Equivariant Scalar Fields for Molecular Docking with Fast Fourier Transforms

Molecular docking is critical to structure-based virtual screening, yet the throughput of such workflows is limited by the expensive optimization of scoring functions involved in most docking algorithms. We explore how machine learning can accelerate this process by learning a scoring function with a functional form that allows for more rapid optimization. Specifically, we define the scoring function to be the cross-correlation of multi-channel ligand and protein scalar fields parameterized by equivariant graph neural networks, enabling rapid optimization over rigid-body degrees of freedom with fast Fourier transforms. The runtime of our approach can be amortized at several levels of abstraction, and is particularly favorable for virtual screening settings with a common binding pocket. We benchmark our scoring functions on two simplified docking-related tasks: decoy pose scoring and rigid conformer docking. Our method attains similar but faster performance on crystal structures compared to the widely-used Vina and Gnina scoring functions, and is more robust on computationally predicted structures. Proteins are the macromolecular machines that drive almost all biological processes, and much of early-stage drug discovery focuses on finding molecules which bind to and modulate their activity. Molecular docking--the computational task of predicting the binding pose of a small molecule to a protein target--is an important step in this pipeline. Traditionally, molecular docking has been formulated as an optimization problem over a scoring function designed to be a computational proxy for the free energy (Torres et al., 2019; Fan et al., 2019). Such scoring functions are typically a sum of pairwise interaction terms between atoms with physically-inspired functional forms and empirically tuned weights (Quiroga & Villarreal, 2016). While these terms are simple and hence fast to evaluate, exhaustive sampling or optimization over the space of ligand poses is difficult and leads to the significant runtime of docking software.