A Novel Construction of Genome Space with Biological Geometry

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

The genomes of lentiviruses are single-stranded linear RNA. RNA has the base uracil (U) rather than thymine (T) that is present in DNA. In fact, these RNA genome sequences downloaded from GenBank have already been transformed into DNA sequences (change U by T). Thus, we treat them as linear DNA sequences. Using the nucleotide vector system shown in Fig. 1 , the sequence graphs of the genomes of the 33 lentiviruses were obtained. Here, we use the first 12 components of the moment vector to characterize these 33 genome graphical curves, and thus we obtained 33 twelve-dimensional vectors. These 33 vectors can be viewed as 33 points in a 12-dimensional genome space. By computing the Euclidean distance between these points, we reconstructed the phylogenetic tree of these primate lentiviruses (Fig. 4) using UPGMA program in the MEGA 4 package. 23 The figure illustrates that both the HIV-1 and HIV-2 lineages fall within that of the SIVs which are isolated from other primates, thus they represent the independent cross-species transmission events. In agreement with In addition, we apply our genome space to another field of virology: the taxonomy of coronavirus. To study the classification and phylogeny of coronaviruses clearly, we apply our genome space to a large set of 30 complete coronavirus genomes from GenBank, including the two newly sequenced human coronaviruses, HCoV-NL63 and HCoV-HKU1, along with four genomes from Flaviviridae and Togaviridae which are not coronaviruses (outgroups). The coronavirus genomes are also single-stranded linear RNA. So, similar to the above lentivirus case, we treat these coronavirus genomes as linear DNA sequences. Their abbreviation, accession number, description, and classification are shown in Table 1 . First, we used our two-dimensional genome space (actually, it is a two-dimensional plane with the first two moments M 1 and M 2 being x-axis and y-axis) to characterize these '34' virus genomes and calculated '34' points in Fig. 5A . Four groups, group 1, group 2, group 3, and outgroups, can be seen in this figure as four distinct clusters. To study the classification for coronavirus clearly, we expanded it and obtained Fig. 5B .