Polynomial-Time Amoeba Neighborhood Membership and Faster Localized Solving

We derive efficient algorithms for coarse approximation of algebraic hypersurfaces, useful for estimating the distance between an input polynomial zero set and a given query point. Our methods work best on sparse polynomials of high degree (in any number of variables) but are nevertheless completely general. The underlying ideas, which we take the time to describe in an elementary way, come from tropical geometry. We thus reduce a hard algebraic problem to high-precision linear optimization, proving new upper and lower complexity estimates along the way.Comment: 15 pages, 9 figures. Submitted to a conference proceeding

A Free-Standing Homing Endonuclease Targets an Intron Insertion Site in the psbA Gene of Cyanophages

Homing endonuclease genes are mobile elements that promote their duplication into cognate sites that lack the endonuclease gene [1, 2]. The homing endonuclease initiates this event through site-specific DNA cleavage. Copying of the endonuclease gene follows as a consequence of DNA repair. A genome containing a homing endonuclease gene is subject to self-cleavage. Protection is accomplished through DNA sequence polymorphisms, as is the case in intronless homing of free-standing endonuclease genes [3, 4], or by disruption of the recognition site by a group I intron (or intein) into which the endonuclease ORF is embedded. We describe here a novel free-standing homing endonuclease from cyanobacteriophage S-PM2, which is similar to the DNA resolvase of bacteriophage T4 and is encoded adjacent to an intron-containing psbA gene [5, 6]. The endonuclease makes a specific double-strand cut near the intron insertion site (IIS), its DNA recognition site spans the IIS, and it is unable to cleave intron-containing psbA genes. This interdependence of a free-standing endonuclease gene and a group I intron, which we denote "collaborative homing," has not been reported previously and gives support to a hypothesis of formation of composite mobile introns by independent convergence of an intron and an endonuclease gene on the same target sequence. © 2009 Elsevier Ltd. All rights reserved

I-BasI and I-HmuI: two phage intron-encoded endonucleases with homologous DNA recognition sequences but distinct DNA specificities

I-HmuI and I-BasI are two highly similar nicking DNA endonucleases, which are each encoded by a group I intron inserted into homologous sites within the DNA polymerase genes of Bacillus phages SPO1 and Bastille, respectively. Here, we present a comparison of the DNA specificities and cleavage activities of these enconucleases with homologous target sites. I-BasI has properties that are typical of homing endonucleases, nicking the intron-minus polymerase genes in either host genome, three nucleotides downstream of the intron insertion site. In contrast, I-HmuI nicks both the intron-plus and intron-minus site in its own host genome, but does not act on the target from Bastille phage. Although the enzymes have distinct DNA substrate specificities, both bind to an identical 25bp region of their respective intron-minus DNA polymerase genes surrounding the intron insertion site. The endonucleases appear to interact with the DNA substrates in the downstream exon 2 in a similar manner. However, whereas I-HmuI is known to make its only base-specific contacts within this exon region, structural modeling analyses predict that I-BasI might make specific base contacts both upstream and downstream of the site of intron insertion. The predicted requirement for base-specific contacts in exon 1 for cleavage by I-BasI was confirmed experimentally. This explains the difference in substrate specificities between the two enzymes, including the observation that the former enzyme is relatively insensitive to the presence of an intron upstream of exon 2. These differences are likely a consequence of divergent evolutionary constraints

DNA binding and cleavage by the HNH homing endonuclease I-HmuI

The structure of I-HmuI, which represents the last family of homing endonucleases without a defining crystallographic structure, has been determined in complex with its DNA target. A series of diverse protein structural domains and motifs, contacting sequential stretches of nucleotide bases, are distributed along the DNA target. I-HmuI contains an N-terminal domain with a DNA-binding surface found in the I-PpoI homing endonuclease and an associated HNH/N active site found in the bacterial colicins, and a C-terminal DNA-binding domain previously observed in the I-TevI homing endonuclease. The combination and exchange of these features between protein families indicates that the genetic mobility associated with homing endonucleases extends to the level of independent structural domains. I-HmuI provides an unambiguous structural connection between the His-Cys box endonucleases and the bacterial colicins, supporting the hypothesis that these enzymes diverged from a common ancestral nuclease