Force Distribution Reveals Signal Transduction in E. coli Hsp90

Abstract

Heat-shock protein 90 (Hsp90) is an ubiquitous chaperone that is essential for cell function in that it promotes client-protein folding and stabilization. Its function is tightly controlled by an ATP-dependent large conformational transition between the open and closed states of the Hsp90 dimer. The underlying allosteric pathway has remained largely unknown, but it is revealed here in atomistic detail for the Escherichia coli homolog HtpG. Using force-distribution analysis based on molecular-dynamics simulations (>1 μs in total), we identify an internal signaling pathway that spans from the nucleotide-binding site to an ∼2.3-nm-distant region in the HtpG middle domain, that serves as a dynamic hinge region, and to a putative client-protein-binding site in the middle domain. The force transmission is triggered by ATP capturing a magnesium ion and thereby rotating and bending a proximal long α-helix, which represents the major force channel into the middle domain. This allosteric mechanism is, with statistical significance, distinct from the dynamics in the ADP and apo states. Tracking the distribution of forces is likely to be a promising tool for understanding and guiding experiments of complex allosteric proteins in general.

Introduction

Molecular chaperones like heat-shock protein 90 (Hsp90, molecular mass 90 kDa) promote the correct folding of other proteins. Hsp90 primarily stabilizes proteins involved in signaling pathways (1). Homologs of Hsp90 can be found in most organisms and are highly conserved (2). Hsp90 is a dimerized ATPase protein consisting of three domains: an N-terminal nucleotide-binding domain (NTD); a middle domain; and a C-terminal dimerization domain (CTD). Hsp90 homologs share an allosteric mechanism in which binding of nucleotides regulates conformational changes and thereby chaperone function (3,4). Despite recent success in revealing the structural and dynamic basis of Hsp90 allostery, the molecular signal transduction pathway has remained largely elusive. HtpG, the Escherichia coli homolog of Hsp90, has been experimentally studied in great detail, because, among other reasons, it is not dependent on cochaperones, which means the allosteric model is less complex. For HtpG (Fig. 1 a), large conformational changes have been proposed that involve opening and closing of the NTD and middle domain (5). The binding of a nucleotide (ATP/ADP) influences the conformation: in the apo state, the NTD is very flexible and therefore remains in a mostly open state; with ADP bound, the NTD is less flexible and tends more often to stay in a closed state; with ATP bound, the NTD is at its most rigid, primarily populating a closed state (Fig. 1 b) (6,7).

Figure 1.

HtpG dimer structure. (a)Cartoon representation of the Hsp90 homolog HtpG. The closed dimeric structure was used as the initial structure in the simulations, with N-terminal domain (green), middle domain (orange), C-terminal (blue), ATP (red), and magnesium (gold). (b) Scheme of the HtpG dimer with the same color code as in a. ATP holds HtpG in a closed confirmation. Without ATP, the structure is more flexible and can easily open.

We address the question of how the signal of the nucleotide-binding state is communicated to the regions of conformational change in HtpG, triggering opening and closure and influencing chaperone activity. This is one of the many puzzling aspects of allosteric mechanisms, which rely on molecular communication between regions at nanometer distances from each other. A number of computational techniques have been developed to reveal allosteric communication. These techniques mostly rely on detection of correlated motions in the protein, as observed in molecular-dynamics (MD) simulations (8–11) or in approximate elastic network models (12,13). However, the computation of an allosteric mechanism is very challenging, because the signal propagation can be hidden in only very minor conformational changes. To overcome this limitation, we here used Force Distribution Analysis (FDA) based on MD simulations to investigate the underlying mechanism of HtpG signal transduction. FDA reveals the propagation of internal forces within a protein structure upon ligand binding or other perturbations, and it has been proven successful in revealing a different allosteric mechanism (14). It is able to detect signals in the form of high forces in stiff structures with only small conformational changes, like the bending of α-helices. These are not easily recognized using exclusively structural data-analysis techniques.

