Summary of Bioinformatics: Sequence Analysis and Prediction
Bioinformatics: Sequence Analysis and Prediction Guide for Students
Introduction
Protein sequence scoring matrices quantify how likely one amino acid is substituted by another during evolution. They are essential for interpreting sequence similarity, guiding database searches, and scoring local or global alignments. This material explains the principles behind log-odds scores, PAM and BLOSUM matrices, how to read matrix values, and practical considerations for choosing matrices.
Definition: A log-odds score compares the observed frequency of a substitution to the frequency expected by chance.
1. Foundations: log-odds scores
What is a log-odds score?
A log-odds score $S_{i,j}$ for residues $i$ and $j$ is defined as:
$$S_{i,j} = \log\frac{q_{i,j}}{p_i p_j}$$
where $p_i$ and $p_j$ are the background probabilities of residues $i$ and $j$, and $q_{i,j}$ is the empirical frequency with which $i$ aligns with $j$.
Definition: The background probability $p_i$ is the frequency of residue $i$ among proteins; $q_{i,j}$ is the observed alignment frequency of $i$ with $j$ in a dataset.
Key points about log-odds:
- If $S_{i,j} > 0$, the substitution occurs more often than expected by chance.
- If $S_{i,j} < 0$, the substitution occurs less often than expected by chance.
- Diagonal entries $S_{i,i}$ are usually positive and larger for rare residues (e.g., Trp).
Example interpretation
- Trp vs Trp might have $S_{W,W}=11$ (strongly favored because Trp is rare and conserved).
- Tyr replacing Trp might have $S_{W,Y}=2$ (a conservative substitution observed more than by chance).
- Val replacing Trp might have $S_{W,V}=-3$ (observed less often than by chance).
2. Two major families of scoring matrices
We compare PAM and BLOSUM matrices to understand how they are built and when to use them.
| Feature | PAM matrices | BLOSUM matrices |
|---|---|---|
| Origin data | Closely related proteins (global alignments) | Conserved ungapped blocks (local alignments) |
| Year | 1978 | 1992 |
| Typical use | Modeling evolutionary divergence via extrapolation | Direct empirical matrices for different identity thresholds |
| Construction | Start from PAM1 (1% change) and extrapolate | Derived directly for different sequence identity cutoffs (e.g., BLOSUM62) |
| Assumptions | Substitutions independent of past changes; all sites equally mutable | Uses observed substitutions in conserved blocks; clusters similar sequences to adjust contributions |
Definition: PAM stands for point accepted mutation; 1 PAM ≈ 1% change (one substitution per 100 residues). BLOSUM62 is derived from blocks clustered at 62% identity.
PAM: details
- Dayhoff et al. analyzed closely related proteins (>85% identity) and compiled observed substitutions.
- PAM1 tabulates substitution probabilities corresponding to roughly 1% divergence.
- Higher PAM matrices (PAM250, etc.) are extrapolated by matrix exponentiation assuming constant substitution processes.
- Limitations: extrapolations assume the same evolutionary forces across long times and equal site mutability; the original dataset was small and biased.
BLOSUM: details
- Henikoff & Henikoff examined conserved blocks from the BLOCKS database and computed substitution frequencies directly for different sequence identity thresholds.
- BLOSUM62 clusters sequences with >62% identity so that no more than 62% identical sequences overly bias counts; it is widely used for general protein comparisons.
- Strengths: empirical across varied distances, built from local conserved regions, and not extrapolated.
3. Reading and using a scoring matrix (BLOSUM62 example)
- Each cell gives the log-odds score for substituting the row residue with the column residue.
- Positive scores: substitutions more frequent than random; negative scores: less frequent.
- Diagonal cells (m
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Protein Scoring Matrices
Klíčové pojmy: Log-odds score: $S_{i,j}=\log\frac{q_{i,j}}{p_i p_j}$, Positive score means substitution occurs more often than by chance, Diagonal entries are usually positive and larger for rare conserved residues, PAM derived from global alignments of closely related proteins; PAM1 ≈ 1% change, PAM matrices for large distances are extrapolated from PAM1, BLOSUM derived from conserved ungapped blocks; BLOSUM62 clusters at 62% identity, Choose lower BLOSUM number or higher PAM for distant homolog detection, Matrix choice must be paired with appropriate gap penalties, Physico-chemical similarity often yields positive substitution scores, Matrices assume site independence and average over positions, so contextual data needed, Use BLOSUM62 for general-purpose searches; switch matrices for specific divergence levels