Modeling Macromolecular Complexes: A Journey Across Scales - Modeling in Computational Biology and Biomedicine - page 23

from that of the free protein surface. Subsequent studies have suggested core
residues are more likely to include hotspot residues [ 32 ].
While the core-rim distinction is inherently binary, the shelling-order introduced
in Sect. 1.2.5 measures the depth of an interfacial atom with an integer. The
SO has been used to refine the understanding of the several physico-chemical
properties, based on statistics gathered on 18 homodimers and 36 heterodimers
protein complexes. We have seen that the composition of the core and the rim of
an interface are different [ 17 ], and one would tend to believe that charged or polar
amino-acids tend to be located near the rim, where electrostatic interactions with
the solvent are favored. However, the correlation between SO and the electrostatic
properties of amino acids is not statistically significant in general [ 11 ]. It has also
beenshownin[ 31 ], based on a statistical meta-analysis, that conserved residues
tend to locate in the interface core. (Conservation of a residue refers to its repeated
presence at a particular position within a non redundant set of protein sequences.
The reader is referred to Sect. 1.2.1 for the Shannon entropy based evaluation
of conservation.) Replacing the binary core-rim partitioning by the SO confirms
this finding at the dataset level, but also shows that the conclusion does not hold
in general on a per-complex basis [ 11 ]. Finally, another important property of
interfacial residues is their dryness , i.e., their isolation from mobile solvent. Using
all-atom molecular dynamics simulations on the aforementioned 54 complexes, it
was shown in [ 46 ] that dryness is correlated to residue conservation. But as shown
in [ 11 ], the dryness of a residue is in fact determined by its SO. Thus dryness
can be evaluated from a mere Voronoı interface calculation, as opposed to a costly
molecular dynamics simulation.
This is a case in which appropriate geometric analysis naturally spotlights the
important biological determinants of protein-protein interactions.

Predicting the structure of protein complexes. The power diagram has also been
used in deriving new scoring functions to be used in ranking candidate solutions for
the structure of a protein-protein complex from docking studies. In one such study,
amino-acid residue centroids and synthetic solvent molecule positions were used to
create the Voronoı descriptions, and parameters such as the cell volumes, interface
areas, and centroid-to-centroid distances of known interfaces were integrated into
the final scoring function using machine learning techniques [ 6 ].
The more general α -complex has also been employed, obviating the need
for solvent-atom positions, notably in defining volume derivatives of the macro-
molecule [ 26 ]. Such results should also prove important in improving implicit-
solvent models in molecular simulations, in which modifications in the coordinates
of the protein must be taken into account.

1.3 Modeling Large Assemblies

Having dealt with binary protein complexes, we now consider the problem of
modeling large assemblies, that is, complexes involving on the order of hundreds
of polypeptide chains. In doing so, we shall focus on the Nuclear Pore Complex