Residue interaction network is constructed on the base of the three-dimensional
atomic coordinates of protein structure and consists of nodes and edges. Each node
represents amino acid residue (or C a atom) that is connected to the neighbor node.
In the simplest variant, the edges are defined on the base of predefined cutoff of the
distances in 3D structure between nodes. The values of distance may be varied
based on nature of interactions (van der Waals, hydrophobic, electrostatic interactions, etc.). Frequently, the covalent backbones are included as edges in the
networks. The edges can be weighed based on energy of interactions,
knowledge-based potentials, or amino acid fluctuations in molecular dynamics
simulation [30, 31]. The differential network (DDN) method was proposed where
network formed by unique edges that are present only in one state but are absent in
other ones [32].
Networks have several most common characteristics; some of them that frequently
have been used for analysis of biological systems are listed below [28, 31, 33].
A degree of a node is a number of edges in a network that connect node with its
neighbors. In a directed network, there might be two types of degrees, the in-degree,
and the out-degree depending on the orientation of the edges. An average degree is
the average number of connections that the nodes have in a network.
A connectivity represents a minimum number edges that need to be removed to
make a disconnected graph. The connectivity structure and the degree of nodes
analysis in RINs help to identify important residues, i.e., participating in ligand
binding sites.
A shortest path is a path in which the two nodes are connected by the smallest
number of intermediate nodes. A characteristic path length is defined as the
number of edges in the shortest path between two nodes, averaged over all pairs of
nodes. Residues with small shortest path lengths are often located in the active or
ligand binding sites of proteins [17] and participate in allosteric pathways [34, 35].
A betweenness centrality of a node is the number of times that a node is included
in the shortest path between each pair of nodes, normalized by the total number of
pairs.
A closeness centrality of a node is the reciprocal of the average shortest path
length.
The network concept is widely used to analyze and predict properties in different
biological systems, from intramolecular interaction to whole cells and organisms.
Biological networks are small worlds that means that two nodes are connected to
each other via only a few other nodes [23, 30]. There are several network
parameters for characterizing different aspects of biological networks.
A hub is defined as a node with a high degree or connectivity in a network. Hubs
may play a structural role in proteins increasing the thermodynamic stability of
proteins [14, 36].
A cluster is a set of nodes with the number of connections, which is higher than
in the other nodes. Clusters often are equivalent to a domain of protein and participate in intramolecular interactions.
58
D. Shcherbinin and A. Veselovsky
atomic coordinates of protein structure and consists of nodes and edges. Each node
represents amino acid residue (or C a atom) that is connected to the neighbor node.
In the simplest variant, the edges are defined on the base of predefined cutoff of the
distances in 3D structure between nodes. The values of distance may be varied
based on nature of interactions (van der Waals, hydrophobic, electrostatic interactions, etc.). Frequently, the covalent backbones are included as edges in the
networks. The edges can be weighed based on energy of interactions,
knowledge-based potentials, or amino acid fluctuations in molecular dynamics
simulation [30, 31]. The differential network (DDN) method was proposed where
network formed by unique edges that are present only in one state but are absent in
other ones [32].
Networks have several most common characteristics; some of them that frequently
have been used for analysis of biological systems are listed below [28, 31, 33].
A degree of a node is a number of edges in a network that connect node with its
neighbors. In a directed network, there might be two types of degrees, the in-degree,
and the out-degree depending on the orientation of the edges. An average degree is
the average number of connections that the nodes have in a network.
A connectivity represents a minimum number edges that need to be removed to
make a disconnected graph. The connectivity structure and the degree of nodes
analysis in RINs help to identify important residues, i.e., participating in ligand
binding sites.
A shortest path is a path in which the two nodes are connected by the smallest
number of intermediate nodes. A characteristic path length is defined as the
number of edges in the shortest path between two nodes, averaged over all pairs of
nodes. Residues with small shortest path lengths are often located in the active or
ligand binding sites of proteins [17] and participate in allosteric pathways [34, 35].
A betweenness centrality of a node is the number of times that a node is included
in the shortest path between each pair of nodes, normalized by the total number of
pairs.
A closeness centrality of a node is the reciprocal of the average shortest path
length.
The network concept is widely used to analyze and predict properties in different
biological systems, from intramolecular interaction to whole cells and organisms.
Biological networks are small worlds that means that two nodes are connected to
each other via only a few other nodes [23, 30]. There are several network
parameters for characterizing different aspects of biological networks.
A hub is defined as a node with a high degree or connectivity in a network. Hubs
may play a structural role in proteins increasing the thermodynamic stability of
proteins [14, 36].
A cluster is a set of nodes with the number of connections, which is higher than
in the other nodes. Clusters often are equivalent to a domain of protein and participate in intramolecular interactions.
58
D. Shcherbinin and A. Veselovsky