A Novel Construction of Genome Space with Biological Geometry

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

For the circular single-strand genomes, the construction of genome space is more complicated because we do not know which point is the start point in this circular DNA sequence. In this case, we treat every point as the start point in this circular sequence of length n, and then we get n linear single-strand genomes. For every linear single-strand genome sequence, we can compute its n-dimensional moment vector. Then, we take average by n for these n n-dimensional moment vectors to get a normalized moment vector (M 1 , M 2 , . . . , M n ). For circular singlestrand genomes, we use the first N components (M 1 , M 2 , . . . , M N ) of this normalized moment vector to represent a genome as a point in an N-dimensional space. Thus, we obtain an N-dimensional genome space as a subspace in R N .