Complexity of colouring problems restricted to unichord-free and \{square,unichord\}-free graphs

A \emph{unichord} in a graph is an edge that is the unique chord of a cycle. A \emph{square} is an induced cycle on four vertices. A graph is \emph{unichord-free} if none of its edges is a unichord. We give a slight restatement of a known structure theorem for unichord-free graphs and use it to show that, with the only exception of the complete graph $K_4$, every square-free, unichord-free graph of maximum degree~3 can be total-coloured with four colours. Our proof can be turned into a polynomial time algorithm that actually outputs the colouring. This settles the class of square-free, unichord-free graphs as a class for which edge-colouring is NP-complete but total-colouring is polynomial

Genomic distance under gene substitutions

Dias Vieira Braga M, Machado R, Ribeiro LC, Stoye J. Genomic distance under gene substitutions. BMC Bioinformatics. 2011;12(Suppl 9: Proc. of RECOMB-CG 2011): S8.Background: The distance between two genomes is often computed by comparing only the common markers between them. Some approaches are also able to deal with non-common markers, allowing the insertion or the deletion of such markers. In these models, a deletion and a subsequent insertion that occur at the same position of the genome count for two sorting steps. Results: Here we propose a new model that sorts non-common markers with substitutions, which are more powerful operations that comprehend insertions and deletions. A deletion and an insertion that occur at the same position of the genome can be modeled as a substitution, counting for a single sorting step. Conclusions: Comparing genomes with unequal content, but without duplicated markers, we give a linear time algorithm to compute the genomic distance considering substitutions and double-cut-and-join (DCJ) operations. This model provides a parsimonious genomic distance to handle genomes free of duplicated markers, that is in practice a lower bound to the real genomic distances. The method could also be used to refine orthology assignments, since in some cases a substitution could actually correspond to an unannotated orthology

Phenotype Sequencing: Identifying the Genes That Cause a Phenotype Directly from Pooled Sequencing of Independent Mutants

Random mutagenesis and phenotype screening provide a powerful method for dissecting microbial functions, but their results can be laborious to analyze experimentally. Each mutant strain may contain 50–100 random mutations, necessitating extensive functional experiments to determine which one causes the selected phenotype. To solve this problem, we propose a “Phenotype Sequencing” approach in which genes causing the phenotype can be identified directly from sequencing of multiple independent mutants. We developed a new computational analysis method showing that 1. causal genes can be identified with high probability from even a modest number of mutant genomes; 2. costs can be cut many-fold compared with a conventional genome sequencing approach via an optimized strategy of library-pooling (multiple strains per library) and tag-pooling (multiple tagged libraries per sequencing lane). We have performed extensive validation experiments on a set of E. coli mutants with increased isobutanol biofuel tolerance. We generated a range of sequencing experiments varying from 3 to 32 mutant strains, with pooling on 1 to 3 sequencing lanes. Our statistical analysis of these data (4099 mutations from 32 mutant genomes) successfully identified 3 genes (acrB, marC, acrA) that have been independently validated as causing this experimental phenotype. It must be emphasized that our approach reduces mutant sequencing costs enormously. Whereas a conventional genome sequencing experiment would have cost $7,200 in reagents alone, our Phenotype Sequencing design yielded the same information value for only$1200. In fact, our smallest experiments reliably identified acrB and marC at a cost of only $110–$340