# Energy-Based Models for Predicting Mutational Effects on Proteins

arXiv: https://arxiv.org/abs/2508.10629 · HTML: https://mlsanity.com/paper/2508.10629/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 67 references that are in the map.
- First posted on arXiv 14 Aug 2025.

## Builds on (most cited first, 14 of 14)

- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields](https://mlsanity.com/paper/2206.07697/) (2022)
- [Learning Local Equivariant Representations for Large-Scale Atomistic Dynamics](https://mlsanity.com/paper/2204.05249/) (2022)
- [Tranception: protein fitness prediction with autoregressive transformers and inference-time retrieval](https://mlsanity.com/paper/2205.13760/) (2022)
- [Two for One: Diffusion Models and Force Fields for Coarse-Grained Molecular Dynamics](https://mlsanity.com/paper/2302.00600/) (2023)
- [When Attention Meets Fast Recurrence: Training Language Models with Reduced Compute](https://mlsanity.com/paper/2102.12459/) (2021)
- [Unsupervised Protein-Ligand Binding Energy Prediction via Neural Euler's Rotation Equation](https://mlsanity.com/paper/2301.10814/) (2023)
- [Blocks: Collaborative and Persistent Augmented Reality Experiences](https://mlsanity.com/paper/1908.02409/) (2019)
- [Learning to Predict Mutation Effects of Protein-Protein Interactions by Microenvironment-aware Hierarchical Prompt Learning](https://mlsanity.com/paper/2405.10348/) (2024)
- [Score-Based Generative Models for Molecule Generation](https://mlsanity.com/paper/2203.04698/) (2022)
- [Multi-level Interaction Modeling for Protein Mutational Effect Prediction](https://mlsanity.com/paper/2405.17802/) (2024)
- [Posterior sampling via Langevin dynamics based on generative priors](https://mlsanity.com/paper/2410.02078/) (2024)

## Abstract (arXiv)

Predicting changes in binding free energy (DeltaDelta 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 DeltaDelta G and entropy, using probabilities of biologically important objects such as side chain angles and residue identities to estimate DeltaDelta G. However, estimating the full conformational distribution of a protein complex is generally considered intractable. In this work, we propose a new approach to DeltaDelta 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 DeltaDelta 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 DeltaDelta G prediction with a new DeltaDelta E term grounded in statistical mechanics. We demonstrate superiority over existing state-of-the-art structure and sequence-based deep learning methods in DeltaDelta G prediction and antibody optimization against SARS-CoV-2.