Graph analysis of β2 adrenergic receptor structures: a "social network" of GPCR residues

G protein-coupled receptors (GPCRs) are a superfamily of membrane proteins of vast pharmaceutical interest. Here, we describe a graph theory-based analysis of the structure of the β2 adrenergic receptor (β2 AR), a prototypical GPCR. In particular, we illustrate the network of direct and indirect interactions that link each amino acid residue to any other residue of the receptor.

Networks of interconnected amino acid residues in proteins are analogous to social networks of interconnected people. Hence, they can be studied through the same analysis tools typically employed to analyze social networks - or networks in general - to reveal patterns of connectivity, influential members, and dynamicity. We focused on the analysis of closeness-centrality, which is a measure of the overall connectivity distance of the member of a network to all other members.

The residues endowed with the highest closeness-centrality are located in the middle of the seven transmembrane domains (TMs). In particular, they are mostly located in the middle of TM2, TM3, TM6 or TM7, while fewer of them are located in the middle of TM1, TM4 or TM5. At the cytosolic end of TM6, the centrality detected for the active structure is markedly lower than that detected for the corresponding residues in the inactive structures. Moreover, several residues acquire centrality when the structures are analyzed in the presence of ligands. Strikingly, there is little overlap between the residues that acquire centrality in the presence of the ligand in the blocker-bound structures and the agonist-bound structures.

Our results reflect the fact that the receptor resembles a bow tie, with a rather tight knot of closely interconnected residues and two ends that fan out in two opposite directions: one toward the extracellular space, which hosts the ligand binding cavity, and one toward the cytosol, which hosts the G protein binding cavity. Moreover, they underscore how interaction network is by the conformational rearrangements concomitant with the activation of the receptor and by the presence of agonists or blockers.