A path collective variable for extracting free energy profiles from cryo-electron microscopy

Abstract

ABSTRACT: Cryo-electron microscopy (or cryo-EM) is an experimental technique to obtain structures of biomolecules. Although single-particle cryo-EM is widely used for 3D reconstruction, it has the potential to provide information about a biomolecule’s conformational variability, which leads to the underlying free-energy landscape of the system. However, cryo-EM as a single-molecule technique uses the 2D projections of individual particles with low signal-to-noise ratio (SNR), making it difficult to work directly with the raw cryo-EM data. Even though there are some methods that overcome the SNR issue, those normally need a big image data bank or are difficult to reproduce. This work proposes a new method called cryo-BIFE (cryo-EM Bayesian Inference of Free-Energy profiles), which uses a path collective variable to extract free-energy profiles and their uncertainties from cryo-EM images. The method is tested for different realistic experimental conditions, leading to a very good performance of extracting free energy profiles for different benchmark systems using different sets of synthetic images. The results show that, to recover the underlying free energy, the SNR in the cryoEM images and the accuracy in estimating the orientation of biomolecule’s projection, are crucial factors. Then, the method is used to study the conformational transitions of a calcium-activated channel with real cryo-EM particles. Interestingly, we recover not only the most probable conformation (used to generate a high-resolution reconstruction of the calcium-bound state) but also a metastable state that corresponds to the calcium-unbound conformation. As expected for turnover transitions within the same sample, the activation barriers are on the order of kBT. We expect our tool for extracting free-energy profiles from cryo-EM images will enable more complete characterization of the thermodynamic ensemble of biomolecules.