A Novel Construction of Genome Space with Biological Geometry

Yu, Chenglong; Liang, Qian; Yin, Changchuan; He, Rong L.; Yau, Stephen S.-T.

In this paper, we report a two-dimensional graphical representation for DNA sequences. A moment vector system to represent a DNA sequence is introduced, and the correspondence between a DNA sequence and its moment vector is mathematically proven to be one-to-one. With this moment vector system, each genome sequence can be represented as a point in a Euclidean space, and the genome space is constructed as a subspace of this Euclidean space. Genomes with close evolutionary relationship and similar properties plot close together in this genome space. Thus, it will provide a new powerful tool for analyzing the classification of genomes and their phylogenetic relationships. Our method is easier and quicker in handling whole or partial genomes than multiple alignment methods. There are two major advantages to our method. (i) Once a genome space has been constructed, it can be stored in a database. There is no need to reconstruct the genome space for any subsequent application, whereas in multiple alignment methods, realignment is needed for add-on new sequences. (ii) One can have global comparison of all genomes simultaneously, which no other existing method can achieve. Furthermore, in our method, the results in twodimensional genome space can be displayed and viewed graphically; this is user-friendly and allows even non-expert to understand the relationship among different genomes via viewing the graph of genome space.