Two computational primitives for algorithmic self-assembly: Copying and counting

Copying and counting are useful primitive operations for computation and construction. We have made DNA crystals that copy and crystals that count as they grow. For counting, 16 oligonucleotides assemble into four DNA Wang tiles that subsequently crystallize on a polymeric nucleating scaffold strand, arranging themselves in a binary counting pattern that could serve as a template for a molecular electronic demultiplexing circuit. Although the yield of counting crystals is low, and per-tile error rates in such crystals is roughly 10%, this work demonstrates the potential of algorithmic self-assembly to create complex nanoscale patterns of technological interest. A subset of the tiles for counting form information-bearing DNA tubes that copy bit strings from layer to layer along their length

Proofreading tile sets: Error correction for algorithmic self-assembly

For robust molecular implementation of tile-based algorithmic self-assembly, methods for reducing errors must be developed. Previous studies suggested that by control of physical conditions, such as temperature and the concentration of tiles, errors (ε) can be reduced to an arbitrarily low rate - but at the cost of reduced speed (r) for the self-assembly process. For tile sets directly implementing blocked cellular automata, it was shown that r ≈ βε^2 was optimal. Here, we show that an improved construction, which we refer to as proofreading tile sets, can in principle exploit the cooperativity of tile assembly reactions to dramatically improve the scaling behavior to r ≈ βε and better. This suggests that existing DNA-based molecular tile approaches may be improved to produce macroscopic algorithmic crystals with few errors. Generalizations and limitations of the proofreading tile set construction are discussed

An information-bearing seed for nucleating algorithmic self-assembly

Self-assembly creates natural mineral, chemical, and biological structures of great complexity. Often, the same starting materials have the potential to form an infinite variety of distinct structures; information in a seed molecule can determine which form is grown as well as where and when. These phenomena can be exploited to program the growth of complex supramolecular structures, as demonstrated by the algorithmic self-assembly of DNA tiles. However, the lack of effective seeds has limited the reliability and yield of algorithmic crystals. Here, we present a programmable DNA origami seed that can display up to 32 distinct binding sites and demonstrate the use of seeds to nucleate three types of algorithmic crystals. In the simplest case, the starting materials are a set of tiles that can form crystalline ribbons of any width; the seed directs assembly of a chosen width with >90% yield. Increased structural diversity is obtained by using tiles that copy a binary string from layer to layer; the seed specifies the initial string and triggers growth under near-optimal conditions where the bit copying error rate is 17 kb of sequence information. In sum, this work demonstrates how DNA origami seeds enable the easy, high-yield, low-error-rate growth of algorithmic crystals as a route toward programmable bottom-up fabrication

Algorithmic Self-Assembly of DNA Sierpinski Triangles

Algorithms and information, fundamental to technological and biological organization, are also an essential aspect of many elementary physical phenomena, such as molecular self-assembly. Here we report the molecular realization, using two-dimensional self-assembly of DNA tiles, of a cellular automaton whose update rule computes the binary function XOR and thus fabricates a fractal pattern—a Sierpinski triangle—as it grows. To achieve this, abstract tiles were translated into DNA tiles based on double-crossover motifs. Serving as input for the computation, long single-stranded DNA molecules were used to nucleate growth of tiles into algorithmic crystals. For both of two independent molecular realizations, atomic force microscopy revealed recognizable Sierpinski triangles containing 100–200 correct tiles. Error rates during assembly appear to range from 1% to 10%. Although imperfect, the growth of Sierpinski triangles demonstrates all the necessary mechanisms for the molecular implementation of arbitrary cellular automata. This shows that engineered DNA self-assembly can be treated as a Turing-universal biomolecular system, capable of implementing any desired algorithm for computation or construction tasks

Contrasting Geometric Variations of Mathematical Models of Self-assembling Systems

