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

Abstract

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 β2 adrenergic receptor (β2AR), 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.FigureThe significance of surface roughness for protein structure and function.

The dopamine D2 receptor dimer and its interaction with homobivalent antagonists: homology modeling, docking and molecular dynamics

“…In this protocol, populations of dimers compatible with membrane integration are generated, taking into account all possible interfaces. The method involves external scoring (as protein–protein docking itself fails in case of GPCR dimers [ 14 ]), followed by consensus scoring of the resulting dimers according to (1) Rosetta total score, (2) Rosetta interface score, (3) surface of the dimer interface, (4) polar contribution to the dimer interface, (5) fractal dimension of the dimer interface [ 15 , 16 ], (6) evolutionary conservation score [ 17 , 18 ], (7) shape complementarity, (8) electrostatic complementarity, (9) potential energy [ 19 ], (10) free energy of binding [ 19 ], and (11) energy of hydrogen bond interactions [ 12 , 20 ]. The protocol was tested by prediction of the dimer structure of GPCR dimers with existing X-ray structures, and it was concluded from these studies that the Rosetta interface score, interface area, free energy of binding and the energy of hydrogen bond interactions were the best performing scoring factors [ 12 ].…”

Helicalised fractals

“…In general, there have been some efforts to study various fractal properties associated to the structure of DNA [9,10] as well as the structure of protein [11][12][13][14][15] -albeit not specifically dealing with how the structure of chromosomes enables DNA to be packed efficiently. Nev-ertheless, an intriguing idea was to think of the coding parts of a DNA sequence as clusters of connected sites in a random Cantor-like set (and conversely for the non-coding regions) [9].…”

Multi‐Component Protein – Protein Docking Based Protocol with External Scoring for Modeling Dimers of G Protein‐Coupled Receptors

“…In particular, one would expect that, in membrane environments, the polar contribution of protein residues to the dimer’s interface to be high in order to avoid interactions of polar amino acids with the hydrophobic core of the membrane. On the basis of our earlier studies41 we also expected a GPCR dimer interface to exhibit relatively low surface roughness (measured as fractal dimension) as interactions between rough protein surfaces and the membrane are entropically favored. Furthermore, we also determined previously53 that protein‐protein docking of transmembrane proteins may be successfully guided by the evolutionary conservation score33 in cases where the interface is evolutionary conserved.…”

“…where SES denotes solvent excluded surface and r denotes the radius of the probe size used to characterize the surface. Fractal dimension was calculated according to our previously described approach2 based on the study by Renthal 41…”