Background selection in single genes may explain patterns of codon bias

Abstract

Background selection involves the reduction in effective population size caused by the removal of recurrent deleterious mutations from a population. Previous work has examined this process for large genomic regions. Here we focus on the level of a single gene or small group of genes and investigate how the effects of background selection caused by nonsynonymous mutations are influenced by the lengths of coding sequences, the number and length of introns, intergenic distances, neighboring genes, mutation rate, and recombination rate. We generate our predictions from estimates of the distribution of the fitness effects of nonsynonymous mutations, obtained from DNA sequence diversity data in Drosophila. Results for genes in regions with typical frequencies of crossing over in Drosophila melanogaster suggest that background selection may influence the effective population sizes of different regions of the same gene, consistent with observed differences in codon usage bias along genes. It may also help to cause the observed effects of gene length and introns on codon usage. Gene conversion plays a crucial role in determining the sizes of these effects. The model overpredicts the effects of background selection with large groups of nonrecombining genes, because it ignores Hill-Robertson interference among the mutations involved.

Figure 1.—

Background selection in a single gene with the fixed selection coefficient approximation, showing the effects of gene conversion and mutation rates with a crossover rate of 10⁻⁸. The selection coefficient s was set equal to the harmonic mean heterozygous selection coefficient, estimated from a DDME with a width of σ_g = 50, which gives an N_es value of 12.7 and a frequency of effectively neutral mutations, c_ne, of 12.6%. All curves are paired, with the bottom curve representing the coding sequence of a gene without introns and the top curve that of a gene with four equidistant introns. (A) Different gene conversion rates for u = 4 × 10⁻⁹; pairs of solid lines from top to bottom are for r_g = 5 × 10⁻⁶, 2.5 × 10⁻⁶, 0.5 × 10⁻⁶; the dashed line is for r_g = 0. (B) Different mutation rates for r_g = 2.5 × 10⁻⁶; pairs of lines from top to bottom are for u = 2 × 10⁻⁹, u = 4 × 10⁻⁹, and u = 8 × 10⁻⁹. The scale for the bottom two curves is on the right.

Figure 2.—

Background selection in a single gene: average of 100 samples from a DDME, showing the effects of gene conversion and mutation rate. Otherwise this is similar to Figure 1.

Figure 3.—

Longer exons experience more background selection. Mean values of B = N_e/N₀ for a gene are shown, assuming no neighboring genes, no introns, and r_g = 2.5 × 10⁻⁶. The thickness of the curves denotes the crossing-over rate (thick, 3 × 10⁻⁸; medium, 1 × 10⁻⁸; thin, 1 × 10⁻⁹), line type represents the mutation rate (dotted, 2 × 10⁻⁹; dashed, 4 × 10⁻⁹; solid, 8 × 10⁻⁹), and the highlighted curve indicates a typical gene (dashed line with medium thickness). (A) Fixed selection coefficient is as in Figure 1. (B) Average of 100 samples from the DDME. The bottom three curves belong to the scale on the right.

Figure 4.—

Longer introns reduce background selection. Mean values of B for a gene of the standard length are shown, assuming no neighboring genes, four equidistant introns, and r_g = 2.5 × 10⁻⁶. Other features of the curves are as in Figure 3. (A) Fixed selection coefficients. The bottom three lines belong to the scale on the right. (B) Average of 100 samples from the DDME. The bottom three lines belong to the scale on the right.

Figure 5.—

The effect of neighboring genes on the mean B for a gene under background selection. Both plots show a focal gene and assume four equidistant introns of 100 bp length, 6000 bp intergenic distance, 2000 bp coding sequence for all genes, and r_g = 2.5 × 10⁻⁶. Other features of the curves are as in Figure 3. (A) Fixed selection coefficient. (B) Average of 100 samples from the DDME.

Figure 6.—

Neighboring genes do not affect the patterns of background selection within a gene. This plot is like Figure 2A, except that five neighboring genes were located on both sides of the focal gene (with features as in Figure 5).

Figure 7.—

The effect of neighboring genes on background selection without crossing over. Both plots show the mean B for a focal gene, with the same features of neighboring genes as in Figure 5. However, crossing over is assumed to be absent and curve thickness denotes the rate of gene conversion r_g (thick, 5 × 10⁻⁶; medium, 2.5 × 10⁻⁶; thin, 0.5 × 10⁻⁶). Line type represents the mutation rate (dotted, 2 × 10⁻⁹; dashed, 4 × 10⁻⁹; solid, 8 × 10⁻⁹) and the highlighted line indicates a typical gene (dashed line with medium thickness). (A) Fixed selection coefficient. (B) Average of 100 samples from the DDME.

Figure 8.—

Longer intergenic distances reduce background selection in a region. This plot shows the fixed selection coefficient prediction for the mean B of a focal gene with varying intergenic distances, when five neighboring genes are located on both sides (with features as in Figure 5) and r_g = 2.5 × 10⁻⁶. Other features of the curves are as in Figure 3.

Figure 9.—

Predictions of background selection are insensitive to uncertainty in realistic DDME width estimates. For each assumed DDME shape (x-axis), a corresponding estimate of the location parameter was made from the diversity data. The standard gene structure without neighboring genes was assumed, with r_g = 2.5 × 10⁻⁶. Other features of the curves are as in Figure 3. The bottom three lines belong to the axis on the right. Note that realistic shapes in this case are in the range 20–100, as narrower shapes predict too few lethal mutations and wider shapes predict too many lethal mutations (on the basis of estimates in Loewe and Charlesworth 2006). Details of the assumed DDMEs can be found in Table 1.