3.5 Scoring matrices
8 min read•august 21, 2024
Scoring matrices are essential tools in bioinformatics for quantifying sequence similarities. They assign values to matches, mismatches, and gaps, enabling accurate alignments and homology detection. Different types of matrices, like and , cater to various evolutionary distances and sequence relationships.
These matrices form the backbone of sequence analysis algorithms. By incorporating evolutionary and biochemical principles, they help distinguish meaningful biological similarities from random matches. Understanding scoring matrices is crucial for optimizing alignments, detecting remote homologs, and interpreting sequence comparison results in various bioinformatics applications.
Types of scoring matrices
- Scoring matrices play a crucial role in bioinformatics by quantifying the similarity between biological sequences
- These matrices form the foundation for various sequence analysis tasks, including alignment, homology detection, and evolutionary studies
PAM vs BLOSUM matrices
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- PAM (Point Accepted Mutation) matrices model evolutionary changes over time
- Based on observed amino acid substitutions in closely related proteins
- Higher PAM numbers indicate greater evolutionary distance (PAM250 for more divergent sequences)
- BLOSUM (BLOcks ) matrices derived from local alignments of distantly related proteins
- Numbered by percent identity of sequences used to construct them (BLOSUM62 for sequences with 62% identity)
- BLOSUM matrices generally perform better for detecting distant homologs
Position-specific scoring matrices
- Tailored to specific protein families or functional domains
- Capture position-dependent conservation patterns within sequences
- Constructed by aligning multiple sequences and calculating residue frequencies at each position
- Improve sensitivity in detecting remote homologs compared to general-purpose matrices
- Widely used in profile-based search tools (PSI-BLAST)
Substitution vs gap matrices
- Substitution matrices assign scores for aligning different amino acids or nucleotides
- Reflect the likelihood of one residue mutating into another during evolution
- Gap matrices penalize the introduction of insertions or deletions in sequence alignments
- Include gap opening penalties (cost of creating a new gap) and gap extension penalties (cost of extending an existing gap)
- Balancing substitution and gap scores critical for accurate alignment and homology detection
Components of scoring matrices
Match and mismatch scores
- Match scores assigned when identical residues align (typically positive values)
- Mismatch scores given for non-identical residue alignments (can be positive or negative)
- Scores reflect biochemical properties and evolutionary relationships between residues
- Higher scores for chemically similar amino acids (leucine and isoleucine)
- Lower scores for dissimilar residues (tryptophan and glycine)
Gap penalties
- (GOP) applied when introducing a new gap in the alignment
- (GEP) added for each position the gap continues
- model: Total gap penalty = GOP + (length of gap × GEP)
- GOP typically larger than GEP to discourage excessive fragmentation of alignments
- Proper tuning of gap penalties crucial for balancing sensitivity and specificity in alignments
Scoring scheme rationale
- Based on evolutionary and biochemical principles of sequence conservation
- Aims to distinguish biologically meaningful similarities from random matches
- Incorporates amino acid substitution frequencies observed in known homologous proteins
- Accounts for varying mutation rates among different types of residues
- Designed to maximize the for truly related sequences while minimizing scores for unrelated sequences
Construction of scoring matrices
Observed vs expected frequencies
- Observed frequencies calculated from alignments of known homologous sequences
- Count occurrences of each possible residue pair in the aligned positions
- Expected frequencies derived from background amino acid or nucleotide compositions
- Assumes random association of residues in unrelated sequences
- Ratio of observed to expected frequencies forms the basis for scoring matrix values
Log-odds ratios
- Convert frequency ratios to additive scoring system using logarithms
- Log-odds score = log(observed frequency / expected frequency)
- Positive scores indicate substitutions occurring more often than expected by chance
- Negative scores for substitutions less common than random expectation
- Base of logarithm determines the scale of the scores (2 for bit scores, 10 or e for other scales)
Normalization techniques
- Adjust raw log-odds scores to a standardized scale
- Facilitate comparison between different scoring systems
