The Hsp90 from *E. coli* (HtpG) populates three conformations that can be clearly resolved by SAXS. The influence of osmolytes on these states was investigated by measurements of this chaperone in the presence of 1*M* each of the osmolyte solutions (TMAO, betaine, sarcosine, glycerol, or urea). Other well studied osmolytes such as sucrose, trehalose, and sorbitol show substantial background scattering that complicates their analysis (data not shown) and are not included. The scattering intensity was measured between Q values (4πsinθ /λ where 2θ is the scattering angle) of 0.01 to 0.3 Å^{−1}, radially averaged and then buffer subtracted. The resulting data were transformed to an interatomic distance distribution, P(r), by Fourier transform. In the absence of osmolytes [Fig. 2(A), red curve], the distance distribution for HtpG at pH 7.5 agrees with previous studies.22

The addition of osmolytes produces striking structural changes that are evident in the distance distribution [Fig. 2(A)]. For the protecting osmolytes TMAO, betaine and sarcosine there is a noticeable contraction toward smaller distances, whereas for the denaturant urea there is a clear expansion. Glycerol, a weakly stabilizing osmolyte, has a minimal influence on the distance distribution. The differing influence of these osmolytes can be rank ordered by their respective P(r) values at a reference distance, such as 50 Å [dashed line, Fig. 2(A)]. This ordering: TMAO > betaine > sarcosine > glycerol > urea, is the same ranking for the degree to which these osmolytes affect protein stability, as discussed next.

The backbone transfer free energy of an osmolyte is the key metric that quantifies its influence on folding free energy.9, 25 For example, the stabilizing osmolyte TMAO has a positive value (89 cal/mol/*M*) indicating an unfavorable backbone interaction (thus raising the free energy of the unfolded state and thereby providing relative stability to the native state), whereas the denaturant urea has a negative value (-41 cal/mol/*M*). These energetic values provide the dominant contribution of an osmolyte to protein stability. The rank ordering of these transfer free energies, TMAO (89 cal/mol/*M*) > betaine (65 cal/mol/*M*) > sarcosine (56 cal/mol/*M*) > glycerol (22 cal/mol/*M*) > urea (-41 cal/mol/*M*), is the same as their rank order influence on the P(r) value for HtpG. Indeed, we observe a strong correlation (R = 0.90) between the backbone transfer free energy values of each osmolyte and the P(r) value at 50 Å [Fig. 2(B)]. Since P(r) reflects the ratio of a conformational equilibrium, the quantity ln[P(r)] may be more appropriate for comparison against an energetic value. This comparison also yields a similarly high correlation coefficient (0.90, Supporting Information Fig. 1). This favorable correlation immediately suggests that the same physical principles that govern the osmolyte influence on protein folding also apply to large-scale conformational changes within the HtpG native ensemble.

The Hsp90 chaperone is highly conserved, with homologs in every kingdom of life.26 The domain structure is consistent among species, but the conformational ensemble in the absence of nucleotide is species-specific,21 with human and yeast Hsp90s favoring the open state, whereas the bacterial homolog (HtpG) populates a mixture of open and closed states. However, like HtpG, both yeast and human Hsp90 exhibit TMAO-induced contractions in their respective SAXS distance distributions (Supporting Information Fig. 2), indicating that the osmolyte effect is maintained within this chaperone family.

#### Osmolyte-driven conformation changes

Previous work with HtpG demonstrated that SAXS data can be fit to determine the relative populations of different conformers, which differ by only rigid body domain rearrangements.20 As expected for rigid body motion, the conformational changes induced by 1*M* TMAO are not associated with an increase in circular dichroism or fluorescence (data not shown), in contrast to large scale folding events. Indeed, similar to previous studies, the scattering data is well fit with a simple linear combination of the open and closed states. The computational method behind this procedure simply involves a linear least squares fit of additive combinations of precalculated P(r) curves for the different HtpG conformations (see Methods).

This two-state treatment results in an excellent agreement with the data. For example, the P(r) curves for HtpG in the absence of osmolytes and at 1*M* TMAO are shown with their respective fits in Figure 3. The fitting demonstrates that the open/closed equilibrium, 81/19%, is shifted to 34/66% in 1*M* TMAO. The visual agreement between the model and data is apparent, and is quantified by a low R-factor (similar to a crystallographic R-factor, see equation in Methods) of 2.1 and 2.2%, respectively.

This two-state model suggests that the open/closed transition is highly cooperative, with both monomers acting in concert despite the fact that neither the M-C nor the NTD interfaces are in contact (Fig. 1). This high cooperativity can be corroborated by investigating two alternative models [shown in Fig. 3(C)] that can be excluded by structure-based fitting. In the first (model *ii*), the individual monomers undergo independent transitions between the open and closed state, which would add a third mixed conformation into the equilibrium. In the absence of cooperativity, this mixed state would be maximally populated (50%) at an osmolyte concentration at the midpoint of the open/closed equilibrium. At 0.6*M* TMAO the open/closed equilibrium is 46.7/53.3% with an R-factor of 2.55%, providing an excellent opportunity to test this prediction. A three state fit indicates that a mixed state is either very minimally populated or not populated at all (open/closed/mixed is 53.1/46.1/0.8 with a minimally changed R-factor of 2.54%).

