Transposition distances between genomes

Author(s)

Vinicius Jose Fortuna

• Document type: Master's Dissertation
• Press: Campinas, SP.
• Institution: Universidade Estadual de Campinas (UNICAMP). Instituto de Computação
• Defense date: 2005-03-28

Examining board members

João Meidanis; Maria Emilia Machado Telles Walter; Zanoni Dias

• Advisor: João Meidanis

Abstract

One of the main ways of measuring the evolution distance among species is to evaluate how large chunks have moved when comparing two genomes. Such changes are know as genome rearrangements. In this work we analyze a rearrangement event called transposition that changes the position of two consecutive blocks of genes in a chromosome. More specifically, we look for the minimum number of transpositions needed to transform a chromosome into another. This value is called the transposition distance. Mathematically, chromosomes are regarded as permutations and changing one genome into another can be seen as a sorting problem. In our study, we introduce an operation of element removal from permutations, which has not been fully explored, but allowed us to find an upper bound for the transposition distance. We also suggest new ways of making use of element removal and the analysis of permutation subsequences. In the hope of obtaining new knowledge about the problem of transposition distance, we considered the variation of the problem where we allow prefix transpositions only. Zanoni Dias developed a polynomial algorithm that changes any permutation into its reverse using f3n/41 steps, but without a proof of its correctness. We have modified this algorithm, keeping the number of steps, and presented a complete proof of the correction of the modified algorithm. Still about the prefix transposition distance, we have analyzed those permutations whose distance equals the breakpoint lower bound. Such permutations are easily sorted by prefix transpositions in polynomial time, since they have a unique and well-defined optimum sorting. Finally, we concluded that the permutations that are easily sorted in the prefix transposition problem are also easily sorted in the transposition problem, which proves that the variation of the problem helps the study of the original problem (AU)