A Novel Construction of Genome Space with Biological Geometry

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

For the double-stranded genomes, we need to point out that the moment vector of reverse complementary sequence is not the same as the original sequence. Generally, when meeting the double-stranded genomes, we treat them as two single-stranded genomes. We use the above method (linear or circular) to get two n-dimensional moment vectors for these two single-stranded sequences, and then take average to get a general moment vector (M 1 , M 2 , . . . , M n ). By using the first N components (M 1 , M 2 , . . . , M N ) of this general moment vector to represent a genome as a point in N-dimensional space. Thus, we obtain an N-dimensional genome space as a subspace in R N . Here, we need to point out that the two strands of some genomes (e.g. mitochondrial genomes, some bacterial genomes) are differentiated by their nucleotide content, which are called the heavy strand and the light strand, respectively. The two strands have different masses because one has a higher proportion of heavier nucleic acids and its complement a lower proportion. In this case, we just treat them as the single-stranded (by using the heavy strand) genomes to make the genome space.