Predicting equilibrium distributions for molecular systems with deep learning

Advances in deep learning have greatly improved structure prediction of molecules. However, many macroscopic observations that are important for real-world applications are not functions of a single molecular structure but rather determined from the equilibrium distribution of structures. Conventional methods for obtaining these distributions, such as molecular dynamics simulation, are computationally expensive and often intractable. Here we introduce a deep learning framework, called Distributional Graphormer (DiG), in an attempt to predict the equilibrium distribution of molecular systems. Inspired by the annealing process in thermodynamics, DiG uses deep neural networks to transform a simple distribution towards the equilibrium distribution, conditioned on a descriptor of a molecular system such as a chemical graph or a protein sequence. This framework enables the efficient generation of diverse conformations and provides estimations of state densities, orders of magnitude faster than conventional methods. We demonstrate applications of DiG on several molecular tasks, including protein conformation sampling, ligand structure sampling, catalyst–adsorbate sampling and property-guided structure generation. DiG presents a substantial advancement in methodology for statistically understanding molecular systems, opening up new research opportunities in the molecular sciences. Methods for predicting molecular structure predictions have so far focused on only the most probable conformation, but molecular structures are dynamic and can change when performing their biological functions, for example. Zheng et al. use a graph transformer approach to learn the equilibrium distribution of molecular systems and show that this can be helpful for a number of downstream tasks, including protein structure prediction, ligand docking and molecular design.