  In computer-aided drug discovery (CADD), virtual screening (VS) is used for
identifying the drug candidates that are most likely to bind to a molecular
target in a large library of compounds. Most VS methods to date have focused on
using canonical compound representations (e.g., SMILES strings, Morgan
fingerprints) or generating alternative fingerprints of the compounds by
training progressively more complex variational autoencoders (VAEs) and graph
neural networks (GNNs). Although VAEs and GNNs led to significant improvements
in VS performance, these methods suffer from reduced performance when scaling
to large virtual compound datasets. The performance of these methods has shown
only incremental improvements in the past few years. To address this problem,
we developed a novel method using multiparameter persistence (MP) homology that
produces topological fingerprints of the compounds as multidimensional vectors.
Our primary contribution is framing the VS process as a new topology-based
graph ranking problem by partitioning a compound into chemical substructures
informed by the periodic properties of its atoms and extracting their
persistent homology features at multiple resolution levels. We show that the
margin loss fine-tuning of pretrained Triplet networks attains highly
competitive results in differentiating between compounds in the embedding space
and ranking their likelihood of becoming effective drug candidates. We further
establish theoretical guarantees for the stability properties of our proposed
MP signatures, and demonstrate that our models, enhanced by the MP signatures,
outperform state-of-the-art methods on benchmark datasets by a wide and highly
statistically significant margin (e.g., 93% gain for Cleves-Jain and 54% gain
for DUD-E Diverse dataset).
