Analysis of feedback loops and robustness in network evolution based on Boolean models.

Yung-Keun Kwon,Kwang-Hyun Cho

doi:10.1186/1471-2105-8-430

Yung-Keun Kwon, Kwang-Hyun Cho

Open Access

https://doi.org/10.1186/1471-2105-8-430

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Abstract

BackgroundMany biological networks such as protein-protein interaction networks, signaling networks, and metabolic networks have topological characteristics of a scale-free degree distribution. Preferential attachment has been considered as the most plausible evolutionary growth model to explain this topological property. Although various studies have been undertaken to investigate the structural characteristics of a network obtained using this growth model, its dynamical characteristics have received relatively less attention.ResultsIn this paper, we focus on the robustness of a network that is acquired during its evolutionary process. Through simulations using Boolean network models, we found that preferential attachment increases the number of coupled feedback loops in the course of network evolution. Whereas, if networks evolve to have more coupled feedback loops rather than following preferential attachment, the resulting networks are more robust than those obtained through preferential attachment, although both of them have similar degree distributions.ConclusionThe presented analysis demonstrates that coupled feedback loops may play an important role in network evolution to acquire robustness. The result also provides a hint as to why various biological networks have evolved to contain a number of coupled feedback loops.

Highlights

Many biological networks such as protein-protein interaction networks, signaling networks, and metabolic networks have topological characteristics of a scale-free degree distribution
The simulations showed that the networks evolved by preferential attachment (PA) are more robust and produce more coupled feedback loops than random networks
To further investigate this relationship, we have examined the networks evolved by the "Feedback" model which favors a larger number of feedback loops under a selection pressure (D). (In this simulation, three values, 1, 10, and 30, were chosen for D) Compared with the networks evolved using the "PA" model, the networks evolved using the Feedback" model showed very similar results for D = 1 with respect to both robustness and the number of coupled feedback loops

Summary

Introduction

Many biological networks such as protein-protein interaction networks, signaling networks, and metabolic networks have topological characteristics of a scale-free degree distribution. There have been various studies on the topological properties of biological networks, and one prominent result is about the scale-free property indicating the power-law distribution in the number of connections (degree) per network node [7]. In this regard, finding a network growth model that can produce a scale-free network has become an issue. Preferential attachment, a way of adding new interactions to a network node in proportion to the connectivity of the node (i.e. the number of links connected to the node), has (page number not for citation purposes)

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Results

Conclusion