have a disassortative Long Range Network and this is in accordance
with the results on the article of Bagler and Sinha [5] about the
global assortativity of LRN. For the Induced Hot Spot Network,
we have 736 assortative networks, 4 neutral networks, and 6 disassortative networks. This could mean that the IHSN mimics the
whole protein network property in order to mask the position of
HSN. In contrast, for HSN that is the network of interfaces
between two chains of the protein, we find 68 assortative networks,
9 neutral networks, and 669 disassortative networks.
The first direct interpretation comes simply by the fact that
HSN is by construction a bipartite graph. Indeed, for a complete
bipartite graph K m,n we have r ¼ À1 if m 6 ¼ n and r ¼ 1 if m ¼ n.
Thus, a complete bipartite graph is either fully assortative or fully
disassortative. Nevertheless, HSN is bipartite but far from being
complete. This is why we think that the disassortative property of
the interface between two chains could be the signature of a disassortative barrier. In fact, we have seen already that in the interface
a high degree node is protected from damages by placing a low
degree node near, as perturbation propagates to the neighbors of
the high degree nodes instead of impacting the low degree node
connections [ASVSL].
Now we would like to study the independence of the topology
of network two by two by using information of the assortativity and
proving that there are only few correlations between the assortativity measures of each network. Indeed, if we plot for each protein the
assortativity values of PCN versus the assortativity values of HSN,
all values are almost on a circle. This is the signature of noncorrelated variables and in particular the R
2 is near zero (the value is
around 0.0076) (see Fig. 25). In conclusion the assortativity property of the whole protein is independent of the assortativity property of the interface.
Fig. 25 Assortativity of PCN versus HSN
Topology Results on Adjacent Amino Acid Networks of Oligomeric Proteins
133
with the results on the article of Bagler and Sinha [5] about the
global assortativity of LRN. For the Induced Hot Spot Network,
we have 736 assortative networks, 4 neutral networks, and 6 disassortative networks. This could mean that the IHSN mimics the
whole protein network property in order to mask the position of
HSN. In contrast, for HSN that is the network of interfaces
between two chains of the protein, we find 68 assortative networks,
9 neutral networks, and 669 disassortative networks.
The first direct interpretation comes simply by the fact that
HSN is by construction a bipartite graph. Indeed, for a complete
bipartite graph K m,n we have r ¼ À1 if m 6 ¼ n and r ¼ 1 if m ¼ n.
Thus, a complete bipartite graph is either fully assortative or fully
disassortative. Nevertheless, HSN is bipartite but far from being
complete. This is why we think that the disassortative property of
the interface between two chains could be the signature of a disassortative barrier. In fact, we have seen already that in the interface
a high degree node is protected from damages by placing a low
degree node near, as perturbation propagates to the neighbors of
the high degree nodes instead of impacting the low degree node
connections [ASVSL].
Now we would like to study the independence of the topology
of network two by two by using information of the assortativity and
proving that there are only few correlations between the assortativity measures of each network. Indeed, if we plot for each protein the
assortativity values of PCN versus the assortativity values of HSN,
all values are almost on a circle. This is the signature of noncorrelated variables and in particular the R
2 is near zero (the value is
around 0.0076) (see Fig. 25). In conclusion the assortativity property of the whole protein is independent of the assortativity property of the interface.
Fig. 25 Assortativity of PCN versus HSN
Topology Results on Adjacent Amino Acid Networks of Oligomeric Proteins
133