more ways to utilize such devices become more popular, algorithms for directing the activities of mobile sensors must expand in order to automate their work. This work explores algorithms used to direct the behavior of networks of autonomous mobile sensors, and in particular how such networks can operate to achieve coverage of a field using mobility. We focus special attention to the way limited mobility affects the performance (and other factors) of algorithms traditionally applied to area coverage and event detection problems. Strategies for maximizing event detection and minimizing detection delay as mobile sensors with limited mobility are explored in the first part of this work. Next we examine exploratory coverage, a new way of analyzing sensor coverage, concerned more with covering each part of the coverage field once, while minimizing mobility required to achieve this level of 1-coverage. This analysis is contained in the second part of this work. Extending the analysis of mobility, we next strive to explore the novel topic of disabled mobility in mobile sensors, and how algorithms might react to increase effectiveness given that some sensors have lost mobility while retaining other senses. This work analyzes algorithm effectiveness in light of disabled mobility, demonstrates how this particular failure mode impacts common coverage algorithms, and presents ways to adjust algorithms to mitigate performance losses. --Abstract, page iv

Diverse and robust molecular algorithms using reprogrammable DNA self-assembly

Molecular biology provides an inspiring proof-of-principle that chemical systems can store and process information to direct molecular activities such as the fabrication of complex structures from molecular components. To develop information-based chemistry as a technology for programming matter to function in ways not seen in biological systems, it is necessary to understand how molecular interactions can encode and execute algorithms. The self-assembly of relatively simple units into complex products is particularly well suited for such investigations. Theory that combines mathematical tiling and statistical–mechanical models of molecular crystallization has shown that algorithmic behaviour can be embedded within molecular self-assembly processes, and this has been experimentally demonstrated using DNA nanotechnology with up to 22 tile types. However, many information technologies exhibit a complexity threshold—such as the minimum transistor count needed for a general-purpose computer—beyond which the power of a reprogrammable system increases qualitatively, and it has been unclear whether the biophysics of DNA self-assembly allows that threshold to be exceeded. Here we report the design and experimental validation of a DNA tile set that contains 355 single-stranded tiles and can, through simple tile selection, be reprogrammed to implement a wide variety of 6-bit algorithms. We use this set to construct 21 circuits that execute algorithms including copying, sorting, recognizing palindromes and multiples of 3, random walking, obtaining an unbiased choice from a biased random source, electing a leader, simulating cellular automata, generating deterministic and randomized patterns, and counting to 63, with an overall per-tile error rate of less than 1 in 3,000. These findings suggest that molecular self-assembly could be a reliable algorithmic component within programmable chemical systems. The development of molecular machines that are reprogrammable—at a high level of abstraction and thus without requiring knowledge of the underlying physics—will establish a creative space in which molecular programmers can flourish

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