Dynamics and processing in finite self-similar networks

Author:

DeDeo Simon1,Krakauer David C.231

Affiliation:

1. Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA

2. Department of Genetics, University of Wisconsin, Madison, WI 53706, USA

3. Wisconsin Institute for Discovery, University of Wisconsin, Madison, WI 53706, USA

Abstract

A common feature of biological networks is the geometrical property of self-similarity. Molecular regulatory networks through to circulatory systems, nervous systems, social systems and ecological trophic networks show self-similar connectivity at multiple scales. We analyse the relationship between topology and signalling in contrasting classes of such topologies. We find that networks differ in their ability to contain or propagate signals between arbitrary nodes in a network depending on whether they possess branching or loop-like features. Networks also differ in how they respond to noise, such that one allows for greater integration at high noise, and this performance is reversed at low noise. Surprisingly, small-world topologies, with diameters logarithmic in system size, have slower dynamical time scales, and may be less integrated (more modular) than networks with longer path lengths. All of these phenomena are essentially mesoscopic, vanishing in the infinite limit but producing strong effects at sizes and time scales relevant to biology.

Publisher

The Royal Society

Subject

Biomedical Engineering,Biochemistry,Biomaterials,Bioengineering,Biophysics,Biotechnology

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