  Cryo-electron microscopy (cryo-EM) has recently become a premier method for
obtaining high-resolution structures of biological macromolecules. However, it
is limited to biomolecular samples with low conformational heterogeneity, where
all the conformations can be well-sampled at many projection angles. While
cryo-EM technically provides single-molecule data for heterogeneous molecules,
most existing reconstruction tools cannot extract the full distribution of
possible molecular configurations. To overcome these limitations, we build on a
prior Bayesian approach and develop an ensemble refinement framework that
estimates the ensemble density from a set of cryo-EM particles by reweighting a
prior ensemble of conformations, e.g., from molecular dynamics simulations or
structure prediction tools. Our work is a general approach to recovering the
equilibrium probability density of the biomolecule directly in conformational
space from single-molecule data. To validate the framework, we study the
extraction of state populations and free energies for a simple toy model and
from synthetic cryo-EM images of a simulated protein that explores multiple
folded and unfolded conformations.
