Age-Dependent Evolution of the Yeast Protein Interaction Network Suggests a Limited Role of Gene Duplication and Divergence

Wan Kyu Kim,Edward M Marcotte

doi:10.1371/journal.pcbi.1000232

Abstract

Proteins interact in complex protein–protein interaction (PPI) networks whose topological properties—such as scale-free topology, hierarchical modularity, and dissortativity—have suggested models of network evolution. Currently preferred models invoke preferential attachment or gene duplication and divergence to produce networks whose topology matches that observed for real PPIs, thus supporting these as likely models for network evolution. Here, we show that the interaction density and homodimeric frequency are highly protein age–dependent in real PPI networks in a manner which does not agree with these canonical models. In light of these results, we propose an alternative stochastic model, which adds each protein sequentially to a growing network in a manner analogous to protein crystal growth (CG) in solution. The key ideas are (1) interaction probability increases with availability of unoccupied interaction surface, thus following an anti-preferential attachment rule, (2) as a network grows, highly connected sub-networks emerge into protein modules or complexes, and (3) once a new protein is committed to a module, further connections tend to be localized within that module. The CG model produces PPI networks consistent in both topology and age distributions with real PPI networks and is well supported by the spatial arrangement of protein complexes of known 3-D structure, suggesting a plausible physical mechanism for network evolution.

Highlights

Life is highly organized at all levels of molecules, cells, tissues, and organisms, and such relationships among biological entities are often represented as networks, with vertices representing e.g. genes or proteins, and edges representing e.g. physical protein interactions, transcriptional regulation, or metabolic reactions
Several models have been proposed over the past decade—in particular, a ‘‘rich get richer’’ model and a model based upon gene duplication and divergence—often based only on network topologies
We show that real yeast protein interaction networks show a unique age distribution among interacting proteins, which rules out these canonical models

Summary

Introduction

Life is highly organized at all levels of molecules, cells, tissues, and organisms, and such relationships among biological entities are often represented as networks, with vertices representing e.g. genes or proteins, and edges representing e.g. physical protein interactions, transcriptional regulation, or metabolic reactions. The topology of biological networks shows many interesting characteristics, such as scale-free topology (power-law or broad degree distribution) and hierarchical modularity (reviewed in [1]). One important question is how these important network architectures originate, and what driving forces underlie the observed networks It has not been clear whether network architecture results from the mosaic sum of each gene or protein’s inherent properties, such as stickiness or interactive promiscuity [6,7], or from a stochastic mechanism underlying network evolution, in which the trajectory of network evolution is conditioned on the previous state of the network [8]. This problem has been of wide interest because it raises fundamental questions about design principles of molecular networks and the role of natural selection in the evolution of network structure [9]

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