Tree decompositions with small cost

The f-cost of a tree decomposition ({Xi | i e I}, T = (I;F)) for a function f : N -> R+ is defined as EieI f(|Xi|). This measure associates with the running time or memory use of some algorithms that use the tree decomposition. In this paper we investigate the problem to find tree decompositions of minimum f-cost. A function f : N -> R+ is fast, if for every i e N: f(i+1) => 2*f(i). We show that for fast functions f, every graph G has a tree decomposition of minimum f-cost that corresponds to a minimal triangulation of G; if f is not fast, this does not hold. We give polynomial time algorithms for the problem, assuming f is a fast function, for graphs that has a polynomial number of minimal separators, for graphs of treewidth at most two, and for cographs, and show that the problem is NP-hard for bipartite graphs and for cobipartite graphs. We also discuss results for a weighted variant of the problem derived of an application from probabilistic networks

Application of GFAT as a Novel Selection Marker to Mediate Gene Expression

The enzyme glutamine: fructose-6-phosphate aminotransferase (GFAT), also known as glucosamine synthase (GlmS), catalyzes the formation of glucosamine-6-phosphate from fructose-6-phosphate and is the first and rate-limiting enzyme of the hexosamine biosynthetic pathway. For the first time, the GFAT gene was proven to possess a function as an effective selection marker for genetically modified (GM) microorganisms. This was shown by construction and analysis of two GFAT deficient strains, E. coli ΔglmS and S. pombe Δgfa1, and the ability of the GFAT encoding gene to mediate plasmid selection. The gfa1 gene of the fission yeast Schizosaccharomyces pombe was deleted by KanMX6-mediated gene disruption and the Cre-loxP marker removal system, and the glmS gene of Escherichia coli was deleted by using λ-Red mediated recombinase system. Both E. coli ΔglmS and S. pombe Δgfa1 could not grow normally in the media without addition of glucosamine. However, the deficiency was complemented by transforming the plasmids that expressed GFAT genes. The xylanase encoding gene, xynA2 from Thermomyces lanuginosus was successfully expressed and secreted by using GFAT as selection marker in S. pombe. Optimal glucosamine concentration for E. coli ΔglmS and S. pombe Δgfa1 growth was determined respectively. These findings provide an effective technique for the construction of GM bacteria without an antibiotic resistant marker, and the construction of GM yeasts to be applied to complex media