Current algorithms can find optimal alignments of two nucleic acid or protein sequences, often by using dynamic programming. While the choice of algorithm penalty parameters greatly influences the quality of the resulting alignments, this choice has been done in an ad hoc manner. In this work, we present an algorithm to efficiently find the optimal alignments for all choices of the penalty parameters. It is then possible to systematically explore these alignments for those with the most biological or statistical interest. Several examples illustrate the method.

Abstract Sequencing of DNA has precipitated a revolution in biology. Rapid sequencing techniques were introduced a little more than a decade ago, and the rate of sequencing continues to accelerate. As of spring 1991 the international databanks (EMBL, Gen Bank, and DDBJ) contained approximately 50 x 106 base pairs (bp) of DNA sequences with an average sequence length of about 1,000 bp.

The algorithm of Smith & Waterman for identification of maximally similar subsequences is extended to allow identification of all non-intersecting similar subsequences with similarity score at or above some preset level. The resulting alignments are found in order of score, with the highest scoring alignment first. In the case of single gaps or multiple gaps weighted linear with gap length, the algorithm is extremely efficient, taking very little time beyond that of the initial calculation of the matrix. The algorithm is applied to comparisons of tRNA-rRNA sequences from Escherichia coli. A statistical analysis is important for proper evaluation of the results, which differ substantially from the results of an earlier analysis of the same sequences by Bloch and colleagues.

The basic nature of the sequence features that define a promoter sequence for Escherichia coli RNA polymerase have been established by a variety of biochemical and genetic methods. We have developed rigorous analytical methods for finding unknown patterns that occur imperfectly in a set of several sequences, and have used them to examine a set of bacterial promoters. The algorithm easily discovers the “consensus” sequences for the −10 and −35 regions, which are essentially identical to the results of previous analyses, but requires no prior assumptions about the common patterns. By explicitly specifying the nature of the search for consensus sequences, we give a rigorous definition to this concept that should be widely applicable. We also have provided estimates for the statistical significance of common patterns discovered in sets of sequences.