Preferential protection of protein interaction network hubs in yeast: evolved functionality of genetic redundancy

Abstract

The widely observed dispensability of duplicate genes is typically interpreted to suggest that a proportion of the duplicate pairs are at least partially redundant in their functions, thus allowing for compensatory affects. However, because redundancy is expected to be evolutionarily short lived, there is currently debate on both the proportion of redundant duplicates and their functional importance. Here, we examined these compensatory interactions by relying on a genome wide data analysis, followed by experiments and literature mining in yeast. Our data, thus, strongly suggest that compensated duplicates are not randomly distributed within the protein interaction network but are rather strategically allocated to the most highly connected proteins. This design is appealing because it suggests that many of the potentially vulnerable nodes that would otherwise be highly sensitive to mutations are often protected by redundancy. Furthermore, divergence analyses show that this association between redundancy and protein connectivity becomes even more significant among the ancient duplicates, suggesting that these functional overlaps have undergone purifying selection. Our results suggest an intriguing conclusion-although redundancy is typically transient on evolutionary time scales, it tends to be preserved among some of the central proteins in the cellular interaction network.

Fig. 1.

Proportion of redundant duplicates as a function of connectivity in the protein interaction network. (A) Proportion of duplicates with a viable knockout phenotype is shown as a function of the number of their physical association partners in the protein interaction network. Plots were calculated separately for genes with duplicates (blue) and singletons (black). For drawing the curve for the duplicate genes, all duplicated genes at each value of degree connectivity were pooled. Then, the proportion of dispensable genes in each pool was computed and shown on the y axis. P values for the two slopes, calculated by means of logistic regression, were 1.4 × 10⁻³⁵ for singletons and 5 × 10⁻⁵ for duplicates. (B) Estimated proportion of redundant duplicates as a function of their connectivity in the protein interaction network (for calculation details, see SI Appendix 2). The P value on the slope calculated by means of logistic regression was 1.5 × 10⁻¹⁰.

Fig. 2.

Joint dependence of gene dispensability on connectivity within the protein interaction network and on expression similarity among paralogs. (A) Proportion of dispensable genes from the total set of paralogs is shown (blue, low proportion of dispensable genes and red, high proportion of dispensable genes) as a function of their degree of connectivity in the protein interaction network and the expression similarity between the paralogous pair members. A version including also the relatively few negatively correlated duplicate pairs is qualitatively similar, although with less statistical power (see SI Fig. 7). (B) P values (plotted in red) illustrating the association between degree connectivity and dispensability were tested for paralogous pair populations and stratified according to expression similarity. These are compared with the P values (plotted in black) illustrating the enrichment of functionally redundant paralogs. The plot was generated by sliding a window of width 0.3, along the expression similarity axis. For statistical details on P value calculations, see Materials and Methods.

Fig. 3.

Results of the synthetic sick and lethal double-knockout experiments. (A) Pairs of dispensable genes for which genetic interaction was tested are connected by a solid red line in cases where SSL interaction was found and by a dashed blue line in cases where no interaction was observed. The hub-paralog pairs are arranged clockwise, starting from 12:00 (hub YJL138C, followed by its paralog YKR059W); all hubs are designated in boldface type. As a negative control, we codeleted hubs and randomly picked paralogs of other hubs. In instances of double knockout of the following hubs (YER081W and YMR105C) and their respective paralogs (YIL074C and YKL127W, respectively), SSL interactions were obtained only in specific growth conditions (lack of serine and galactose as a carbon source, respectively). Four hubs (YER081W, YDL226C, YJL098W, and YOR136W) were found to have two or three paralogs. For these cases, we searched for SSL interactions with all paralogs, yet we never found additional interactions (data not shown). For two hubs, we were unable to examine genetic interactions, either because of the essential nature of the hub itself (YDL047W, which in the database appears as viable, yet in our experiments, with specific genetic background, is extremely sick) or because of very low spore viability (YDL160C). (B) Proportions of the different genetic interactions obtained in all three double-knockout experiments are shown. Highly connected, double-knockout experiments in which both the highly connected gene and its duplicate were deleted; sparsely connected, double-knockout experiments in which both the sparsely connected gene and its duplicate were deleted; random pairs, double-knockout experiments in which both the highly connected gene and a randomly chosen paralog of another hub were deleted; SL, synthetic lethality; conditional SSL, lethality under specific conditions and slow growth; no interaction, no detectable fitness effect under the conditions tested.

Fig. 4.

Relationships among gene dispensability, connectivity, expression similarity, and evolutionary divergence. (A) Dispensability as a function of degree and expression similarity among paralogs (as in Fig. 3A), tested separately for pairs with different Ks values. (B) The proportion of remote (Ks > 1) pairs in each window of degree connectivity. Similarity to data in Fig. 2, all duplicated genes at each value of degree connectivity were pooled. Then, the proportion of genes in each pool that have a remote paralog was computed and shown on the y axis.

Fig. 5.

Proportion of functionally redundant duplicate pairs in a literature curated dataset as a function of their connectivity in the protein interaction network. The data for the analysis consisted of a list of 766 duplicate-gene pairs selected by a sequence similarity criterion (BLAST e value <3 × 10⁻¹⁰⁸). Each of these pairs was subjected to a manual literature examination in search of evidence for functional redundancy. This procedure resulted in 112 redundant pairs. At each degree connectivity, the value at the y axis denotes the fraction of genes with that degree that have an annotated redundant paralog in the set of 112 pairs. Proportions were calculated by normalizing to the total set of curated paralogs, thus avoiding potential biases associated with literature over-representation of highly connected proteins. Both color and size of the data points represent the number of genes in a given category (colors specified by the color bar at Right). Analysis was performed by applying a sliding window of width = 2 on the degree axis.

Fig. 6.

Schematic drawing of a proposed evolutionary time flow chart, describing duplicate retention in the genome.