  Many factors influence biomolecules binding, and its assessment constitutes
an elusive challenge in computational structural biology. In this respect, the
evaluation of shape complementarity at molecular interfaces is one of the main
factors to be considered. We focus on the particular case of antibody-antigen
complexes to quantify the complementarities occurring at molecular interfaces.
We relied on a method we recently developed, which employs the 2D Zernike
descriptors, to characterize investigated regions with an ordered set of
numbers summarizing the local shape properties. Collected a structural dataset
of antibody-antigen complexes, we applied this method and we statistically
distinguished, in terms of shape complementarity, pairs of interacting regions
from non-interacting ones. Thus, we set up a novel computational strategy based
on \textit{in-silico} mutagenesis of antibody binding site residues. We
developed a Monte Carlo procedure to increase the shape complementarity between
the antibody paratope and a given epitope on a target protein surface. We
applied our protocol against several molecular targets in SARS-CoV-2 spike
protein, known to be indispensable for viral cell invasion. We, therefore,
optimized the shape of template antibodies for the interaction with such
regions. As the last step of our procedure, we performed an independent
molecular docking validation of the results of our Monte Carlo simulations.
