Approximate Self-Assembly of the Sierpinski Triangle

The Tile Assembly Model is a Turing universal model that Winfree introduced in order to study the nanoscale self-assembly of complex (typically aperiodic) DNA crystals. Winfree exhibited a self-assembly that tiles the first quadrant of the Cartesian plane with specially labeled tiles appearing at exactly the positions of points in the Sierpinski triangle. More recently, Lathrop, Lutz, and Summers proved that the Sierpinski triangle cannot self-assemble in the "strict" sense in which tiles are not allowed to appear at positions outside the target structure. Here we investigate the strict self-assembly of sets that approximate the Sierpinski triangle. We show that every set that does strictly self-assemble disagrees with the Sierpinski triangle on a set with fractal dimension at least that of the Sierpinski triangle (roughly 1.585), and that no subset of the Sierpinski triangle with fractal dimension greater than 1 strictly self-assembles. We show that our bounds are tight, even when restricted to supersets of the Sierpinski triangle, by presenting a strict self-assembly that adds communication fibers to the fractal structure without disturbing it. To verify this strict self-assembly we develop a generalization of the local determinism method of Soloveichik and Winfree

Scaled tree fractals do not strictly self-assemble

In this paper, we show that any scaled-up version of any discrete self-similar {\it tree} fractal does not strictly self-assemble, at any temperature, in Winfree's abstract Tile Assembly Model.Comment: 13 pages, 3 figures, Appeared in the Proceedings of UCNC-2014, pp 27-39; Unconventional Computation and Natural Computation - 13th International Conference, UCNC 2014, London, ON, Canada, July 14-18, 2014, Springer Lecture Notes in Computer Science ISBN 978-3-319-08122-

Key Experimental Approaches in DNA Nanotechnology

DNA nanotechnology combines unusual DNA motifs with sticky‐ended cohesion to build polyhedral objects, topological targets, nanomechanical devices, and both crystalline and aperiodic arrays. The goal of DNA nanotechnology is control of the structure of macroscopic matter on the finest possible scale. Applications are expected to arise in the areas of X‐ray crystallography, nanoelectronics, nanorobotics, and DNA‐based computation. DNA and its close molecular relatives appear extremely well suited for these goals. This overview covers the generation of new DNA motifs, construction methods (synthesis, hybridization, phosphorylation, ligation), and a variety of methods for characterization of motifs, devices, and arrays. Finally, the use of DNA nanotechnology as a tool in biochemistry is discussed.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/143741/1/cpnc1201.pd

Negative Interactions in Irreversible Self-Assembly

This paper explores the use of negative (i.e., repulsive) interaction the abstract Tile Assembly Model defined by Winfree. Winfree postulated negative interactions to be physically plausible in his Ph.D. thesis, and Reif, Sahu, and Yin explored their power in the context of reversible attachment operations. We explore the power of negative interactions with irreversible attachments, and we achieve two main results. Our first result is an impossibility theorem: after t steps of assembly, Omega(t) tiles will be forever bound to an assembly, unable to detach. Thus negative glue strengths do not afford unlimited power to reuse tiles. Our second result is a positive one: we construct a set of tiles that can simulate a Turing machine with space bound s and time bound t, while ensuring that no intermediate assembly grows larger than O(s), rather than O(s * t) as required by the standard Turing machine simulation with tiles

Computer-aided design of nano-filter construction using DNA self-assembly

Computer-aided design plays a fundamental role in both top-down and bottom-up nano-system fabrication. This paper presents a bottom-up nano-filter patterning process based on DNA self-assembly. In this study we designed a new method to construct fully designed nano-filters with the pores between 5 nm and 9 nm in diameter. Our calculations illustrated that by constructing such a nano-filter we would be able to separate many molecules

Knots in Charged Polymers

The interplay of topological constraints and Coulomb interactions in static and dynamic properties of charged polymers is investigated by numerical simulations and scaling arguments. In the absence of screening, the long-range interaction localizes irreducible topological constraints into tight molecular knots, while composite constraints are factored and separated. Even when the forces are screened, tight knots may survive as local (or even global) equilibria, as long as the overall rigidity of the polymer is dominated by the Coulomb interactions. As entanglements involving tight knots are not easy to eliminate, their presence greatly influences the relaxation times of the system. In particular, we find that tight knots in open polymers are removed by diffusion along the chain, rather than by opening up. The knot diffusion coefficient actually decreases with its charge density, and for highly charged polymers the knot's position appears frozen.Comment: Revtex4, 9 pages, 9 eps figure

Rate-equation calculations of the current flow through two-site molecular device and DNA-based junction

Here we present the calculations of incoherent current flowing through the two-site molecular device as well as the DNA-based junction within the rate-equation approach. Few interesting phenomena are discussed in detail. Structural asymmetry of two-site molecule results in rectification effect, which can be neutralized by asymmetric voltage drop at the molecule-metal contacts due to coupling asymmetry. The results received for poly(dG)-poly(dC) DNA molecule reveal the coupling- and temperature-independent saturation effect of the current at high voltages, where for short chains we establish the inverse square distance dependence. Besides, we document the shift of the conductance peak in the direction to higher voltages due to the temperature decrease.Comment: 12 pages, 6 figure

Tight-binding parameters for charge transfer along DNA

We systematically examine all the tight-binding parameters pertinent to charge transfer along DNA. The $\pi$ molecular structure of the four DNA bases (adenine, thymine, cytosine, and guanine) is investigated by using the linear combination of atomic orbitals method with a recently introduced parametrization. The HOMO and LUMO wavefunctions and energies of DNA bases are discussed and then used for calculating the corresponding wavefunctions of the two B-DNA base-pairs (adenine-thymine and guanine-cytosine). The obtained HOMO and LUMO energies of the bases are in good agreement with available experimental values. Our results are then used for estimating the complete set of charge transfer parameters between neighboring bases and also between successive base-pairs, considering all possible combinations between them, for both electrons and holes. The calculated microscopic quantities can be used in mesoscopic theoretical models of electron or hole transfer along the DNA double helix, as they provide the necessary parameters for a tight-binding phenomenological description based on the $\pi$ molecular overlap. We find that usually the hopping parameters for holes are higher in magnitude compared to the ones for electrons, which probably indicates that hole transport along DNA is more favorable than electron transport. Our findings are also compared with existing calculations from first principles.Comment: 15 pages, 3 figures, 7 table

Strategies for Controlled Placement of Nanoscale Building Blocks

The capability of placing individual nanoscale building blocks on exact substrate locations in a controlled manner is one of the key requirements to realize future electronic, optical, and magnetic devices and sensors that are composed of such blocks. This article reviews some important advances in the strategies for controlled placement of nanoscale building blocks. In particular, we will overview template assisted placement that utilizes physical, molecular, or electrostatic templates, DNA-programmed assembly, placement using dielectrophoresis, approaches for non-close-packed assembly of spherical particles, and recent development of focused placement schemes including electrostatic funneling, focused placement via molecular gradient patterns, electrodynamic focusing of charged aerosols, and others