Commensurate distances and similar motifs in genetic congruence and protein interaction networks in yeast

Background In a genetic interaction, the phenotype of a double mutant differs from the combined phenotypes of the underlying single mutants. When the single mutants have no growth defect, but the double mutant is lethal or exhibits slow growth, the interaction is termed synthetic lethality or synthetic fitness. These genetic interactions reveal gene redundancy and compensating pathways. Recently available large-scale data sets of genetic interactions and protein interactions in Saccharomyces cerevisiae provide a unique opportunity to elucidate the topological structure of biological pathways and how genes function in these pathways. Results We have defined congruent genes as pairs of genes with similar sets of genetic interaction partners and constructed a genetic congruence network by linking congruent genes. By comparing path lengths in three types of networks (genetic interaction, genetic congruence, and protein interaction), we discovered that high genetic congruence not only exhibits correlation with direct protein interaction linkage but also exhibits commensurate distance with the protein interaction network. However, consistent distances were not observed between genetic and protein interaction networks. We also demonstrated that congruence and protein networks are enriched with motifs that indicate network transitivity, while the genetic network has both transitive (triangle) and intransitive (square) types of motifs. These results suggest that robustness of yeast cells to gene deletions is due in part to two complementary pathways (square motif) or three complementary pathways, any two of which are required for viability (triangle motif). Conclusion Genetic congruence is superior to genetic interaction in prediction of protein interactions and function associations. Genetically interacting pairs usually belong to parallel compensatory pathways, which can generate transitive motifs (any two of three pathways needed) or intransitive motifs (either of two pathways needed).


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Supp. Randomizations were conducted as shown in Supp. Fig. S3. Transitive motifs triad2 (triangle) and tetrad6 (4-clique) have significantly higher counts in the observed network than the random networks. Intransitive motifs triad1, tetrad1, tetrad2, and tetrad4 have lower counts in the observed network than the random networks. Supp. Fig.  S5C Supp. Fig. S1. The distribution of network size over different congruence scores or confidence scores for congruence and protein networks.
Supp. Fig. S2 -Prediction of high confidence protein interaction (with confidence score greater than 0.5 [2]) using congruence score is presented as a receiver operating characteristic (ROC) curve.
The numbers labeled next to the symbols are cut-off values for congruence scores.
Supp. Fig. S3. Randomization scheme. The observed synthetic lethal interaction network was randomized 100 times keeping the mean number of interaction partners fixed for each gene, congruence scores were calculated for each of the 100 randomized networks, and congruence networks were constructed by choosing a threshold that yielded as many congruence edges as in the observed network. The mean thresholds were 3.2 (asymmetric) and 1.8 (symmetric), compared with 8 (asymmetric) and 6 (symmetric) for the observed congruence network. Motifs counts in the observed congruence network and the congruence network constructed from the randomized networks are compared in Supp. Table S3. The patterns of motif enrichment are compared in Supp. Fig. S4.
Supp. Fig. S4. Motif enrichment in congruence networks constructed from random networks. Congruence networks were constructed from a series of 100 randomized synthetic lethal interaction networks (see Supp. Fig. S3 and Supp. Table S3). The motif enrichment for the random networks displays a different pattern from the observed network. Although triad2 (triangle) is enriched in the observed and random networks, the raw number of triangles is far larger in the observed network (Supp. Table S3). The intransitive motif tetrad4 (square) is depleted in the observed network and enriched in the random networks, and the transitive motif tetrad6 (4-clique) is enriched in the observed network and depleted in the random networks.
A B C Supp. Fig. S5. By using highest score path distance in protein network, the path length is still incommensurate for genetic and protein networks but commensurate for congruence and protein networks. A. The path distance in the protein network slightly declines with the corresponding distance in the genetic network (compare with Fig. 2A). B. The path distance in the protein network increases monotonically with congruence score (compare with Fig. 2C). C. The path distance in the protein network increases with the corresponding distance in the congruence network (compare with Fig. 2D). Results are displayed for the observed and randomized networks. Error bars indicate one standard error. The random value if present is comparable to the observed value (P-value > 0.05).
Supp. Fig. S6. The distribution of probability for protein interaction given the congruence score in the asymmetric congruence network.
The blue circles indicate the probability, which is fit with the sigmoid function represented by the red curve. The values a = 13.5 and b = 5 were used for the distance calculation in the asymmetric congruence network instead of the best-fit values a = 15.9 and b = 1.6 (compare A with Figure  2D, and B with Figure S4C for asymmetric congruence network).