Large Scale Topological Properties of Molecular Networks

Sergei Maslov* and Kim Sneppen Abstract

Bio-molecular networks lack the top-down design. Instead, selective forces of biological evolution shape them from raw material provided by random events such as gene duplications and single gene mutations. As a result individual connections in these networks are characterized by a large degree of randomness. One may wonder which connectivity patterns are indeed random, while which arose due to the network growth, evolution, and/or its fundamental design principles and limitations?

Here we introduce a general method allowing one to construct a random null-model version of a given network while preserving the desired set of its low-level topological features, such as, e.g., the number of neighbors of individual nodes, the average level of modularity, preferential connections between particular groups of nodes, etc. Such a null-model network can then be used to detect and quantify the nonrandom topological patterns present in large networks.

In particular, we measured correlations between degrees of interacting nodes in protein interaction and regulatory networks in yeast. It was found that in both these networks, links between highly connected proteins are systematically suppressed. This effect decreases the likelihood of cross-talk between different functional modules of the cell, and increases the overall robustness of a network by localizing effects of deleterious perturbations. It also teaches us about the overall computational architecture of such networks and points at the origin of large differences in the number of neighbors of individual nodes.

Introduction

Complex networks appear in biology on many different levels:

• All biochemical reactions taking place in a single cell constitute its metabolic network, where nodes are individual metabolites, and edges are metabolic reactions converting them to each other.

• Virtually every one of these reactions is catalyzed by an enzyme and the specificity of this catalytic function is ensured by the key and lock principle of the physical interaction with its substrate. Often the functional enzyme is formed by several mutually interacting proteins. Thus the structure of the metabolic network is shaped by the network of physical interactions of cell's proteins with their substrates and each other.

'Corresponding author: Sergei Maslov—Department of Physics, Brookhaven National Laboratory, Upton, New York 11973, U.S.A. Email: [email protected]

Power Laws, Scale-Free Networks and Genome Biology, edited by Eugene V. Koonin, Yuri I. Wolf and Georgy P. Karev. ©2006 Eurekah.com and Springer Science+Business Media.

• The abundance and the level of activity of each of the proteins in the physical interaction network in turn is controlled by the regulatory network of the cell. Such regulatory network includes all of the multiple mechanisms in which proteins in the cell exert control on each other including transcriptional and translational regulation, regulation of mRNA editing and its transport out of the nucleus, specific targeting of individual proteins for degradation, modification of their activity e.g., by phosphorylation/dephosphorylation or allosteric regulation, etc.

• On yet higher level individual cells in a multicellular organism exchange signals with each other. This gives rise to several new networks such as e.g., nervous, hormonal, and immune systems of animals. The inter-cellular signaling network stages the development of a multicellular organism from the fertilized egg.

• Finally, on the grandest scale, the interactions between individual species in ecosystems determine their food webs.

In this review we concentrate on large-scale topological properties of complex biological networks operating on the levels of physical protein-protein interactions and transcriptional regulation.

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