Previous simulations of HtpG (15–17) portrayed the nucleotide-dependent opening and closing of the NTD of HtpG. Here, we present an allosteric signaling pathway in HtpG based on all-atom simulations with explicit TIP4P water lasting >1 μs. Our model successfully explains the nucleotide-induced conformational transition that we were able to observe within the timescale of our simulations. It is obtained from the analysis of internal forces and correlations in minor, yet significant, structural changes upon ligand binding. Our results are in line with experimental findings, and they suggest a mechanism that primarily involves the bending and torsion of a helix connecting the nucleotide-binding site with the hinge responsible for opening and closing of the NTD dimer interface.

In addition, typical timescales of allosteric transitions such as those in HtpG are on the order of milliseconds to seconds, whereas atomistic simulations cover femtoseconds to microseconds. As forces within a protein generated by perturbation equilibrate relatively fast compared to the conformational change they trigger (18), FDA makes it possible to recognize those mechanisms before structural changes lead to allostery.

Materials and Methods

Molecular dynamics (MD) simulations

The MD simulations were performed using GROMACS 4.0.5 (19) with the optimized potentials for liquid simulations (OPLS) all-atom force field (20) with an optimized OPLS phosphonucleotide parameter set and TIP4P (21) water model. The crystal structures of full-length HtpG (PDB: 2IOP; chains A and B) and the NTD of HtpG (PDB: 2IOR) (22) were used for the MD simulations. Because of an incorrect stereo center in ADP in the 2IOP crystal structure, ADP and Mg²⁺ were transferred from the 2IOR NTD crystal structure by superimposing 2IOR with 2IOP. Missing loops (chain A, 494–499; chain B, 118–120 and 494–499) were inserted with the modloop server software (23). The protonation states of the amino acids were calculated with the WHAT IF software package (24). A rhombic dodecahedral simulation box was filled with TIP4P (21) water and sodium/chloride ions at a physiological concentration of 120 mM with a resulting overall system charge of zero. All simulations were run in the NPT ensemble, and temperature was kept constant at 300 K by coupling to the Nose-Hoover thermostat with ${\tau }_t$ = 0.1 ps. The pressure was kept constant at p = 1 bar using isotropic coupling to a Parinello-Rahman barostat with ${\tau }_p$ = 1 ps and a compressibility of 4.5 × 10⁻⁵ bar⁻¹. After energy minimization, the LINCS algorithm (25) was used to constrain all bonds. Lennard-Jones interactions were calculated using a cutoff of 1 nm. Long-range electrostatics were calculated by particle-mesh Ewald summation (26). The step size of the production run was set to 2 fs, with a length for each run of 20 ns. System coordinates were saved every 20 ps. At the beginning, the rhombic dodecahedron simulation box had a distance of at least 1.1 nm between the protein and the next boundary, resulting in a system volume of 2985 nm³ and 387,306 particles.

Every state (apo, ADP-bound, and ATP-bound) of the HtpG system was minimized, using the robust steepest-descent algorithm (further minimization with the conjugate-gradient or quasi-Newtonian algorithm led to only small changes and has therefore been omitted). For each state, nine trajectories with different random starting velocities were calculated, first in a 1-ns position restraint run (restraint force constant = 1000 kJ∙mol⁻¹ nm²; step size = 1 fs), then in a 20-ns production run, resulting in 27 trajectories with a total length of 540 ns. Analog simulations of the HtpG monomer were performed.

