Approximate Statistics of Gapped Alignments

A heuristic approximation to the score distribution of gapped alignments in the logarithmic domain is presented. The method applies to comparisons between random, unrelated protein sequences, using standard score matrices and arbitrary gap penalties. It is shown that gapped alignment behavior is essentially governed by a single parameter, alpha, depending on the penalty scheme and sequence composition. This treatment also predicts the position of the transition point between logarithmic and linear behavior. The approximation is tested by simulation and shown to be accurate over a range of commonly used substitution matrices and gap-penalties.