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Biology · Glossary

What is Alignment and score?

Definition 5.1 University Biology — Year 3 · Chapter 5 — Bioinformatics and Sequence Analysis

An alignment of two sequences writes them one above the other, with gaps (–) inserted so that the columns pair a residue with a residue or a residue with a gap, and no column pairs two gaps. Its score is the sum over columns of a substitution score s(a,b)s(a,b) for each pair of residues and a gap penalty for each gap: a linear penalty −d-d per gap position, or, more realistically, an affine penalty −d−(k−1)e-d - (k-1)e for a run of kk gaps, with the opening cost dd larger than the extension cost ee, since one insertion of several residues is a single evolutionary event. A global alignment covers both sequences end to end; a local alignment finds the highest-scoring pair of substrings and ignores the rest, which is what one wants when a shared domain sits in two otherwise unrelated proteins.

The Needleman–Wunsch table for GAT against GCAT (match +1, mismatch -1, gap -1). Each cell is the best score for the two prefixes ending there; the red path traced back from the corner is the optimal alignment.
The Needleman–Wunsch table for GAT against GCAT (match +1+1, mismatch −1-1, gap −1-1). Each cell is the best score for the two prefixes ending there; the red path traced back from the corner is the optimal alignment.

Examples

Example 5.3 (A four-by-three table)

Align GAT with GCAT, scoring +1+1 for a match, −1-1 for a mismatch, d=1d = 1. The borders are 0,−1,−2,−3,−40, -1, -2, -3, -4 along the top and 0,−1,−2,−30, -1, -2, -3 down the side. Filling row by row: F(G,G)=1F(\text{G},\text{G}) = 1, F(G,C)=0F(\text{G},\text{C}) = 0, F(G,A)=−1F(\text{G},\text{A}) = -1, F(G,T)=−2F(\text{G},\text{T}) = -2; F(A,G)=0F(\text{A},\text{G}) = 0, F(A,C)=0F(\text{A},\text{C}) = 0, F(A,A)=1F(\text{A},\text{A}) = 1, F(A,T)=0F(\text{A},\text{T}) = 0; F(T,G)=−1F(\text{T},\text{G}) = -1, F(T,C)=−1F(\text{T},\text{C}) = -1, F(T,A)=0F(\text{T},\text{A}) = 0, F(T,T)=2F(\text{T},\text{T}) = 2. The optimum is 22, and tracing back — diagonal from (T,T), diagonal from (A,A), then left from (G,C) to (G,G), then diagonal — gives

G-ATGCAT\begin{array}{c} \texttt{G-AT}\\ \texttt{GCAT} \end{array}

three matches and one gap: 3−1=23 - 1 = 2.

Example 5.10 (Reading an E-value)

A query of 250250 residues against a database of 5×10105\times 10^{10} residues has mn=1.25×1013≈243.5mn = 1.25\times 10^{13} \approx 2^{43.5}. A hit with a bit score of 6060 has E=243.5−60=2−16.5≈10−5E = 2^{43.5 - 60} = 2^{-16.5} \approx 10^{-5}: essentially certainly a homologue. A hit with S′=40S' = 40 has E=23.5≈11E = 2^{3.5} \approx 11: eleven such scores are expected by chance, and the hit means nothing. The same alignment, with the same bit score, searched against a database ten times larger, has an EE ten times larger — significance is a property of the search, not of the pair. The threshold in common use is E<10−3E < 10^{-3} for a confident homologue; E≈0.01E \approx 0.01–11 deserves a second look with a profile method.

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