The evolution of protein-protein interactions over time has led to a complex network whose character is modular in the cellular function and highly correlated in its connectivity. The question of the characterization and emergence of modularity following principles of evolution remains an important challenge as there is no encompassing theory to explain the resulting modular topology. Here, we perform an empirical study of the yeast protein-interaction network . We find a novel large-scale URLanization of the functional classes of proteins characterized in terms of scale-invariant laws of modularity. We develop a mathematical framework and demonstrate a relationship between the modular structure and the evolution growth rate of the interactions, conserved proteins , and topological length-scales in the system revealing a hierarchy of mutational events giving rise to the modular topology. These results are expected to apply to other complex networks providing a general theoretical framework to describe their URLanization and dynamics.
Cellular functions are based on the complex interplay of proteins, therefore the structure and dynamics of these protein-protein interaction (PPI) networks are the key to the functional understanding of cells. In the last years, large-scale PPI networks of several URLanisms were investigated. Methodological improvements now allow the analysis of PPI networks of URLanisms simultaneously as well as the direct modeling of ancestral networks. This provides the opportunity to challenge existing assumptions on network evolution. We utilized present-day PPI networks from integrated datasets of seven URLanisms and developed a theoretical and bioinformatic framework for studying the evolutionary dynamics of PPI networks. A novel filtering approach using percolation analysis was developed to remove low confidence interactions based on topological constraints. We then reconstructed the ancient PPI networks of different ancestors, for which the ancestral proteomes, as well as the ancestral interactions, were inferred. Ancestral proteins were reconstructed using orthologous groups on different evolutionary levels. A stochastic approach, using the duplication-divergence model, was developed for estimating the probabilities of ancient interactions from today's PPI networks. The growth rates for nodes, edges, sizes and modularities of the networks indicate multiplicative growth and are consistent with the results from independent static analysis. Our results support the duplication-divergence model of evolution and indicate fractality and multiplicative growth as general properties of the PPI network structure and dynamics.
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The evolution of
Cellular functions are based on the complex interplay of proteins, therefore the structure and dynamics of these
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interactions over time has led to a complex network whose character is modular in the cellular function and highly correlated in its connectivity. The question of
interaction (PPI) networks are the key to
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characterization and emergence of modularity following principles of evolution remains an important challenge as there is no encompassing theory to explain the resulting modular topology. Here, we perform an empirical study of the yeast protein-interaction network . We find a novel
functional understanding of cells. In the last years,
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URLanization of the functional classes of proteins characterized in terms of scale-invariant laws of modularity. We develop a mathematical framework and demonstrate a relationship between the modular structure and the evolution growth rate of the interactions, conserved proteins , and topological length-scales in the system revealing a hierarchy of mutational events giving rise to the modular topology. These results are expected to apply to other complex networks providing a general theoretical framework to describe their URLanization
PPI networks of several URLanisms were investigated. Methodological improvements now allow the analysis of PPI networks of URLanisms simultaneously as well as the direct modeling of ancestral networks. This provides the opportunity to challenge existing assumptions on network evolution. We utilized present-day PPI networks from integrated datasets of seven URLanisms and developed a theoretical and bioinformatic framework for studying the evolutionary dynamics of PPI networks. A novel filtering approach using percolation analysis was developed to remove low confidence interactions based on topological constraints. We then reconstructed the ancient PPI networks of different ancestors, for which the ancestral proteomes, as well as the ancestral interactions, were inferred. Ancestral proteins were reconstructed using orthologous groups on different evolutionary levels. A stochastic approach, using the duplication-divergence model, was developed for estimating the probabilities of ancient interactions from today's PPI networks. The growth rates for nodes, edges, sizes and modularities of the networks indicate multiplicative growth and are consistent with the results from independent static analysis. Our results support the duplication-divergence model of evolution and indicate fractality and multiplicative growth as general properties of the PPI network structure