Robustness leads close to the edge of chaos in coupled map networks: toward the understanding of biological networks

Nen Saito,Macoto Kikuchi

doi:10.1088/1367-2630/15/5/053037

Abstract

Dynamics in biological networks are, in general, robust against several perturbations. We investigate a coupled map network as a model motivated by gene regulatory networks and design systems that are robust against phenotypic perturbations (perturbations in dynamics), as well as systems that are robust against mutation (perturbations in network structure). To achieve such a design, we apply a multicanonical Monte Carlo method. Analysis based on the maximum Lyapunov exponent and parameter sensitivity shows that systems with marginal stability, which are regarded as systems at the edge of chaos, emerge when robustness against network perturbations is required. This emergence of the edge of chaos is a self-organization phenomenon and does not need a fine tuning of parameters.

Highlights

Complex dynamical behaviors on a network can be found in a variety of biological networks, such as gene regulatory networks, neural networks and food-web
We investigate a coupled chaotic map network motivated by gene regulatory networks and show that systems at the edge of chaos are selected with only the requirement of robustness against network perturbations
Using multicanonical Monte Carlo method, we have observed emergence of the systems at the edge of chaos as a self-organization phenomenon with only the requirement of robustness against network perturbations, which can be interpreted as mutational robustness in the context of the gene regulatory network

Summary

Introduction

Complex dynamical behaviors on a network can be found in a variety of biological networks, such as gene regulatory networks, neural networks and food-web. Such systems share a common characteristic: observed dynamics are robust against disturbance introduced in its dynamics, as well as against disturbance in its network [1, 2, 3]. Robustness in biological networks has attracted much attention of many researchers and has been thought to be one of fundamental properties of life [1, 2, 3, 4]

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Methods

Conclusion