Saul B. Needleman coauthored the 1970 matrix-based approach to comparing complete protein sequences, associated with the Needleman-Wunsch algorithm. The approach replaces an exhaustive comparison of all possible arrangements by a structured accumulation of similarity scores.[ref]
A general method applicable to the search for similarities in the amino acid sequence of two proteins by Saul B. Needleman and Christian D. Wunsch. 1970, pp. 443–453: iterative matrix approach to sequence similarity
A modern global-alignment formulation optimizes scores over pairs of prefixes, considering a paired residue or a gap as the final column. The boundary conditions penalize unmatched prefixes, unlike local alignment's option to restart freely. This distinction makes the scientific question explicit: comparing entire sequences is different from searching for one shared internal region. The choice of substitution scores and gap costs remains part of the biological model.
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