problems root in the information theory [12, 13]. On the web,
libraries in Java and Python are available to compute shortest
paths, mainly based on Dijkstra’s algorithms [13].
The average shortest path, also known as network characteristic length, plays a key role in signal transmission throughout protein contact networks and is of a major relevance in
protein functionality [15]. Notice that the shortest path is
averaged over all possible node pairs
N ˜
n NÀ1
ð
Þ
2
3. Centrality metrics: how central is a role is the first address to
topological role of nodes in the network. This concept flanks
the continuous quest for functional role of residues in proteins,
which is also a topic in allostery identification. The simplest
centrality metrics is the above-mentioned node degree, which
describes the local structure of networks (and of proteins).
However, allostery and, more in general, cooperativity have
to do with global signatures of protein structures, which are
represented by corresponding global network properties. In
this perspective, the functional relevance of centrality must
pass through a global analysis of protein structures and
corresponding contact networks. Global centrality metrics
pass by shortest paths computation [16]: the most relevant in
the protein contact networks analysis are:
(a) closeness centrality [17]: it is defined as the inverse of
fairness, in turn defined for a node, as the sum of the
shortest paths with all other nodes. Given a set of vertices
V, the closeness centrality of a node i is defined as:
close i
ð Þ ¼
1
P
u∈V ,u6 ¼i sp ui
ð4Þ
Amitai and coworkers [18] demonstrated that residues in active
sites show high closeness, but no clue comes as for residues acting
in cooperative processes (allostery).
(b) betweenness centrality (see Note 2): it describes for a node the
number of shortest paths coming through it. Given a set of
vertices V, the betweenness centrality of a node i is defined as:
betw i
ð Þ ¼
X
v∈V , v6 ¼i
X
u∈V , u6 ¼i
σ uv i
ð Þ
σ uv
ð5Þ
σ uv being the total number of shortest paths connecting nodes
u and v and σ uv (i) the number of shortest paths connecting the
two nodes and also coming through the node i.
The betweenness centrality is among the most relevant descriptor to identify the role of residues (nodes) in the signal transmission
network of protein structures. In terms of network robustness, the
focused removal of high betweenness nodes is detrimental in the
whole network connectivity.
Disclosing Allostery Through Protein Contact Networks
13
libraries in Java and Python are available to compute shortest
paths, mainly based on Dijkstra’s algorithms [13].
The average shortest path, also known as network characteristic length, plays a key role in signal transmission throughout protein contact networks and is of a major relevance in
protein functionality [15]. Notice that the shortest path is
averaged over all possible node pairs
N ˜
n NÀ1
ð
Þ
2
3. Centrality metrics: how central is a role is the first address to
topological role of nodes in the network. This concept flanks
the continuous quest for functional role of residues in proteins,
which is also a topic in allostery identification. The simplest
centrality metrics is the above-mentioned node degree, which
describes the local structure of networks (and of proteins).
However, allostery and, more in general, cooperativity have
to do with global signatures of protein structures, which are
represented by corresponding global network properties. In
this perspective, the functional relevance of centrality must
pass through a global analysis of protein structures and
corresponding contact networks. Global centrality metrics
pass by shortest paths computation [16]: the most relevant in
the protein contact networks analysis are:
(a) closeness centrality [17]: it is defined as the inverse of
fairness, in turn defined for a node, as the sum of the
shortest paths with all other nodes. Given a set of vertices
V, the closeness centrality of a node i is defined as:
close i
ð Þ ¼
1
P
u∈V ,u6 ¼i sp ui
ð4Þ
Amitai and coworkers [18] demonstrated that residues in active
sites show high closeness, but no clue comes as for residues acting
in cooperative processes (allostery).
(b) betweenness centrality (see Note 2): it describes for a node the
number of shortest paths coming through it. Given a set of
vertices V, the betweenness centrality of a node i is defined as:
betw i
ð Þ ¼
X
v∈V , v6 ¼i
X
u∈V , u6 ¼i
σ uv i
ð Þ
σ uv
ð5Þ
σ uv being the total number of shortest paths connecting nodes
u and v and σ uv (i) the number of shortest paths connecting the
two nodes and also coming through the node i.
The betweenness centrality is among the most relevant descriptor to identify the role of residues (nodes) in the signal transmission
network of protein structures. In terms of network robustness, the
focused removal of high betweenness nodes is detrimental in the
whole network connectivity.
Disclosing Allostery Through Protein Contact Networks
13