July 25, 2006
Major advances in large-scale yeast two hybrid (Y2H) screening have provided a global view of binary protein-protein interactions across species as dissimilar as human, yeast, and bacteria. Remarkably, these analyses have revealed that all species studied have a degree distribution of protein-protein binding that is approximately scale-free (varies as a power law) even though their evolutionary divergence times differ by billions of years. The universal power-law shows only the surface of the rich information harbored by these high-throughput data. We develop a detailed mathematical model of the protein-protein interaction network based on association free energy, the biochemical quantity that determines protein-protein interaction strength. This model reproduces the degree distribution of all of the large-scale Y2H data sets available and allows us to extract the distribution of free energy, the likelihood that a pair of proteins of a given species will bind. We find that across-species interactomes have significant differences that reflect the strengths of the protein-protein interaction. Our results identify a global evolutionary shift: more evolved organisms have weaker binary protein-protein binding. This result is consistent with the evolution of increased protein unfoldedness and challenges the dogma that only specific protein-protein interactions can be biologically functional..
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September 23, 2003
We present a simple model for the underlying structure of protein-protein pairwise interaction graphs that is based on the way in which proteins attach to each other in experiments such as yeast two-hybrid assays. We show that data on the interactions of human proteins lend support to this model. The frequency of the number of connections per protein under this model does not follow a power law, in contrast to the reported behaviour of data from large scale yeast two-hybrid s...
July 30, 2002
The structure of molecular networks derives from dynamical processes on evolutionary time scales. For protein interaction networks, global statistical features of their structure can now be inferred consistently from several large-throughput datasets. Understanding the underlying evolutionary dynamics is crucial for discerning random parts of the network from biologically important properties shaped by natural selection. We present a detailed statistical analysis of the prote...
August 31, 2005
It has recently been demonstrated that many biological networks exhibit a scale-free topology where the probability of observing a node with a certain number of edges (k) follows a power law: i.e. p(k) ~ k^-g. This observation has been reproduced by evolutionary models. Here we consider the network of protein-protein interactions and demonstrate that two published independent measurements of these interactions produce graphs that are only weakly correlated with one another de...
July 12, 2002
The next step in the understanding of the genome organization, after the determination of complete sequences, involves proteomics. The proteome includes the whole set of protein-protein interactions, and two recent independent studies have shown that its topology displays a number of surprising features shared by other complex networks, both natural and artificial. In order to understand the origins of this topology and its evolutionary implications, we present a simple model...
January 5, 2009
We test the claim by Yu et al. -- presented in Science 322, 104 (2008) -- that the degree distribution of the yeast (Saccharomyces cerevisiae) protein-interaction network is best approximated by a power law. Yu et al. consider three versions of this network. In all three cases, however, we find the most likely power-law model of the data is distinct from and incompatible with the one given by Yu et al. Only one network admits good statistical support for any power law, and in...
April 9, 2003
The budding yeast {\it Saccharomyces cerevisiae} is the first eukaryote whose genome has been completely sequenced. It is also the first eukaryotic cell whose proteome (the set of all proteins) and interactome (the network of all mutual interactions between proteins) has been analyzed. In this paper we study the structure of the yeast protein complex network in which weighted edges between complexes represent the number of shared proteins. It is found that the network of prot...
February 11, 2004
We employed the random graph theory approach to analyze the protein-protein interaction database DIP (Feb. 2004), for seven species (S. cerevisiae, H. pylori, E. coli, C. elegans, H. sapiens, M. musculus and D. melanogaster). Several global topological parameters (such as node connectivity, average diameter, node connectivity correlation) were used to characterize these protein-protein interaction networks (PINs). The logarithm of the connectivity distribution vs. the logarit...
June 26, 2006
Successive whole genome duplications have recently been firmly established in all major eukaryote kingdoms. It is not clear, however, how such dramatic evolutionary process has contributed to shape the large scale topology of protein-protein interaction (PPI) networks. We propose and analytically solve a generic model of PPI network evolution under successive whole genome duplications. This demonstrates that the observed scale-free degree distributions and conserved multi-pro...
July 3, 2005
The degree distribution of many biological and technological networks has been described as a power-law distribution. While the degree distribution does not capture all aspects of a network, it has often been suggested that its functional form contains important clues as to underlying evolutionary processes that have shaped the network. Generally, the functional form for the degree distribution has been determined in an ad-hoc fashion, with clear power-law like behaviour ofte...
January 6, 2015
We model the evolution of eukaryotic protein-protein interaction (PPI) networks. In our model, PPI networks evolve by two known biological mechanisms: (1) Gene duplication, which is followed by rapid diversification of duplicate interactions. (2) Neofunctionalization, in which a mutation leads to a new interaction with some other protein. Since many interactions are due to simple surface compatibility, we hypothesize there is an increased likelihood of interacting with other ...