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

ALCH: An Imperative Language for Chemical Reaction Network-Controlled Tile Assembly

In 2015 Schiefer and Winfree introduced the chemical reaction network-controlled tile assembly model (CRN-TAM), a variant of the abstract tile assembly model (aTAM), where tile reactions are mediated via non-local chemical signals. In this paper, we introduce ALCH, an imperative programming language for specifying CRN-TAM programs. ALCH contains common features like Boolean variables, conditionals, and loops. It also supports CRN-TAM-specific features such as adding and removing tiles. A unique feature of the language is the branch statement, a nondeterministic control structure that allows us to query the current state of tile assemblies. We also developed a compiler that translates ALCH to the CRN-TAM, and a simulator that simulates and visualizes the self-assembly of a CRN-TAM program. Using this language, we show that the discrete Sierpinski triangle can be strictly self-assembled in the CRN-TAM. This solves an open problem that the CRN-TAM is capable of self-assembling infinite shapes at scale one that the aTAM cannot. ALCH allows us to present this construction at a high level, abstracting species and reactions into C-like code that is simpler to understand. Our construction utilizes two new CRN-TAM techniques that allow us to tackle this open problem. First, it employs the branching feature of ALCH to probe the previously placed tiles of the assembly and detect the presence and absence of tiles. Second, it uses scaffolding tiles to precisely control tile placement by occluding any undesired binding sites

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

Algorithmic Assembly of Nanoscale Structures

The development of nanotechnology has become one of the most significant endeavors of our time. A natural objective of this field is discovering how to engineer nanoscale structures. Limitations of current top-down techniques inspire investigation into bottom-up approaches to reach this objective. A fundamental precondition for a bottom-up approach is the ability to control the behavior of nanoscale particles. Many abstract representations have been developed to model systems of particles and to research methods for controlling their behavior. This thesis develops theories on two such approaches for building complex structures: the self-assembly of simple particles, and the use of simple robot swarms. The concepts for these two approaches are straightforward. Self-assembly is the process by which simple particles, following the rules of some behavior-governing system, naturally coalesce into a more complex form. The other method of bottom-up assembly involves controlling nanoscale particles through explicit directions and assembling them into a desired form. Regarding the self-assembly of nanoscale structures, we present two construction methods in a variant of a popular theoretical model known as the 2-Handed Tile Self-Assembly Model. The first technique achieves shape construction at only a constant scale factor, while the second result uses only a constant number of unique particle types. Regarding the use of robot swarms for construction, we first develop a novel technique for reconfiguring a swarm of globally-controlled robots into a desired shape even when the robots can only move maximally in a commanded direction. We then expand on this work by formally defining an entire hierarchy of shapes which can be built in this manner and we provide a technique for doing so

Cell-Free Synthetic Biology Platform for Engineering Synthetic Biological Circuits and Systems

Synthetic biology brings engineering disciplines to create novel biological systems for biomedical and technological applications. The substantial growth of the synthetic biology field in the past decade is poised to transform biotechnology and medicine. To streamline design processes and facilitate debugging of complex synthetic circuits, cell-free synthetic biology approaches has reached broad research communities both in academia and industry. By recapitulating gene expression systems in vitro, cell-free expression systems offer flexibility to explore beyond the confines of living cells and allow networking of synthetic and natural systems. Here, we review the capabilities of the current cell-free platforms, focusing on nucleic acid-based molecular programs and circuit construction. We survey the recent developments including cell-free transcription– translation platforms, DNA nanostructures and circuits, and novel classes of riboregulators. The links to mathematical models and the prospects of cell-free synthetic biology platforms will also be discussed.11Yscopu

Small Tile Sets That Compute While Solving Mazes

We ask the question of how small a self-assembling set of tiles can be yet have interesting computational behaviour. We study this question in a model where supporting walls are provided as an input structure for tiles to grow along: we call it the Maze-Walking Tile Assembly Model. The model has a number of implementation prospects, one being DNA strands that attach to a DNA origami substrate. Intuitively, the model suggests a separation of signal routing and computation: The input structure (maze) supplies a routing diagram, and the programmer's tile set provides the computational ability. We ask how simple the computational part can be. We give two tiny tile sets that are computationally universal in the Maze-Walking Tile Assembly Model. The first has four tiles and simulates Boolean circuits by directly implementing NAND, NXOR and NOT gates. Our second tile set has 6 tiles and is called the Collatz tile set as it produces patterns found in binary/ternary representations of iterations of the Collatz function. Using computer search we find that the Collatz tile set is expressive enough to encode Boolean circuits using blocks of these patterns. These two tile sets give two different methods to find simple universal tile sets, and provide motivation for using pre-assembled maze structures as circuit wiring diagrams in molecular self-assembly based computing.ISSN:1868-896