Force-distribution analysis

In FDA (27), the forces between each atom pair i and j, $F_{ij}$, are analyzed at each MD step. For this study, the GROMACS 4.0.5 implementation of the FDA and the corresponding FDAtools 1.0 were used. Atomic or residue forces $F_i$ or $F_u$ average to zero over time in equilibrated systems according to Newton's third axiom:

$$\left|\langle {\overrightarrow{F}}_{ij}\rangle \right|\in \mathbb{Q};\left|\langle \sum _j{\overrightarrow{F}}_{ij}\rangle \right|=0,$$ (1)

because the net force acting on an atom or residue is zero by definition as long as the net translation of that atom or residue is zero. In contrast, forces between pairs of atoms, i and j, or residues, u and v, can be different from zero even when considering time averages. The force vectors between residues have been summed up to reduce the amount of data and to allow the analysis of residue interactions. More specifically, interresidue forces, $F_{uv}^{\text{res}}$, were calculated from the norm of the force vector resulting from summing up over all force vectors, ${\overrightarrow{F}}_{ij}$, between atom pairs i and j in the two residues u and v:

$$F_{uv}^{\text{res}}=\left|\sum _{ij}{\overrightarrow{F}}_{ij}\right|;i\in u,j\in v.$$ (2)

To enhance the signal/noise ratio, the pairwise forces, $F_{uv}^{\text{res}}$, calculated from each frame in the trajectories were averaged over time, the two protomers, and the nine independent runs of the three states, apo, ADP-bound, and ATP-bound. The pairwise forces within the atoms of the protein, magnesium, and ligands were used, whereas forces from water, sodium, and chloride were neglected.

Signal transduction upon nucleotide binding was measured from differences between the interresidue forces obtained from the three different states, apo, ADP-bound, and ATP-bound. This resulted in three distinct force-distribution patterns, namely, apo-ADP, apo-ATP, and ADP-ATP, for which the absolute differences are shown (see, e.g., Fig. 4). With this technique, it was possible to track down signaling pathways even in the absence of large atomic displacements during the MD simulations. For the detection of connected signal pathways, a vertex-count algorithm was implemented that searches for the largest network of connected pairwise force differences beyond a given cutoff, i.e., a minimal pairwise force.

Figure 4.

Force distribution upon nucleotide binding. The network of force differences is shown as magenta sticks in HtpG (green). Only the largest connected network of forces beyond a certain cutoff is shown. The positions of ATP (gray) and magnesium (yellow) are shown at representative positions, as observed during the HtpG-ATP simulations. (a) Force differences between apo and ATP-bound state simulations. The cutoff used for the representation is 50 pN. (b) Same as in a, but with a cutoff of 40 pN. (c) Force differences between apo and ADP-bound state simulations beyond a cutoff of 30 pN. Even for this cutoff, which is smaller than those in a and b, this force network does not extend into the middle domain, hinting toward a functionally relevant difference between ATP and ADP binding. (d) Force differences between all ADP- and ATP-bound HtpG simulations beyond a cutoff of 35 pN.

Statistics

Focusing on regions that show large differences in interresidue forces, we analyzed in greater detail the structural changes upon nucleotide binding, and the correlations between these changes. Correlation coefficients of structural parameters (helix bending, torsions, interresidue distances) were calculated with Spearman's rank-based rho statistics, because the data do not necessarily come from a bivariate normal distribution. Unless otherwise noted, the mean values and standard deviations given are for 18,017 degrees of freedom (df). The level of significance (probability of error) is α = 0.05.

Results

Structural analysis

A common theme of Hsp90 function is an opening/closing transition. We monitored the opening and closing at the N-terminal side of the dimer by calculating the minimal distance between the NTDs of the two HtpG protomers. For each of the three states (apo, ADP-bound, and ATP-bound), a dimer and a monomer system were created, based on the HtpG structures 2IOP and 2IOR (22). To achieve a statistically significant result, each simulation system was calculated nine times for 20 ns each. All dimer structures were initiated from the closed state of the crystal structure. Conformations observed during the MD simulations are here considered closed if their NTDs feature a minimal distance of <0.25 nm.

