Quantitative Characterization of Binding Pockets and Binding Complementarity by Means of Zernike Descriptors

Abstract

In this work, we describe the application of the Zernike formalism to quantitatively characterize the binding pockets of two sets of biologically relevant systems. Such an approach, when applied to molecular dynamics trajectories, is able to pinpoint the subtle differences between very similar molecular regions and their impact on the local propensity to ligand binding, allowing us to quantify such differences. The statistical robustness of our procedure suggests that it is very suitable to describe protein binding sites and protein–ligand interactions within a rigorous and well-defined framework.

2D Zernike polynomial expansion: Finding the protein-protein binding regions

“…Describing a surface region with a set of numbers independent of its orientation in space (expansion coefficients) allows a quick and easy comparison between regions of different proteins. In recent years indeed, some computational approaches based on the 3D Zernike formalism have been developed to exploit the compactness and the rotation invariance of this formalism [40] , [38] , [41] , [37] , [42] . Moreover, even the Zernike 2D formalism was also used to study protein regions, but only considering pockets for small compounds [48] .…”

“…While widely used in optics, its application to structural biology was possible only after that Canterakis extended the formalism to 3D space [54] . The compact representation of the protein surface in terms of a numerical vector together with the possibility to easily define rotational invariant observables make the Zernike formalism very suitable for shape and complementarity investigations [40] , [38] , [41] , [37] , [42] , although at the cost of increasing the dimension of the basis space and the consequences of the computational cost (an expansion to the 20th order has 1771 coefficients in 3D against the 121 complex coefficients in 2D).…”

“…To this end, recently some of the authors and other groups used the three-dimensional (3D) Zernike polynomials, a method to effectively capture the local molecular shape and analyzing its functional relevance [37] , [38] , [39] , [40] , [41] , [42] . The Zernike expansion associates each portion of molecular surfaces with an ordered set of numerical descriptors, invariant under rotation, allowing easy metric comparison between the shape of different protein regions for similarity or complementarity evaluation, without the considerable computational cost that would be required if we had to consider all possible relative angles between the surfaces.…”

Molecular Dynamics Simulations Reveal Canonical Conformations in Different pMHC/TCR Interactions

“…Then, we extracted by means of a voxelization procedure the three Zernike 3D functions (3DZD) [32,33], representing the shape, the positive electrostatics and the negative electrostatics of the selected region, i.e., the binding groove. Such a procedure was recently implemented and applied in our recent work on similar systems [34,35].…”

Insights into the Interaction Mechanism of DTP3 with MKK7 by Using STD-NMR and Computational Approaches

“…Once the molecular surfaces are described with the Zernike descriptors, complementarity metrics for both the shape and the electrostatics can be easily defined using a pairwise distance (we adopted the Cosine distance). It results that the lower the distance between their Zernike descriptors, the higher the complementarity between the two potentially interacting molecular regions (See Experimental Section) [ 28 , 29 ]. By such an approach, we can quantitatively assess the complementarity between two molecular regions, belonging to different molecular partners, that are supposed to interact.…”