  Single molecule X-ray scattering experiments with free electron lasers have
opened a new route to the structure determination of biomolecules. Because
typically only very few photons per scattering image are recorded and thus the
signal-to-noise ratio is very low in this extreme Poisson regime, structure
refinement is quite challenging. In addition, in each scattering event the
orientation of the biomolecule is random and unknown. As a further layer of
complexity, many biomolecules show structural heterogeneity and conformational
transitions between different distinct structures; these structural dynamics
are averaged out by existing refinement methods. To overcome these limitations,
here we developed and tested a rigorous Bayesian approach and demonstrate that
it should be possible to determine not only a single structure, but an entire
structural ensemble from these experiments. Using $10^6$ synthetic scattering
images generated from molecular dynamics trajectories, our approach was able to
resolve ensembles of eight alanine dipeptide conformers at $2\,$\r{A}
resolution; similarly, we determined the unfolded ensemble of the protein
chignolin at $4-7\,$\r{A} resolution using $1.2\cdot 10^7$ images.
Unexpectedly, much fewer images are required to determine an ensemble of $n$
structures of $m$ atoms each than a single structure of $n\times m$ atoms,
i.e., of the same total number of degrees of freedom. These findings show that
X-ray scattering experiments using state-of-the-art free electron lasers should
allow one to determine not only biomolecular structures, but whole structure
ensembles and, ultimately, 'molecular movies'.
