Variability analysis of HIV-1 gp120 V3 region: I. Point estimators for the amino acid distribution characteristics

Enumerating procedure for symbol sequences is proposed. Relationship between Hamming distance for symbol sequences and Euclidean distance for corresponding enumerations is established, and more universal Hamming-transformed Euclidean measure is constructed. A distribution function of amino acid substitutions and some of its point estimators (consensus, subconsensus, sample mean, sample central moments and asymmetry coefficient) are introduced. Hamming-transformed Euclidean measures between consensus, subconsensus and sample means for ten HIV-1 taxons of gp120 V3 regions are calculated. It is demonstrated that these taxons have a complicated pattern which is significant for their classification.