From Network Structure to Dynamics and Back Again: Relating dynamical stability and connection topology in biological complex systems

TL;DR

This paper explores how the structure of biological networks influences their dynamics and how dynamical stability constrains network topology, revealing that natural networks evolve to modular, hub-rich configurations.

Contribution

It reviews recent work demonstrating the bidirectional relationship between network structure and dynamics in biological systems, highlighting the evolution of optimal, modular networks.

Findings

Network structure dictates dynamical behavior.

Dynamical constraints limit possible network topologies.

Biological networks tend to evolve modular, hub-rich configurations.

Abstract

The recent discovery of universal principles underlying many complex networks occurring across a wide range of length scales in the biological world has spurred physicists in trying to understand such features using techniques from statistical physics and non-linear dynamics. In this paper, we look at a few examples of biological networks to see how similar questions can come up in very different contexts. We review some of our recent work that looks at how network structure (e.g., its connection topology) can dictate the nature of its dynamics, and conversely, how dynamical considerations constrain the network structure. We also see how networks occurring in nature can evolve to modular configurations as a result of simultaneously trying to satisfy multiple structural and dynamical constraints. The resulting optimal networks possess hubs and have heterogeneous degree distribution similar to those seen in biological systems.