Figure 1.
Model of evolution after gene duplication.
After whole genome duplication (A), duplicated genes preserve their functions (and therefore genetic interactions: here indicated with colour-labelled circles) interacting (indicated by solid lines between circles) with their partners (x, m, w, z). The partners of a duplicated gene also interact functionally with one another (dashed lines) and are stoichiometrically balanced. Because of genetic redundancy, stochastic loss of genes (functions) takes place, with the final combinations of genes being preserved if they satisfy the overall stoichiometric balance of the cell, with complete partitioning of ancestral functions between the two gene copies (sub-functionalization) being the extreme solution. (B) Duplication of one or few genes in the genome (also known as small-scale duplication: SSD) generates genetic robustness (phenotype resistance to loosing one of the gene copies) if the stoichiometry is not dramatically unbalanced after duplication. This genetic robustness imposes a selective pressure to keep a large overlap in the genetic interaction patterns (functions) of gene copies. The persistence of both gene copies in the genome for long evolutionary periods allows the functional divergence of one gene copy (á) and the acquisition of novel functions (novel genetic interactions: k and f).
Figure 2.
Gene duplicated by small-scale duplications (SSD) present a larger number of genetic interactions (#GI) than those duplicated by whole-genome duplication (WGD) and singletons.
(A) Gene duplicated by small-scale duplications (SSD) present a larger number of genetic interactions (#GI) than those duplicated by whole-genome duplication (WGD) and singletons. (B) To determine whether greater genetic redundancy of WGDs may spuriously generate lower number of genetic interactions, we generated bins of duplicated genes according to the JTT amino acid divergences between the gene copies. These bins ranged between 0.4 (that included duplicated genes with the two copies diverging up to 0.4 substitutions per site) and 1.8 (when the divergence between the gene copies was equal or greater than 1.8 amino acid substitutions per site). We noticed no significant differences in the number of genetic interactions between the different bins. (C) The epistatic effects (ε), both positive epistasis (ε+) and negative epistasis (ε−), of singletons were stronger than those of SSD and WGDs, and the effects of SSDs were stronger than those of WGDs. Differences in the number of genetic interactions (#GI) or their effects between the three categories of genes (singletons, SSD and WGD) were identified using Wilcoxon rank test.
Figure 3.
Distinct functional fates for genes duplicated by small-scale duplication (SSD) and whole-genome duplication (WGD).
(A) After the duplication of a gene by SSD (circles), one of the gene copies (black circle) maintains the ancestral functions (squares), while the other (white circle) loses (discontinuous lines) some ancestral functions while establishing novel genetic interactions (functions) through the process of neo-functionalization. (B) Genes duplicated by WGD sub-functionalize through the partitioning of ancestral functions so that each gene copy specializes in a subset of the ancestral functions.
Figure 4.
Small-scale duplication (SSD) generates gene copies sharing more ancestral functions than whole-genome duplication (WGD).
We tested the partitioning of ancestral functions after duplication by SSD and WGD. We calculated partitioning of ancestral functions by estimating the proportion of shared genetic interactions between the copies of a duplicated gene. This proportion was calculated as ΘSSD|WGD = (2nS(i,j))/(GIi+GIj), with nS(i,j) being the number of genetic interactions (GI) in common between gene copies i and j. To determine the significance of this partitioning (or sharing) we compared ΘSSD|WGD to that calculated for a distribution of such values estimated from 106 randomly paired singletons. WGDs shared on average (solid green arrow line) as many GIs as random pairs of singletons (for example, the mean indicated by an arrow is within the 90% density of the curve), indicating that they have partitioned their ancestral functions to a point that they could be almost considered as singletons. Conversely, SSD gene copies share ancestral functions (solid red arrow line) significantly more than expected by chance (indicated by asterisks *). The classification of the average number of shared partners between duplicates for different categories of amino acid sequence divergence (amino acid divergence between duplicates was estimated using JTT model) followed the same patterns, with all divergence bins (bins were built with 0.2 divergence levels intervals, except for the first bin) of WGDs (green dashed lines) being not significant while bins of SSDs (red dashed lines) being significant (*: P<0.01, **: P<10−6).
Figure 5.
Interaction partners of duplicated genes are more functionally related than those of singletons.
(A) We calculated the functional relatedness of the interaction partners (blue circles) of a gene as the proportion of links (l) between these partners (black thick lines) taking into account the number of partners (n): k = 2l/n(n−1). For example, in (A), there are 7 links between the 5 partners of a gene (black circle), which yields k = 2×7/5×4 = 0.7. (B) Clustering coefficients for singletons, small-scale duplications (SSDs) and whole-genome duplications (WGDs). The columns represent the mean clustering coefficient and the standard error of the mean associated to that particular set of genes. Probabilities were calculated by the Wilcoxon rank test. Duplicates interact with genes more functionally related than those with which singletons interact. SSDs interact with genes that are more functionally dispersed (unrelated) than the interaction partners of WGDs.
Figure 6.
Distribution of single nucleotide polymorphisms in a mutation-accumulation experiment.
(A) Normalized mean number of single nucleotide polymorphisms (SNPs) per chromosome after experimental evolution of 5 S. cerevisiae lineages for up to 2200 generations. The number of SNPs per chromosome was normalized by length to that of the longest chromosome (chrIV) and error bars represent the standard deviation. (B) The number of SNPs detected in the genome of each lineage increased linearly with the number of generations for total, non-synonymous and synonymous SNPs. (C) The fraction of SSDs (black columns) and WGDs (grey columns) affected by non-synonymous single nucleotide polymorphisms (Nsyn-SNPs) across the five mutation-accumulation (MA1 to MA5) experimental lines. In all five MA lines, the fraction of SSDs with Nsyn-SNPs is larger than that of WGDs. The fraction of SSDs that have fixed Nsyn-SNPs is significantly larger than that of WGDs in four of the five MA experimental lines (significance is indicated by * = P<0.05; ** = P<0.01 and *** = P<0.001).