Biomedical Engineering Reference
In-Depth Information
business networks represent further examples of complex networks of techno-
logical, scientific or economic interest.
In biological systems networks emerge in many disguises, from food webs
in ecology to various biochemical nets in molecular biology. In particular, the
wide range of interactions between genes, proteins, and metabolites in a cell are
best represented by various complex networks. During the last decade, genomics
has produced an incredible quantity of molecular interaction data, contributing
to maps of specific cellular networks. The emerging fields of transcriptomics
and proteomics have the potential to join the already extensive data sources pro-
vided by the genome-wide analysis of gene expression at the mRNA and protein
levels (10,11,40). Indeed, extensive protein-protein interaction maps have been
generated for a variety of organisms including viruses (16,34), prokaryotes, like
H. pylori
(45), and eukaryotes, like
S. cerevisiae
(17,22-24,49,52) and
C. ele-
gans
(58). Beyond the current focus on uncovering the structure of the genomes,
proteomes, and interactomes of various organisms, some of the most extensive
data sets are the metabolic maps (28,39), catalyzing an increasing number of
studies, focusing on the architecture of the metabolism (15,26,57).
Networks offer us a new way to categorize systems of very different origin
under a single framework. This approach has uncovered unexpected similarities
between the organization of various complex systems, indicating that the net-
works describing them are governed by generic organization principles and
mechanisms. Understanding the driving forces that invest different networks
with similar topological features enables systems biology to combine the nu-
merous details about molecular interactions into a single framework, offering
means to address the structure of the cell as a whole.
2.
BASIC NETWORK FEATURES
A node's degree (or connectivity), giving the number of links
k
the node
has, is the most elementary network measure. For example, in Figure 1 node
i
has exactly three links (
k
i
= 3). The overall graph, however, is characterized by
the average degree, <
k
>, which has the value <
k
> = 2.6 for this example. Yet,
the average degree does not capture the potential degree variations present in the
network. This is better characterized by the degree distribution,
P
(
k
), which
gives the number of nodes with exactly
k
links (see Table 1).
Planing a trip from Anchorage, Alaska, to Alice Springs in the outbacks of
Australia requires finding the shortest paths through a particular airline's trans-
portation network. As in most networks, there are multiple paths between any
two nodes
i
and
j
; a useful distance measure is the length of the shortest path,
l
ij
(see Figure 1). In a network of
N
nodes, the mean path length is defined as
2
N
,
l
=
l
[1]
ij
NN
(
)
jl
v
i
=
1
