A Novel Construction of Genome Space with Biological Geometry

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

We introduce graphical representation of DNA sequence to construct the genome space. The graphical representation of DNA sequence provides a simple way of viewing, sorting, and comparing various gene structures. Thus, it is an attractive and promising research direction. The first important method in this direction is due to Hamori. 7 He used a three-dimensional curve to represent a DNA sequence. Gates 8 later constructed a two-dimensional graphical representation that is simpler than the Hamori curve. However, Gates' graphical representation has high degeneracy. Recently, we reported a new two-dimensional graphical representation of gene sequences 9 which has no circuit or degeneracy, so that the correspondence between gene sequences and gene graphs is one-to-one. In this way, the original DNA sequence can be recovered from its graph mathematically without loss of biological information. In this paper, we make a minor modification of our previous method and obtain a new graphical representation approach for DNA sequences. The breakthrough of the subject is that we can construct the moment vectors from DNA sequences using this new graphical method, and we can prove that the correspondence between moment vectors and DNA sequences is one-to-one. The novelty and uniqueness of our approach is that by using these moment vectors of DNA sequences, we have constructed a genome space as a subspace in Euclidean space. Each genome sequence can be represented as a point in this space. Therefore, this genome space can be used to make comparative analysis to study the clustering and phylogenetic relationship among genomes. The biological (evolutionary) distance between two genomes can be obtained through the Euclidean distance among the corresponding points in the genome space.