In Chapter 3 we considered the problem of aligning DNA sequences that had been read from the same source but with errors introduced by laboratory procedures. Rather arbitrarily, we assigned a reward of +1 for a match and penalties of -1 and -2 for mismatches and gaps. In this chapter, we will examine how to align protein sequences that differ as a result of evolution itself rather than owing to experimental error. The outcome will be a method for constructing substitution matrices for scoring alignments. Potentially, these matrices can assign a different reward or penalty for each of the 210 possible unordered pairs of amino acids that may appear in a column of an alignment.

The function of a protein is determined by its shape and charge distribution, not by the exact sequence of amino acids. During DNA replication, various mutations can alter the protein produced by a gene. Some types of mutations are:

• point mutations, in which the machinery of replication randomly substitutes an incorrect nucleotide for the correct one;

• indels, or insertions and deletions, in which extra bases are randomly inserted or bases are omitted;

• translocations, in which longer pieces of DNA – possibly including one or more entire genes – are moved from one part of the chromosome to another part, or to another chromosome; and

• duplications, in which long pieces of DNA are copied and integrated into a chromosome.