Analytical Study of Certain Magnetohydrodynamic-alpha Models

In this paper we present an analytical study of a subgrid scale turbulence model of the three-dimensional magnetohydrodynamic (MHD) equations, inspired by the Navier-Stokes-alpha (also known as the viscous Camassa-Holm equations or the Lagrangian-averaged Navier-Stokes-alpha model). Specifically, we show the global well-posedness and regularity of solutions of a certain MHD-alpha model (which is a particular case of the Lagrangian averaged magnetohydrodynamic-alpha model without enhancing the dissipation for the magnetic field). We also introduce other subgrid scale turbulence models, inspired by the Leray-alpha and the modified Leray-alpha models of turbulence. Finally, we discuss the relation of the MHD-alpha model to the MHD equations by proving a convergence theorem, that is, as the length scale alpha tends to zero, a subsequence of solutions of the MHD-alpha equations converges to a certain solution (a Leray-Hopf solution) of the three-dimensional MHD equations.Comment: 26 pages, no figures, will appear in Journal of Math Physics; corrected typos, updated reference

Processing DNA molecules as text

Polymerase Chain Reaction (PCR) is the DNA-equivalent of Gutenberg’s movable type printing, both allowing large-scale replication of a piece of text. De novo DNA synthesis is the DNA-equivalent of mechanical typesetting, both ease the setting of text for replication. What is the DNA-equivalent of the word processor? Biology labs engage daily in DNA processing—the creation of variations and combinations of existing DNA—using a plethora of manual labor-intensive methods such as site-directed mutagenesis, error-prone PCR, assembly PCR, overlap extension PCR, cleavage and ligation, homologous recombination, and others. So far no universal method for DNA processing has been proposed and, consequently, no engineering discipline that could eliminate this manual labor has emerged. Here we present a novel operation on DNA molecules, called Y, which joins two DNA fragments into one, and show that it provides a foundation for DNA processing as it can implement all basic text processing operations on DNA molecules including insert, delete, replace, cut and paste and copy and paste. In addition, complicated DNA processing tasks such as the creation of libraries of DNA variants, chimeras and extensions can be accomplished with DNA processing plans consisting of multiple Y operations, which can be executed automatically under computer control. The resulting DNA processing system, which incorporates our earlier work on recursive DNA composition and error correction, is the first demonstration of a unified approach to DNA synthesis, editing, and library construction

Efficient assembly of very short oligonucleotides using T4 DNA Ligase

<p>Abstract</p> <p>Background</p> <p>In principle, a pre-constructed library of all possible short oligonucleotides could be used to construct many distinct gene sequences. In order to assess the feasibility of such an approach, we characterized T4 DNA Ligase activity on short oligonucleotide substrates and defined conditions suitable for assembly of a plurality of oligonucleotides.</p> <p>Findings</p> <p>Ligation by T4 DNA Ligase was found to be dependent on the formation of a double stranded DNA duplex of at least five base pairs surrounding the site of ligation. However, ligations could be performed effectively with overhangs smaller than five base pairs and oligonucleotides as small as octamers, in the presence of a second, complementary oligonucleotide. We demonstrate the feasibility of simultaneous oligonucleotide phosphorylation and ligation and, as a proof of principle for DNA synthesis through the assembly of short oligonucleotides, we performed a hierarchical ligation procedure whereby octamers were combined to construct a target 128-bp segment of the beta-actin gene.</p> <p>Conclusions</p> <p>Oligonucleotides as short as 8 nucleotides can be efficiently assembled using T4 DNA Ligase. Thus, the construction of synthetic genes, without the need for custom oligonucleotide synthesis, appears feasible.</p