SAXS refinement simulations

For LBP simulations, the target curves for the refinement were modeled from calculated SAXS curves of the closed state I_closed(q) (Fig 2C, solid dark blue curve) and open state I_open(q) (Fig 2C, solid light blue curve), as follows:

In this study, we tested ensemble refinement against SAXS data computed with the following wopenexp: 0, 25%, 50%, 75%, or 100% (Fig 2C, solid and dashed curves). Hence, since I_exp,w(q) was computed theoretically, the true weight of the open state was known, allowing us

to validate that the SAXS-guided refinement starting from the closed state is capable of reproducing the true weight (wopenexp) and the true structure of the open state (used to compute I_open(q)), and

to derive the uncertainty (or ambiguity) of the weight and structure in the light of the SAXS curve and the MD force field, as given by the width of the posterior distributions.

All simulations of LBP were started from the closed state (Fig 2A). The simulations were coupled to the target SAXS curve at N_q = 25 q-points, which were evenly distributed between 0 and 8 nm⁻¹. The two-state ensemble refinement was conducted using umbrella sampling along the weight w_open of the open state (see above). Each umbrella window was simulated for 40 ns, where the first 2 ns were removed for equilibration. The posterior distributions of w_open and of the interdomain distance derived from these simulations are presented in Figs ​Figs2D,2D, ​,3A3A and S1A Fig.

For comparison, a single state (instead of the ensemble of two states) was refined against each of the five curves I_exp,w(q), using five simulations of 10 ns each and removing the first 2 ns for equilibration. S1B Fig presents the posteriors of the interdomain distance d_NC resulting from refining a single structure against SAXS curves that, in truth, represent heterogenous open/closed ensemble. Notably, the single-state refinements try to explain those SAXS curves with intermediate (partially open) structures.

For the refinement simulations of Hsp90, the simulations were coupled to the target SAXS curve at N_q = 30 q-points, which were evenly distributed between 0.1 and 3 nm⁻¹. The q-range below 0.1 nm⁻¹ was omitted because the experimental data exhibited some deviation from the ideal Guinier behaviour. For some umbrella windows, Hsp90 was required to carry out large-scale conformational transitions. To accelerate those transitions, each window was first simulated for 8 ns with a ten-fold increased experiment-derived energy E_exp. Subsequently, the simulation of each umbrella window was continued for another 20 ns using the statistically founded E_exp that leads to the correct posterior (eq 18). From those simulations, the first 2 ns were removed for further equilibration, and the remaining simulation time was used to compute the posterior. An example of the umbrella histograms along the weight coordinate is shown in S4 Fig. To further improve the sampling close to the maxima of the posteriors, the simulations of the umbrella window at the peak of p(w_open|D, K) plus two neighboring windows were prolonged for another 15 ns.