MathDL: mathematical deep learning for D3R Grand Challenge 4.

Area of Science:

• Computational chemistry
• Machine learning
• Structural biology

Background:

• Drug discovery relies on accurate prediction of molecular interactions.
• The D3R Grand Challenge 4 (GC4) benchmarked computational models for BACE and CatS.
• Existing methods face challenges in efficiently representing complex molecular interactions.

Purpose of the Study:

• To present the performance of novel mathematical deep learning (MathDL) models in GC4.
• To evaluate MathDL models for BACE ligand pose prediction, affinity ranking, and free energy estimation.
• To assess MathDL models for Cathepsin S (CatS) affinity ranking and free energy estimation.

Main Methods:

• Developed MathDL models integrating differential geometry, algebraic graph, and topology.
• Created low-dimensional, rotation/translation invariant representations of physical/chemical interactions.
• Employed generative adversarial networks (GANs) for pose prediction and convolutional neural networks (CNNs) for energy evaluation.

Main Results:

• Achieved top ranking in BACE ligand pose prediction (Stage 1a).
• Secured the highest Spearman correlation for CatS compound affinity ranking.
• Obtained the smallest centered root mean square error for CatS free energy estimation.
• Demonstrated significant improvement in docking pose prediction accuracy over previous methods.

Conclusions:

• MathDL models show high efficacy in molecular docking and binding affinity prediction.
• The integration of advanced mathematics with deep learning offers a powerful approach for drug discovery.
• The developed methods provide accurate and efficient tools for BACE and CatS related research.