Variables

Our multivariate data come from alignment reports generated by biological sequence similarity algorithms. Each report consists of an input sequence and many alignments. Each alignment is a match between a subsequence of the input sequence and a subsequence of a sequence from the database. Thus, an alignment indicates a region of similarity between two sequences. Such alignments are the basic elements in our visualization system. Associated with each alignment is the following information:

• Position. The position in the input sequence where the alignment starts.
• Frame, or frame number. The frame number defines how the DNA sequence is translated into a protein sequence. DNA sequences are composed of a four letter alphabet, which are used to encode the sequence of nucleotides (also called a base). Three DNA bases encode one protein residue (also called an amino acid). A DNA sequence can encode a protein sequence starting from the first, second, or third position. The starting point determines how bases are grouped into residues. When comparing a DNA sequence to a protein sequence, each encoding is tried separately.
• Length. The length of the alignment measured in residues.
• Entry Date. The submission date of the database sequence for the alignment into the database.
• Similarity Scores and Residue Pair Scores. Similarity algorithms such as BLAST compute the similarity score of each alignment [2]. For each pair of residues in an alignment, BLAST looks up the entry in a substitution matrix and gets the residue pair score, a measure of the match strength. A positive entry corresponds to a good match, and a negative entry corresponds to a bad match [8]. BLAST then sums all residue pair scores in the alignment to obtain the similarity score.
• P-value. The Poisson P-value for an alignment measures the statistical probability that an alignment could have occurred by chance. Because of its large range, P-value is commonly represented by the negative logarithm. Thus, an alignment with P-value of 10^-45 is represented by 45.
• Percent Identities. The percentage of exact matches to the total alignment length.
• Percent Positives. The percentage of positive matches to the total alignment length.
• Bits. The amount of information in the alignment measured in ``bits'' using information theory [17].
• PAM Evolutionary Distance. Different substitution matrices allow different degrees of mismatches and mutations. These matrices are either experimentally or theoretically derived. The PAM (Point Accepted Mutations) matrices use a rough measure of how many generations of evolution it would take to mutate one sequence into another [8]. For example, the PAM120 matrix allows fewer mutations than PAM250. We can obtain a rough estimate of the evolutionary distance of the alignments by statistically recomputing and normalizing the similarity scores obtained by using different PAM matrices [17].
• BLOSUM Evolutionary Distance. The evolutionary distance measured using the BLOSUM matrices, which are experimentally derived from sequence data. In contrast to the PAM matrices, a low number signifies a large evolutionary distance [13].
• Matrix Used. The number designating the substitution matrix used for the alignment report. For a single input sequence, AV has the ability to read in multiple alignment reports that were computed using different substitution matrices.

The PAM and BLOSUM Evolutionary Distances are not given by the alignment report, rather AV computes these as needed. The entry date is also not given in the report, but is retrieved from a separate database as the report is read into the system.

For an alignment, in addition to the above variables, there is the matching vector itself. This vector, represented by an array of integers, contains the residue pair scores of the matches starting from the first matching position. Therefore, an alignment can be viewed as a twelve dimensional point (for the above twelve variables), plus a matching vector.