The function of a large number of proteins and enzymes is determined by the synergic interplay of structure and dynamics, often modulated by substrate binding or covalent modifications. Although many mechanisms have been elucidated 
, the question of how atomic fluctuations are connected to the large-scale functional motions remains a major open problem that is actively investigated experimentally and computationally.
Here, we focus on a specific aspect of this general problem by considering how the large-scale internal dynamics of members of the Hsp90 family is affected by the bound nucleotide. In fact, the conformational turnover of these chaperones depends primarily on ATP binding and hydrolysis (though interaction with co-chaperones and even client proteins is expectedly important for the balance of alternative states in vivo 
). Characterizing the salient aspects of these chaperones' functional dynamics using atomistic MD simulations has proved challenging. Besides the unavoidable time-span limitations of MD simulations, a key obstacle is the very large-scale character of the chaperones' conformational rearrangements. As a consequence, powerful techniques such as principal component analysis 
, where the internal dynamics is projected on the linear space spanned by a small number of essential dynamical modes 
, cannot be used for a faithful representation of the simulated trajectory.
To overcome these difficulties and to gain insight into the functional dynamical aspects that are common to various members of the Hsp90 family, we introduced a novel multiscale method for analyzing and comparing MD simulations of related, but structurally-different, proteins. Specifically, the method is applied to atomistic MD simulations of the Apo, ADP-bound and ATP-bound states of mammalian Grp94 
, yeast Hsp90 
. The molecules differ noticeably for structural organization and are therefore ideal benchmarks for general methods aimed at identifying common, corresponding dynamical traits in the proteins. Indeed, our integrated results allowed to pinpoint common mechanistic properties and to obtain a unified view of the relevant motions linked to function at different levels of resolution.
Multiscale analysis of Hsp90 chaperones
Our analysis proceeded by comparing the dynamics of Hsp90, Grp94 and HtpG in various ligand-bound states at increasing length-scales: from the atomistic level to the protein domain one.
We started by considering the fluctuations of the distances of all pairs of amino acids and identified the regions experiencing the largest deformation of their local structural neighborhood (strain) 
upon change of the bound ligand.
Importantly, across all three chaperones, four common regions were identified: the nucleotide binding site in the N-terminal domain (ATP-lid, N-M interface), the aromatic cluster in the H4–H6 helix bundle located in the Middle domain, the core of the C-terminal domain and finally the C-terminal loops defining the allosteric binding pocket for C-terminal inhibitors of Hsp90 
By analyzing the various terms of the proteins' internal energy it is established that the ligand-dependent changes in the protomeric structures correlate with the strength of the electrostatic interaction between the bound nucleotide and the positively charged Arginine in the Middle domain (see , and , S3).
The modulation of this attraction affects the catalytic loop (containing Arg448 in Grp94, Arg380 in Hsp90 and Arg336 in HtpG) and, more notably, the cluster of aromatic residues at the end of the H4–H6 three-helix bundle in the Middle domain. In fact, going from the ATP to the ADP state, the increased separation of the nucleotide-binding domain and the catalytic loop in the Middle domain causes the end of the H4–H6 bundle to partially unfold/unpack. This, in turn, leads to the opening of the dimeric clamp. By contrast, the presence of ATP favors the stabilization of the aromatic cluster in an optimally-packed organization.
The fluctuation analysis of the 1800-ns-long “meta-trajectory”, obtained by combining the atomistic trajectories of the single protomers of the three chaperones in all considered ligand-bound states, was next used to subdivide the protomers of the Hsp90, Grp94 and HtpG chaperones into corresponding quasi-rigid domains. The subdivision into quasi-rigid domains lends naturally to describe the large-scale motion of the chaperones with a minimal number of degrees of freedom. In fact, as much as 61% of the “meta-trajectory” mean square fluctuations can be accounted for by the relative rigid-like movements (translations and rotations) of merely 3 quasi-rigid domain (see , , ,
). With reference to the structural subdomains, the quasi-rigid (dynamical) ones correspond to: the N-terminal domain, the portion of Middle domain corresponding to the M-large subdomain (including β-sheets S1 to S5 and α-helices H1 to H5) 
, and to the combination of the M-small (comprising H6 to H10) and C-terminal domains (see , , ,
A minimalistic, though viable, description of the large-scale dynamics that is shared by the three chaperones is obtained by restricting the motion of the two side quasi-rigid domains to consist exclusively of rotations around axes that are fixed (same position and orientation) to the corresponding core of Hsp90, Grp94 and HtpG. By doing so, only two degrees of freedom (the instantaneous rotation angles) are needed to parameterize the “meta-trajectory” and yet it is still possible to account for 55% of its covariance.