As shown in Fig. 2 top, the apo structures of HtpG visit a very large range of inter-NTD distances up to 4 nm. Thus, the closed structure, which was experimentally determined in the presence of an ATP analog, transits into a highly mobile open state. This large-scale conformational change leading to an open HtpG dimer (Fig. 2, inset) is remarkable given the 20-ns timescale of our simulations. It can be primarily characterized by a hinge motion between the middle and NTD domains, as determined by principal-component analysis (PCA; Fig. S1 in the Supporting Material). The hinge region is highlighted in the open apo state in Fig. 2. In contrast, the ATP-bound structures tend to remain in the closed state (Fig. 2, bottom) at our nanosecond timescale, with an inter-NTD distance of <0.25 nm for 75% of the time. A second minor conformational ensemble was observed for ATP-bound HtpG, exhibiting a distinct and relatively narrow range of distances around 1.5 nm. The ADP-bound state samples a broader distance range than the ATP-bound HtpG, yet opens up much less than the apo state. An opening of the C-terminal dimerization site could not be observed (Fig. S2).

Figure 2.

HtpG undergoes an opening/closing transition that is nucleotide-dependent. Histograms of the normalized occurrence (1 = 100%) of the minimal distance between the NTDs of HtpG for the apo, ADP-bound, and ATP-bound states. The first bar in each histogram is truncated, and the value of this bar is given above each bar. The apo state shows the widest spectrum of minimal distances, whereas the ATP-bound state remains largely closed.

Force-distribution analysis

Apparently, the signal of ATP or ADP bound to the nucleotide-binding site propagates to the hinge region between the NTD and middle domain responsible for the opening/closing transition. How are these two regions, over a 2.3-nm distance from each other, mechanistically connected? We could not observe any obvious structural changes within the NTD domain, the fluctuations of which were primarily restricted to the lid at the NTD-NTD interface and outer loops. However, stiff protein cores like that of the NTD could potentially propagate allosteric signals in terms of high forces, which we analyzed here by means of FDA. Matrices of interresidue forces were averaged over time, over the two monomers, and over the nine trajectories for each state (apo, ADP-bound, and ATP-bound). Details are given in the Methods section.

We first calculated the force changes in HtpG upon binding of ATP. The resulting network of pairwise residue forces >50 pN is shown in Fig. 4 a as sticks connecting the respective residues. To further reduce noise, only the connected graph with the largest number of residues as vertices is shown. The binding of ATP leads to a spatially connected force signal that is restricted to the nucleotide-binding pocket. The magnesium ion serves as a crucial hub by propagating forces from ATP to the adjacent α-helix 3 (H3; I30–A50). We note that the magnesium ion was firmly bound to H3 in all our simulations, even in the apo state (see below). Thus, the high force signals observed between magnesium and protein can be traced back not to a dissociation of magnesium from HtpG, but to a structural adjustment of the ion. With decreasing cutoff, the signal reaches the interface between the NTD and the middle domain (Fig. 4 b), comprising the hinge region described above (Fig. 2, open structure).

In the case of ADP, the force signal is confined to the NTD even for a reduced cutoff of 30 pN (Fig. 4 c). Hence, ADP binding leads to an allosteric force network in HtpG that is remarkably different from that of ATP, even though the two molecules differ by no more than one phosphate group. For clarity, the force differences between ATP and ADP are shown in Fig. 4 d and in Movie S1. In contrast to the nucleotide-binding niche, for which the two nucleotides exhibit similar forces, it is only the γ-phosphate of ATP that causes the force signal to extend along H3 to the hinge at one end of H3 and to the NTD binding area at the other end of H3. The signal caused by ATP expands even into the middle domain, including α-helix 11 (H11; D190–Y200). The signal that reaches the NTD binding area (helix 2; A12–Y25) is transmitted through the small loop between H2 and H3.

