Key Formulas & Code Examples
Sequence Identity: Identity (%) = (matches / alignment length) ร 100
Bit Score: S' = (ฮปS โ ln K) / ln 2
E-value: E = K ร m ร n ร eโฮปS
m = query length, n = database length, K and ฮป are parameters
Bit Score: S' = (ฮปS โ ln K) / ln 2
E-value: E = K ร m ร n ร eโฮปS
m = query length, n = database length, K and ฮป are parameters
Hamming Distance: dH = number of mismatched positions in equal-length sequences
GC Content: GC% = (G + C) / (A + T + G + C) ร 100
GC Content: GC% = (G + C) / (A + T + G + C) ร 100
Phred Quality Score: Q = โ10 ร log10(Perror)
Probability of error: P = 10โQ/10
Probability of error: P = 10โQ/10
Needleman-Wunsch Score: F(i,j) = max { F(iโ1,jโ1) + s(xi,yj), F(iโ1,j) โ d, F(i,jโ1) โ d }
s = substitution score, d = gap penalty
s = substitution score, d = gap penalty
Python Example โ Count Nucleotides:
seq = "ATCGATCG"
counts = {base: seq.count(base) for base in "ATCG"}
# Output: {'A': 2, 'T': 2, 'C': 2, 'G': 2}
seq = "ATCGATCG"
counts = {base: seq.count(base) for base in "ATCG"}
# Output: {'A': 2, 'T': 2, 'C': 2, 'G': 2}
Core Concepts
1. Sequence Alignment
Comparing DNA, RNA, or protein sequences to identify regions of similarity. Global alignment (Needleman-Wunsch) aligns entire sequences; local alignment (Smith-Waterman) finds the best matching subsequences.
Comparing DNA, RNA, or protein sequences to identify regions of similarity. Global alignment (Needleman-Wunsch) aligns entire sequences; local alignment (Smith-Waterman) finds the best matching subsequences.
2. BLAST Algorithm
Basic Local Alignment Search Tool โ compares a query sequence against a database. Uses seed words, extension, and statistical evaluation (E-value) to rapidly find significant matches.
Basic Local Alignment Search Tool โ compares a query sequence against a database. Uses seed words, extension, and statistical evaluation (E-value) to rapidly find significant matches.
3. Phylogenetic Trees
Diagrams showing evolutionary relationships among species or genes. Built using distance methods (UPGMA, Neighbor-Joining) or character-based methods (Maximum Parsimony, Maximum Likelihood, Bayesian).
Diagrams showing evolutionary relationships among species or genes. Built using distance methods (UPGMA, Neighbor-Joining) or character-based methods (Maximum Parsimony, Maximum Likelihood, Bayesian).
4. Genome Assembly
Reconstructing complete genomes from short sequencing reads. De Bruijn graph methods (Velvet, SPAdes) break reads into k-mers and reconstruct paths through the graph.
Reconstructing complete genomes from short sequencing reads. De Bruijn graph methods (Velvet, SPAdes) break reads into k-mers and reconstruct paths through the graph.
5. Structural Bioinformatics
Prediction and analysis of 3D protein structures. Homology modeling, ab initio prediction, and molecular dynamics simulations (GROMACS, AMBER) study protein folding and interactions.
Prediction and analysis of 3D protein structures. Homology modeling, ab initio prediction, and molecular dynamics simulations (GROMACS, AMBER) study protein folding and interactions.
Core Definitions
k-mer: A substring of length k. In genome assembly, reads are decomposed into k-mers of length k to build de Bruijn graphs.
Homology: Shared ancestry between sequences or structures. Orthologs: separated by speciation; paralogs: separated by duplication; xenologs: transferred horizontally.
Annotation: The process of identifying gene locations and functions in a genome. Includes structural annotation (finding genes) and functional annotation (assigning biological roles).
Read Depth (Coverage): The average number of times each base in a genome is represented in sequencing reads. 30ร coverage means each base is sequenced 30 times on average.
SNP (Single Nucleotide Polymorphism): A single base pair variation at a specific genome position occurring in >1% of the population. Used in GWAS studies and pharmacogenomics.
Worked Examples
Example 1: BLAST E-value
A BLAST hit with bit score S = 50, ฮป = 0.267, K = 0.041, m = 200, n = 10โท:
E = 0.041 ร 200 ร 10โท ร eโ0.267ร50 โ 0.041 ร 2ร10โน ร eโ13.35 โ ~10โปโด (significant)
A BLAST hit with bit score S = 50, ฮป = 0.267, K = 0.041, m = 200, n = 10โท:
E = 0.041 ร 200 ร 10โท ร eโ0.267ร50 โ 0.041 ร 2ร10โน ร eโ13.35 โ ~10โปโด (significant)
Example 2: GC Content
Sequence: ATGCGCTA (3 G/C out of 8 bases)
GC% = 3/8 ร 100 = 37.5%
High GC content indicates thermostability (three H-bonds in G-C pairs).
Sequence: ATGCGCTA (3 G/C out of 8 bases)
GC% = 3/8 ร 100 = 37.5%
High GC content indicates thermostability (three H-bonds in G-C pairs).
Example 3: Phred Score
If a base has Phred Q = 30: Perror = 10โ30/10 = 10โ3 = 0.001
Accuracy = 99.9%. Q20 = 99% accuracy, Q30 = 99.9% accuracy.
If a base has Phred Q = 30: Perror = 10โ30/10 = 10โ3 = 0.001
Accuracy = 99.9%. Q20 = 99% accuracy, Q30 = 99.9% accuracy.
Practice Problems
Problem 1: Calculate GC content of sequence ATGCGATCGATCG (5 G/C out of 13 bases).
Answer: GC% = 5/13 ร 100 = 38.5%
Answer: GC% = 5/13 ร 100 = 38.5%
Problem 2: What is the Hamming distance between "ATCGAT" and "ATGGCT"?
Answer: Position 3: Cโ G, Position 5: Aโ C. Distance = 2
Answer: Position 3: Cโ G, Position 5: Aโ C. Distance = 2
Problem 3: A BLAST search returns E = 0.001. Is this significant? Explain.
Answer: Yes. E = 0.001 means we expect 0.001 random hits of this quality by chance. Below the standard 0.05 threshold.
Answer: Yes. E = 0.001 means we expect 0.001 random hits of this quality by chance. Below the standard 0.05 threshold.
Problem 4: What is the difference between orthologs and paralogs?
Answer: Orthologs diverged through speciation (same gene in different species). Paralogs diverged through gene duplication (different genes in same genome).
Answer: Orthologs diverged through speciation (same gene in different species). Paralogs diverged through gene duplication (different genes in same genome).
Problem 5: A genome is 3 million bp and sequencing produced 90 million 150 bp reads. What is the coverage?
Answer: Total bases = 90M ร 150 = 13.5 billion. Coverage = 13.5B / 3B = 45ร
Answer: Total bases = 90M ร 150 = 13.5 billion. Coverage = 13.5B / 3B = 45ร