Abstract
BackgroundSuccessive whole genome duplications have recently been firmly established in all major eukaryote kingdoms. Such exponential evolutionary processes must have largely contributed to shape the topology of protein-protein interaction (PPI) networks by outweighing, in particular, all time-linear network growths modeled so far.ResultsWe propose and solve a mathematical model of PPI network evolution under successive genome duplications. This demonstrates, from first principles, that evolutionary conservation and scale-free topology are intrinsically linked properties of PPI networks and emerge from i) prevailing exponential network dynamics under duplication and ii) asymmetric divergence of gene duplicates. While required, we argue that this asymmetric divergence arises, in fact, spontaneously at the level of protein-binding sites. This supports a refined model of PPI network evolution in terms of protein domains under exponential and asymmetric duplication/divergence dynamics, with multidomain proteins underlying the combinatorial formation of protein complexes. Genome duplication then provides a powerful source of PPI network innovation by promoting local rearrangements of multidomain proteins on a genome wide scale. Yet, we show that the overall conservation and topology of PPI networks are robust to extensive domain shuffling of multidomain proteins as well as to finer details of protein interaction and evolution. Finally, large scale features of direct and indirect PPI networks of S. cerevisiae are well reproduced numerically with only two adjusted parameters of clear biological significance (i.e. network effective growth rate and average number of protein-binding domains per protein).ConclusionThis study demonstrates the statistical consequences of genome duplication and domain shuffling on the conservation and topology of PPI networks over a broad evolutionary scale across eukaryote kingdoms. In particular, scale-free topologies of PPI networks, which are found to be robust to extensive shuffling of protein domains, appear to be a simple consequence of the conservation of protein-binding domains under asymmetric duplication/divergence dynamics in the course of evolution.
Highlights
Successive whole genome duplications have recently been firmly established in all major eukaryote kingdoms
About 90% of the initial pairs of duplicated proteins from this whole genome duplications (WGDs) have since undergone reciprocal gene loss, leaving about 549 remaining pairs in the extant genome, amongst which 259 have both duplicated proteins included in the available protein-protein interaction (PPI) network [38]
The same trend has been reported when considering protein pairs with a significant sequence homology [40]. This direct experimental evidence for the effect of WGD on PPI network evolution is even more compelling when considering protein pairs sharing more than one partner in the PPI network; for instance, duplicated pairs from this 150 MY-old WGD are about 1,000 times more likely to share 10 or more partners as compared to randomly picked pairs of the PPI network, Fig. 1
Summary
Mathematical solution of the modelOur formal approach is based on the use of generating functions to capture the statistical properties of emergingPPI networks under WGD. The generating function of the average number of protein nodes with k binding partners after n WGD steps is defined as, (7) k≥0. As discussed in Results, a general model for PPI network evolution under WGD allows for an asymmetric divergence of duplicated genes, Fig. 2. Since each node is initially duplicated, F(n+1)(x), which essentially counts the number of nodes according to their degree k ≥ 0, is the sum of two F(n)(x) corresponding, respectively, to the "old" and "new" nodes in the duplicated network. At each WGD step (n) (n + 1), the generating function recurrence for PPI network evolution with asymmetric divergence of duplicated proteins becomes Eq 8 (see Supporting Information for proof details)
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