Computational Drug Discovery and Design

acidαin the full MSA, which serves as the background frequency.

The quantity S¼

P 20

α¼ 1 pi

αlogp

i

α=p

α



can be regarded as the

relative entropy, andS¼0ifpiαis no different thanpαfor allα.

Note that larger values ofΔGidenote better sequence conservation

at positioni. In class A GPCR family, the conserved residues are

mainly located at the cytoplasmic region, where G-proteins may

bind. On the contrary, the residues at the extracellular ligand

binding site in AR family are highly conserved affecting ligand

binding selectivity. Especially, in A2AAR, 15 out of 18 microswitches

(except for P189, S281, and E228) are highly conserved, satisfying

ΔG(GPCR)/kBT*0.2.

2.2.2 Construction
of the Residue-Interaction
Network Model

By using 3D structures of proteins, we constructed the 3D-network

where each amino acid residue was represented as a single node. To

take into account the effect of side chain, we considered two coarse-

grained centers per residue, i.e., the alpha carbon (Cα) for backbone

and a farthest heavy atom fromCαfor the side chain (SC). The

mutual distance between residue A and residue B was assumed by

the shortest distance among the ones between Cα(residue

A)Cα(residue B),Cα(A)SC(B), SC(A)Cα(B), and SC

(A)SC(B). By doing so, we incorporated the cases of back-

bone–backbone, backbone–side chain, and side chain–side chain

contacts. In our network model, a link was established between two

residues (Cα), where any pair of backbone and side chain distance is

less than 7 A ̊ [30]. Thus, the side chain effects were implicitly

included in our network analysis.

2.2.3 Centrality Analysis Measuring centrality, which is the most studied concept in social
network analysis, can be a practical way of selecting essential nodes
in the network [11, 31, 32](seeNote 3). This centrality calculation
was successfully applied in identifying functional residues, such as in
the active site or metal binding site of proteins [13, 16]. Also, this
method is considered to be useful in the investigation of allosteric
communications in protein structures [14, 15, 33]. For example,
allosteric propagation was modeled by considering all possible
signaling routes in a monomeric structure [33]. There are three
most popular centrality measures, i.e., degree, closeness, and
betweenness [11, 31]:

1. The degree centrality,CD(v), measures the total number of
   edges linked to a nodev. This value is identical to the number
   of contacts with its neighboring residues.

CDðÞ¼v degðÞv ð 2 Þ

2. The closeness centrality,CC(v), is an inverse of the mean geo-
   desic distance (shortest path length) from all other nodes to the
   nodev. It measures how fast a signal from the nodevcan be
   transmitted to other nodes.

462 Shaherin Basith et al.