Now that we have a scoring scheme, we can apply it to finding optimal alignments - we seek the alignment that maximizes the score. A famous algorithm to determine the global optimal alignments of two sequences is based on a mathematical technique called dynamic programming. (Details are described at the end of this section.) This algorithm has been extremely important in molecular biology. Two of several noteworthy features are

• The good news is that the method is guaranteed to give a global optimum. It will find the best alignment score, given the choice of parameters - substitution matrix and gap penalty - with no approximation.

  Substitution matrices used for scoring amino acid sequence similarity. The entries are in alphabetical order of the THREE-letter amino acid names. Only the lower triangles of the matrices are shown, as the substitution probabilities are taken as symmetric. (This is not because we are sure that the rate of any substitution is the same as the rate of its reverse, but because we cannot determine the differences between the two rates.)

  The Dayhoff PAM250 matrix

  Ala (A)	2
  Arg (R)	-2	6
  Asn (N)	0	0	2