The location of the two optimal axes of rotation for the quasi-rigid domains was next used to single out regions that have a crucial mechanical role in the large-scale motion of all three chaperones and hence ought to represent good target sites for inhibiting drugs. Consistently with this observation, one of them is the interface between the N-terminal and Middle domains which corresponds to a previously identified functional site 
. The second one is centered on the aromatic cluster at the end of the three-helix bundle located at the interface between the large and small sub-portions of the protomeric Middle domain. This latter site was not pointed out before as being functionally relevant and hence could represent a new druggable site for the discovery/design of a novel class of allosteric inhibitors active on the chaperones, thus increasing the chemical space of possible Hsp90 inhibitors for the treatment of different diseases.
Model for the conformational mechanisms of Hsp90 chaperones
Based on the above results it is possible to formulate a consistent, unified framework for the conformational mechanisms of Hsp90, Grp94 and HtpG.
The primary direct effect ascribable to the specific nucleotides in all three proteins is the modulation of the Coulombic interactions with the positively charged residues in the catalytic loop and in Middle domain (see ). These interactions are highest in the presence of ATP, and their attractive character favors the approach of the N-terminal domains through a rotation around the hinge passing at the interfaces with the Middle domains. In fact, ATP-binding to different, more open conformations, here exemplified by the starting structures of Grp94 and HtpG, results in the activated state which can eventually evolve to the final closed compact structure of ATP-bound Hsp90, in which the two N-terminal domains share a large and compact interface. In particular, the importance of the inter-protomer contacts at the N-terminal domains for the efficiency of the Grp94 hydrolysis was demonstrated by the experiments of Dollins and coworkers 
who reported a reduction of the activity in mutants lacking β-strand1 or β-strand1 plus α-helix 1, which are required for N-terminal dimerization. These closure motions are linked to modulations of the fluctuation and strain patterns that extend through the whole structure, which are strikingly similar across the three proteins, independent of the global 3D organization. In particular, the boundary region between M-small and C-terminal domain increases its mobility, which is compatible with maintaining a significant twist at the C-terminal interface, as observed in the closed activated structure.
Switching from ATP to ADP, the catalytic loop containing Arg448 in Grp94, Arg380 in Hsp90 and Arg336 in HtpG experiences particularly high geometrical strain. The deformation of the contact network of this loop correlates to that of the ordered cluster of aromatic residues at the basis of the H4–H6 three-helix bundle in the Middle domain. The electrostatic attraction of the N-terminal and Middle domains decreases and the protomers relax from the closed state (reference structure Hsp90-ADP), through a rotation that causes a partial unfolding of the basis of the three-helix bundle. This sequence results in an opening of the structures with increased mobility of the Middle domains (Grp94-ADP, HtpG-ADP) and in the collapse of the N-terminal domains over the M-domains, as well as in the population of the “open-compact” conformations described by Agard and coworkers (Grp94-ADP). In this framework, the catalytic loop provides a direct mechanical response to the type of bound nucleotide.
Finally, the release of the nucleotide leads to states with no specific dynamic signatures, which can be correlated to the absence of conformational preferences in the absence of ligand. The release of the ligand induces a strain that favors a reduced twist at the C-terminal interface in all Apo systems, converging to the values typical of HtpG, which can be related to the tendency of the proteins to evolve to fully open structures.
Model comparison and validation against experimental data
As discussed hereafter, the results of the present multiscale analysis are in accord with several experimental findings and contribute to establishing a comprehensive view of the functional mechanics of these chaperones.
The Neckers group identified a conserved hydrophobic motif in β-strands at the C-terminal boundary of the N-domain, whose mutation abrogated Hsp90 function. Hsp90 mutants lacked chaperone activity in vitro and failed to support yeast viability. Chaperone activity was restored by truncation of the charged linker connecting the N-terminal and Middle domains, consistently with the key “mechanical” role of hydrophobic contacts in the N-M hinge region found in our study 
In a different study, Vasko and co-workers identified Sansalvamide A (SanA) as a structurally novel Hsp90 inhibitor. Through the use of pull-down experiments in the presence of the three isolated domains of Hsp90, a construct containing only the N-terminal/Middle domains, and the WT protein, the authors were able to show that SanA binds exclusively to the N-terminal/Middle construct of the protein 
. Building on this experimental evidence, their studies were extended to synthetic SanA derivatives with different activities 
. Using a docking-based strategy, they were able to generate structure activity relationships for the small molecules, based on their predicted binding to the N-terminal/Middle interface, as indicated by the pull-downs.
Finally, Matts and coworkers 
considered different classes of modulators/inhibitors of Hsp90 activity and showed that the action of several inhibitors (whose binding site is still unknown) made the hinge located at the Middle domain three-helix bundle not accessible to trypsin-proteolysis. In particular, in the presence of celastrol, gedunin, or H2-gamendazole the cleavage site Lys398 (together with Arg291) in HtpG (corresponding to Lys508 in Grp94, in close proximity to the location of the hinge located in the Middle domain) is protected from degradation. This suggests that this key site identified by our study is shielded either by direct binding of the drugs or by conformational changes induced through allosteric mechanisms 
The three-helix bundle in the Middle domain and the N-M interface hinge have also been shown to be involved in the interaction with the ATPase stimulating co-chaperone Aha1 
. Indeed, one Aha1 molecule is found to interact in an asymmetric manner with the Hsp90 dimer: the N-terminal domain of Aha1 engages Hsp90 Middle domain making contacts both with the three-helix bundle, and with the residues at the N-M interface (as seen from NMR perturbation studies), which we found to be crucial for the chaperones' functional mechanics.
