Fig 1.
Envelopes of (A) leucine binding protein (LBP) and (B) heat shock protein 90 (Hsp90), illustrated as a white surface.
Water molecules (red/white sticks) inside the envelope contributed to the explicit-solvent calculations used to compute the SAXS curves and the SAXS curve gradients, as required for the refinement simulations. (A) The N- and C-terminal domains of LBP are shown in red and blue cartoon representation, respectively. (B) The N-terminal, middle, and C-terminal domains of Hsp90 are shown in red, yellow, and blue cartoon representation, respectively.
Fig 2.
Bayesian ensemble refinement of leucine binding protein (LBP).
(A) Cartoon representation of LBP in closed and (B) open states. N- and C-terminal domains are colored in red and blue, respectively. (C) Solid lines: Computed SAXS curves of the open (light blue) and closed state (dark blue). Dashed lines: SAXS curves of open/closed heterogeneous ensembles, computed with open/closed weights of 25:75, 50:50, and 75:25. Inset: Complete SAXS curves up to q = 10 nm−1. Large figure: closeup view highlighting the differences between the SAXS curves. (D) Posterior distribution of the refined two-state ensemble, projected onto the weight wopen and the interdomain distance dNC of the open state. The one-dimensional marginalized distributions are shown in Fig 3A and S1 Fig.
Fig 3.
(A) Marginalized posterior of the weight of the open state from refinement of leucine binding protein (LBP). (B) Odds that a single state vs. a two-state ensemble underlies the SAXS curves, presented as pedge/pmax. For details, see text.
Fig 4.
Bayesian ensemble refinement of Hsp90.
(A/B) Cartoon representation of Hsp90, the first protomer shown in grey, and the second protomer in color. C-terminal, middle, and N-terminal domains are shown in blue, yellow, and red, respectively. (A) Closed state, modelled from the 2CG9 structure [36]. (B) Open state, refined against SAXS data. (C) Experimental SAXS curves (colored lines, taken from ref. [37]) and calculated SAXS curves (black) computed from the refined ensembles. For clarity, curves for AMPPNP- and ATP-bound states were vertically offset, and experimental data points with very large errors were removed. (D) Posterior distribution of refined Hsp90 ensemble plotted as function of the weight (wopen) and radius of gyration () of the open state. For reference, The radius of gyration Rg of the closed Hsp90 structure (2CG9) and of the partially open E. coli HptG structure (2IOQ) are indicated as pale red and grey circles [36, 38]. In addition, Rg of the experimental ensembles, taken from Guinier fits to the SAXS curves in (C), are indicated as colored bars (color coding according to C). (E) Posterior of wopen, computed from the maps in (D) by marginalizing out Rg.
Fig 5.
Residuals between the calculated SAXS curves and the experimental SAXS curves, evaluated at the q-points applied during the refinement simulations of Hsp90 (color code see legend).
(A) Residuals ΔI/σexp normalized with respect to purely statistical experimental errors σexp. Large residuals at low q reflect that the MD force field prohibited structures that would accurately match the data within statistical errors. (B) Residuals ΔI(q)/σtot, where σtot denotes the total error including both statistical and estimated systematic errors (see Methods for details). The reduced residuals compared to panel (A) reflect that the Bayesian analysis suggested substantial systematic errors as the most plausible explanation for discrepancies between calculated and experimental SAXS curves.
Fig 6.
Lines: Marginalized posteriors of the radius of gyration of the refined open state from two-state refinement of Hsp90+AMPPNP, Hsp90+ATP, and apo Hsp90 (for color code, see legend).
The posteriors characterize a wide open conformation. For comparison, pale green, purple, and pale blue bars indicate the Rg values for the ensembles of Hsp90+AMPPNP, Hsp90+ATP, and apo Hsp90, respectively, estimated from a Guinier fit to the experimental data [37]. The pale red bar indicates Rg of the closed crystal structure of Hsp90 (2CG9), and the grey bar indicates Rg of the partially open crystal structure of E. coli HptG (2IOQ) [36, 38].
Fig 7.
Overview of the algorithm used to compute the posteriors.
For more details, see text.