Glen Tesler, Department of Mathematics, University of California, San Diego
Reconstructing the Genomic Architecture of Ancestral Mammals
Coauthors:
Pavel Pevzner, UCSD, Department of Computer Science and Engineering
Guillaume Bourque, Genome Institute of Singapore
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 also describe the relationship between our combinatorial analysis and the classical Nadeau-Taylor random breakage theory of evolution.
I have also done theoretical work using combinatorial methods (generating functions, commutative and noncommutative formal power series, asymptotics, recursions, and enumeration formulas) to study the distributions of the number and lengths of conserved segments of genes between two or more unichromosomal genomes, including signed and unsigned genomes, and linear and circular genomes. This 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).