# Graduate Student Seminar-Mathematical Models for Genome Rearrangements and Whole Genome Duplications

Title: Mathematical Models for Genome Rearrangements and Whole Genome Duplications

Speaker: Pavel, Avdeev

Date and Time: Monday, April 23, 2:30-3:30pm

Place: Rome 204

Abstract: One of the key computational problems in comparative genomics is the reconstruction of genomes of ancestral species based on genomes of extant species. Since most dramatic changes in genomic architectures are caused by genome rearrangements, this problem is often posed as minimization of the number of genome rearrangements between extant and ancestral genomes.

Place: Rome 204

Abstract: One of the key computational problems in comparative genomics is the reconstruction of genomes of ancestral species based on genomes of extant species. Since most dramatic changes in genomic architectures are caused by genome rearrangements, this problem is often posed as minimization of the number of genome rearrangements between extant and ancestral genomes.

The basic case of three given genomes is known as the genome median problem. Whole genome duplications (WGDs) represent yet another type of dramatic evolutionary events and inspire the reconstruction of pre-duplicated ancestral genomes, referred to as the genome halving problem.

We start with a description of genome evolution and most dramatic evolutionary events such genome rearrangements and whole genome duplication. Then. we move to the most common mathematical model of genome rearrangements, called Double-Cut-and-Join (DCJ). We further describe generalizations and applications of the DCJ model. We also consider the

problem of ancestral genome reconstruction and its particular instances such as genome median and halving problems. Finally, we discuss topological and integer linear programming approaches to these problems.