Codon usage bias has been known to reflect the expression level of a protein-coding gene under the evolutionary theory that selection favors certain synonymous codons. Although measuring the effect of selection in simple organisms such as yeast and E. coli has proven to be effective and accurate, codon-based methods perform less well in plants and humans. In this paper, we extend a prior method that incorporates another evolutionary factor, namely mutation bias and its effect on codon usage. Our results indicate that prediction of gene expression is significantly improved under our framework, and suggests that quantification of mutation bias is essential for fully understanding synonymous codon usage. We also propose an improved method, namely MLE-Φ, with much greater computation efficiency and a wider range of applications. An implementation of this method is provided at https://github.com/luzhixiu1996/MLE-Phi.
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