Self-assembly is the process by which complex systems are formed and behave due to the interactions of relatively simple units. In this thesis, we explore multiple augmentations of well known models of self-assembly to gain a better understanding of the roles that geometry and space play in their dynamics. We begin in the abstract Tile Assembly Model (aTAM) with some examples and a brief survey of previous results to provide a foundation. We then introduce the Geometric Thermodynamic Binding Network model, a model that focuses on the thermodynamic stability of its systems while utilizing geometrically rigid components (dissimilar to other thermodynamic models). We show that this model is computationally universal, an ability conjectured to be impossible in similar models with non-rigid components. We continue by introducing the Flexible Tile Assembly Model, a generalization of the 2D aTAM that allows bonds between tiles to flex and assemblies to therefore reconfigure. We show how systems in this model can deterministically assemble shapes that adhere to a number of certain restrictions. Finally, we introduce the Spatial abstract Tile Assembly Model, a variation of the 3D aTAM that restricts tiles from attaching without a diffusion path. We show that this model is intrinsically universal, a property of computational models to simulate themselves which has been shown for the 3D aTAM and other similar models. We conclude this thesis with a summary of the presented results, a brief impact analysis, and potential directions for future research within this area

Pattern recognition in the nucleation kinetics of non-equilibrium self-assembly

Inspired by biology’s most sophisticated computer, the brain, neural networks constitute a profound reformulation of computational principles. Analogous high-dimensional, highly interconnected computational architectures also arise within information-processing molecular systems inside living cells, such as signal transduction cascades and genetic regulatory networks. Might collective modes analogous to neural computation be found more broadly in other physical and chemical processes, even those that ostensibly play non-information-processing roles? Here we examine nucleation during self-assembly of multicomponent structures, showing that high-dimensional patterns of concentrations can be discriminated and classified in a manner similar to neural network computation. Specifically, we design a set of 917 DNA tiles that can self-assemble in three alternative ways such that competitive nucleation depends sensitively on the extent of colocalization of high-concentration tiles within the three structures. The system was trained in silico to classify a set of 18 grayscale 30 × 30 pixel images into three categories. Experimentally, fluorescence and atomic force microscopy measurements during and after a 150 hour anneal established that all trained images were correctly classified, whereas a test set of image variations probed the robustness of the results. Although slow compared to previous biochemical neural networks, our approach is compact, robust and scalable. Our findings suggest that ubiquitous physical phenomena, such as nucleation, may hold powerful information-processing capabilities when they occur within high-dimensional multicomponent systems

Nucleic Acid Architectures for Therapeutics, Diagnostics, Devices and Materials

Nucleic acids (RNA and DNA) and their chemical analogs have been utilized as building materials due to their biocompatibility and programmability. RNA, which naturally possesses a wide range of different functions, is now being widely investigated for its role as a responsive biomaterial which dynamically reacts to changes in the surrounding environment. It is now evident that artificially designed self-assembling RNAs, that can form programmable nanoparticles and supra-assemblies, will play an increasingly important part in a diverse range of applications, such as macromolecular therapies, drug delivery systems, biosensing, tissue engineering, programmable scaffolds for material organization, logic gates, and soft actuators, to name but a few. The current exciting Special Issue comprises research highlights, short communications, research articles, and reviews that all bring together the leading scientists who are exploring a wide range of the fundamental properties of RNA and DNA nanoassemblies suitable for biomedical applications

Sensing and Regulation from Nucleic Acid Devices

abstract: The highly predictable structural and thermodynamic behavior of deoxynucleic acid (DNA) and ribonucleic acid (RNA) have made them versatile tools for creating artificial nanostructures over broad range. Moreover, DNA and RNA are able to interact with biological ligand as either synthetic aptamers or natural components, conferring direct biological functions to the nucleic acid devices. The applications of nucleic acids greatly relies on the bio-reactivity and specificity when applied to highly complexed biological systems. This dissertation aims to 1) develop new strategy to identify high affinity nucleic acid aptamers against biological ligand; and 2) explore highly orthogonal RNA riboregulators in vivo for constructing multi-input gene circuits with NOT logic. With the aid of a DNA nanoscaffold, pairs of hetero-bivalent aptamers for human alpha thrombin were identified with ultra-high binding affinity in femtomolar range with displaying potent biological modulations for the enzyme activity. The newly identified bivalent aptamers enriched the aptamer tool box for future therapeutic applications in hemostasis, and also the strategy can be potentially developed for other target molecules. Secondly, by employing a three-way junction structure in the riboregulator structure through de-novo design, we identified a family of high-performance RNA-sensing translational repressors that down-regulates gene translation in response to cognate RNAs with remarkable dynamic range and orthogonality. Harnessing the 3WJ repressors as modular parts, we integrate them into biological circuits that execute universal NAND and NOR logic with up to four independent RNA inputs in Escherichia coli.Dissertation/ThesisDoctoral Dissertation Biochemistry 201