Power law tails in phylogenetic systems

Area of Science:

• Computational Biology
• Bioinformatics
• Structural Biology

Background:

• Covariance analysis of protein sequence alignments identifies coevolving positions to predict protein structure and function.
• Current methods often overlook phylogenetic relationships, potentially leading to inaccurate identification of covarying positions.

Purpose of the Study:

• To differentiate covariance signals arising from phylogeny versus structural interactions in protein sequence alignments.
• To develop a method for improving the prediction of protein 3D structure contacts by accounting for phylogenetic effects.

Main Methods:

• Application of random matrix theory to analyze the covariance spectrum of protein sequence alignments.
• Identification of a power law tail characteristic of phylogenetic covariance.
• Demonstration that this power law is largely independent of phylogenetic tree topology.

Main Results:

• A distinct power law tail in the covariance spectrum reliably distinguishes phylogenetic signals from structural interactions.
• These power law tails are prevalent in large protein sequence alignments used for contact prediction.
• Removing or down-weighting eigenvectors associated with the largest eigenvalues significantly enhances contact prediction accuracy.

Conclusions:

• Phylogenetic relationships introduce a confounding factor in covariance analysis that must be addressed.
• The proposed method effectively decouples phylogenetic effects from true structural interactions.
• Truncating specific eigenvectors of the covariance matrix is a validated strategy for improving protein contact prediction.