Optimal self-assembly of finite shapes at temperature 1 in 3D

Working in a three-dimensional variant of Winfree's abstract Tile Assembly Model, we show that, for an arbitrary finite, connected shape $X \subset \mathbb{Z}^2$, there is a tile set that uniquely self-assembles into a 3D representation of a scaled-up version of $X$ at temperature 1 in 3D with optimal program-size complexity (the "program-size complexity", also known as "tile complexity", of a shape is the minimum number of tile types required to uniquely self-assemble it). Moreover, our construction is "just barely" 3D in the sense that it only places tiles in the $z = 0$ and $z = 1$ planes. Our result is essentially a just-barely 3D temperature 1 simulation of a similar 2D temperature 2 result by Soloveichik and Winfree (SICOMP 2007)

Reflections on Tiles (in Self-Assembly)

We define the Reflexive Tile Assembly Model (RTAM), which is obtained from the abstract Tile Assembly Model (aTAM) by allowing tiles to reflect across their horizontal and/or vertical axes. We show that the class of directed temperature-1 RTAM systems is not computationally universal, which is conjectured but unproven for the aTAM, and like the aTAM, the RTAM is computationally universal at temperature 2. We then show that at temperature 1, when starting from a single tile seed, the RTAM is capable of assembling n x n squares for n odd using only n tile types, but incapable of assembling n x n squares for n even. Moreover, we show that n is a lower bound on the number of tile types needed to assemble n x n squares for n odd in the temperature-1 RTAM. The conjectured lower bound for temperature-1 aTAM systems is 2n-1. Finally, we give preliminary results toward the classification of which finite connected shapes in Z^2 can be assembled (strictly or weakly) by a singly seeded (i.e. seed of size 1) RTAM system, including a complete classification of which finite connected shapes be strictly assembled by a "mismatch-free" singly seeded RTAM system.Comment: New results which classify the types of shapes which can self-assemble in the RTAM have been adde

Self-replication and evolution of DNA crystals

Is it possible to create a simple physical system that is capable of replicating itself? Can such a system evolve interesting behaviors, thus allowing it to adapt to a wide range of environments? This paper presents a design for such a replicator constructed exclusively from synthetic DNA. The basis for the replicator is crystal growth: information is stored in the spatial arrangement of monomers and copied from layer to layer by templating. Replication is achieved by fragmentation of crystals, which produces new crystals that carry the same information. Crystal replication avoids intrinsic problems associated with template-directed mechanisms for replication of one-dimensional polymers. A key innovation of our work is that by using programmable DNA tiles as the crystal monomers, we can design crystal growth processes that apply interesting selective pressures to the evolving sequences. While evolution requires that copying occur with high accuracy, we show how to adapt error-correction techniques from algorithmic self-assembly to lower the replication error rate as much as is required

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 Power of Duples (in Self-Assembly): It's Not So Hip To Be Square

In this paper we define the Dupled abstract Tile Assembly Model (DaTAM), which is a slight extension to the abstract Tile Assembly Model (aTAM) that allows for not only the standard square tiles, but also "duple" tiles which are rectangles pre-formed by the joining of two square tiles. We show that the addition of duples allows for powerful behaviors of self-assembling systems at temperature 1, meaning systems which exclude the requirement of cooperative binding by tiles (i.e., the requirement that a tile must be able to bind to at least 2 tiles in an existing assembly if it is to attach). Cooperative binding is conjectured to be required in the standard aTAM for Turing universal computation and the efficient self-assembly of shapes, but we show that in the DaTAM these behaviors can in fact be exhibited at temperature 1. We then show that the DaTAM doesn't provide asymptotic improvements over the aTAM in its ability to efficiently build thin rectangles. Finally, we present a series of results which prove that the temperature-2 aTAM and temperature-1 DaTAM have mutually exclusive powers. That is, each is able to self-assemble shapes that the other can't, and each has systems which cannot be simulated by the other. Beyond being of purely theoretical interest, these results have practical motivation as duples have already proven to be useful in laboratory implementations of DNA-based tiles

DNA-based Self-Assembly of Chiral Plasmonic Nanostructures with Tailored Optical Response

Surface plasmon resonances generated in metallic nanostructures can be utilized to tailor electromagnetic fields. The precise spatial arrangement of such structures can result in surprising optical properties that are not found in any naturally occurring material. Here, the designed activity emerges from collective effects of singular components equipped with limited individual functionality. Top-down fabrication of plasmonic materials with a predesigned optical response in the visible range by conventional lithographic methods has remained challenging due to their limited resolution, the complexity of scaling, and the difficulty to extend these techniques to three-dimensional architectures. Molecular self-assembly provides an alternative route to create such materials which is not bound by the above limitations. We demonstrate how the DNA origami method can be used to produce plasmonic materials with a tailored optical response at visible wavelengths. Harnessing the assembly power of 3D DNA origami, we arranged metal nanoparticles with a spatial accuracy of 2 nm into nanoscale helices. The helical structures assemble in solution in a massively parallel fashion and with near quantitative yields. As a designed optical response, we generated giant circular dichroism and optical rotary dispersion in the visible range that originates from the collective plasmon-plasmon interactions within the nanohelices. We also show that the optical response can be tuned through the visible spectrum by changing the composition of the metal nanoparticles. The observed effects are independent of the direction of the incident light and can be switched by design between left- and right-handed orientation. Our work demonstrates the production of complex bulk materials from precisely designed nanoscopic assemblies and highlights the potential of DNA self-assembly for the fabrication of plasmonic nanostructures.Comment: 5 pages, 4 figure