In this context, results from the Agard group support the importance of the HtpG region around residue 450 as important in regulating conformational changes. Using small-angle X-ray scattering and EM studies, the authors showed that the conformational equilibrium of HtpG can be shifted with pH, and identified His446, in the immediate proximity of the identified dynamic hotspot, as a key residue that controls this pH-dependent equilibrium. Mutagenesis of His446 was shown to successfully modulate the conformational equilibrium at neutral pH.
With regards to the dynamics of the C-terminal domains, the calculated ATP-induced increase in motion amplitude in the core of the C-terminal domain correlates well with the observed increase of hydrogen-deuterium exchange in the C-terminal core of HtpG upon ATP binding 
. This supports ligand-dependent changes in flexibility/rigidity in this region, in agreement with our data.
Finally, our model of the ATP-induced transition towards a compact state is consistent with available biochemical and structural data for Grp94. In this context, Dollins and coworkers 
observed that Glu103Ala and Arg448Ala mutations caused an 85% reduction of the ATPase activity. Our findings about the ligand-responsive dynamics of Glu103 and Arg448 – and particularly their small-amplitude, yet correlated motion in the catalytically-competent ATP state – are consistent with this experimental result.
The ligand-dependent internal dynamics of three Hsp90 chaperones with markedly different structural organization, mammalian Grp94, yeast Hsp90 and E.coli HtpG, was studied by advanced numerical schemes. For each chaperone, the dynamics in the ATP-bound, ADP-bound and Apo states was studied using extensive atomistic molecular dynamics simulations, covering a total time span of 900 ns.
The collected data were analyzed within a novel comparative scheme that is aptly used to single out the salient, common traits of the chaperones' internal dynamics. The proposed analysis scheme has a multiscale character in that it allows to bridge between the ligand-dependent local modifications of the chaperones and the resulting large-scale conformational rearrangements of the chaperones' protomers. Compared to other powerful techniques - such as essential dynamics or principal component - the proposed approach overcomes the structural distortions (e.g. of Cα-Cα virtual bonds) caused by reconstructing the very large amplitude internal dynamics by the linear superposition of very few modes. In fact, it is shown that most of the covariance observed across the 900 ns-long combined trajectories can be captured - with no structural distortion - by using merely two degrees of freedom, which are the angles of rotation of the two side quasi-rigid domains relative to the middle, core one. Based on this result we envisage that the same strategy could be profitably used in cryo-em and SAXS contexts as an effective computational aid for structural modeling.
From this analysis, which is general and hence transferable to other contexts, it emerges that the ligand-dependent modulation of the structural rearrangements in both chaperones is governed by a common underlying mechanism. Specifically, the bound ATP favors the closed protomer conformation by the electrostatic attraction of the N-terminal and Middle domains. The interaction strength decreases significantly going from the ATP-state to the ADP-state and finally to the Apo one. As a result, the relative positioning of the N-terminal and Middle domains is progressively less constrained and favors the open and open-extended conformations, respectively.
The closing/opening rearrangements that are crucial for the chaperones' activity cycle are made possible by the presence of two primary hinge regions at the interface of the quasi-rigid middle domain with the two side ones. These hinges appear to be key players in modulating the protomeric conformations of all Grp94, Hsp90 and HtpG chaperones in response to the type of bound ligand. The first hinge site is located at the interface of the N-terminal and Middle structural domains, while the second is located at the end of the H4–H6 helix-bundle at the boundary between the M-small and the M-large structural subdomains. The first hinge site has already been validated as a potential target for inhibition of the Hsp90 activity 
. Based on our results and on consistent experimental indications, we therefore suggest that the second hinge region could be a good candidate target for inhibition of the Hsp90 chaperones. Hence, in view of further experimental validation, we propose, as a working hypothesis, that the Middle-domain hinge-region, shared by all
three chaperones despite their different conformational organization and with a distance of about 40 Å from the nucleotide-binding site, is a possible novel allosteric site. Targeting this site by mutations or small molecules might affect the mechanisms of conformational transition that are crucial for chaperone activity. The strategy to discover putative new inhibitors has been described in 
, where we successfully identified C-terminal targeted drug-like compounds with interesting anticancer activities.
The overall approach we propose may represent a novel and effective means of modulating the functions of different members of the Hsp90 family with drugs that intervene by specifically addressing regions crucial for the functional dynamics of the molecule other than the classically targeted active site.