have utilized specialized algorithms of spectral analysis of weighted
networks to obtain re-grouping of residues as clusters in response
to binding of different ligands or proteins. The information at such
a level obtained on protein structures has been presented in the
context of allostery and protein-ligand complex formation. The
protocol of interpreting the metrics like Fiedler vector has been
demonstrated, and the biological relevance of the methods discussed here has been highlighted with the example of β 2 adrenergic
receptor, a member of GPCR family.
6 Additional Notes
1. While comparing PSNs using edge weight difference, sufficient
care is to be taken such that comparison is being made between
nodes corresponding to same residues. A Needleman-Wunsch
alignment [44] can be used with default settings for this node
correspondence. Any missing residues are either to be compensated by adding additional dummy rows and columns in the
network with missing ones or to be removed from the other
network.
2. The spectral decomposition of the networks using Laplacian
matrix requires that there are no isolated nodes (nodes with
zero edges) in the network. Hence any such nodes are to be
made non-isolated by adding an edge to those nodes with a
logically relevant node. For example, for backbone network,
the node with nearest C
α distance can be selected. For sidechain networks, the node can be connected to that of a residue
with atom contacts nearest to it. The weight of the edge added
should be of very low value (for example, 10
À32
) so that it does
not interfere with the spectral information.
3. Clusters in a network are identified by cutting the Fiedler
vector of the Laplacian matrix of the PSN. If the clusters are
well separated as in the case of antagonist in GPCR case-study
(Fig. 5, panel b), they are also well separated in their Fiedler
vector components, nodes in the same cluster possessing very
close values. In the case of clusters well interspersed with each
other like that of agonist in case study (Fig. 5, panel a) making
the sorted Fiedler vector a continuous increasing one, the cut
in the Fiedler vector to obtain clusters is to be done judiciously.
Acknowledgments
S.V. thanks National Academy of Sciences (NASI), Allahabad,
India, for Senior Scientist Fellowship. V.G. thanks IISc for incentive
research support grant and CSIR for Research Associate fellowship.
110
Vasundhara Gadiyaram et al.
networks to obtain re-grouping of residues as clusters in response
to binding of different ligands or proteins. The information at such
a level obtained on protein structures has been presented in the
context of allostery and protein-ligand complex formation. The
protocol of interpreting the metrics like Fiedler vector has been
demonstrated, and the biological relevance of the methods discussed here has been highlighted with the example of β 2 adrenergic
receptor, a member of GPCR family.
6 Additional Notes
1. While comparing PSNs using edge weight difference, sufficient
care is to be taken such that comparison is being made between
nodes corresponding to same residues. A Needleman-Wunsch
alignment [44] can be used with default settings for this node
correspondence. Any missing residues are either to be compensated by adding additional dummy rows and columns in the
network with missing ones or to be removed from the other
network.
2. The spectral decomposition of the networks using Laplacian
matrix requires that there are no isolated nodes (nodes with
zero edges) in the network. Hence any such nodes are to be
made non-isolated by adding an edge to those nodes with a
logically relevant node. For example, for backbone network,
the node with nearest C
α distance can be selected. For sidechain networks, the node can be connected to that of a residue
with atom contacts nearest to it. The weight of the edge added
should be of very low value (for example, 10
À32
) so that it does
not interfere with the spectral information.
3. Clusters in a network are identified by cutting the Fiedler
vector of the Laplacian matrix of the PSN. If the clusters are
well separated as in the case of antagonist in GPCR case-study
(Fig. 5, panel b), they are also well separated in their Fiedler
vector components, nodes in the same cluster possessing very
close values. In the case of clusters well interspersed with each
other like that of agonist in case study (Fig. 5, panel a) making
the sorted Fiedler vector a continuous increasing one, the cut
in the Fiedler vector to obtain clusters is to be done judiciously.
Acknowledgments
S.V. thanks National Academy of Sciences (NASI), Allahabad,
India, for Senior Scientist Fellowship. V.G. thanks IISc for incentive
research support grant and CSIR for Research Associate fellowship.
110
Vasundhara Gadiyaram et al.