Explaining complex codon usage patterns with selection for translational efficiency, mutation bias, and genetic drift

Abstract

The genetic code is redundant with most amino acids using multiple codons. In many organisms, codon usage is biased toward particular codons. Understanding the adaptive and nonadaptive forces driving the evolution of codon usage bias (CUB) has been an area of intense focus and debate in the fields of molecular and evolutionary biology. However, their relative importance in shaping genomic patterns of CUB remains unsolved. Using a nested model of protein translation and population genetics, we show that observed gene level variation of CUB in Saccharomyces cerevisiae can be explained almost entirely by selection for efficient ribosomal usage, genetic drift, and biased mutation. The correlation between observed codon counts within individual genes and our model predictions is 0.96. Although a variety of factors shape patterns of CUB at the level of individual sites within genes, our results suggest that selection for efficient ribosome usage is a central force in shaping codon usage at the genomic scale. In addition, our model allows direct estimation of codon-specific mutation rates and elongation times and can be readily applied to any organism with high-throughput expression datasets. More generally, we have developed a natural framework for integrating models of molecular processes to population genetics models to quantitatively estimate parameters underlying fundamental biological processes, such a protein translation.

Fig. 1.

Effect of varying relative mutation rate (μ_i/μ_j), elongation time (Δt_ij), and protein production rate (φ) on the expected codon frequencies (E[f]) in a hypothetical two-codon amino acid. (A) Effect of changing μ_i/μ_j on E[f] with φ. Solid lines represent the codon with a longer elongation time t₁, and dotted lines represent the codon with a shorter elongation time t₂. Mutation bias has a greater effect on E[f] at low φ, whereas at very high φ, the E[f] of codons converge to the same values, irrespective of μ_i/μ_j. (B) Effect of changing t_i − t_j on their expected frequencies E[f] with respect to φ. Solid lines represent the codon with a lower relative mutation rate μ₁, and dotted lines represent the codon with a higher mutation rate μ₂. Differences in elongation times between the two codons t_i − t_j has little effect on E[f] at low φ. However, at high φ, as t_i − t_j changes, so does the difference in their expected frequencies E[f].

Fig. 2.

Observed and predicted changes in codon frequencies with gene expression, specifically protein production rate φ. A–S correspond to specific amino acids, where codons ending in A or T are shown in shades of blue and codons ending in G or C are shown in shades of red. Solid dots and vertical bars represent mean ±1 SD of observed codon frequencies of genes in a given bin. The expected codon frequencies under our model are represented by solid lines. (T) Histogram of genes in each bin. We used k − 1 codons of an amino acid with k codons in estimating correlation coefficients. ρ_M represents the Pearson correlation between the mean of observed codon frequencies within a bin and predicted codon frequencies at mean φ value. ρ_c represents the Pearson correlation between observed codon counts and predicted codon counts of all genes at their individual φ value.

Fig. 3.

Correlation between observed codon counts and predicted codon counts of individual genes. We used codon counts of k − 1 codons of an amino acid with k codons. Ignoring Met and Trp (one-codon amino acids) and splitting Ser into two blocks of four and two codons, there are 19 unique amino acid sets. Hence, the number of data points used is 4,674 × (59 − 19) = 186,960. We find a very high correlation (ρ = 0.959, P < 10¹⁵) between our model predictions and observed counts. (Inset) Distribution of correlation coefficients at the level of individual amino acids, indicating that our high correlation is not biased by specific amino acids and that we have a high correlation across all amino acids.

Fig. 4.

Correlation between our model-based estimates of Δt_ij with Δt_ij estimated using tRNA gene copy numbers. We find a strong correlation (ρ = 0.801, P < 10⁻⁹) between our model estimates and estimates of Δt_ij based on tRNA gene copy numbers, indicating that our estimates can be related to other biological estimates, such as tRNA abundances, directly.