Exponential Replication of Patterns in the Signal Tile Assembly Model

Chemical self-replicators are of considerable interest in the field of nanomanufacturing and as a model for evolution. We introduce the problem of self-replication of rectangular two-dimensional patterns in the practically motivated Signal Tile Assembly Model (STAM) [9]. The STAM is based on the Tile Assembly Model (TAM) which is a mathematical model of self-assembly in which DNA tile monomers may attach to other DNA tile monomers in a programmable way. More abstractly, four-sided tiles are assigned glue types to each edge, and self-assembly occurs when singleton tiles bind to a growing assembly, if the glue types match and the glue binding strength exceeds some threshold. The signal tile extension of the TAM allows signals to be propagated across assemblies to activate glues or break apart assemblies. Here, we construct a pattern replicator that replicates a two-dimensional input pattern over some fixed alphabet of size φ with O(φ) tile types, O(φ) unique glues, and a signal complexity of O(1). Furthermore, we show that this replication system displays exponential growth in n, the number of replicates of the initial patterned assembly

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

Determining hydrodynamic forces in bursting bubbles using DNA nanotube mechanics

Quantifying the mechanical forces produced by fluid flows within the ocean is critical to understanding the ocean’s environmental phenomena. Such forces may have been instrumental in the origin of life by driving a primitive form of self-replication through fragmentation. Among the intense sources of hydrodynamic shear encountered in the ocean are breaking waves and the bursting bubbles produced by such waves. On a microscopic scale, one expects the surface-tension–driven flows produced during bubble rupture to exhibit particularly high velocity gradients due to the small size scales and masses involved. However, little work has examined the strength of shear flow rates in commonly encountered ocean conditions. By using DNA nanotubes as a novel fluid flow sensor, we investigate the elongational rates generated in bursting films within aqueous bubble foams using both laboratory buffer and ocean water. To characterize the elongational rate distribution associated with a bursting bubble, we introduce the concept of a fragmentation volume and measure its form as a function of elongational flow rate. We find that substantial volumes experience surprisingly large flow rates: during the bursting of a bubble having an air volume of 10 mm^3, elongational rates at least as large as ϵ = 1.0×10^8 s^(−1) are generated in a fragmentation volume of ∼2×10^(−6) μL. The determination of the elongational strain rate distribution is essential for assessing how effectively fluid motion within bursting bubbles at the ocean surface can shear microscopic particles and microorganisms, and could have driven the self-replication of a protobiont

Design, Synthesis and Analysis of Self-Assembling Triangulated Wireframe DNA Structures

The field of DNA nanotechnology offers a wide range of design strategies with which nanometer-sized structures with a desired shape, size and aspect ratio can be built. The most established techniques in the field rely on close-packed 'solid' DNA nanostructures produced with either the DNA origami or the single-stranded tile techniques. These structures depend on high-salt buffer solutions and require more material than comparable size hollow wireframe structures. This dissertation explores the construction of hollow wireframe DNA nanostructures composed of equilateral triangles. To achieve maximal material efficiency the design is restricted to use a single DNA double helix per triangle edge. As a proof of principle, the DNA origami technique is extended to produce a series of truss structures including the flat, tetrahedral, octahedral, or irregular dodecahedral truss designs. In contrast to close packed DNA origami designs these structures fold at low-salt buffer conditions. These structures have defined cavities that may in the future be used to precisely position functional elements such as metallic nanoparticles or enzymes. The design process of these structures is simplified by a custom design software. Next, the triangulated construction motif is extended to the single-stranded DNA tile technique. A collection of finite structures, as well as one-dimensional crystalline assemblies is explored. The ideal assembly conditions are determined experimentally and using molecular dynamics simulations. A custom design software is presented to simplify the design and handling of these structures. At last, the cost-effective prototyping of triangulated wireframe DNA origami structures is explored. This is achieved through the introduction of single-stranded “gap” regions along the triangle edges. These gap regions are then filled using a DNA polymerase rather than by synthetic oligonucleotides. This technique also allows the mechanical transformation of these structures, which is exemplified by the transition of a bent into a straight structure upon completion of the gap filling.:Abstract v Publications vii Acknowledgements ix Contents xi Chapter 1 A short introduction into DNA nanotechnology 1 1.1 Nanotechnology 1 1.1.1 Top down 1 1.1.2 Bottom up 3 1.2 Deoxyribonucleic acid (DNA) 4 1.3 DNA Nanotechnology 6 1.3.1 Tile based assembly 9 1.3.2 DNA origami and single-stranded tiles 10 1.3.3 Some applications of DNA nanotechnology 12 1.3.4 Wireframe structures 15 1.3.5 Computational tools and DNA nanotechnology. 17 Chapter 2 Motivation and objectives 19 Chapter 3 Design and Synthesis of Triangulated DNA Origami Trusses 20 3.1 Introduction 20 3.2 Results and Discussion 21 3.2.1 Design 21 3.2.2 Nomenclature and parameters of the tube structures 23 3.2.3 Gel electrophoreses analysis 25 3.2.4 Imaging of the purified structures 26 3.2.5 Optimizing the folding conditions 28 3.2.6 Comparison to vHelix 29 3.3 Conclusions 29 3.4 Methods 30 3.4.1 Standard DNA origami assembly reaction. 30 3.4.2 Gel purification. 30 3.4.3 AFM sample preparation. 31 3.4.4 TEM sample preparation. 31 3.4.5 Instructions for mixing the staple sets. 31 Chapter 4 Triangulated wireframe structures assembled using single-stranded DNA tiles 33 4.1 Introduction 33 4.2 Results and Discussion 35 4.2.1 Designing the structures 35 4.2.2 Synthesis of test structures 37 4.2.3 Molecular dynamics simulations of 6-arm junctions 38 4.2.4 Assembly of the finite structures 40 4.2.5 Influence of salt concentration and folding times 42 4.2.6 Molecular dynamics simulations of the rhombus structure 43 4.2.7 1D SST crystals 44 4.2.8 Controlling the crystal growth 46 4.3 Conclusions 48 4.4 Methods 49 4.4.1 SST Folding 49 4.4.2 Agarose Gel Electrophoresis 49 4.4.3 tSEM Characterization 49 4.4.4 AFM Imaging 49 4.4.5 AGE-Based Folding-Yield Estimation 49 4.4.6 Molecular Dynamics Simulations 50 Chapter 5 Structural transformation of wireframe DNA origami via DNA polymerase assisted gap-filling 52 5.1 Introduction 52 5.2 Results and Discussion 54 5.2.1 Design of the Structures 54 5.2.2 Folding of Gap-Structures 56 5.2.3 Inactivation of Polymerase. 57 5.2.4 Secondary Structures. 58 5.2.5 Folding Kinetics of Gap Origami. 60 5.3 Conclusions 61 5.4 Methods 62 5.4.1 DNA origami folding 62 5.4.2 Gap filling of the wireframe DNA origami structures 63 5.4.3 Agarose gel electrophoresis 63 5.4.4 PAGE gel analysis 63 5.4.5 tSEM characterization 64 5.4.6 AFM imaging 64 5.4.7 AGE based folding-yield estimation 64 5.4.8 Gibbs free energy simulation using mfold 65 5.4.9 List of sequence for folding the DNA origami triangulated structures 65 Chapter 6 Summary and outlook 67 Appendix 69 A.1 Additional figures from chapter 369 A.2 Additional figures from chapter 4 77 A.3 Additional figures from chapter 5 111 Bibliography 127 Erklärung 13