'Genome order index' should not be used for defining compositional constraints in nucleotide sequences - a case study of the Z-curve

'Genome order index' should not be used for defining compositional constraints in nucleotide sequences - a case study of the Z-curve

Biology Direct, February 2010

20158921

Eran Elhaik, Dan Graur, Krešimir Josić

The Z-curve is a three dimensional representation of DNA sequences proposed over a decade ago and has been extensively applied to sequence segmentation, horizontal gene transfer detection, and sequence analysis. Based on the Z-curve, a "genome order index," was proposed, which is defined as S = a2+ c2+t2+g2, where a, c, t, and g are the nucleotide frequencies of A, C, T, and G, respectively. This index was found to be smaller than 1/3 for almost all tested genomes, which was taken as support for the existence of a constraint on genome composition. A geometric explanation for this constraint has been suggested. Each genome was represented by a point P whose distance from the four faces of a regular tetrahedron was given by the frequencies a, c, t, and g. They claimed that an inscribed sphere of radius r = 1/ square root 3 contains almost all points corresponding to various genomes, implying that S <r2. The distribution of the points P obtained by S was studied using the Z-curve.