Interaction detection methods have led to the discovery of thousands of interactions between proteins, and discerning relevance within large-scale data sets is important to present-day biology. Here, a spectral method derived from graph theory was introduced to uncover hidden topological structures (i.e. quasi-cliques and quasi-bipartites) of complicated protein-protein interaction networks. Our analyses suggest that these hidden topological structures consist of biologically relevant functional groups. This result motivates a new method to predict the function of uncharacterized proteins based on the classification of known proteins within topological structures. Using this spectral analysis method, 48 quasi-cliques and six quasi-bipartites were isolated from a network involving 11,855 interactions among 2617 proteins in budding yeast, and 76 uncharacterized proteins were assigned functions.

Thermoanaerobacter tengcongensis is a rod-shaped, gram-negative, anaerobic eubacterium that was isolated from a freshwater hot spring in Tengchong, China. Using a whole-genome-shotgun method, we sequenced its 2,689,445-bp genome from an isolate, MB4T (Genbank accession no. AE008691). The genome encodes 2588 predicted coding sequences (CDS). Among them, 1764 (68.2%) are classified according to homology to other documented proteins, and the rest, 824 CDS (31.8%), are functionally unknown. One of the interesting features of the T. tengcongensis genome is that 86.7% of its genes are encoded on the leading strand of DNA replication. Based on protein sequence similarity, the T. tengcongensis genome is most similar to that of Bacillus halodurans, a mesophilic eubacterium, among all fully sequenced prokaryotic genomes up to date. Computational analysis on genes involved in basic metabolic pathways supports the experimental discovery that T. tengcongensis metabolizes sugars as principal energy and carbon source and utilizes thiosulfate and element sulfur, but not sulfate, as electron acceptors. T. tengcongensis, as a gram-negative rod by empirical definitions (such as staining), shares many genes that are characteristics of gram-positive bacteria whereas it is missing molecular components unique to gram-negative bacteria. A strong correlation between the G + C content of tDNA and rDNA genes and the optimal growth temperature is found among the sequenced thermophiles. It is concluded that thermophiles are a biologically and phylogenetically divergent group of prokaryotes that have converged to sustain extreme environmental conditions over evolutionary timescale

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In the theoretical part of this paper, we introduce a simplified proof technique for error bounds and convergence of a variation of E. Kansa's well-known unsymmetric meshless collocation method. For a numerical implementation of the convergent variation, a previously proposed greedy technique is coupled with linear optimization. This algorithm allows a fully adaptive on-the-fly data-dependent meshless selection of test and trial spaces. The new method satisfies the assumptions of the background theory, and numerical experiments demonstrate its stability.