- Methods include scaling to a specific range (e.g., -4 to +11 for BLOSUM62)
- Centering scores around zero by subtracting the mean score
- Entropy-based normalization to account for information content of the matrix
Applications in bioinformatics
Sequence alignment optimization
- Guide dynamic programming algorithms in finding optimal alignments
- Influence gap placement and residue matching decisions
- Enable accurate identification of conserved regions and domains
- Critical for both global alignment (entire sequence length) and local alignment (subsequence matching)
- Affect alignment accuracy in multiple tools (ClustalW, MUSCLE)
Homology detection
- Facilitate identification of evolutionarily related sequences across species
- Enhance sensitivity in detecting remote homologs with low sequence identity
- Power sequence similarity search tools (BLAST, FASTA)
- Enable functional annotation transfer between well-characterized and novel proteins
- Support and evolutionary studies
Protein structure prediction
- Aid in identifying structurally conserved regions in protein sequences
- Guide threading algorithms in protein fold recognition
- Improve accuracy of secondary structure prediction methods
- Support template selection in homology modeling approaches
- Contribute to scoring functions in ab initio protein structure prediction
Statistical significance
E-value calculation
- Estimates the number of alignments with a given score expected by chance
- Depends on database size, query sequence length, and alignment score
- Calculated using extreme value distribution theory
- Lower E-values indicate higher statistical significance
- Formula: E = Kmn * e^(-λS), where K and λ are matrix-specific parameters, m and n are sequence lengths, and S is the alignment score
P-value interpretation
- Probability of obtaining an alignment score at least as extreme as the observed score by chance
- Derived from : = 1 - e^(-E-value)
- Smaller P-values indicate stronger evidence against the null hypothesis of random similarity
- Often used in hypothesis testing for sequence homology
- Critical for controlling false positive rates in large-scale sequence comparisons
Bit scores vs raw scores
- Raw scores directly calculated from scoring matrix values
- Bit scores normalized to a standard scale using matrix-specific parameters
- Bit score = (λ * raw score - ln K) / ln 2
- Allows comparison of alignment qualities across different scoring systems
- Independent of query sequence length and database size, unlike E-values
- Useful for assessing the absolute quality of an alignment
Matrix selection criteria
Sequence similarity levels
- Choose matrices optimized for the expected evolutionary distance between sequences
- Use PAM matrices for closely related sequences (PAM30 or PAM70)
- Employ BLOSUM matrices for more divergent sequences (BLOSUM62 or BLOSUM50)
- Consider using multiple matrices to capture different levels of conservation within a single analysis
- Adjust matrix selection based on preliminary sequence identity assessments
Evolutionary distance considerations
- Select matrices that reflect the evolutionary time separating the sequences
- Use matrices derived from more closely related sequences for recent divergences
- Opt for matrices based on more distant relationships for ancient homologies
- Consider domain-specific matrices for highly conserved functional regions
- Adapt matrix choice to the specific phylogenetic context of the analysis
Task-specific matrix choice
- Tailor matrix selection to the specific bioinformatics application
- Use sensitive matrices (e.g., BLOSUM45) for detecting remote homologs
- Employ stricter matrices (e.g., BLOSUM80) for fine-grained comparisons of closely related sequences
- Consider codon-based matrices for analyzing coding DNA sequences
- Utilize structure-based matrices when incorporating protein structural information
Limitations and challenges
Evolutionary model assumptions
- Scoring matrices based on simplified models of sequence evolution
- Assume uniform substitution rates across all positions in a sequence
- May not accurately capture site-specific evolutionary constraints
- Struggle to model complex evolutionary processes (gene duplication, recombination)
- Limited ability to account for context-dependent mutational patterns
Compositional bias effects
- Sequences with unusual amino acid or nucleotide compositions can skew alignment scores
- May lead to artificially high scores for unrelated sequences with similar compositional biases
- Particularly problematic in low-complexity regions or repetitive sequences
- Can result in false positive homology predictions or inaccurate alignments
- Requires careful interpretation and potential use of composition-adjusted scoring techniques
Low complexity region issues
