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Review: An Improved General Amino Acid Replacement Matrix

Citation

  • Le, S. Q., & Gascuel, O. (2008). An improved general amino acid replacement matrix. Molecular Biology and Evolution, 25(7), 1307–1320.
  • DOI

Abstract

A new general amino acid replacement matrix, LG, is estimated from a large database of protein alignments. The matrix is derived using a maximum likelihood approach and provides a significantly better fit to empirical protein evolution than earlier matrices (WAG, JTT). It is recommended as the default matrix for protein phylogenetic analysis.

Empirical amino acid substitution matrices encode the observed relative rates at which one amino acid is replaced by another across large databases of aligned protein sequences. Rather than specifying the 20×20 rate matrix \( Q \) from mechanistic first principles, these matrices estimate it directly from data, capturing the aggregate effect of biochemical constraints, structural requirements, and selection.

The LG matrix was estimated by Le and Gascuel (2008) using a maximum-likelihood approach on a curated database of 3,912 protein alignments, substantially larger than the datasets used for earlier matrices. The estimation procedure maximizes the log-likelihood of the observed amino acid replacements given a rate matrix \( Q \) and a set of associated stationary frequencies, subject to the time-reversibility constraint \( \pi_i r_{ij} = \pi_j r_{ji} \). The result is a 190-parameter symmetric rate matrix (one exchangeability \( r_{ij} \) per pair of amino acids) plus 20 stationary frequencies.

Likelihood ratio tests and cross-validation against held-out alignments show that LG fits protein evolution better than the previously recommended WAG and JTT matrices for most modern protein datasets.

In Hifuku, LG is one of the built-in fixed-rate matrices available for protein sequence likelihood computation. The exchangeability matrix and stationary frequencies are stored as constants in src/hifuku/substitution.py and passed to the EigenDecomp class to construct the \( Q \) matrix and its eigendecomposition. Hifuku also supports WAG (see Whelan & Goldman 2001) and JTT (see Jones et al. 1992) as alternatives.