Controlled assembly of SNAP-PNA-fluorophore systems on DNA templates to produce fluorescence resonance energy transfer

The SNAP protein is a widely used self-labeling tag that can be used for tracking protein localization and trafficking in living systems. A model system providing controlled alignment of SNAP-tag units can provide a new way to study clustering of fusion proteins. In this work, fluorescent SNAP-PNA conjugates were controllably assembled on DNA frameworks forming dimers, trimers, and tetramers. Modification of peptide nucleic acid (PNA) with the O6-benzyl guanine (BG) group allowed the generation of site-selective covalent links between PNA and the SNAP protein. The modified BG-PNAs were labeled with fluorescent Atto dyes and subsequently chemo-selectively conjugated to SNAP protein. Efficient assembly into dimer and oligomer forms was verified via size exclusion chromatography (SEC), electrophoresis (SDS-PAGE), and fluorescence spectroscopy. DNA directed assembly of homo- and hetero-dimers of SNAP-PNA constructs induced homo- and hetero-FRET, respectively. Longer DNA scaffolds controllably aligned similar fluorescent SNAP-PNA constructs into higher oligomers exhibiting homo-FRET. The combined SEC and homo-FRET studies indicated the 1:1 and saturated assemblies of SNAP-PNA-fluorophore:DNA formed preferentially in this system. This suggested a kinetic/stoichiometric model of assembly rather than binomially distributed products. These BG-PNA-fluorophore building blocks allow facile introduction of fluorophores and/or assembly directing moieties onto any protein containing SNAP. Template directed assembly of PNA modified SNAP proteins may be used to investigate clustering behavior both with and without fluorescent labels which may find use in the study of assembly processes in cells

Random, blocky and alternating ordering in supramolecular polymers of chemically bidisperse monomers

As a first step to understanding the role of molecular or chemical polydispersity in self-assembly, we put forward a coarse-grained model that describes the spontaneous formation of quasi-linear polymers in solutions containing two self-assembling species. Our theoretical framework is based on a two-component self-assembled Ising model in which the bidispersity is parameterized in terms of the strengths of the binding free energies that depend on the monomer species involved in the pairing interaction. Depending upon the relative values of the binding free energies involved, different morphologies of assemblies that include both components are formed, exhibiting paramagnetic-, ferromagnetic- or anti ferromagnetic-like order,i.e., random, blocky or alternating ordering of the two components in the assemblies. Analyzing the model for the case of ferromagnetic ordering, which is of most practical interest, we find that the transition from conditions of minimal assembly to those characterized by strong polymerization can be described by a critical concentration that depends on the concentration ratio of the two species. Interestingly, the distribution of monomers in the assemblies is different from that in the original distribution, i.e., the ratio of the concentrations of the two components put into the system. The monomers with a smaller binding free energy are more abundant in short assemblies and monomers with a larger binding affinity are more abundant in longer assemblies. Under certain conditions the two components congregate into separate supramolecular polymeric species and in that sense phase separate. We find strong deviations from the expected growth law for supramolecular polymers even for modest amounts of a second component, provided it is chemically sufficiently distinct from the main one.Comment: Submitted to Macromolecules, 6 figures. arXiv admin note: substantial text overlap with arXiv:1111.176

Single-molecule derivation of salt dependent base-pair free energies in DNA

Accurate knowledge of the thermodynamic properties of nucleic acids is crucial to predicting their structure and stability. To date most measurements of base-pair free energies in DNA are obtained in thermal denaturation experiments, which depend on several assumptions. Here we report measurements of the DNA base-pair free energies based on a simplified system, the mechanical unzipping of single DNA molecules. By combining experimental data with a physical model and an optimization algorithm for analysis, we measure the 10 unique nearest-neighbor base-pair free energies with 0.1 kcal mol-1 precision over two orders of magnitude of monovalent salt concentration. We find an improved set of standard energy values compared with Unified Oligonucleotide energies and a unique set of 10 base-pair-specific salt-correction values. The latter are found to be strongest for AA/TT and weakest for CC/GG. Our new energy values and salt corrections improve predictions of DNA unzipping forces and are fully compatible with melting temperatures for oligos. The method should make it possible to obtain free energies, enthalpies and entropies in conditions not accessible by bulk methodologies.Comment: Main text: 27 pages, 4 figures, 2 tables. Supporting Information: 51 pages, 19 figures, 4 table