Comprehensive Bioinformatics and Functional Genomics Notes: Combined 2021-2025 Exam Guides

Sequencing Technologies: Advantages and Disadvantages

• Illumina   - Advantages: Generates huge amounts of data, is currently the cheapest method, has a low sequence error rate, and features very few indels (insertions/deletions). It has established wet-lab and dry-lab (bioinformatics) protocols.   - Disadvantages: Produces short reads. Requires large, expensive machines.

• Pacific Biosciences (PacBio)   - Advantages: Produces long reads and has a low sequence error rate compared to some other long-read tech.   - Disadvantages: High cost. Requires large amounts of DNA. Wet-lab and dry-lab pipelines are less established than Illumina.

• Nanopore (Oxford Nanopore Technologies)   - Advantages: Produces long reads and is highly portable (small devices). The technology is rapidly improving.   - Disadvantages: Traditionally high error rates, specifically a high incidence of indel errors. Less established wet/dry lab protocols.

Sequencing Depth and Genome Assembly

• Sequencing Depth (D) Calculation   - The formula for sequencing depth is: $D = \frac{N \times L}{G}$     - $N$ = number of reads     - $L$ = length of reads     - $G$ = genome size (base pairs)   - Example 1: For a genome of $5 \times 10^6$ base pairs, reads of length $125$, and a target depth of $50$, the number of reads needed is: $N = \frac{50 \times 5,000,000}{125} = 2,000,000$.   - Example 2: For a genome of $3 \times 10^6$ bp, $1,000,000$ read pairs (meaning $2,000,000$ total reads), and length $150$, the depth is: $D = \frac{1,000,000 \times 2 \times 150}{3,000,000} = 100$.

• Probability of Coverage   - The probability that a random read covers a specific position in a circular genome of length $G$ is: $P = \frac{L}{G}$.

• Genome Assembly Concepts   - Contigs: Pieces of the genome assembled from overlapping reads.   - N50 Value: A metric for assembly quality. Given a set of contigs (lengths: $100, 200, 300, 400, 500, 600, 700$), the total length is $2800$. The N50 is the length of the smallest contig such that the sum of it and all larger contigs is at least $50\%$ of the total ($1400$. Here: $700 + 600 + 500 = 1800$, so N50 is $500$.   - De Bruijn Graphs (DBG): A method for genome assembly that avoids comparing all reads directly (faster than OLC for many reads). Reads are cut into shorter sequences of length $K$ ($k-mers$). Each unique $k-mer$ is a node; edges are created for overlaps of length $K-1$.

• Sequencing Strategies   - Amplicon sequencing: Sequences a specific marker or region (e.g., 16S rRNA).   - Shotgun sequencing: Sequences all DNA fragments in a sample.   - Metabarcoding: Mapping biological composition from environment-specific marker sequences.

Pairwise Sequence Alignment and Scoring

• Dynamic Programming Algorithms   - Global Alignment (Needleman-Wunsch): Finds the best alignment over the whole length. Starts filling a matrix from the top-left (score 0, then accumulated gap penalties). The final score is in the bottom-right cell.   - Local Alignment (Smith-Waterman): Finds the best matching sub-segments. Matrix initialization and the recursion rule allow cells to reset to $0$ (no negative values). The optimal score is the highest value anywhere in the matrix.

• Scoring Logic   - Log-Likelihood Ratio Score: $S(a,b) = \log_{10} \left( \frac{Pr(a,b|related)}{Pr(a,b|unrelated)} \right)$.     - Positive score: Pair occurs more often in related sequences than by chance.     - Negative score: Pair occurs less often in related sequences than by chance.   - Example Calculation: If $Pr(A,B) = 0.1$, $Pr(A) = 0.01$, and $Pr(B) = 0.1$, then the score is $\log_{10} \left( \frac{0.1}{0.01 \times 0.1} \right) = \log_{10}(100) = 2$.

• Gap Penalties   - Linear Gap Penalty: Fixed penalty per gap position.   - Affine Gap Penalty: Distinguishes between starting a gap (Gap-open, high cost) and extending a gap (Gap-extension, lower cost). $Score_{gap} = Open + (Length - 1) \times Extension$.

Sequence Databases and BLAST Statistics

• Data Formats   - FASTA: Header starts with >. Sequence follows. To count sequences, count lines starting with >.   - Accession Number: A unique address/identifier for an object (e.g., a sequence) in a database.   - Newick: A format describing tree topology and branch lengths.

• BLAST Metrics   - E-value: The expected number of hits with a score at least as high as the observed score that would be found by chance in a database of a certain size. Smaller E-values indicate higher significance.   - Bit-score: A normalized version of the raw score that is independent of the scoring matrix scaling. E-value can be calculated from bit-score if search sequence length and database size are known.   - Null Distribution: The distribution of scores expected from aligning unrelated/independent sequences.

• Search Performance   - Sensitivity (Recall): The proportion of actual homologs in the database that appear on the hit list: $TP / (TP + FN)$.   - Precision: The proportion of hits on the list that are actually homologs: $TP / (TP + FP)$.   - Specificity: The proportion of non-homologs correctly excluded: $TN / (TN + FP)$.

