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

End-to-end automated microfluidic platform for synthetic biology: from design to functional analysis

DNAConstructor scripts.zip. Zip file containing files gfp_DNAConstructor.txt and rfp_DNAConstructor.txt, input script files for DNA Constructor. (ZIP 1.7 kb

Synthesis and cell-free cloning of DNA libraries using programmable microfluidics

Microfluidics may revolutionize our ability to write synthetic DNA by addressing several fundamental limitations associated with generating novel genetic constructs. Here we report the first de novo synthesis and cell-free cloning of custom DNA libraries in sub-microliter reaction droplets using programmable digital microfluidics. Specifically, we developed Programmable Order Polymerization (POP), Microfluidic Combinatorial Assembly of DNA (M-CAD) and Microfluidic In-vitro Cloning (MIC) and applied them to de novo synthesis, combinatorial assembly and cellfree cloning of genes, respectively. Proof-of-concept for these methods was demonstrated by programming an autonomous microfluidic system to construct and clone libraries of yeast ribosome binding sites and bacterial Azurine, which were then retrieved in individual droplets and validated. The ability to rapidly and robustly generate designer DNA molecules in an autonomous manner should have wide application in biological research and development

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

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

Recursive construction of perfect DNA molecules from imperfect oligonucleotides

Making faultless complex objects from potentially faulty building blocks is a fundamental challenge in computer engineering, nanotechnology and synthetic biology. Here, we show for the first time how recursion can be used to address this challenge and demonstrate a recursive procedure that constructs error-free DNA molecules and their libraries from error-prone oligonucleotides. Divide and Conquer (D&C), the quintessential recursive problem-solving technique, is applied in silico to divide the target DNA sequence into overlapping oligonucleotides short enough to be synthesized directly, albeit with errors; error-prone oligonucleotides are recursively combined in vitro, forming error-prone DNA molecules; error-free fragments of these molecules are then identified, extracted and used as new, typically longer and more accurate, inputs to another iteration of the recursive construction procedure; the entire process repeats until an error-free target molecule is formed. Our recursive construction procedure surpasses existing methods for de novo DNA synthesis in speed, precision, amenability to automation, ease of combining synthetic and natural DNA fragments, and ability to construct designer DNA libraries. It thus provides a novel and robust foundation for the design and construction of synthetic biological molecules and organisms

Algorithms for automated DNA assembly

Generating a defined set of genetic constructs within a large combinatorial space provides a powerful method for engineering novel biological functions. However, the process of assembling more than a few specific DNA sequences can be costly, time consuming and error prone. Even if a correct theoretical construction scheme is developed manually, it is likely to be suboptimal by any number of cost metrics. Modular, robust and formal approaches are needed for exploring these vast design spaces. By automating the design of DNA fabrication schemes using computational algorithms, we can eliminate human error while reducing redundant operations, thus minimizing the time and cost required for conducting biological engineering experiments. Here, we provide algorithms that optimize the simultaneous assembly of a collection of related DNA sequences. We compare our algorithms to an exhaustive search on a small synthetic dataset and our results show that our algorithms can quickly find an optimal solution. Comparison with random search approaches on two real-world datasets show that our algorithms can also quickly find lower-cost solutions for large datasets