BLOSUM

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    1. BLOSUM Matrices

BLOSUM (Blocks Substitution Matrix) is a scoring matrix used for aligning protein sequences. These matrices are fundamental tools in bioinformatics and are applied extensively in programs like BLAST and FASTA for sequence similarity searches and multiple sequence alignment. Understanding BLOSUM matrices is crucial for anyone engaged in biological sequence analysis, and even has surprising connections to understanding risk assessment in complex systems, analogous to some concepts used in binary options trading. This article provides a comprehensive overview of BLOSUM matrices, their construction, interpretation, and application, geared towards beginners.

Introduction to Substitution Matrices

Before diving into BLOSUM specifically, it's important to understand the broader concept of substitution matrices. When aligning two sequences, we aim to identify regions of similarity that suggest evolutionary relationships or functional homology. However, not all amino acid substitutions are equally likely. Some substitutions are more common because they involve amino acids with similar biochemical properties (e.g., swapping between two hydrophobic amino acids). Others are less common because they involve drastic changes in properties (e.g., swapping between a hydrophobic and a charged amino acid).

A substitution matrix quantifies these differences by assigning a score to each possible amino acid substitution. A positive score indicates that the substitution is relatively common and therefore suggests a higher degree of similarity, while a negative score indicates a rare substitution suggesting a lower degree of similarity. These scores are the backbone of algorithms used in sequence alignment.

The Genesis of BLOSUM

Early substitution matrices, like the PAM (Point Accepted Mutation) matrices, were based on an evolutionary model that extrapolated substitution frequencies over long evolutionary distances. However, the PAM matrices suffered from limitations; they became less reliable as the evolutionary distance increased, and weren't necessarily representative of the substitutions observed in closely related sequences.

The BLOSUM matrices, developed by Henikoff and Henikoff in 1992, took a different approach. Instead of extrapolating from distant relationships, BLOSUM matrices were derived directly from observed substitutions in conserved blocks of protein sequences. These blocks were identified from a database of protein families, ensuring that the matrix reflects substitutions actually seen in functionally important regions of proteins. This focus on conserved blocks makes BLOSUM matrices particularly effective for aligning sequences that are relatively closely related.

Constructing a BLOSUM Matrix

The construction of a BLOSUM matrix involves several key steps:

1. Block Identification: The process begins with identifying conserved blocks within multiple sequence alignments of protein families. These blocks represent regions of the protein that are essential for its function and are therefore less prone to mutation. 2. Multiple Sequence Alignment: High-quality multiple sequence alignments of these conserved blocks are generated. This is a critical step, as errors in the alignment will propagate into the matrix. 3. Counting Substitutions: The frequency of each amino acid substitution within these blocks is then counted. For example, how often does Alanine (A) get substituted by Valine (V)? 4. Normalization: The raw counts are normalized to account for the frequencies of each amino acid. This prevents biases towards amino acids that occur more frequently in the dataset. 5. Log-Odds Calculation: The core of the BLOSUM score is calculated using log-odds. The observed frequency of a substitution is divided by the expected frequency under the assumption that the substitutions occur randomly. The logarithm of this ratio is then taken. This log-odds score reflects how much more or less frequently a substitution occurs than expected by chance.

Formula: BLOSUM(a, b) = log2(P(a→b) / P(a) * P(b))

Where:

  • a and b are amino acids
  • P(a→b) is the observed frequency of amino acid 'a' being substituted by amino acid 'b' in the conserved blocks.
  • P(a) and P(b) are the overall frequencies of amino acids 'a' and 'b' in the dataset.

BLOSUM Matrix Numbers: What Do They Mean?

BLOSUM matrices are identified by a number, such as BLOSUM62, BLOSUM80, or BLOSUM45. This number represents the percentage identity of the blocks used to construct the matrix. For example:

  • BLOSUM62: Constructed from blocks with at least 62% sequence identity. This is the most commonly used BLOSUM matrix and is generally a good choice for aligning moderately divergent sequences. It offers a balance between sensitivity and specificity. It’s akin to using a shorter expiration time in binary options trading – focusing on more immediate, stronger signals.
  • BLOSUM80: Constructed from blocks with at least 80% sequence identity. This matrix is suitable for aligning very closely related sequences. It’s a more conservative matrix, meaning it will only score highly similar substitutions. Think of this as a low-risk, low-reward strategy in high/low binary options.
  • BLOSUM45: Constructed from blocks with at least 45% sequence identity. This matrix is more sensitive and can detect more distant relationships, but it may also produce more false positives. It parallels a high-risk, high-reward strategy in touch/no touch binary options.

The lower the number, the more divergent the sequences the matrix is designed to align. Choosing the appropriate BLOSUM matrix is crucial for achieving optimal alignment results. Consider the expected evolutionary distance between the sequences being compared.

Interpreting BLOSUM Scores

The scores within a BLOSUM matrix represent the likelihood of a particular amino acid substitution. Here's how to interpret them:

  • Positive Scores: Indicate that the substitution is more frequent than expected by chance, suggesting a degree of similarity. Higher positive scores indicate stronger similarity.
  • Negative Scores: Indicate that the substitution is less frequent than expected by chance, suggesting a lower degree of similarity. Larger negative scores indicate a more significant difference.
  • Zero Scores: Represent substitutions that occur at the expected frequency.

