Relative Entropy Calculator

Calculate expected information per position and critical alignment lengths for sequence comparison

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Relative Entropy (bits)
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Critical Length
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% Identity
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Expected Score

Relative Entropy vs Evolutionary Distance

Critical Alignment Length vs Distance

Note: Relative entropy H = Σ q_ij log(q_ij/p_ip_j) represents the expected information per aligned position. Higher entropy means more information for distinguishing homologs from random alignments.

What is Relative Entropy?

Relative entropy (H) measures the expected information per position in aligned sequences. It quantifies how much better a scoring matrix distinguishes homologs from random alignments, calculated as H = Σ q_ij log(q_ij/p_ip_j) bits.

How to Use This Calculator

Calculate information content at different evolutionary distances:

  1. Choose PAM distance or scoring matrix
  2. Set noise threshold for significance
  3. View entropy and critical length calculations

When to Use

This tool is useful when you need to:

  • Determine minimum alignment length for significance
  • Compare information content of different matrices
  • Understand detection limits at various distances

Example Input

Parameters for twilight zone analysis:

PAM Distance: 250
Noise Threshold: 30 bits
Type: Protein sequences

Shows ~20% identity requires 120+ residues.

Example Output

Information theory metrics:

Relative Entropy: 0.356 bits
Critical Length: 84 residues
Percent Identity: 20%

Minimum length for significant detection.

FAQ

Q: What is critical length?
A: The minimum alignment length needed to rise above background noise at a given evolutionary distance.

Q: Why does entropy decrease with distance?
A: As sequences diverge, amino acid pairs become more random, reducing information content.