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Shelling Protein Interfaces
Raik
1
Grünberg *,
Benjamin
2
Bouvier* ,
Michael
3
Nilges ,
Frederic
2
Cazals
1
2
* equally contributing; EMBL-CRG Systems Biology Unit, CRG – Centre de Regulacio Genomica, Barcelona; INRIA
3
Sophia-Antipolis, Project Geometrica, France; 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.
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):584-95. (Figure reproduced
from Mihalek et al.)
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).
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.
Conservation across interface shells
Heterodimers
Homodimers
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).
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.