Sequence Logo

The total height of a stack of letters at a position represents the information content (R_sequence) measured in bits. It quantifies the reduction in uncertainty about which nucleotide occupies that position.

• Formula: R_sequence = 2 - (H_position + e_n)
• Maximum: 2 bits for a perfectly conserved position in DNA.
• Minimum: 0 bits for a completely random, unconserved position.
• Interpretation: A taller stack indicates a stronger biological constraint and higher binding specificity.

The height of an individual letter within a stack is directly proportional to its observed frequency at that position, weighted by the total information content.

• Calculation: height = f(b,i) * R_sequence
• Dominant Letters: A single tall letter indicates a highly conserved nucleotide.
• Co-dominant Letters: Two half-height letters (e.g., A and G) indicate a purine preference.
• Visual Weight: The area of each letter is a direct visual proxy for its probability in the binding site model.

The logo provides an immediate visual readout of the consensus sequence, which is the most frequent nucleotide at each position.

• Primary Consensus: Read the tallest letter at each position from left to right.
• Ambiguity Codes: If two letters are nearly equal in height, standard IUPAC ambiguity codes (e.g., R for A/G, Y for C/T) are implied.
• Utility: This string is used for rapid database searching and designing mutagenesis experiments.

For logos built from a limited number of aligned sequences, the raw information content is an overestimate. An approximate correction factor (e_n) is subtracted to account for sampling error.

• Formula: e_n = (s - 1) / (2 * ln(2) * n)
• Variables: 's' is the alphabet size (4 for DNA), 'n' is the number of sequences.
• Effect: This correction prevents low-sample, spurious alignments from appearing as high-information, biologically significant motifs.

A position where the total stack height is effectively zero indicates a gap or insertion hotspot. The model has no nucleotide preference here.

• Biological Meaning: This region is structurally flexible or a linker where the specific base identity is irrelevant to function.
• Logo Representation: These positions are often collapsed or shown as a thin line to emphasize the lack of constraint.
• Contrast: The sharp transition from a tall, conserved stack to a zero-height gap delineates the functional core of a binding domain.

For DNA-binding proteins that bind as homodimers, the sequence logo often exhibits palindromic symmetry. The pattern in the first half is the reverse complement of the second half.

• Visual Check: A logo with a clear center of symmetry strongly suggests a dimeric binding mechanism.
• Information Redundancy: The information content is mirrored, reflecting the physical interaction of two identical protein subunits with inverted DNA half-sites.
• Exception: Asymmetric logos indicate monomeric binding or heterodimeric complexes.

The foundational class of algorithms that assign a relevance score to each input nucleotide for a specific prediction. These scores form the raw data from which sequence logos are generated.

• Post-hoc methods: Explain a trained model without modifying it
• Key approaches: Gradient-based (Integrated Gradients), perturbation-based (ISM), and game-theoretic (SHAP)
• Output: A vector of importance values aligned to the input sequence length

A systematic perturbation technique that computationally mutates every nucleotide in a sequence to quantify its impact on model predictions.

• Saturation mutagenesis: Tests all 3 alternative bases at each position
• Delta score: The difference between reference and alternate allele predictions
• Ground truth alignment: ISM results are often used to validate gradient-based attribution maps before logo generation

A method that clusters high-contribution genomic subsequences identified by attribution maps into recurring, biologically meaningful motif patterns.

• Input: Per-nucleotide importance scores from any attribution method
• Output: Consolidated motifs that can be rendered as sequence logos
• Significance: Bridges raw attribution scores and human-interpretable motifs by grouping similar patterns across thousands of sequences

The mathematical foundation of sequence logo letter heights, measured in bits. It quantifies the reduction in uncertainty at each position relative to a background nucleotide distribution.

• Formula: IC = log₂(4) - H(position), where H is Shannon entropy
• High IC (>1 bit): Strongly conserved position, tall letters
• Low IC (~0 bits): Random or degenerate position, short or flat letters
• Derivation: Can be computed from alignment frequencies or from averaged attribution scores

Quantitative measures that evaluate how accurately an attribution map reflects the true decision-making logic of a genomic model before it is visualized as a logo.

• Perturbation tests: Remove high-attribution nucleotides and measure prediction drop
• ROAR: Iteratively retrain after removing top features to test fidelity
• AOPC: Area Over the Perturbation Curve — measures prediction decay as salient bases are sequentially masked
• Purpose: Ensures the logo represents real model logic, not artifacts

The quantitative difference in a model's prediction score between a reference and an alternate allele, used to assess the functional impact of genomic variants.

• Calculation: ΔScore = Prediction(Alt) - Prediction(Ref)
• Visualization: Often displayed alongside sequence logos to highlight variant effects
• Clinical relevance: High absolute delta scores indicate potentially pathogenic variants
• Integration: Delta scores validate that logo-highlighted positions are functionally consequential