Deriving an Amino Acid Distance Matrix

Various methods were investigated to convert an amino acid similarity matrix into a low-dimensional, metric distance matrix. Using projection techniques, no unique transformation was found and of the many inversion forms investigated, simple negation normalized by the diagonal elements produced a good fit to the original data. An inter-row distance also gave a comparable fit and when evaluated by weighted least-squares minimization was found to be preferable. A rank-ordered form of the matrices was also derived by constraining neighbours to be equidistant in 3D-space. This produced a network configuration not unlike that produced in a previous analysis of amino acid physicochemical properties. The derived forms might find applications in sequence alignment, including pattern-matching algorithms, and the construction of phylogenetic trees.