The magnitude of the score is also important. A score of 10 is generally considered a strong match, while a score of -4 indicates a significant mismatch. The scores are relative and should be interpreted in the context of the specific matrix being used.

Example BLOSUM62 Matrix Snippet

BLOSUM62 Matrix (Snippet)
| A | C | D | E |
4 | 0 | -1 | -2 | 0 | 9 | -3 | -4 | -1 | -3 | 6 | -3 | -2 | -4 | -3 | 5 |

In this snippet, you can see that substituting Alanine (A) with Alanine (A) scores 4, indicating a very good match. Substituting Alanine with Cysteine (C) scores 0, suggesting no significant similarity. Substituting Alanine with Aspartic Acid (D) scores -1, indicating a weak dissimilarity.

Application in Sequence Alignment Algorithms

BLOSUM matrices are integral to many sequence alignment algorithms, including:

  • Needleman-Wunsch Algorithm: A dynamic programming algorithm used for global alignment, aligning the entire length of two sequences.
  • Smith-Waterman Algorithm: A dynamic programming algorithm used for local alignment, identifying regions of high similarity within two sequences.
  • BLAST (Basic Local Alignment Search Tool): A widely used algorithm for searching sequence databases for similar sequences. BLAST uses a BLOSUM matrix (typically BLOSUM62) to score the alignments.
  • FASTA: Another popular sequence database search tool that utilizes BLOSUM matrices.

These algorithms use the BLOSUM scores to calculate an alignment score, which reflects the overall similarity between the two sequences. The algorithm then seeks to maximize this score by finding the optimal alignment. The choice of BLOSUM matrix significantly impacts the results of these algorithms.

BLOSUM and Gap Penalties

In addition to substitution scores, sequence alignment algorithms also incorporate gap penalties. Gaps represent insertions or deletions in one of the sequences. Gap penalties are subtracted from the alignment score to discourage the introduction of unnecessary gaps. The appropriate gap penalty depends on the expected evolutionary distance between the sequences. A higher gap penalty will result in fewer gaps, while a lower gap penalty will allow for more gaps. Balancing substitution scores (from the BLOSUM matrix) and gap penalties is crucial for accurate alignment. It’s similar to balancing your risk tolerance and potential payout in binary options.

Choosing the Right BLOSUM Matrix

Selecting the appropriate BLOSUM matrix is a critical step in sequence alignment. Here's a guide:

  • Closely Related Sequences (high % identity): Use BLOSUM80 or BLOSUM90.
  • Moderately Divergent Sequences (40-60% identity): Use BLOSUM62 (the default choice for many applications).
  • Distantly Related Sequences (low % identity): Use BLOSUM45 or PAM matrices.

The best approach is often to experiment with different matrices and evaluate the results based on biological knowledge and the specific application. Consider the expected evolutionary relationship between the sequences and the potential for gaps. It's analogous to backtesting different trading strategies in binary options to find the best fit for your market conditions.

BLOSUM beyond Bioinformatics: Analogies to Financial Risk

Interestingly, the principles behind BLOSUM matrices have parallels in financial risk assessment, particularly in binary options trading. The concept of assigning scores based on observed frequencies and probabilities is mirrored in evaluating the likelihood of different market outcomes.

  • Substitution Scores as Probability Assessments: In BLOSUM, scores reflect the probability of one amino acid changing to another. In binary options, we assess the probability of an asset price moving above or below a certain level within a specific timeframe.
  • Gap Penalties as Transaction Costs: Gap penalties discourage unnecessary insertions/deletions. Similarly, transaction costs (brokerage fees, spreads) discourage excessive trading.
  • Matrix Selection as Strategy Choice: Choosing the right BLOSUM matrix depends on the expected evolutionary distance. Choosing the right trading strategy depends on market volatility and your risk appetite.
  • Log-Odds as Risk-Reward Ratio: The log-odds score in BLOSUM reflects the relative likelihood of an event. The risk-reward ratio in binary options represents the potential profit relative to the potential loss.
  • BLOSUM62 as a Balanced Approach: BLOSUM62’s widespread use reflects its balance between sensitivity and specificity, much like a balanced trading plan that considers both potential gains and risks.
  • Analyzing trading volume can provide insight similar to analyzing conserved blocks of protein sequences.

While the contexts are vastly different, the underlying principle of assigning scores based on probabilistic assessments is remarkably similar.

Resources and Further Learning

Conclusion

BLOSUM matrices are powerful tools for aligning protein sequences and uncovering evolutionary relationships. Understanding their construction, interpretation, and application is crucial for anyone working in bioinformatics. By carefully selecting the appropriate BLOSUM matrix and considering gap penalties, researchers can achieve accurate and meaningful sequence alignments. Furthermore, the underlying principles of probabilistic scoring and risk assessment have surprising connections to fields like financial trading, demonstrating the broad applicability of these concepts.

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