- Scoring matrices often perform poorly in regions with simple repeat patterns
- Can lead to overestimation of sequence similarity in these areas
- May result in biologically meaningless alignments driven by repetitive elements
- Necessitates the use of sequence masking or filtering techniques (SEG, DUST)
- Challenges the development of scoring systems that can handle both globular and disordered protein regions
Advanced scoring techniques
Profile-based scoring
- Utilize position-specific scoring matrices (PSSMs) derived from multiple sequence alignments
- Capture conservation patterns and allowed variations at each position
- Improve sensitivity in detecting remote homologs compared to single sequence methods
- Form the basis for powerful search tools (PSI-BLAST, HMMER)
- Enable more accurate functional and structural predictions based on sequence families
Hidden Markov models
- Probabilistic models representing sequence families or motifs
- Incorporate position-specific insertion, deletion, and match states
- Allow for variable-length gaps and flexible alignment of sequences to the model
- Provide a rigorous statistical framework for sequence comparison and annotation
- Widely used in protein domain databases (Pfam) and gene prediction tools
Machine learning approaches
- Employ neural networks or support vector machines to learn optimal scoring functions
- Can integrate multiple features beyond simple residue substitutions (secondary structure, solvent accessibility)
- Adapt to specific sequence analysis tasks through training on curated datasets
- Potential to capture complex, non-linear relationships in sequence evolution
- Challenges include interpretability and the need for large, high-quality training data
Software tools and databases
BLAST matrix options
- BLAST (Basic Local Alignment Search Tool) offers various built-in scoring matrices
- Default protein matrix: BLOSUM62 for general-purpose searches
- Allows users to select alternative matrices (PAM30, BLOSUM45) based on search requirements
- Provides options for nucleotide-specific matrices (MATCH, MISMATCH)
- Supports custom matrix input for specialized applications
PFAM scoring systems
- Pfam (Protein Families Database) uses profile (HMMs) for domain annotation
- Each Pfam entry has a specific scoring model built from curated seed alignments
- Employs HMMER software for searching and scoring sequences against Pfam models
- Provides gathering thresholds (GA) for determining significant matches to each family
- Allows for nested and overlapping domain architectures through competing HMM scores
Custom matrix creation
- Tools available for generating task-specific scoring matrices (BLOSUM programs, SEQBOOT)
- Requires careful curation of training sequence alignments
- Involves choices in frequency counting methods and pseudocount strategies
- Necessitates proper normalization and scaling of the resulting matrix
- Enables optimization for specific sequence families or evolutionary scenarios
Performance evaluation
Sensitivity vs specificity
- Sensitivity measures the ability to detect true positive relationships
- Specificity quantifies the ability to avoid false positive predictions
- Trade-off exists between maximizing sensitivity and maintaining high specificity
- Different scoring matrices and parameters can shift the balance between these metrics
- Optimal choice depends on the specific requirements of the bioinformatics task
ROC curve analysis
- Receiver Operating Characteristic (ROC) curves plot true positive rate vs false positive rate
- Allows visualization of classifier performance across various threshold settings
- Area Under the Curve (AUC) provides a single metric for comparing different scoring systems
- Higher AUC indicates better overall performance in distinguishing true from false relationships
- Useful for optimizing scoring matrix and gap penalty parameters
Benchmarking datasets
- Curated sets of sequences with known evolutionary relationships
- Include both closely related and distantly homologous sequences
- Often contain challenging cases that push the limits of current methods
- Examples include SCOP (Structural Classification of Proteins) superfamilies
- Critical for fair comparison of different scoring approaches and parameter settings
Key Terms to Review (22)
Affine gap penalty: An affine gap penalty is a scoring scheme used in sequence alignment that applies a cost for opening a gap and a different, typically lower, cost for extending that gap. This method is designed to better reflect biological realities where gaps in sequences often arise from insertions or deletions during evolution, and it allows for more accurate alignments by penalizing the initiation of gaps more heavily than the continuation of existing gaps.
