This equation constitutes the model of peptide similarity used throughout subsequent analysis. S(x,y) measures how much peptide y resembles x in terms of the number and magnitude of conservative substitutions. A x max is the auto-peptide-similarity score of x. Thus, A x max = A(x,x). If peptide y is a mimic of x then S(x,y) should be close to 1. The other extreme value (A x min ) is found by comparing x with a peptide x, where on each position the amino acid in x corresponds to the substitution in x with the smallest value i.e. the least likely substitution. In this way 0#S(x,y)#1 for all peptides y. The peptide-similarity score is asymmetric i.e. S(a,b)?S(b,a) despite W being symmetric. The reason is that the extreme values (A min ,A max ) cannot be guarantied to be identical for any pair of peptides (a,b). Reference peptides x which are dominated by amino acids like tryptophan that hardly ever substitute, will have few highly similar peptides (y) which satisfy the condition: S(x,y) < 1. In contrast, reference peptides which are enriched in amino acids that are more likely to substitute (given the matrix W) have a greater number of highly similar peptides. This property is captured by the asymmetry of S.