Energy-Based Models for Predicting Mutational Effects on Proteins

Predicting changes in binding free energy ($\Delta\Delta G$) is a vital task in protein engineering and protein-protein interaction (PPI) engineering for drug discovery. Previous works have observed a high correlation between $\Delta\Delta G$ and entropy, using probabilities of biologically important objects such as side chain angles and residue identities to estimate $\Delta\Delta G$. However, estimating the full conformational distribution of a protein complex is generally considered intractable. In this work, we propose a new approach to $\Delta\Delta G$ prediction that avoids this issue by instead leveraging energy-based models for estimating the probability of a complex's conformation. Specifically, we novelly decompose $\Delta\Delta G$ into a sequence-based component estimated by an inverse folding model and a structure-based component estimated by an energy model. This decomposition is made tractable by assuming equilibrium between the bound and unbound states, allowing us to simplify the estimation of degeneracies associated with each state. Unlike previous deep learning-based methods, our method incorporates an energy-based physical inductive bias by connecting the often-used sequence log-odds ratio-based approach to $\Delta\Delta G$ prediction with a new $\Delta\Delta E$ term grounded in statistical mechanics. We demonstrate superiority over existing state-of-the-art structure and sequence-based deep learning methods in $\Delta\Delta G$ prediction and antibody optimization against SARS-CoV-2.