Fractal dimension as a measure of surface roughness of G protein-coupled receptors: implications for structure and function

Protein surface roughness is a structural property associated with ligand-protein and protein-protein binding interfaces. In this work we apply for the first time the concept of surface roughness, expressed as the fractal dimension, to address structure and function of G protein-coupled receptors (GPCRs) which are an important group of drug targets. We calculate the exposure ratio and the fractal dimension for helix-forming residues of the β(2) adrenergic receptor (β(2)AR), a model system in GPCR studies, in different conformational states: in complex with agonist, antagonist and partial inverse agonists. We show that both exposure ratio and roughness exhibit periodicity which results from the helical structure of GPCRs. The pattern of roughness and exposure ratio of a protein patch depends on its environment: the residues most exposed to membrane are in general most rough whereas parts of receptors mediating interhelical contacts in a monomer or protein complex are much smoother. We also find that intracellular ends (TM3, TM5, TM6 and TM7) which are relevant for G protein binding and thus receptor signaling, are exposed but smooth. Mapping the values of residual fractal dimension onto receptor 3D structures makes it possible to conclude that the binding sites of orthosteric ligands as well as of cholesterol are characterized with significantly higher roughness than the average for the whole protein. In summary, our study suggests that identification of specific patterns of roughness could be a novel approach to spot possible binding sites which could serve as original drug targets for GPCRs modulation.