A second model with less cooperativity could involve a gradual shift to intermediate conformations that are between the open and closed states [Fig. 3(C), model *iii*], reminiscent of one-state protein folding models.27 This model implies that at intermediate TMAO concentrations, the conformational equilibrium would be better fit by a combination of the closed state and a new state that is more closed than the open state. We tested this prediction at 0.4*M* TMAO, where the open/closed equilibrium is 53/47% (R-factor of 2.3%). By fitting these data with the closed state and a state with rigid body freedom to explore intermediate conformations via different M-C opening angles (see Methods), we found that the optimal fit involved a state that is similar to the open state (Supporting Information Fig. 3).

Finally, the cooperativity is supported by an equivalent distribution of R-factors for the two-state fit at TMAO concentrations taken at regular intervals. These R-factors (which represent the quality of the two-state model) are: 2.2, 2.5, 2.3, 2.6, 2.6, 2.1% for TMAO concentrations of 0.0, 0.2, 0.4, 0.6, 0.8, 1.0*M*. This indicates that the two-state model is similarly appropriate over a wide range of the open/closed equilibrium.

Given that a two-state transition is an appropriate description of the osmolyte-induced conformational change, we can determine an open/closed equilibrium constant and subsequently its free energy. Since the open/closed equilibrium is controlled by a simple domain-domain interaction that buries a significant surface area, this should allow for a comparison with folding studies where a clear correlation has been observed between the folding-induced change in surface area and *m*-value (slope of the free energy change vs TMAO concentration). An equivalent conformational *m*-value can be determined from an osmolyte concentration series.

The TMAO titration shows a smooth change in the P(r) curves (Figure 4A) and subsequently the open/closed population (Figure 4B) and the associated free energy (inset). The linear extrapolation model28, 29 predicts a linear relationship (with a slope of *m*) between *RT*ln(*K*) and [TMAO], where *K* is the open/closed equilibrium constant. This concentration series shows an initially large slope of 2 kcal/mol/*M* at TMAO concentrations less than 0.4*M*, and above this concentration the slope reduces to 0.85 kcal/mol/*M* (inset, dashed lines). This change of *m*-value suggests larger surface area burial contributing to the conformational change at low TMAO concentrations. As discussed next, we can use the Tanford transfer model to suggest a structural interpretation of this behavior.

The open/closed conformational change involves rigid body rearrangements at the M-C interface (residue 500 marks the division between these domains). A predicted TMAO *m*-value associated with making/breaking this domain-domain interface can be determined from the Tanford transfer model, which scales the number of backbone and sidechain groups against the sum of experimentally measured transfer free energies associated with each group (details of this calculation method are given in other publications15). The predicted value for making/breaking the M-C interface is 0.7 kcal/mol/*M*, which is close to the limiting *m*-value at high TMAO concentrations (0.85 kcal/mol/*M*). This suggests that in the higher TMAO concentration regime the structural influence of TMAO is given by its role in forming the M-C domain interface. By contrast, at lower TMAO concentrations there are likely additional processes with significant surface area changes not reflected in the rigid rotation model. As discussed later, this type of variable *m*-value shows similarities to subglobal folding transitions that have been observed in osmolyte-induced protein folding/unfolding measurements.

#### Comparison of ligand-induced and osmolyte-induced conformational changes

The ATPase activity of Hsp90 is required for viability in eukaryotes30 and the binding of ATP is associated with an additional conformational change involving N-terminal dimerization (Fig. 1). This allows us to investigate the interplay between ligand- and osmolyte-induced conformational changes. The addition of a saturating concentration of 10 m*M* AMPPNP causes a significant change in conformation [compare Fig. 5(A) and Fig. 3(A)]. The two-state open/closed model no longer fits the data well (R-factor of 10%, Figure 5A dashed line), but a three-state open/closed/ATP fit results in good agreement (R-factor of 2.5%, solid line), similar to previous studies.22

The addition of 10 m*M* AMPPNP and 1*M* TMAO shows this osmolyte affects the open/closed equilibrium but not the ATP population. The fitting (solid line, Figure 5B) indicates a similar population of the ATP state (57 versus 55% with and without 1*M* TMAO, respectively), but a dramatically different open/closed equilibrium (13/30% versus 45/0%). These changes are indicated by the relative height of the red/blue bars in Figure 5. To explore this effect over a broad range of conditions, we performed a concentration series of AMPPNP with and without TMAO, which demonstrates only modest TMAO-induced changes in the population of the ATP state [Supporting Information Fig. 4(A)]. Consistent with the lack of TMAO-induced changes in the ATP population, we measured no change in the rate of ATP hydrolysis by HtpG in 1*M* TMAO (data not shown).

The ATP state has a fully formed M-C interface and buries an additional 1900 Å2 via N-terminal dimerization, and yet the addition of TMAO alone does not populate this conformation. The observation that TMAO does not populate the more buried ATP state is possibly because of the complex, ligand-specific, reorganizations required to access this state. Indeed, ATP binding (i) restructures an N-terminal lid region that makes important dimer contacts, (ii) dramatically changes the organization with the middle domain via an interaction between an arginine (residue 336 in HtpG), and the ATP γ-phosphate, and (iii) is associated with the release of a β-strand which then makes cross monomer interactions that stabilize the N-terminal dimerization.18, 19 These ligand-specific effects are unique to ATP, as ADP has been shown by SAXS to promote a conformational equilibrium similar to apo conditions. As expected then, in the presence of 1*M* TMAO the subsequent addition of ADP has no significant effect on the conformational equilibrium [Supporting Information Fig. 4(B)].