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networks where links have a directionality associated to them, the degree of
a node can be further subdivided into links going in or out of the node (in
and out degrees, respectively) (
Fig. 9.1
C).
The degree distribution is an important property of large-scale network
organization, and it measures how the connectivity is distributed overall in
the network. Most molecular networks studied to date such as protein-
protein, signaling, or TF-gene networks have a degree distribution that
deviates from random (i.e., a normal distribution) and follows instead an
exponential distribution or a power law (
Barab´si and Oltvai, 2004
;
Martinez and Walhout, 2009
). In such networks, the majority of nodes
have a low to medium number of links, while a few nodes, called hubs, are
highly connected to other nodes (
Fig. 9.1
B). Hubs mediate interactions
among numerous and less connected nodes, allowing rapid coordination
between different parts of the network. This type of system is robust to
random loss of the less connected nodes but is sensitive to deletion of the
hubs (
Albert
et al
., 2000
). For example, in protein-protein interaction
networks, there is a lethality-centrality relationship where highly connected
components induce lethality when lost (
Jeong
et al
., 2001
;
Zotenko
et al
.,
2008
).
Do miRNAs exhibit this lethality-centrality relationship? Systematic
mutagenesis of many individual miRNA genes (
Miska
et al
., 2007
) and
paralogous families of miRNA genes (
Alvarez-Saavedra and Horvitz, 2010
)
were performed in the nematode
Caenorhabditis elegans
. Most miRNAs
either individually or in collective families are not essential for viability or
development. Only miRNAs like
let-7
, one of the most highly connected
miRNAs in the animal (
Martinez
et al
., 2008
), elicit observable lethal
phenotypes when knocked out (
Reinhart
et al
., 2000
). The degree distribu-
tion of
C. elegans
miRNA-TF networks could explain why most miRNAs
trigger subtle or nondetectable mutant phenotypes. If a miRNA node
has only one or a few links to target within a given network, then loss of
this node would generally have a small impact on network behavior. In
C. elegans
, there is a significant difference between nodes composed of TFs
and nodes composed of miRNAs. TFs bind promoters in a scale-free
manner, that is, the TF-out degree distribution follows a power law,
and there are clear TF hubs binding many promoters. In contrast, the
miRNA-out degree distribution follows an exponential distribution,
that is, there are no clear miRNA hubs even though some miRNAs are
more connected than others (
Martinez and Walhout, 2009
;
Martinez
et al
.,
2008
).
Although miRNAs do not exhibit hub-like properties, frequently the
direct targets of miRNAs behave as network hubs. These target hubs often
contain many in-links from different miRNAs (
Fig. 9.2
). In the
C. elegans
and human miRNA-mRNA target networks, the target in-links follow a
power law distribution (
Martinez
et al.
, 2008
;
Mookherjee
et al
., 2009a
).
