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Encoding and processing information in DNA-, RNA- and other biomolecule-based devices is an important requirement for DNA-based computing with potentially important applications. Recent experimental and theoretical advances have produced and tested new methods to obtain large code sets of oligonucleotides to support virtually any kind of application. We report results of a to conduct an exhaustive search to produce code sets that are arguably of sizes comparable to that of maximal sets while guaranteeing high quality, as measured by the minimum Gibbs energy between any pair of code words and other criteria. The method is constructive and directly produces the actual composition of the sets, unlike their counterpart . The sequences allow a quantitative characterization of their composition. We also present a new technique to generate code sets with desirable more stringent constraints on their possible interaction under a variety of conditions, as measured by Gibbs energies of duplex formation. The results predict close agreement with known results for 20–mers. Consequences of these results are bounds on the capacity of DNA for information storage and processing in wet tubes for a given oligo length, as well as many other applications where specific and complex self-directed assembly of large number of components may be required.

We propose a local-search based algorithm to design DNA sequence sets that satisfy several combinatorial constraints about hamming-distance criteria. To deal with the constraints in the local search, we adopt elaborate (and dynamic) neighborhood search frameworks called the (VNS) and the (VDS). Although our algorithm can deal with many types of hamming distance-based constraints and is easy to extend (e.g., also applicable for other constraints), in computational experiments, we succeeded in generating better sequence sets than the ones generated by exiting methods of more specified constraints.

DNA tile nanostructures have lately attracted a lot of attention as a new calculation technique and material on the nanometer scale. In forming DNA tiles, sequences need to bond in tile conformation. Conventional work can design sequences using overlapping subsequence. In this paper, we design tile sequences based on free energy. As a result of optimization, we show that we can design tile sequences as stable as conventional tiles. Moreover, we illustrate that the tile designed by the proposed method is perhaps more stable than conventional one. This method will be useful to design many tiles when forming large scale and complex DNA nanostructures.

We examine scattered hairpins, which are structures formed when a single strand folds into a partially hybridized stem and a loop. To specify different classes of hairpins, we use the concept of DNA trajectories, which allows precise descriptions of valid bonding patterns on the stem of the hairpin. DNA trajectories have previously been used to describe bonding between separate strands.

We are interested in the mathematical properties of scattered hairpins described by DNA trajectories. We examine the complexity of set of hairpin-free words described by a set of DNA trajectories. In particular, we consider the closure properties of language classes under sets of DNA trajectories of differing complexity. We address decidability of recognition problems for hairpin structures.

Self-repair is essential to all living systems, providing the ability to remain functional in spite of gradual damage. In the context of self-assembly of self-repairing synthetic biomolecular systems, recently Winfree developed a method for transforming a set of DNA tiles into its self-healing counterpart at the cost of increasing the lattice area by a factor of 25. The overall focus of this paper, however, is to develop designs for self-repairing tiling assemblies with reasonable constraints on crystal growth. Specifically, we use a special class of DNA tiling designs called tiling which when carefully designed can provide inherent self-repairing capabilities to patterned DNA lattices. We further note that we can transform any irreversible computational DNA tile set to its reversible counterpart and hence improve the self-repairability of the computational lattice. But doing the transform with an optimal number of tiles, is still an open question.

We study the times to grow structures within the tile self-assembly model proposed by Winfree, and the possible shapes that can be achieved during the self-assembly. Our earlier work was confined to the growth of rectangular structures, in which the border tiles are prefabricated. By varying the relative rates between the border-tile and rule-tile attachment, one can engineer interesting new shapes, which have been observed in the laboratory. We show that the results from an extension of our earlier stochastic models agree remarkably closely with experimental results. This is an important further demonstration of the validity and usefulness of our stochastic models, which have also been used successfully in studies of error correction in DNA self assembly.

Winfree’s pioneering work led the foundations in the area of error-reduction in algorithmic self-assembly[26], but the construction resulted in increase of the size of assembly. Reif et. al. contributed further in this area with compact error-resilient schemes [15] that maintained the original size of the assemblies, but required certain restrictions on the Boolean functions to be used in the algorithmic self-assembly. It is a critical challenge to improve these compact error resilient schemes to incorporate arbitrary Boolean functions, and to determine how far these prior results can be extended under different degrees of restrictions on the Boolean functions. In this work we present a considerably more complete theory of compact error-resilient schemes for algorithmic self-assembly in two and three dimensions. First we consider two-dimensional algorithmic self-assembly. We present an error correction scheme for reduction of errors from to for arbitrary Boolean functions in two dimensional algorithmic self-assembly. Then we characterize the class of Boolean functions for which the error reduction can be done from to , and present an error correction scheme that achieves this reduction. Then we prove ultimate limits on certain classes of compact error resilient schemes: in particular we show that they can not provide reduction of errors from to is for any Boolean functions. Further, we develop the first provable compact error resilience schemes for three dimensional tiling self-assemblies. We also extend the work of Winfree on self-healing in two-dimensional self-assembly[25] to obtain a self-healing tile-set for three-dimensional self-assembly.

Understanding the structure of viruses is an important first step in terms of many applications in virology, including the protein engineering of containers to enable more effective drug delivery. In particular, the viral capsids, i.e. the protective shells on the exterior of viruses containing the important genetic code, play an important role in the context of gene therapy, where small amounts of therapeutic DNA is packaged into a capsid which then penetrates the cell membrane and delivers its payload. Cross-linking structures are particular additional covalent bonds that can occur in addition to the already present hydrophobic interactions and hydrogen bonds between the proteins. Their importance lies in the fact that they render the capsid particularly stable. Here we shall introduce a mathematical method to predict possible locations for these additional bonds of cross-linking. We will give examples of failed cases as well as of cases where cross-linking structures are possible. These results serve as a pointer for experimentalists as to which types of cross-linking structures may possibly be engineered and exploited in the framework of drug delivery.

In this paper, we propose a framework for a discrete event simulator for simulating the DNA based nano-robotical systems. We describe a physical model that captures the conformational changes of the solute molecules. We also present methods to simulate various chemical reactions due to the molecular collisions, including hybridization, dehybridization and strand displacement. The feasibility of such a framework is demonstrated by some preliminary results.

We developed a computer-software with graphic interfaces for generating DNA sequences of various DNA motifs for DNA nanotechnology research. The software is free of charge for academic and non-profit organizations.