Coronavirus phylogeny based on a geometric approach

Abstract

A novel coronavirus has been identified as the cause of the outbreak of severe acute respiratory syndrome (SARS). Previous phylogenetic analyses based on sequence alignments show that SARS-CoVs form a new group distantly related to the other three groups of previously characterized coronaviruses. In this paper, a geometric approach based on the Z-curve representation of the whole genome sequence is proposed to analyze the phylogenetic relationships of coronaviruses. The evolutionary distances are obtained through measuring the differences among the three-dimensional Z-curves. The Z-curve is approximately described by its geometric center and the associated three eigenvectors, which indicate the center position and the trend of the Z-curve, respectively. Although some information is lost due to the approximate description of the Z-curve, the phylogenetic tree constructed based on these parameters is consistent with those of previous analyses. The present method has the merits of simplicity and intuitiveness, but it is still in its premature stage. Because the phylogenetic relationships are inferred from the whole genome, instead of some individual genes, the present method represents a new direction of phylogeny study in the post-genome era.

Fig. 1

The three-dimensional Z-curves (x, y, z′) for three complete coronavirus genomes. (A–C) The Z-curves of BJ01, TOR2, and BCoV, respectively. It can be clearly seen that the Z-curves of BJ01 and TOR2 are very similar, while the Z-curve of BCoV is significantly different from the former two. This forms the basis of the present method. (D) A sketch of the three eigenvectors for a certain genome (TOR2), which illustrates the relationship between the three eigenvectors and the Z-curve.

Fig. 2

The three groups of eigenvectors (denoted with different arrows). The vectors in the X, Y, and Z′ groups are denoted by dark, dot, and grey arrows, respectively. (A and B) The eigenvectors of the 24 genomes observed from different directions. It can be seen from (A) that the three groups can be separated according to their three-dimensional space distribution. (B) The vectors in Y group of the 24 genomes are coplanar and they are almost in the x–y plane.

Fig. 3

The phylogenetic tree constructed with the current method. The result shows that four groups exist in the genus Coronavirus. Note that group I (HCoV-229E, TGEV, and PEDV) and group II (BCoVM, BCoVL, BCoVQ, BCoV, MHVM, MHV2, MHVP, and MHV) cluster together forming a bigger group firstly. Second, this group joins group III (IBV) to form a much bigger group. Finally, SARS-CoVs join them and result in the phylogenetic tree shown here. Also note that the resulting monophyletic clusters agree perfectly with the established taxonomic groups.