HOMEWORK READING:
Ch.3 (textbook);

Sections 4.1-4.4; (supp. textbook);

pp. 129-135 (supp. textbook);
OR
Eddy, 2004 (Moodle);

Sections 5.1,5.2,5.4 (supp. textbook); [optional, detailed theory]

Fitch, 2000 (Moodle)

Two sequences are HOMOLOGOUS if they share common ancestry, i.e. they are evolved from the same ancestral sequence [More on types of homology later in the course].

For DNA and protein sequences, homology is inferred by showing significant similarity between sequences. Sequence similarity is expressed either as percent of identical matches (sequence identity) or (for protein sequences) as percent of identical matches AND matches of amino acids with similar physicochemical properties (sequence similarity).

Because two sequence of potentially different lengths are involved in the comparison, either average length (L_avg) of two sequences used, or the length of the shorter sequence (L_short) used. That is, sequence similarity

S=N_s/L_avg*100

or

S=N_s(short)/L_short*100

where N_s is number of similar residues and N_s(short) is number of similar residues in the shorter sequence.

Homology is a qualitative statement. As Walter Fitch wrote, "[H]omology, like pregnancy is indivisible. You either are homologous (pregnant) or you are not" (Fitch, Trends in Genetics, 2000, 16: p.228; See Moodle for the article). If quantitative assessment is needed, IDENTITY or SIMILARITY is used (for example, two DNA sequences are 75% identical).

Aligning Two Sequences

RECIPE FOR INFERENCE OF HOMOLOGY BETWEEN TWO SEQUENCES:

Take two sequences
Align them (or parts of them)
Assess similarity between the sequences (by assigning a score)
Decide if the alignment score is significant or if two randomly selected sequences can have the same score
If significant, claim homology

The goal of alignment of two sequences (pairwise alignment) is to find the relative positioning of them that maximizes the number of matching residues (or more precisely, maximizes the alignment score). When sequences are aligned across their whole lengths, the alignment is global. Local alignment refers to alignments of subsequences (i.e. only pieces of sequences are aligned).

During the alignment procedure it is almost always necessary to introduce gaps. Gaps are either insertions or deletions in a sequence. Sometimes they are also called indels. Introduction of gaps is penalized (no widely accepted theory on gap penaties). The idea is to find the least costly solution in terms of mismatches and gaps.

Matches and mismatches in alignments are quantified through scoring matrices, also called Substitution Matrices. For nucleotide sequences, Unitary Matrix (or Identity Matrix) is used: a match scores +1, a mismatch scores 0 (Another scoring scheme that involves considering gaps is +1 for a match, -1 for mismatch and -2 for insertion of a gap). For protein sequences, either matrices taking into account physicochemical properties of amino acids or, more commonly, empirically derived scoring matrices are used. The latter types of matrices are based on substitution frequencies determined in alignments of homologous sequences.

Fig. BLOSUM62 matrix.[Source: Wikipedia]

The numbers in the matrix are log-odds scores (ratios), i.e. logarithm of a ratio of observed frequency of substitution to the substitution frequency expected by chance. More frequently observed amino acid substitutions have positive scores. A score of zero means that this type of substitution is as likely to be by chance alone.

LINKS:

Commonly used types of alignment algorithms:

Visual: Dot Plots
Dynamic Programming (e.g., Needleman-Wunsch and Smith-Waterman algorithms) - slow, but guaranteed to find optimal alignment
Heuristic Search - fast (BLAST)

Dot Plots

Fig. Dot Plot Example. P24014.2: Drosophila melanogaster SLIT protein aligned against itself.
Generated with DotMatcher.

Fig. Domain organization of Drosophila melanogaster SLIT protein.

Fig. Dot Plot Example. P24014.2: Drosophila melanogaster SLIT mRNA aligned against itself.
Generated with DotMatcher.

Variation of Needleman-Wunsch Alignment Algorithm (an example of Dynamic Programming Algorithm)

We are going to align two hypothetical protein sequences "THISLINE" and "ISALIGNED", using BLOSUM62 substitution matrix and a simple gap penalty g(n_gap)=-E*n_gap, where n_gap is the number of gaps. We will try E=-8 and E=-4. [read pp. 129-135 (supp. textbook)]

Fig. 5.8 [Source]. Starting to fill out matrix.

Fig. 5.9 [Source]. Optimal global alignment with E=-8.

Fig. 5.11 [Source]. Optimal global alignment with E=-4.

Usually a more sophisticated gap penalty formula is used, where penalties for initiating (opening) and extending gaps are different: g(n_gap)=-I-E*(n_gap-1).

Statistical Significance of Sequence Alignment

P-values give the probability of finding a match of this quality or better. P values can take values in range of [0,1]. E-value (expectation value) describes how many matches with this alignment score or better are expected to be found in a pool of sequences by chance. For small values, E-value is approximately equal to P-value. Z-scores give the distance between the actual alignment score and the mean of the scores for the randomized sequences expressed as multiples of the standard deviation calculated for the randomized scores. For example: a Z-score of 3 means that the actual alignment score is 3 standard deviations better than the average for the randomized sequences. Z-scores > 3 are usually considered as suggestive of homology.

Given an alignment and its score, how probable is it to find an alignment of this score or better by chance alone? One way to assess is to use algorithm implemented in PRSS (Probability of Random Sequence Shuffles) program, developed by William R. Pearson at the University of Virginia (W.R. Pearson, 1991, Genomics 11:635-650).