Alignment score: An alignment score is a numerical value that quantifies the quality of a sequence alignment, reflecting the degree of similarity or dissimilarity between two sequences. It is crucial in comparing biological sequences, helping to determine how well sequences match with each other through substitutions, insertions, and deletions. The alignment score can significantly influence the outcome of various alignment methods, including pairwise, global, and local alignments, as well as the effectiveness of scoring matrices and structural comparisons.
BLOSUM: BLOSUM (Block Substitution Matrix) is a scoring matrix used to assess the likelihood of amino acid substitutions during protein sequence alignment. It is particularly useful in bioinformatics for evaluating the similarity between sequences by providing scores for aligning different amino acids based on observed substitutions in related proteins. BLOSUM matrices are essential tools in various alignment algorithms, impacting how accurately and efficiently sequences can be compared, particularly in the context of analyzing evolutionary relationships and structural similarities.
Dynamic programming matrix: A dynamic programming matrix is a structured table used in algorithm design to solve optimization problems by breaking them down into simpler subproblems. This matrix facilitates the systematic organization of computed values, allowing for efficient calculation of optimal solutions by storing intermediate results and reducing redundant computations. It is particularly important in the context of scoring matrices and sequence alignment, as it allows for the quantification of similarity between biological sequences.
E-value: The e-value, or expect value, is a statistical measure used in bioinformatics to indicate the number of times one might expect to see a match between sequences purely by chance. It helps assess the significance of alignments in various applications such as sequence databases, pairwise alignment, local alignment, and scoring matrices. A lower e-value indicates a more significant match, which is crucial for identifying biologically relevant similarities between sequences.
Gap extension penalty: The gap extension penalty is a score subtracted from a sequence alignment score each time an existing gap in the alignment is extended by one additional position. This penalty is crucial because it influences how gaps are treated in pairwise sequence alignments, where maintaining a balance between matches and gaps is essential for accurate alignments. Understanding this penalty helps in utilizing scoring matrices effectively and determining the overall alignment score based on gap penalties.
Gap Opening Penalty: A gap opening penalty is a numerical value assigned to the introduction of a gap in a sequence alignment, used to discourage the insertion of gaps in sequences during pairwise alignment. It plays a critical role in optimizing alignments by balancing the need to represent gaps accurately against the overall alignment score. The penalty is part of scoring systems, influencing how sequences are aligned and affecting the identification of similarities and differences between them.
Hidden Markov Models: Hidden Markov Models (HMMs) are statistical models that represent systems where the state is not directly observable, but can be inferred through observable outputs. HMMs are particularly useful in bioinformatics for tasks such as sequence alignment and protein structure prediction, relying on probabilistic reasoning to understand relationships between sequences. The hidden states correspond to unobserved biological processes, while the observed events are the sequences or structures derived from those processes.
Log-odds ratios: Log-odds ratios are a statistical measure used to express the odds of an event occurring relative to the odds of it not occurring, often represented on a logarithmic scale. This concept is particularly useful in bioinformatics for evaluating the significance of sequence alignments through scoring matrices, as it helps determine the likelihood of specific substitutions or mutations in biological sequences.
Match score: A match score is a numerical value assigned to indicate the degree of similarity or alignment between sequences, such as DNA, RNA, or protein sequences. This score plays a crucial role in evaluating the quality of sequence alignments, helping researchers identify conserved regions, mutations, or evolutionary relationships. By utilizing scoring matrices, match scores help quantify how well sequences fit together, guiding further analysis and interpretations in bioinformatics.
Mismatch score: A mismatch score is a numerical value used to quantify the penalty incurred when two compared sequences differ at a specific position. This score is essential in scoring matrices, as it helps to evaluate the quality of alignments between DNA, RNA, or protein sequences, ultimately impacting the overall alignment score. A higher mismatch score indicates a less favorable alignment and assists in distinguishing between more and less similar sequences.
