  Efficient molecular featurization is one of the major issues for machine
learning models in drug design. Here we propose persistent Ricci curvature
(PRC), in particular Ollivier persistent Ricci curvature (OPRC), for the
molecular featurization and feature engineering, for the first time. Filtration
process proposed in persistent homology is employed to generate a series of
nested molecular graphs. Persistence and variation of Ollivier Ricci curvatures
on these nested graphs are defined as Ollivier persistent Ricci curvature.
Moreover, persistent attributes, which are statistical and combinatorial
properties of OPRCs during the filtration process, are used as molecular
descriptors, and further combined with machine learning models, in particular,
gradient boosting tree (GBT). Our OPRC-GBT model is used in the prediction of
protein-ligand binding affinity, which is one of key steps in drug design.
Based on three most-commonly used datasets from the well-established
protein-ligand binding databank, i.e., PDBbind, we intensively test our model
and compare with existing models. It has been found that our model are better
than all machine learning models with traditional molecular descriptors.
