1. Shelling Protein Interfaces
Raik Grünberg1*, Benjamin Bouvier*2, Michael Nilges3, Frederic Cazals2
* equally contributing; 1EMBL-CRG Systems Biology Unit, CRG – Centre de Regulacio Genomica, Barcelona; 2 INRIA Sophia-Antipolis, Project Geometrica, France; 3 Unité de Bioinformatique Structurale, Institute Pasteur, Paris, France
From a Voronoi description of interfaces to Voronoi Shelling Order (VSO)
Voronoi diagram (light solid lines) for a hypothetical 4 atom molecule. The Voronoi diagram defines an exact partitioning of space into atom cells. The power diagram extension accounts for different atomic radii.
Shelling of the Voronoi interface of a dimer complex. Left: seen from the side (in two dimensions) – red: protein A, blue: protein B, green: water. Voronoi interface facets are depicted as broken line, Delaunay edges, which connect atoms on different partners, are shown as solid line. Interface facets are numbered by their shelling order. The high curvature of this schematic interface leads to high shelling orders around the water molecule. Right: top view with facets colored by Shelling Order from one (light gray) to two (black).
The interface (colored Voronoi facets) and interfacial water molecules W (grey spheres) for two distinct solvation and equilibration procedures based on a very fast (a) and an exhaustive (b) molecular dynamics simulation.
Voronoi Shelling Order (VSO) predicts residue conservation and water dynamics
Case study: 2DOR homodimer
Prediction of dry residues for 18 hetero- and 36 homodimers
Comparison of accuracy (i.e. ROC area) for the prediction of dry residues by Voronoi Shelling Order (solid line) and by residue conservation (broken line).
Voronoi Shelling Order predicts “dry spots” with high accuracy. Both “dryness” and high VSO coincide with high conservation.
The Shelling Order of Voronoi facets (left, color-coded) was projected back to participating atoms (right) and converted to average residue shelling orders.
Conservation across interface shells
Conserved residues (left; from real Evolutionary Trace) and dry residues (right; shielded from exchange with bulk solvent) as determined from molecular dynamics simulations by Mihalek, Res & Lichtarge (2007) J Mol Biol. 369(2): (Figure reproduced from Mihalek et al.)
Heterodimers
Homodimers
VSO, water shielding and conservation for three more homodimer complexes. Voronoi Shelling Order (top), dry residues (each bottom left, colored red) and conservation pattern (each bottom right, determined from relative entropy of Pfam alignments).
Conservation generally increases from rim to interface core but there are also, possibly systematic, deviations from this trend. Crosses: normalized conservation values from all interface residues and their location within the interface. Black line: conservation averaged over a running window spanning ¼ of the interface. Grey area: expected variation of the running average (+- 1 SD).
Conclusions
Voronoi Shelling Order (VSO) provides an unambiguous, quantitative measure for an atom’s “depth” within the protein – protein interface while accounting for both geometry and topology. In contrast to current ad-hoc interface definitions (based on residue contacts or loss of solvent exposed surface), Voronoi interface and Voronoi Shelling Order are efficiently calculated from an exact and parameter-free mathematical model.
VSO correlates very well with the protection of residues from itinerant water fluxes, as computed by Mihalek and colleagues (see above) which, in turn, can be considered a measure of residue activity. The calculation of shelling orders, however, is about five orders of magnitude faster than a typical MD simulation.
Comparison with evolutionary signals reveals a general increase of conservation towards inner interface shells. Systematic deviations from this trend may inform about distinct binding mechanisms, catalytic activities but also modeling errors.
Voronoi Shelling Order thus adds a meaningful dimension along which protein – protein interfaces can be analyzed and compared with each other.
Acknowledgements
We are grateful to Olivier Lichtarge and Tuan Anh Tran for providing us with their detailed dryness results. The automatic generation of conservation profiles was implemented by Johan Leckner. B. Bouvier was supported by the INRIA cooperative project ReflexP. R. Gruenberg is supported by the Human Frontiers Science Program.