Exceptional symmetry by genomic word: a statistical analysis

Single-strand DNA symmetry is pointed as a universal law observed in the genomes from all living organisms. It is a somewhat broadly defined concept, which has been refined into some more specific measurable effects. Here we discuss the exceptional symmetry effect. Exceptional symmetry is the symmetry effect beyond that expected in independence contexts, and it can be measured for each word, for each equivalent composition group, or globally, combining the effects of all possible words of a given length. Global exceptional symmetry was found in several species, but there are genomic words with no exceptional symmetry effect, whereas others show a very high exceptional symmetry effect. In this work, we discuss a measure to evaluate the exceptional symmetry effect by symmetric word pair, and compare it with others. We present a detailed study of the exceptional symmetry by symmetric pairs and take the CG content into account. We also introduce and discuss the exceptional symmetry profile for the DNA of each organism, and we perform a multiple comparison for 31 genomes: 7 viruses; 5 archaea; 5 bacteria; 14 eukaryotes.