An introduction to genome rearrangements

Glenn TeslerUniversity of California, San Diego (UCSD)Mathematics

In addition to frequent single-nucleotide mutations, mammalian and many other genomes undergo rare and dramatic changes in their chromosomal organization, called genome rearrangements. These include inversions, fissions, fusions, and translocations. Although analysis of genome rearrangements was pioneered by Dobzhansky and Sturtevant in 1938, we still know very little about the rearrangement events that produced the existing varieties of genomic architectures. Recovery of mammalian rearrangement history is a difficult combinatorial problem that I will cover in this talk. Our data sets have included sequenced genomes (human, mouse, rat, and others), as well as radiation hybrid maps of additional mammals. I will describe the relationship between our combinatorial analysis and the classical Nadeau-Taylor random breakage theory of evolution.

I will also survey other genome rearrangement models that have been introduced to allow for different types of data and different types of rearrangement operations. Of particular interest is the double cut and join'' (DCJ) operation, which has become very popular due to the relative simplicity of its analysis.

Finally, I will discuss enumeration problems in genome rearrangements, including the number of sorting scenarios, and the distribution of the number and lengths of conserved segments of genes between two or more unichromosomal genomes. The latter problem generalizes classical work on permutations from the 1940s-60s by Wolfowitz, Kaplansky, Riordan, Abramson, and Moser, who studied decompositions of permutations into strips of ascending or descending consecutive numbers. In our setting, their work corresponds to comparison of two unsigned genomes (known gene orders, unknown gene orientations).

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