Difference in gene duplicability may explain the difference in overall structure of protein-protein interaction networks among eukaryotes

Abstract

Background: A protein-protein interaction network (PIN) was suggested to be a disassortative network, in which interactions between high- and low-degree nodes are favored while hub-hub interactions are suppressed. It was postulated that a disassortative structure minimizes unfavorable cross-talks between different hub-centric functional modules and was positively selected in evolution. However, by re-examining yeast PIN data, several researchers reported that the disassortative structure observed in a PIN might be an experimental artifact. Therefore, the existence of a disassortative structure and its possible evolutionary mechanism remains unclear.

Results: In this study, we investigated PINs from the yeast, worm, fly, human, and malaria parasite including four different yeast PIN datasets. The analyses showed that the yeast, worm, fly, and human PINs are disassortative while the malaria parasite PIN is not. By conducting simulation studies on the basis of a duplication-divergence model, we demonstrated that a preferential duplication of low- and high-degree nodes can generate disassortative and non-disassortative networks, respectively. From this observation, we hypothesized that the difference in degree dependence on gene duplications accounts for the difference in assortativity of PINs among species. Comparison of 55 proteomes in eukaryotes revealed that genes with lower degrees showed higher gene duplicabilities in the yeast, worm, and fly, while high-degree genes tend to have high duplicabilities in the malaria parasite, supporting the above hypothesis.

Conclusions: These results suggest that disassortative structures observed in PINs are merely a byproduct of preferential duplications of low-degree genes, which might be caused by an organism's living environment.

Figure 1

Degree distribution of PINs in five eukaryote species. Degree distribution P(k) in the PINs of yeast (black square), worm (magenta plus), fly (blue triangle), human (green cross), and malaria parasite (red diamond). For yeast and human PINs, P(k) for MIPS and Rual et al. datasets, respectively, are shown, because they contain the largest numbers of genes among the PINs for each species. The results for the other yeast and human datasets are provided in Additional file 1: Figure S1. A dashed line represents ${\left(k_0+k\right)}^{-}{}^{\gamma }{\text{e}}^{-k/k_{\text{c}}}$ with γ = 2.7, k₀ = 3.4, and k_C = 50.

Figure 2

Difference in assortativity among eukaryote PINs. (A) <K_nn(k)>, the mean of the degrees among the neighbors of k-degree nodes, in the PINs of yeast (black square), worm (magenta plus), fly (blue triangle), human (green cross), and malaria parasite (red diamond). For yeast and human PINs, <K_nn(k)> for MIPS and Rual et al. datasets, respectively, are shown, and the results for the other yeast and human datasets are provided in Additional file 2: Figure S2. Dashed lines in black, magenta, blue, green, and red represent k^-0.47, k^-0.29, k^-0.35, k^-0.26, and k^-0.02, respectively. (B) Duplication of a node changes the value of ν in <K_nn(k)> ~ k^-ν. A diagram below each network indicates the distribution of <K_nn(k)> and the value of ν. (C) The distribution of <K_nn(k)> in the networks generated by the DDD model with the asymmetric divergence (DDD+A; left) and the symmetric divergence (DDD+S; right). Blue diamonds, green crosses, and red diamonds indicate the results with σ = -0.05 (-0.05), -0.03 (-0.03), and 0 (0), respectively, for DDD+A (DDD+S). These results were obtained by taking the mean among 100 networks generated by simulations. Black squares indicate <K_nn(k)> in the yeast PIN for MIPS. Dashed lines in black, blue, green, and red represent k^-0.47 (k^-0.47), k^-0.51 (k^-0.48), k^-0.37 (k^-0.38), and k^-0.18 (k^-0.26), respectively, for DDD+A (DDD+S).

Figure 3

Degree-dependent duplication (DDD) model. In the DDD model, the probability of a duplication of a node is dependent on the degree of the node. In the network at the left, node A is duplicated to generate node A' with the probability of (1 + 4σ)/1,000, because the degree of node A is four (see Methods). In the asymmetric divergence, each of the links to node A' is removed with a uniform probability α in the divergence process (top, second column). In the symmetric divergence, one of the two duplicated links (e.g. either A-B link or A'-B link) to each node connecting to A and A' (nodes B-E) is eliminated with a probability α (bottom, second column). A new link between nodes A and A' is attached with the probability proportional to the number of common neighbors (n_N) shared by these nodes (third column). In this case, the probability is 2β, because these nodes share two common neighbors (nodes C and D).

Figure 4

Gene duplicability dependent on degrees. Correlation between the degree and the duplicability of proteins in the (A) yeast, (B) worm, (C) fly, (D) human, and (E) malaria parasite PINs. L, M, and H represent low- (k = 1), middle- (k = 2-6), and high-degree (k > 7) proteins, respectively. A vertical axis indicates the mean duplicability in each category. A species name above each diagram denotes the species with which the orthologous relationships were examined. For example, in the top left diagram in (A), gene duplicabilities were investigated using a phylogenetic tree containing S. cerevisiae and S. paradoxus genes. In (A) and (C), the results for MIPS and Rual et al. datasets, respectively, are shown, and those for other yeast and human datasets are provided in Additional file 5: Figure S5. In each diagram, the duplicability of proteins in each category is compared to one another by using the Wilcoxon rank-sum test with the Bonferroni correction. *, P < 0.05; **, P < 0.01; ***, P < 0.001.