Balance of positive and negative regulation for trade-off between efficiency and resilience of high-dimensional networks

Abstract

The study of resilience for high-dimensional systems is a challenging problem in physical sciences. Although a generic dimensional reduction method has been proposed to study the resilience of large-scale networks, an important yet unsolved question is how different types of regulation affect network resilience. Here we propose a new method to reduce the size of a large-scale regulatory network to the number of regulation types in the system. For each type of regulation, a symbolic variable is introduced to represent the function of that regulation in determining the resilience of the high-dimensional network. Using the genetic networks in Escherichia coli and Saccharomyces cerevisiae as the test systems, we examine how positive and negative regulation affect the resilience of these systems. Analytical and numerical studies suggest that the reduction of positive regulation deteriorates network resilience, while the decline of negative regulation enhances the resilience property. More importantly, we show that there is a trade-off between network efficiency and resilience, which is supported by the balance of positive and negative regulation. The proposed method provides a general framework to evaluate the key role of different regulatory mechanisms in determining the resilience of high-dimensional networks.