Computational Design and Study of Structural and Dynamic Nucleic Acid Systems

abstract: DNA and RNA are generally regarded as one of the central molecules in molecular biology. Recent advancements in the field of DNA/RNA nanotechnology witnessed the success of usage of DNA/RNA as programmable molecules to construct nano-objects with predefined shapes and dynamic molecular machines for various functions. From the perspective of structural design with nucleic acid, there are basically two types of assembly method, DNA tile based assembly and DNA origami based assembly, used to construct infinite-sized crystal structures and finite-sized molecular structures. The assembled structure can be used for arrangement of other molecules or nanoparticles with the resolution of nanometers to create new type of materials. The dynamic nucleic acid machine is based on the DNA strand displacement, which allows two nucleic acid strands to hybridize with each other to displace one or more prehybridized strands in the process. Strand displacement reaction has been implemented to construct a variety of dynamic molecular systems, such as molecular computer, oscillators, in vivo devices for gene expression control. This thesis will focus on the computational design of structural and dynamic nucleic acid systems, particularly for new type of DNA structure design and high precision control of gene expression in vivo. Firstly, a new type of fundamental DNA structural motif, the layered-crossover motif, will be introduced. The layered-crossover allow non-parallel alignment of DNA helices with precisely controlled angle. By using the layered-crossover motif, the scaffold can go through the 3D framework DNA origami structures. The properties of precise angle control of the layered-crossover tiles can also be used to assemble 2D and 3D crystals. One the dynamic control part, a de-novo-designed riboregulator is developed that can recognize single nucleotide variation. The riboregulators can also be used to develop paper-based diagnostic devices.Dissertation/ThesisDoctoral Dissertation Chemistry 201

Biological Nanowires: Integration of the silver(I) base pair into DNA with nanotechnological and synthetic biological applications

Modern computing and mobile device technologies are now based on semiconductor technology with nanoscale components, i.e., nanoelectronics, and are used in an increasing variety of consumer, scientific, and space-based applications. This rise to global prevalence has been accompanied by a similarly precipitous rise in fabrication cost, toxicity, and technicality; and the vast majority of modern nanotechnology cannot be repaired in whole or in part. In combination with looming scaling limits, it is clear that there is a critical need for fabrication technologies that rely upon clean, inexpensive, and portable means; and the ideal nanoelectronics manufacturing facility would harness micro- and nanoscale fabrication and self-assembly techniques. The field of molecular electronics has promised for the past two decades to fill fundamental gaps in modern, silicon-based, micro- and nanoelectronics; yet molecular electronic devices, in turn, have suffered from problems of size, dispersion and reproducibility. In parallel, advances in DNA nanotechnology over the past several decades have allowed for the design and assembly of nanoscale architectures with single-molecule precision, and indeed have been used as a basis for heteromaterial scaffolds, mechanically-active delivery mechanisms, and network assembly. The field has, however, suffered for lack of meaningful modularity in function: few designs to date interact with their surroundings in more than a mechanical manner. As a material, DNA offers the promise of nanometer resolution, self-assembly, linear shape, and connectivity into branched architectures; while its biological origin offers information storage, enzyme-compatibility and the promise of biologically-inspired fabrication through synthetic biological means. Recent advances in DNA chemistry have isolated and characterized an orthogonal DNA base pair using standard nucleobases: by bridging the gap between mismatched cytosine nucleotides, silver(I) ions can be selectively incorporated into the DNA helix with atomic resolution. The goal of this thesis is to explore how this approach to “metallize” DNA can be combined with structural DNA nanotechnology as a step toward creating electronically-functional DNA networks. This work begins with a survey of applications for such a transformative technology, including nanoelectronic component fabrication for low-resource and space-based applications. We then investigate the assembly of linear Ag+-functionalized DNA species using biochemical and structural analyses to gain an understanding of the kinetics, yield, morphology, and behavior of this orthogonal DNA base pair. After establishing a protocol for high yield assembly in the presence of varying Ag+ functionalization, we investigate these linear DNA species using electrical means. First a method of coupling orthogonal DNA to single-walled carbon nanotubes (SWCNTs) is explored for self-assembly into nanopatterned transistor devices. Then we carry out scanning tunneling microscope (STM) break junction experiments on short polycytosine, polycationic DNA duplexes and find increased molecular conductance of at least an order of magnitude relative to the most conductive DNA analog. With an understanding of linear species from both a biochemical and nanoelectronic perspective, we investigate the assembly of nonlinear Ag+-functionalized DNA species. Using rational design principles gathered from the analysis of linear species, a de novo mathematical framework for understanding generalized DNA networks is developed. This provides the basis for a computational model built in Matlab that is able to design DNA networks and nanostructures using arbitrary base parity. In this way, DNA nanostructures are able to be designed using the dC:Ag+:dC base pair, as well as any similar nucleobase or DNA-inspired system (dT:Hg2+:dT, rA:rU, G4, XNA, LNA, PNA, etc.). With this foundation, three general classes of DNA tiles are designed with embedded nanowire elements: single crossover Holliday junction (HJ) tiles, T-junction (TJ) units, and double crossover (DX) tile pairs and structures. A library of orthogonal chemistry DNA nanotechnology is described, and future applications to nanomaterials and circuit architectures are discussed

Integrating DNA strand-displacement circuitry with DNA tile self-assembly

DNA nanotechnology has emerged as a reliable and programmable way of controlling matter at the nanoscale through the specificity of Watson–Crick base pairing, allowing both complex self-assembled structures with nanometer precision and complex reaction networks implementing digital and analog behaviors. Here we show how two well-developed frameworks, DNA tile self-assembly and DNA strand-displacement circuits, can be systematically integrated to provide programmable kinetic control of self-assembly. We demonstrate the triggered and catalytic isothermal self-assembly of DNA nanotubes over 10 µm long from precursor DNA double-crossover tiles activated by an upstream DNA catalyst network. Integrating more sophisticated control circuits and tile systems could enable precise spatial and temporal organization of dynamic molecular structures