Needleman-Wunsch Algorithm: The Needleman-Wunsch algorithm is a dynamic programming method used for global sequence alignment of biological sequences, such as DNA, RNA, or proteins. It systematically compares sequences to identify the optimal alignment by maximizing similarity while minimizing mismatches and gaps. This algorithm is foundational in understanding how sequences are compared and aligned within various bioinformatics applications.
Normalized scores: Normalized scores are statistical values that have been adjusted to a common scale, allowing for comparison across different datasets or scoring systems. This process helps eliminate biases caused by variations in measurement units, providing a clearer understanding of relative performance, especially in contexts like scoring matrices, where various alignments or sequences need to be evaluated uniformly.
P-value: A p-value is a statistical measure that helps scientists determine the significance of their experimental results. It indicates the probability of obtaining results at least as extreme as those observed, assuming that the null hypothesis is true. The p-value plays a crucial role in hypothesis testing, guiding researchers in deciding whether to reject or fail to reject the null hypothesis across various scientific fields.
PAM: PAM stands for Point Accepted Mutation and refers to a scoring system used in bioinformatics to evaluate the similarity between protein sequences. It helps in quantifying how likely a mutation is to occur over evolutionary time, with PAM matrices providing numerical values that indicate how substitutions between amino acids are scored. This concept is vital for various sequence alignment techniques and is closely linked with methods that assess the evolutionary relationships among proteins.
Phylogenetic analysis: Phylogenetic analysis is a method used to study the evolutionary relationships among biological species based on their genetic, morphological, or behavioral characteristics. By constructing phylogenetic trees, researchers can visualize how species are related and trace their evolutionary history, which connects to various concepts such as sequence alignment, scoring systems, and models of molecular evolution.
Profile-based scoring matrices: Profile-based scoring matrices are computational tools used to assess the similarity between biological sequences by comparing them to a profile derived from multiple sequence alignments. These matrices help identify conserved regions in protein sequences, allowing for better understanding of protein function and evolutionary relationships. They incorporate information from numerous sequences to create a statistical framework that can predict the likelihood of residue substitutions and detect homologous sequences more accurately.
Sequence Alignment: Sequence alignment is a method used to arrange sequences of DNA, RNA, or protein to identify regions of similarity that may indicate functional, structural, or evolutionary relationships. This technique is fundamental in various applications, such as comparing genomic sequences to study evolution, identifying genes, or predicting protein structures.
Similarity score: A similarity score is a quantitative measure that indicates the degree of similarity between biological sequences, such as DNA, RNA, or protein sequences. It helps in comparing sequences to determine how closely they relate to one another, which is essential for understanding evolutionary relationships, functional predictions, and structural alignments. The calculation of this score often relies on specific algorithms and scoring matrices that assess matches, mismatches, and gaps within the sequences being compared.
Smith-Waterman Algorithm: The Smith-Waterman algorithm is a dynamic programming method used for local sequence alignment, which identifies the optimal alignment between two sequences. It is particularly effective for finding regions of similarity in nucleotide or protein sequences, allowing researchers to highlight conserved sequences even when there are gaps or mutations.
Substitution Matrix: A substitution matrix is a scoring scheme used in sequence alignment to quantify the likelihood of one amino acid or nucleotide being replaced by another during evolution. This matrix plays a critical role in determining the overall similarity between sequences by assigning scores based on biological properties, such as the frequency of substitutions. It is essential in pairwise sequence alignment, local alignment, scoring matrices, and dynamic programming as it helps identify conserved regions and assess evolutionary relationships between sequences.
Two-dimensional matrix: A two-dimensional matrix is a rectangular array of numbers arranged in rows and columns, allowing for the representation and manipulation of data in a structured format. In the context of scoring matrices, these matrices are essential for comparing biological sequences by assigning scores to matches, mismatches, and gaps, facilitating various computational analyses in bioinformatics.