Graph Theory Properties of Cellular Networks - Systems Biology Concepts and Insights - page 167

Chapter 9

Graph Theory Properties of Cellular
Networks

Baruch Barzel, 1 , 2 Amitabh Sharma 1 , 2 and Albert-L ´ szl ´ Barab ´si 1 , 2
1 Center for Complex Network Research, Department of Physics, Northeastern University, 360 Huntington avenue, Boston, Massachusetts 02115, USA,
2 Center for Cancer System Biology (CCSB) and Department of Cancer Biology, the Dana-Farber Cancer Institute and Department of Genetics, Harvard
Medical School, 44 Binney street, Boston, Massachusetts, USA

Chapter Outline
Introduction 177 Party vs. Date Hubs 184

Biological Systems As Graphs 178 Degree Correlations 184

The Tools of Graph Theory 178 Human Disease Network 185

Erd seR´nyi e The Benchmark Network 178 The Building Blocks of Cellular Networks 186

T

Degrees and Degree Distribution 178 Sub-graphs and Motifs 186

Network Paths and the Small World Phenomena 179 Randomized Networks 186

Clustering Coefficient 180 Autoregulation and the Feedforward Loop 187

Successes and Failures of the Erd T seR´nyi Model 180 Going Beyond Topology 187

Biological Small Worlds 180 Assigning the Weights 188

Deviations from the Erd T seR´nyi Model 180 Characterizing the Weighted Topology 188

Scale-Free Nature of Cellular Networks 181 Topology Correlated Weights 188

The Scale-Free Property 181 Controllability 188

Network Integrity and the Role of Hubs 182 Differential Networks 189

The Origins of the Scale-Free Topology 183 From Structure to Dynamics 190

Preferential Attachment in Biological Networks 183 References 191

Hierarchy and Modularity 184

INTRODUCTION
From a conceptual point of view,
the rise of systems biology can be described as the adoption
of a broad-based perspective on biological systems. In that
sense, the classical detailed biological analysis is com-
plemented by a macroscopic description of the cell as
a holistic unit [1 e 4] . This approach, aiming at a system-
level understanding of biology, mandates a crude simplifi-
cation of biological processes. In this light, the graph
theoretic approach to biological systems focuses on the
structural aspects of the interaction patterns, where the
interacting species, be them genes, proteins or other bio-
logical components, are signified by nodes, and their
interactions by the edges drawn between them. These
network systems express the underlying architecture which
enables the cellular functions to be carried out [5 e 9] .

Undoubtedly, the functionality of the cell cannot be
attributed to just one network, but rather to a set of inter-
dependent networks ranging from the level of transcription
to the processes of metabolism. It is common to divide the
cellular functions into three distinct networks, the tran-
scriptional network, the protein interaction network and the
metabolic network [2] . Although we follow this division
throughout this chapter, it should be acknowledged that the
true functionality of the cellular unit is a result of the
interdependence between these networks, and not merely
the interactions in each of them alone. At the current state,
the topology of these three fundamental cellular networks
has been thoroughly mapped using high-throughput tech-
niques. As a result, we now have reliable data on the
interaction maps of many organisms. Some examples are
protein e protein interaction networks, which have been