Bayesian refinement of protein structures and ensembles against SAXS data using molecular dynamics

Small-angle X-ray scattering is an increasingly popular technique used to detect protein structures and ensembles in solution. However, the refinement of structures and ensembles against SAXS data is often ambiguous due to the low information content of SAXS data, unknown systematic errors, and unknown scattering contributions from the solvent. We offer a solution to such problems by combining Bayesian inference with all-atom molecular dynamics simulations and explicit-solvent SAXS calculations. The Bayesian formulation correctly weights the SAXS data versus prior physical knowledge, it quantifies the precision or ambiguity of fitted structures and ensembles, and it accounts for unknown systematic errors due to poor buffer matching. The method further provides a probabilistic criterion for identifying the number of states required to explain the SAXS data. The method is validated by refining ensembles of a periplasmic binding protein against calculated SAXS curves. Subsequently, we derive the solution ensembles of the eukaryotic chaperone heat shock protein 90 (Hsp90) against experimental SAXS data. We find that the SAXS data of the apo state of Hsp90 is compatible with a single wide-open conformation, whereas the SAXS data of Hsp90 bound to ATP or to an ATP-analogue strongly suggest heterogenous ensembles of a closed and a wide-open state.Author summary: In solution, many proteins adopt ensembles of multiple distinct states. The relative concentrations of the states are tightly controlled by factors such as pH, phosphorylation, or ligand binding, and a misbalance between the states underlies diseases such as cancer or neurodegeneration. However, detecting protein ensembles in experimental data has remained challenging. We present a statistically founded procedure for refining protein structures and ensembles against X-ray solution scattering data by combining atomistic simulations with Bayesian inference.