  Cryo-electron microscopy (cryo-EM) extracts single-particle density
projections of individual biomolecules. Although cryo-EM is widely used for 3D
reconstruction, due to its single-particle nature, it has the potential to
provide information about the biomolecule's conformational variability and
underlying free energy landscape. However, treating cryo-EM as a
single-molecule technique is challenging because of the low signal-to-noise
ratio (SNR) in the individual particles. In this work, we developed the
cryo-BIFE method, cryo-EM Bayesian Inference of Free Energy profiles, that uses
a path collective variable to extract free energy profiles and their
uncertainties from cryo-EM images. We tested the framework over several
synthetic systems, where we controlled the imaging parameters and conditions.
We found that for realistic cryo-EM environments and relevant biomolecular
systems, it is possible to recover the underlying free energy, with the pose
accuracy and SNR as crucial determinants. Then, we used the method to study the
conformational transitions of a calcium-activated channel with real cryo-EM
particles. Interestingly, we recover the most probable conformation (used to
generate a high resolution reconstruction of the calcium-bound state), and we
find two additional meta-stable states, one which corresponds to the
calcium-unbound conformation. As expected for turnover transitions within the
same sample, the activation barriers are of the order of a couple $k_BT$.
Extracting free energy profiles from cryo-EM will enable a more complete
characterization of the thermodynamic ensemble of biomolecules.
