AutoMatrix

AutoMatrix computes instantaneous amino acid substitution rate matrices and their eigenvalue decompositions from substitution count matrices as a MATLAB script to model protein evolutionary dynamics and support phylogenetic analysis.

Key Features:

• Instantaneous Rate Matrix Calculation: Computes instantaneous rate matrices from substitution count matrices to model amino acid substitution dynamics over evolutionary time.
• Eigenvalue Decomposition: Performs eigenvalue decomposition on rate matrices to analyze the stability and behavior of substitution processes.
• Compatibility with BLOSUM Matrices: Integrates with the BLOSUM series and extends their use by providing an evolutionary model that accounts for multiple hits.
• PMB (Probability Matrix from Blocks) Model: Implements the PMB model derived from the Blocks database to approximate substitution probabilities as functions of evolutionary distance.
• Blocks Database Usage: Utilizes the Blocks database of protein alignments as the empirical basis for deriving substitution models.
• Substitution Count Matrices from Sequence Identity/Similarity: Accepts substitution count matrices derived from varying levels of sequence identity or similarity.
• Multiple-Hit Correction and Substitution Number Estimation: Provides mechanisms to correct for multiple hits and estimate actual numbers of amino acid substitutions.
• PHYLIP Integration: Facilitates integration with PHYLIP programs for downstream phylogenetic analyses.
• MATLAB Implementation: Implemented as a MATLAB script for matrix computations and numerical analysis.

Scientific Applications:

• Protein Sequence Alignment: Enhances interpretation of BLOSUM-based alignments by linking scoring matrices to an explicit evolutionary model.
• Evolutionary Analysis and Phylogenetic Reconstruction: Estimates amino acid substitution probabilities as functions of evolutionary distance to support phylogenetic tree inference.
• Model Development and Evaluation: Provides the PMB model to approximate substitution probabilities from empirical Blocks data and to evaluate substitution dynamics and multiple-hit corrections.

Methodology:

Derives substitution count matrices from varying sequence identity/similarity levels, uses the Blocks database and the additivity principle of evolutionary distances to derive the PMB model, computes instantaneous rate matrices and their eigenvalue decompositions, and exports results for integration with PHYLIP.