A hypothesis for the origins and evolution of protein complexes. Gene duplication with conservation of protein interactions is frequent [9]. Self-interactions (homomeric interactions) have special structural properties (see text for details) that are conserved into the duplicated interaction between paralogous proteins (light-dark interaction). Interactions between paralogous proteins are more versatile functionally and structurally, and are systematically selected for in evolution. These interactions are central in the establishment and evolution of clusters in PINs and protein complexes.

Clusters in PINs. (a) A small section of a PIN in S. cerevisiae is represented as a graph where nodes correspond to proteins and edges to physical interactions between pairs of proteins. One definition of a module in this work is a highly connected subgraph, such as that shaded in the figure (left), in which the central (green) node has a maximum clustering coefficient (C = 1). A clustering coefficient can be calculated for each protein in the network and measures the number of interactions between neighbors of that protein, divided by the total number of possible interactions between those neighbors. In this example, the green node and its fully connected neighborhood correspond to the protein complex AP-2 [49]. Fully connected subgraphs can also represent interactions that are dissociated in time and/or in space. For example, the shaded cluster on the right represents members of the basic helix-loop-helix transcriptional regulator family, in which duplication of a homodimeric protein with inheritance of interactions resulted in Max existing as a homodimer, as well as distinct dimers of paralogous proteins (c-Myc and Mad1) [34,35]. (b) Cumulative frequency distribution of the clustering coefficients in the Yeast PIN and in randomized networks with exactly the same degree distribution (scale-free random; see the Randomization by link shuffling section in Materials and methods for details). This shows that high clustering of real PINs, and thus their modularity, is a characteristic of their biology and not of the degree distribution. (c) Cartoon illustrating the consequences of duplication with conservation of interactions for the clustering coefficient of node (protein) i (C_i). In each case the network is shown before and after duplication of a protein that either interacts with itself or does not. The bottom part of the cartoon summarizes the effect on the clustering coefficient of the protein. (d) Cumulative frequency distribution of clustering coefficients in the simulated networks, with varying proportions of self-interactors at the start of the simulation. The fraction of proteins with higher clustering coefficients increases with the proportion of self-interactors.

Duplicated subunits in complexes interact. (a) Interactions between paralogous subunits (red) are more frequent than expected given the stoichiometry of subunits within protein complexes. Chains from PQS complexes were binned according to probability of forming a homomeric interaction or interactions between paralogous or different chains (see Materials and methods). The frequencies at which these chains form homodimers and paralogous dimers (averaged for each bin) are shown as blue and red bars, respectively. In a random scenario, all the points lie within the range shown in the black lines. (b) Possible arrangements of two distinct subunits in a hexameric ring like that of the F1 complex. The actual F1 complex is shown on the left. Bars of different colors correspond to different inter-subunit interfaces. (c) If there are multiple identical and paralogous chains within a protein complex, the chains tend to be arranged in three-dimensional space so that the paralogous chains rather than identical chains are contacting each other, corresponding to the scenario shown on the left. Note that when there is a choice, interactions between paralogous proteins are always preferred. This experiment is similar to that described in (a), but considering only the two types of interaction in the calculations. (d) The role of oligomers of paralogues in generating structural diversity. n is the number of protein complexes found in PQS that have identical chains (left) or paralogous chains (right), which contact the same (top) or distinct binding partners (bottom). Hetero-oligomers that contain paralogous dimers are more frequently asymmetrical (10/31) than those containing homomers (6/210), that is, paralogues tend to bind different partners. The complexes shown illustrate the four possible situations. Top left is the tryptophan synthase from Salmonella typhimurium, in which the homomeric α:α dimer (blue) binds one β subunit on each side (yellow) [50], which represents symmetry in binding partners of homomers. Top right is the photosynthetic reaction centre from Rhodopseudomonas viridis, in which both paralogous L and M chains (blue and purple) bind to the H and C subunits (shown in yellow) [51], which illustrates symmetry in the binding partners of a dimer of paralogues. Bottom left is the structure of the Rac1 small GTPase bound to the arfaptin-1 homodimer [52] from Homo sapiens, in which Rac1 binds solely one of the arfaptin chains, but occupies a volume that excludes the possibility of additional Rab molecules binding the other arfaptin chain; this illustrates the rare cases of asymmetry in the binding partners of homomers. Bottom right is the RNA polymerase from S. cerevisiae [53], in which many peripheral subunits decorate the central core formed by the dimer of paralogues A:B, which illustrates the creation of asymmetry by the duplication of the ancestral homodimer [32].

Dimers of paralogues in the protein-protein interaction network. On top is a cartoon illustrating how paralogous dimers result from the duplication of proteins that form homodimers. The bar chart shows the fraction of paralogous dimers (gray bars) in four protein interaction networks compared with random expectation levels, obtained by 10,000 network randomizations by shuffling evolutionary relationships (p < 10^-4; see Materials and methods for details).

Duplication of subunits in protein complexes. (a) Nearly 40% of the protein complexes have homologous subunits (gray bars). These levels are higher than expected by chance (white bars). Random expectation levels are the averages of 10,000 randomized protein complex datasets, where the complex size distribution is kept constant. While the MIPS dataset is the result of manual curation (see table 1), both TAP and HMS-PCI are the result of large-scale experiments, and some redundancy may exist from multiple baits picking up the same complex. For the TAP dataset, the authors provide a smaller set of predicted complexes based on bioinformatics methods. We repeated the calculation on this set of predicted TAP complexes and found that 47% of the complexes have duplicated subunits, while 18 ± 2% would be expected at random. The significance level remains the same for this predicted set of complexes as for the raw purification data. (b) Percentage of complexes of known three-dimensional structure that have duplicated subunits, as a function of complex size. Grey bars are for the complete data set, whereas black bars are from a dataset that excludes purely homomeric complexes, as these dominate the dataset (see Table 1) and may distort the results. On average, between 9% and 30% of the complexes display duplicated subunits (including and excluding purely homomeric complexes, respectively). This is not an artifact introduced by the complex size distribution.