Abstract
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.
Highlights
Proteins are dynamic nanomachines that often populate heterogeneous ensembles of multiple distinct structural states
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
Bayesian ensemble refinement is demonstrated for two test proteins: leucine binding protein (LBP) using calculated Small-angle X-ray scattering (SAXS) data and heat shock protein 90 (Hsp90) using experimental SAXS data
Summary
Proteins are dynamic nanomachines that often populate heterogeneous ensembles of multiple distinct structural states. Detecting, understanding, and manipulating heterogeneous protein ensembles has remained a central goal of molecular biophysics [1]. Bayesian inference may become computationally expensive and technically challenging since it requires explicit sampling of the conformational space of the protein. It holds a number of key advances over more simple optimization algorithms, as it provides statistically founded procedures (i) to weight the experimental data versus prior physical knowledge, and (ii) to quantify the uncertainty (or ambiguity) of the fitted structural model [5]. Following the pioneering work by Rieping et al, we refer to structural modeling based on Bayesian statistics as ‘inferential structure determination’ (ISD) [6]
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