Infinite-Order Percolation and Giant Fluctuations in a Protein Interaction Network

Abstract

We investigate a model protein interaction network whose links represent interactions between individual proteins. This network evolves by the functional duplication of proteins, supplemented by random link addition to account for mutations. When link addition is dominant, an infinite-order percolation transition arises as a function of the addition rate. In the opposite limit of high duplication rate, the network exhibits giant structural fluctuations in different realizations. For biologically-relevant growth rates, the node degree distribution has an algebraic tail with a peculiar rate dependence for the associated exponent.

4 pages, 2 figures, 2 column revtex format, to be submitted to PRL 1; reference added and minor rewording of the first paragraph; Title change and major reorganization (but no result changes) in response to referee comments; to be published in PRE

References in corpus (5)

• Statistical mechanics of complex networks
• Lethality and centrality in protein networks
• Evolution of networks
• Are randomly grown graphs really random?
• Anomalous percolating properties of growing networks

Cited by in corpus (68)

• The structure and function of complex networks
• Critical phenomena in complex networks
• Growing networks with local rules: preferential attachment, clustering hierarchy and degree correlations
• Classification of scale-free networks
• Percolation on complex networks: Theory and application
• Preferential attachment in the protein network evolution
• Duplication-divergence model of protein interaction network
• Inverted Berezinskii-Kosterlitz-Thouless Singularity and High-Temperature Algebraic Order in an Ising Model on a Scale-Free Hierarchical-Lattice Small-World Network
• Percolation on correlated networks
• Vertex Intrinsic Fitness: How to Produce Arbitrary Scale-Free Networks
• Construction and Analysis of Random Networks with Explosive Percolation
• A simple physical model for scaling in protein-protein interaction networks
• Potts model on complex networks
• Recent advances of percolation theory in complex networks
• Structural Transitions in Dense Networks
• Percolation transition in networks with degree-degree correlation
• Phase Transition with the Berezinskii--Kosterlitz--Thouless Singularity in the Ising Model on a Growing Network
• Wikipedia information flow analysis reveals the scale-free architecture of the Semantic Space
• Logarithmic growth dynamics in software networks
• The evolutionary dynamics of protein-protein interaction networks inferred from the reconstruction of ancient networks
• Densification and Structural Transitions in Networks that Grow by Node Copying
• BKT-like transition in the Potts model on an inhomogeneous annealed network
• Tree Networks with Causal Structure
• Dense Power-law Networks and Simplicial Complexes
• Spatially distributed social complex networks
• Solution of the explosive percolation quest. II. Infinite-order transition produced by the initial distributions of clusters
• Homological percolation transitions in growing simplicial complexes
• Cliques and duplication-divergence network growth
• Evolving networks through deletion and duplication
• Complex networks created by aggregation
• The distribution of shortest path lengths in a class of node duplication network models
• Growing Scale-free Networks by a Mediation-Driven Attachment Rule
• Some asymptotic properties of duplication graphs
• Degree Distribution, Rank-size Distribution, and Leadership Persistence in Mediation-Driven Attachment Networks
• Designer Nets from Local Strategies
• Global organization of protein complexome in the yeast Saccharomyces cerevisiae
• Identifying time dependence in network growth
• First Passage Properties of the Polya Urn Process
• On Gene Duplication Models for Evolving Regulatory Networks
• Analytical results for the distribution of shortest path lengths in directed random networks that grow by node duplication
• Large-scale behavior of the partial duplication random graph
• Percolation and Loop Statistics in Complex Networks
• A Structure-Centric View of Protein Evolution, Design and Adaptation
• Percolation properties of growing networks under an Achlioptas process
• Profile and scaling of the fractal exponent of percolations in complex networks
• Laplacian Spectrum and Protein-Protein Interaction Networks
• Modelling temporal and spatial features of collaboration network
• Emergence of Robust and Efficient Networks in a Family of Attachment Models
• The Emergence of Scaling in Sequence-based Physical Models of Protein Evolution
• Analytical results for the in-degree and out-degree distributions of directed random networks that grow by node duplication
• Greedy Connectivity of Geographically Embedded Graphs
• Modeling spatial social complex networks for dynamical processes
• The Magic of Networks Grown by Redirection
• A network model with structured nodes
• Degree-ordered percolation on hierarchical scale-free network
• Growing Hypergraphs with Preferential Linking
• Percolation transitions with nonlocal constraint
• Sensitivity dependent model of protein-protein interaction networks
• Asymptotic behavior of the node degrees in the ensemble average of adjacency matrix
• Percolation Transitions in Growing Networks Under Achlioptas Processes: Analytic Solutions
• Simple evolving random graphs
• Monochromaticity in Neutral Evolutionary Network Models
• Growing Networks with Super-Joiners
• On role extraction for digraphs via neighbourhood pattern similarity
• Critical Percolation Phase and Thermal BKT Transition in a Scale-Free Network with Short-Range and Long-Range Random Bonds
• Scale- free networks in cell biology
• Nonreciprocal random networks and their percolation properties
• Anomalous percolation transitions beyond the BKT transition in growing networks