Models of Genome Evolution

Abstract

The evolutionary theory, ``evolution by duplication{''}, originallyproposed by Susumu Ohno in 1970, can now be verified with the availablegenome sequences. Recently, several mathematical models have beenproposed to explain the topology of protein interaction networks thathave also implemented the idea of ``evolution by duplication{''}. Thepower law distribution with its ``hubby{''} topology (e.g., P53 wasshown to interact with an unusually large number of other proteins) canbe explained if one makes the following assumption: new proteins, whichare duplicates of older proteins, have a propensity to interact onlywith the same proteins as their evolutionary predecessors. Since proteininteraction networks, as well as other higher-level cellular processes,are encoded in genomic sequences, the evolutionary structure, topology,and statistics of many biological objects (pathways, phylogeny,symbiotic relations, etc.) are rooted in the evolution dynamics of thegenome sequences. Susumu Ohno's hypothesis can be tested ``in silico{''}using Polya's urn model. In our model, each basic DNA sequence change ismodelled using several probability distribution functions. The functionscan decide the insert ion/deletion positions of the DNA fragments, thecopy numbers of the inserted fragments, and the sequences of theinserted /deleted pieces. Moreover, those functions can beinterdependent. A mathematically tractable model can be created with adirected graph representation. Such graphs are Eulerian and eachpossible Eulerian path encodes a genome. Every ``genome duplication{''}event evolves these Eulerian graphs, and the probability distributionsand their dynamics themselves give rise to many intriguing and elegantmathematical problems. In this chapter, we explore and survey theseconnections between biology, mathematics and computer science in orderto reveal simple, and yet deep, models of life itself.