Strong Products of Hypergraphs: Unique Prime Factorization Theorems and Algorithms

It is well-known that all finite connected graphs have a unique prime factor decomposition (PFD) with respect to the strong graph product which can be computed in polynomial time. Essential for the PFD computation is the construction of the so-called Cartesian skeleton of the graphs under investigation. In this contribution, we show that every connected thin hypergraph H has a unique prime factorization with respect to the normal and strong (hypergraph) product. Both products coincide with the usual strong graph product whenever H is a graph. We introduce the notion of the Cartesian skeleton of hypergraphs as a natural generalization of the Cartesian skeleton of graphs and prove that it is uniquely defined for thin hypergraphs. Moreover, we show that the Cartesian skeleton of hypergraphs can be determined in O(|E|^2) time and that the PFD can be computed in O(|V|^2|E|) time, for hypergraphs H = (V,E) with bounded degree and bounded rank

Square Property, Equitable Partitions, and Product-like Graphs

Equivalence relations on the edge set of a graph $G$ that satisfy restrictive conditions on chordless squares play a crucial role in the theory of Cartesian graph products and graph bundles. We show here that such relations in a natural way induce equitable partitions on the vertex set of $G$, which in turn give rise to quotient graphs that can have a rich product structure even if $G$ itself is prime.Comment: 20 pages, 6 figure

Methods for producing soluble, biologically-active disulfide-bond containing eukaryotic proteins in bacterial cells

Disclosed are methods of producing eukaryotic disulfide bond-containing polypeptides in bacterial hosts, and compositions resulting therefrom. Co-expression of a eukaryotic foldase and a disulfide bond-containing polypeptide in a bacterial host cell is demonstrated. In particular embodiments, the methods have been used to produce mammalian pancreatic trypsin inhibitor and tissue plasminogen activator (tPA) in soluble, biologically-active forms, which are isolatable from the bacterial periplasm. Also disclosed are expression systems, recombinant vectors, and transformed host cells.Board of Regents, University of Texas Syste

Morphogen-defined patterning of Escherichia coli enabled by an externally tunable band-pass filter

<p>Abstract</p> <p>Background</p> <p>Gradients of morphogens pattern cell fate – a phenomenon that is especially important during development. A simple model system for studying how morphogens pattern cell behavior would overcome difficulties inherent in the study of natural morphogens <it>in vivo</it>. A synthetic biology approach to building such a system is attractive.</p> <p>Results</p> <p>Using an externally-tunable band-pass filter paradigm, we engineered <it>Escherichia coli </it>cells to function as a model system for the study of how multiple morphogens can pattern cell behavior. We demonstrate how our system exhibits behavior such as morphogen crosstalk and how the cells' growth and fluorescence can be patterned in a number of complex patterns. We extend our cell patterning from 2D cultures on the surface of plates to 3D cultures in soft agarose medium.</p> <p>Conclusion</p> <p>Our system offers a convenient, well-defined model system for fundamental studies on how multiple morphogen gradients can affect cell fate and lead to pattern formation. Our design principles could be applied to eukaryotic cells to develop other models systems for studying development or for enabling the patterning of cells for applications such as tissue engineering and biomaterials.</p

A note on quasi-robust cycle bases

We investigate here some aspects of cycle bases of undirected graphs that allow the iterative construction of all elementary cycles. We introduce the concept of quasi-robust bases as a generalization of the notion of robust bases and demonstrate that a certain class of bases of the complete bipartite graphs K m,n with m,n _> 5 is quasi-robust but not robust. We furthermore disprove a conjecture for cycle bases of Cartesian product graphs

In Vitro Recombination of Non-Homologous Genes Can Result in Gene Fusions that Confer a Switching Phenotype to Cells

Regulation of protein activity is central to the complexity of life. The ability to regulate protein activity through exogenously added molecules has biotechnological/biomedical applications and offers tools for basic science. Such regulation can be achieved by establishing a means to modulate the specific activity of the protein (i.e. allostery). An alternative strategy for intracellular regulation of protein activity is to control the amount of protein through effects on its production, accumulation, and degradation. We have previously demonstrated that the non-homologous recombination of the genes encoding maltose binding protein (MBP) and TEM1 β-lactamase (BLA) can result in fusion proteins in which β-lactamase enzyme activity is allosterically regulated by maltose. Here, through use of a two-tiered genetic selection scheme, we demonstrate that such recombination can result in genes that confer maltose-dependent resistance to β-lactam even though they do not encode allosteric enzymes. These ‘phenotypic switch’ genes encode fusion proteins whose accumulation is a result of a specific interaction with maltose. Phenotypic switches represent an important class of proteins for basic science and biotechnological applications in vivo

Circular Permutation in the Ω-Loop of TEM-1 β-Lactamase Results in Improved Activity and Altered Substrate Specificity

Generating diverse protein libraries that contain improved variants at a sufficiently high frequency is critical for improving the properties of proteins using directed evolution. Many studies have illustrated how random mutagenesis, cassette mutagenesis, DNA shuffling and similar approaches are effective diversity generating methods for directed evolution. Very few studies have explored random circular permutation, the intramolecular relocation of the N- and C-termini of a protein, as a diversity-generating step for directed evolution. We subjected a library of random circular permutations of TEM-1 β-lactamase to selections on increasing concentrations of a variety of β-lactam antibiotics including cefotaxime. We identified two circularly permuted variants that conferred elevated resistance to cefotaxime but decreased resistance to other antibiotics. These variants were circularly permuted in the Ω-loop proximal to the active site. Remarkably, one variant was circularly permuted such that the key catalytic residue Glu166 was located at the N-terminus of the mature protein