Cryo-Electron Microscopy Structural Ensemble Optimization Using Individual Particles

Biomolecules are inherently dynamic, transitioning between various conformational states to execute their biological functions; consequently, characterizing their ensemble distributions (the population of these conformations) is essential for understanding their biological roles. Cryo-electron microscopy (cryo-EM), a technique that images individual biomolecules frozen in a thin layer of amorphous ice, has emerged as a leading method for determining the structure of biomolecules at atomic resolution. Recent advances in cryo-EM reconstruction have enabled significant progress in characterizing conformational variability around metastable states. In contrast to reconstruction, a different class of techniques has been used to infer population weights, referred to as ensemble reweighting. These methods have yet to be generalized to infer structures and weights simultaneously. Here, we present a method for cryo-EM ensemble optimization that directly infers the optimal set of conformations and their associated population weights from cryo-EM images using Bayesian optimization techniques. Our method iterates between optimizing the structures and weights using a likelihood defined in terms of cryo-EM particle images (not reconstructions) and projecting onto the domain of a physical prior through an approach inspired by projected gradient descent. We test the method on several systems, ranging from a four-atom toy model to two large protein systems with real cryo-EM data. We find that our approach successfully recovers the structures and their associated weights across a wide range of experimental conditions, even when the number of structures does not match the actual number of metastable states. Our method paves the way for cryo-EM structural ensemble optimization of flexible biomolecules exhibiting complex, multimodal conformational landscapes.