Seminar za biomatematiko in matematično kemijo - Arhiv

Horizontal Gene Transfer (HGT) is the movement of genetic material between coexisting species. Given the true history of the genes, Walter M. Fitch defined in his illuminating paper [Trends Genet. 16 (2000) 227–231, doi:10.1016/s0168-9525(00)02005-9] two genes as “xenologs” if their history since their common ancestor involves HGT of at least one of them. Although this definition of xenology is one of the most commonly used terms in phylogenomics, the mathematics of the xenology-relation X has not been investigated in detail, so-far. In this talk, we consider the following two problems:

1. How much phylogenetic signal is contained in a xenology-relation X? In other words, is it possible to infer phylogenetic trees from X? 
2. Can we characterize xenology-relations? In other words, is it possible to decide whether an arbitrary binary relation is a xenology-relation? 

To this end, we study the graph structure of the relation X. Surprisingly, xenology-relations are characterized by a small set of forbidden induced subgraphs on three vertices and they form a subclass of so-called directed cographs. We provide a linear-time algorithm to recognize such relations and for the reconstruction of least-resolved phylogenetic trees.

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The simplest description of conjugated hydrocarbons is Hückel Molecular Orbital (HMO) Theory, which is in essence a graph theoretical model. Eigenvectors and eigenvalues of the adjacency matrix of the molecular graph are used to model spatial distributions and energies of the mobile electrons that dominate the chemical and physical properties of these important unsaturated systems. Charles Alfred Coulson FRS (1910 – 1974) was a leading figure in the development and exploitation of HMO theory from the early 1940s all the way through to the 1970s. His work with Longuet-Higgins defined key concepts that still shape chemical thinking about benzenoids and have found new applications with the many forms of carbon that have emerged in the decades since his death. This talk will discuss a claim that surfaced in Coulson’s early work, is part of the folklore of HMO theory apparently believed by all chemists, but until recently had no complete published proof, despite tantalising hints sprinkled through 70 years of primary literature and textbooks.

This talk is based on J. Chem. Phys. 151 (2019) 151101, doi:10.1063/1.5128624 but also covers some more recent developments.

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