  The underlying structure of the canonical amino acid substitution matrix
(aaSM) is examined by considering stepwise improvements in the differential
recognition of amino acids according to their chemical properties during the
branching history of the two aminoacyl-tRNA synthetase (aaRS) superfamilies.
The evolutionary expansion of the genetic code is described by a simple
parameterization of the aaSM, in which (i) the number of distinguishable amino
acid types, (ii) the matrix dimension, and (iii) the number of parameters, each
increases by one for each bifurcation in an aaRS phylogeny. Parameterized
matrices corresponding to trees in which the size of an amino acid sidechain is
the only discernible property behind its categorization as a substrate,
exclusively for a Class I or II aaRS, provide a significantly better fit to
empirically determined aaSM than trees with random bifurcation patterns. A
second split between polar and nonpolar amino acids in each Class effects a
vastly greater further improvement. The earliest Class-separated epochs in the
phylogenies of the aaRS reflect these enzymes' capability to distinguish tRNAs
through the recognition of acceptor stem identity elements via the minor (Class
I) and major (Class II) helical grooves, which is how the ancient Operational
Code functioned. The advent of tRNA recognition using the anticodon loop
supports the evolution of the optimal map of amino acid chemistry found in the
later Genetic Code, an essentially digital categorization, in which polarity is
the major functional property, compensating for the unrefined, haphazard
differentiation of amino acids achieved by the Operational Code.
