Alignment scores

Finally, as with most pairwise alignment scores (Arratia and Waterman, 1985), the profile-to-sequence match scores need to be normalized as a function of the sequence and the profile s effective lengths. It was noted empirically that the raw scores of profile optimal matches against negative control sequences varied approximately as the logarithm of the sequence length times the profile s information content. The latter is calculated as the mutual information,... 

In the detection of repeats using SMART an algorithm is used that derives similarity thresholds that are dependent on the number of repeats already found in a protein sequence (Andrade et al., 1999b). These thresholds are based on the assumption that suboptimal local alignment scores of a profile/HMM against a random sequence database are well described by an extreme value distribution (EVD). The result of this protocol is that acceptance thresholds for suboptimal alignments are lowered below the optimal scores of nonhomologous sequences. 

Alignment scores generated from the comparison of a repeat profile with a database of randomized sequences are derived with Searchwise (Birney et al., 1996), which uses a Smith-Waterman comparison (Smith and Waterman, 1981). A number n of score distributions for the 1st (optimal), 2nd (first suboptimal), and up to the wth highest scores of the profile compared with randomized sequences are fitted to n EVDs. Parameters are obtained for each fit that allow the transformation of alignment scores for the top n (sub)optimal alignments into values. Since these E values are dependent on the repeat number, they are sensitive to the number of true-positive repeats in a sequence. 

Figure 2 Overview of alignment scoring system. Sequence alignments are scored by attributing a positive score to each match (+ in the score line) and a negative score to either mismatches (the A—>T transversion) or gaps.

Figure 6.5. Scoring pairwise alignments. Scoring schemes are comprised of a substitution matrix (S) and gap penalty. Here we consider a pairwise comparison of nucleotide sequences, and the matrix S scores +1 for a match and -1 for a mismatch (left). Three alignments of X and Y are shown, and each is scored using both a linear and an affine gap penalty. The score of each residue pair is shown beneath it, and these are summed to produce the alignment score. Note that the affine gap penalty scores neighboring gaps as -3 and -1 the ordering is not determined, but the end result is their sum -4.

Because of the many factors on which BLAST scores and statistics depend, the results of disparate searches may not be directly compared. To standardize across scoring schemes and variable database composition, the formula B = (kx - In K)l (In 2) is used to convert an alignment score x into a bit score B. This conversion effectively removes K and X from subsequent calculations, standardizing all BLAST searches to reference the same EVD. It is the bit score which NCBI-BLAST includes along with the / -value of each reported high-scoring local alignment. We demonstrate in the next section with an example. 

Shuffling. Using the identity-based scoring system (Section 1.2). calculate the alignment score for the alignment of the following two short sequences ... 

Generate a shuffled version of sequence 2 by randomly reordering these 10 amino acids. Align your shuffled sequence with sequence 1 without allowing gaps, and calculate the alignment score between sequence 1 and your shuffled sequence. 

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