Fig. 2c. In this way, the dynamical weighted network represents a
communication network where the residues physically in contact in
the protein structure (for most of the time along the MD simulation) exchanging more information (i.e., have larger paircorrelation coefficients) and are found closer in distance within
the graph with respect to those that, despite being in physical
contact, have lower correlation coefficients and thus communicate
less among each other.
3.2 Community
Network Analysis
The dynamical weighted network, as defined in the above section, it
contains information paths and critical nodes that are important for
communication within the proteic system under study. Such network already contains relevant information for allostery and it can
be analyzed by determining the shortest pathways (SPs) between all
pairs of (not directly linked) nodes/residues. The SPs within the
protein communication network can be calculated using the FloydWarshall algorithm [47], representing the best communication
pathways among pairs of residues. The communication pathways
between physically distant amino acid residues (such as those in the
active and allosteric sites) are of extreme relevance for the elucidation of allosteric mechanisms. Still, it is not straightforward to
identify the allosterically relevant residues among which to calculate
the SPs, since both the allosteric and active sites are generally
characterized by sized domains, possibly involving a relatively
large number of amino acid residues. Thus, it becomes quite useful,
especially for large proteic systems, to use the information embodied in the SPs for partitioning the whole dynamical network,
providing a coarse-grained view of the communication flows within
the protein network that facilitates the understanding of the allosteric mechanisms.
The Girvan-Newman algorithm [48] can be used to split the
dynamical weighted network into “communities,” i.e., local substructures involving groups of nodes within which the connections
are dense but between which they are sparser. This algorithm
exploits as partitioning criterion for the weighted network the
edge betweenness, EB, defined as the number of SPs that cross a
given edge, see Fig. 2d [49], measuring of how much this edge is
responsible for connecting the other pairs of nodes in the network.
Therefore, the edges with the highest between-nesses are those
carrying on the highest amount of information exchange within
the protein network. An iterative procedure that starts from the
whole protein network as a single big community and removes/
cuts the edges with highest between-nesses would, then, isolate the
nodes progressively creating smaller and smaller communities, up
to generation of a number of communities that corresponds to the
number of (isolated) nodes, see Fig. 2e. The iterative procedure
could, however, be interrupted at given step and produce a specific
partition of the dynamical weighted network, namely a community
Community Network Analysis of Allosteric Proteins
143
communication network where the residues physically in contact in
the protein structure (for most of the time along the MD simulation) exchanging more information (i.e., have larger paircorrelation coefficients) and are found closer in distance within
the graph with respect to those that, despite being in physical
contact, have lower correlation coefficients and thus communicate
less among each other.
3.2 Community
Network Analysis
The dynamical weighted network, as defined in the above section, it
contains information paths and critical nodes that are important for
communication within the proteic system under study. Such network already contains relevant information for allostery and it can
be analyzed by determining the shortest pathways (SPs) between all
pairs of (not directly linked) nodes/residues. The SPs within the
protein communication network can be calculated using the FloydWarshall algorithm [47], representing the best communication
pathways among pairs of residues. The communication pathways
between physically distant amino acid residues (such as those in the
active and allosteric sites) are of extreme relevance for the elucidation of allosteric mechanisms. Still, it is not straightforward to
identify the allosterically relevant residues among which to calculate
the SPs, since both the allosteric and active sites are generally
characterized by sized domains, possibly involving a relatively
large number of amino acid residues. Thus, it becomes quite useful,
especially for large proteic systems, to use the information embodied in the SPs for partitioning the whole dynamical network,
providing a coarse-grained view of the communication flows within
the protein network that facilitates the understanding of the allosteric mechanisms.
The Girvan-Newman algorithm [48] can be used to split the
dynamical weighted network into “communities,” i.e., local substructures involving groups of nodes within which the connections
are dense but between which they are sparser. This algorithm
exploits as partitioning criterion for the weighted network the
edge betweenness, EB, defined as the number of SPs that cross a
given edge, see Fig. 2d [49], measuring of how much this edge is
responsible for connecting the other pairs of nodes in the network.
Therefore, the edges with the highest between-nesses are those
carrying on the highest amount of information exchange within
the protein network. An iterative procedure that starts from the
whole protein network as a single big community and removes/
cuts the edges with highest between-nesses would, then, isolate the
nodes progressively creating smaller and smaller communities, up
to generation of a number of communities that corresponds to the
number of (isolated) nodes, see Fig. 2e. The iterative procedure
could, however, be interrupted at given step and produce a specific
partition of the dynamical weighted network, namely a community
Community Network Analysis of Allosteric Proteins
143