Minimal entropy probability paths between genome families.

Area of Science:

• Computational Biology and Bioinformatics
• Information Theory
• Mathematical Biology

Background:

• Biological sequences (DNA, amino acids) are often represented as probability distributions or frequency profiles.
• Comparing these sequences requires robust distance metrics that capture evolutionary or functional relationships.
• Existing metrics may not fully account for the underlying probabilistic nature of sequence transformations.

Purpose of the Study:

• To develop a new distance metric for probability distributions with applications in biological sequence analysis.
• To leverage entropy considerations to create a metric reflecting the efficiency of natural mutations.
• To provide a computationally efficient and accurate method for comparing biological sequences.

Main Methods:

• Developed a distance metric by minimizing a functional defined on paths over probability measures.
• Utilized calculus of variations and numerical methods (Newton's method, linear regression) for optimization.
• Proposed an elementary distance function as a faster, more broadly applicable approximation.

Main Results:

• The proposed metric approximates the minimal entropy path distance, outperforming standard Euclidean distance for probability vectors.
• Computed minimal entropy distance matrices for DNA myostatin genes and amino acid sequences.
• Generated dendrograms based on the new metric and compared them with those from BLAST analysis.

Conclusions:

• The minimal entropy distance metric provides a valuable new tool for biological sequence comparison.
• The metric demonstrates potential for phylogenetic analysis and understanding sequence evolution.
• The elementary distance function offers a practical alternative for large-scale sequence comparisons.