Multiple Sequence Alignment (MSA)

• Algorithms   - Progressive Alignment: Greedy algorithm that builds the MSA based on a guide tree (made via UPGMA or NJ). Once a gap is placed, it is rarely changed (“Once a gap, always a gap”).   - Iterative Methods: Repeatedly realigns groups of sequences in the MSA to improve the total score.

• Guide Trees (UPGMA)   - UPGMA (Unweighted Pair-Group Method with Arithmetic mean): A hierarchical clustering method using Average Linkage, where the distance between two groups is the average of distances between all pairs of members across groups.   - Guide Tree Parsing: In a Newick string like ((A,(B,C)),E), the bracketed pairs closest to the center (inner brackets) are aligned first (e.g., B and C first, then A to the BC profile).

• Scoring   - Sum-of-Pairs (SP) Score: The sum of scores for all possible pairwise combinations of sequences at each position in the MSA.

Sequence Models: PSSM and pHMM

• Position Specific Scoring Matrix (PSSM)   - A table with a row for each symbol (e.g., A, C, G, T) and a column for each sequence position. Values represent the log-ratio of the probability of the symbol at that position vs. background frequency.   - Example: For 20 amino acids over 8 positions, a PSSM requires $20 \times 8 = 160$ probability values.

• Profile Hidden Markov Models (pHMM)   - Describes motifs that can vary in length (including gaps). Includes "Match" states (observing symbols), "Insertion" states, and "Deletion" states (skipping symbols).

• PROSITE Patterns   - Syntax to represent motifs. Example: A-[LK]-[IW]-X-L(3)-S means A followed by L or K, then I or W, then any symbol (X), then L three times, then S.

Molecular Phylogeny

• Homology Concepts   - Orthologs: Genes originated via speciation. Used to describe species evolution.   - Paralogs: Genes originated via gene duplication. Used to describe gene family evolution.   - Note: All orthologs and paralogs are homologs, but not all homologs are orthologs.

• Phylogenetic Trees   - Cladogram: Shows topology (branching order) only; branch lengths have no meaning.   - Phylogram: Branch lengths are proportional to evolutionary distance.   - Additive tree: Sum of branch lengths between nodes equals the distance in the distance matrix.   - Ultrametric tree: All leaves are equidistant from the root (assumes a constant molecular clock).

• Reconstruction Methods   - Distance-based (NJ, UPGMA): Transform sequence data into a distance matrix. Neighbor-Joining (NJ) is a greedy method that seeks the tree with the smallest total length.   - Discrete methods:     - Maximum Parsimony (PM): Finds the tree requiring the fewest total mutations (uses informative positions where at least 2 symbols occur at least 2 times).     - Maximum Likelihood (LM): Finds the tree/model that maximizes the probability of the observed data.     - Bayesian (BM): Finds trees with the highest posterior probability.

• Distance Models   - P-distance: The observed proportion of mismatches: $Mismatches / (Matches + Mismatches)$. Gaps are often excluded.   - Evolutionary Distance: The estimated actual number of substitutions. As p-distance increases, the gap between p-distance and evolutionary distance grows because of multiple substitutions at the same site. Jukes-Cantor model corrects for this; maximum p-distance is $0.75$ (for nucleotides).

• Bootstrapping   - A statistical technique to assess clade stability. Resamples the MSA with replacement to generate many new alignments. The bootstrap value is the frequency with which a specific clade appears in the resulting trees.

Functional Genomics: Transcriptomics and Statistical Analysis

• RNA-Seq Applications   - Quantification of gene expression (coding and non-coding).   - Discovery of novel (unannotated) genes.   - Detection of splice variants.   - Mapping mutations (SNPs) within transcripts.

• Differential Expression Genes (DEGs)   - Multiple Testing Correction: When testing 20,000 genes with a p-value of $0.05$, we expect $1,000$ false positives by chance even if no genes are differentially expressed.     - Bonferroni: Controls the family-wise error rate ($E = p \times N$). Very strict.     - False Discovery Rate (FDR/q-values): Controls the proportion of false positives among the "significant" results. An FDR of $0.05$ for $100$ selected genes means expecting $5$ false positives.   - Volcano Plot: Plots the significance ($-\log_{10}(p)$) vs. effect size ($\log_{2}(Fold Change)$). Genes in the top corners are significant DEGs.

• Enrichment Analysis (Fisher's Exact Test)   - Tests if a specific functional group of genes (e.g., cold stress genes) appears in a set of DEGs or clusters more often than expected by chance.

• Dimensionality Reduction and Exploration   - PCA (Principal Component Analysis): Used on data tables (like RPKM/TPM) to visualize gradients, groups, or outliers.   - PCoA (Principal Coordinate Analysis): Used on distance/dissimilarity tables.   - Clustering: K-means (requires choosing $k$ clusters, randomized) vs. Hierarchical (produces a tree, deterministic).   - Diversity:     - Alpha-diversity: Diversity within a single sample.     - Beta-diversity: Diversity between samples.

• Programming in R   - Vectors vs. Lists: Vectors store elements of the same type; lists can store different types.   - String Manipulation: str_detect() (logical), str_locate() (integer matrix of positions), str_extract() (text).   - Tidyverse: mutate() adds columns, filter() keeps rows based on conditions, select() keeps/excludes columns.