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

TL;DR

This paper studies a model of protein interaction networks, revealing infinite-order percolation transitions and giant fluctuations, with implications for understanding biological network growth and structure.

Contribution

It introduces a model combining protein duplication and mutation, showing novel infinite-order percolation and fluctuation phenomena in biological networks.

Findings

Infinite-order percolation transition at high link addition rates

Giant structural fluctuations at high duplication rates

Algebraic tail in node degree distribution with rate-dependent exponent

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.