C+G content (GC content or G+C content) is known to be correlated with genome/chromosome size in bacteria but the relationship for other kingdoms remains unclear. This study analyzed genome size, chromosome size, and base composition in most of the available sequenced genomes in various kingdoms. Genome size tends to increase during evolution in plants and animals, and the same is likely true for bacteria. The genomic C+G contents were found to vary greatly in microorganisms but were quite similar within each animal or plant subkingdom. In animals and plants, the C+G contents are ranked as follows: monocot plants>mammals>non-mammalian animals>dicot plants. The variation in C+G content between chromosomes within species is greater in animals than in plants. The correlation between average chromosome C+G content and chromosome length was found to be positive in Proteobacteria, Actinobacteria (but not in other analyzed bacterial phyla), Ascomycota fungi, and likely also in some plants; negative in some animals, insignificant in two protist phyla, and likely very weak in Archaea. Clearly, correlations between C+G content and chromosome size can be positive, negative, or not significant depending on the kingdoms/groups or species. Different phyla or species exhibit different patterns of correlation between chromosome-size and C+G content. Most chromosomes within a species have a similar pattern of variation in C+G content but outliers are common. The data presented in this study suggest that the C+G content is under genetic control by both trans- and cis- factors and that the correlation between C+G content and chromosome length can be positive, negative, or not significant in different phyla.

Pre–messenger RNA (mRNA) 3′-end cleavage and subsequent polyadenylation strongly regulate gene expression. In comparison with the upstream or downstream motifs, relatively little is known about the feature differences of polyadenylation [poly(A)] sites among major kingdoms. We suspect that the precise poly(A) sites are very selective, and we therefore mapped mRNA poly(A) sites on complete and nearly complete genomes using mRNA sequences available in the National Center for Biotechnology Information (NCBI) Nucleotide database. In this paper, we describe the mRNA nucleotide [i.e., the poly(A) tail attachment position] that is directly in attachment with the poly(A) tail and the pre-mRNA nucleotide [i.e., the poly(A) tail starting position] that corresponds to the first adenosine of the poly(A) tail in the 29 most-mapped species (2 fungi, 2 protists, 18 animals, and 7 plants). The most representative pre-mRNA dinucleotides covering these two positions were UA, CA, and GA in 17, 10, and 2 of the species, respectively. The pre-mRNA nucleotide at the poly(A) tail starting position was typically an adenosine [i.e., A-type poly(A) sites], sometimes a uridine, and occasionally a cytidine or guanosine. The order was U>C>G at the attachment position but A>>U>C≥G at the starting position. However, in comparison with the mRNA nucleotide composition (base composition), the poly(A) tail attachment position selected C over U in plants and both C and G over U in animals, in both A-type and non-A-type poly(A) sites. Animals, dicot plants, and monocot plants had clear differences in C/G ratios at the poly(A) tail attachment position of the non-A-type poly(A) sites. This study of poly(A) site evolution indicated that the two positions within poly(A) sites had distinct nucleotide compositions and were different among kingdoms.

BackgroundThe polyadenylation of RNA is critical for gene functioning, but the conserved sequence motifs (often called signal or signature motifs), motif locations and abundances, and base composition patterns around mRNA polyadenylation [poly(A)] sites are still uncharacterized in most species. The evolutionary tendency for poly(A) site selection is still largely unknown.ResultsWe analyzed the poly(A) site regions of 31 species or phyla. Different groups of species showed different poly(A) signal motifs: UUACUU at the poly(A) site in the parasite Trypanosoma cruzi; UGUAAC (approximately 13 bases upstream of the site) in the alga Chlamydomonas reinhardtii; UGUUUG (or UGUUUGUU) at mainly the fourth base downstream of the poly(A) site in the parasite Blastocystis hominis; and AAUAAA at approximately 16 bases and approximately 19 bases upstream of the poly(A) site in animals and plants, respectively. Polyadenylation signal motifs are usually several hundred times more abundant around poly(A) sites than in whole genomes. These predominant motifs usually had very specific locations, whether upstream of, at, or downstream of poly(A) sites, depending on the species or phylum. The poly(A) site was usually an adenosine (A) in all analyzed species except for B. hominis, and there was weak A predominance in C. reinhardtii. Fungi, animals, plants, and the protist Phytophthora infestans shared a general base abundance pattern (or base composition pattern) of “U-rich—A-rich—U-rich—Poly(A) site—U-rich regions”, or U-A-U-A-U for short, with some variation for each kingdom or subkingdom.ConclusionThis study identified the poly(A) signal motifs, motif locations, and base composition patterns around mRNA poly(A) sites in protists, fungi, plants, and animals and provided insight into poly(A) site evolution.

We consider the facility location problem with submodular penalties (FLPSP) and the facility location problem with linear penalties (FLPLP), two extensions of the classical facility location problem (FLP). First, we introduce a general algorithmic framework for a class of covering problems with submodular penalties, extending the recent result of Geunes et al. (Math Program 130:85-106, 2011) with linear penalties. This framework leverages existing approximation results for the original covering problems to obtain corresponding results for their counterparts with submodular penalties. Specifically, any LP-based α-approximation for the original covering problem can be leveraged to obtain an 1 − e −1/α −1 -approximation algorithm for the counterpart with submodular penalties. Consequently, any LP-based approximation algorithm for the classical FLP (as a covering problem) can yield, via this framework, an approximation algorithm for the counterpart with submodular penalties. Second, by exploiting some special properties of submodular/linear penalty function, we present 123 Algorithmica an LP rounding algorithm which has the currently best 2-approximation ratio over the previously best 2.375 by Li et al. (Theoret Comput Sci 476:109-117, 2013) for the FLPSP and another LP-rounding algorithm which has the currently best 1.5148-approximation ratio over the previously best 1.853 by Xu and Xu (J Comb Optim 17:424-436, 2008) for the FLPLP, respectively.

The maximum residual flow problem with one-arc destruction is shown to be solvable in strongly polynomial time in [Aneja et al., Networks, 38 (2001), 194-198]. However, the status of the corresponding problem with more than one-arc destruction is left open therein. We resolve the status of the two-arc destruction problem by demonstrating that it is already NP -hard.