In the force-distribution network of the HtpG monomer, force differences between the apo and ADP states and between the apo and ATP states are comparable to the results of the dimer simulations (Fig. S3). Only the effect of the γ-phosphate in the dimer, measured in terms of the force difference between the ADP- and ATP-bound states, could not be reproduced in the monomer simulations of HtpG. We note that over all, the monomeric structure is less stable than the dimer and for this reason requires more extensive sampling to reach the same force precision. Forces from water and ions have not been taken into account in this analysis, since they interchange positions rapidly. However, the force-distribution pattern indirectly reflects the effect of the solvent, as the MD simulations were carried out in the presence of explicit water at physiological ion concentration.

To test the robustness of the forces obtained from FDA, extensive force variance and error calculations were performed. We extended the simulations and the data gathering for the FDA until the pairwise forces rose clearly above the level of noise, which was estimated by the standard error of the mean (SEM) of the pairwise forces. Fig. 5 shows the force network obtained by comparing ADP- and ATP-bound HtpG, the most challenging comparison because of the small signal/noise ratio. Each pairwise force between residues above 44 pN is shown in stick representation. The color code corresponds to the value of the pairwise force minus the SEM of the particular interaction. For clarification, each pairwise force is shown in a bar plot with its corresponding SEM. The majority of interactions, that is, ∼75%, in the analyzed force network are above the noise level. Overall, FDA was able to reveal changes in forces upon ATP binding over 3.2 nm to regions in the hinge and middle domain, thereby giving quantitative insight into the allosteric mechanism of HtpG.

Figure 5.

Noise estimation of the pairwise forces. The network of force differences with a cutoff of 44 pN between the ADP- and the ATP-bound states is shown in stick representation. The color code represents the pairwise force minus the SEM of this particular pairwise force. Red indicates a high force difference with a low SEM (low noise) and blue a low force difference with a high SEM. The bar plot (right) shows all force differences that are shown in the structure on the left as absolute values. The SEM are shown as error bars. The color code of the bar plot is the same as for the sticks representation and defines the ordering of the pairwise forces in the bar plot. The orange arrow indicates exemplarily the same force difference in the structure and the bar plot.

Mechanism details

Having revealed the amino acids participating in the signal transduction from the FDA, we investigated the underlying mechanism in structural detail. The primary hub in the force-distribution network, the magnesium ion, stays coordinated by the H3 residues Asp-41 or Asn-38 throughout the simulations, even for the apo structures. In the ADP- and ATP-bound states, a single bridging water molecule can enter the magnesium coordination complex. Temporary clusters of sodium and chlorine ions can be found at this site, leading to a highly polar area, especially for ADP- and ATP-bound HtpG. Since Mg²⁺ is coordinated by the two amino acids of H3, it mediates a tight interaction between nucleotides ADP or ATP and H3 of HtpG, as also evidenced by the FDA (Fig. 4, b and c).

As a consequence, the binding of ADP or ATP leads to a significant torsion of H3, accompanied by an evident decrease in variance of this torsion (Statistical analysis 1 (Stat1) in the Supporting Material). The boxplot in Fig. 3 a shows the torsion angle of H3 with respect to the β-sheet in NTD (i.e., the torsion of amino acids S68-I30-D41-Mg). Nucleotide binding increases the torsion angle from 203° ± 29° in the apo state to 232° ± 8° and 232° ± 9° in the ADP and ATP states, respectively (Stat1 in the Supporting Material). The ADP and ATP states do not differ significantly (Stat1 in the Supporting Material). In contrast, the bending of helix H3 differs significantly between the ADP- and the ATP-bound states (Stat2 in the Supporting Material), with ATP binding leading to a straightening of H3 as compared to apo and ADP.

Figure 3.

Nucleotide-dependent dynamics of H3 in HtpG. (Left) Boxplot of the torsion (dihedral angle S68-I30-D41-Mg) of α-helix 3 (I30–A50) for the apo, ADP-bound, and ATP-bound states. The whiskers represent the adjacent values (Stat4 in the Supporting Material), the box shows the interquartile range (between the 25th and 75th percentiles), the line represents the median, and the circular points represent outside values. The apo state has the smallest torsion angle as well as the largest variance in this angle. The torsion angles of the ADP- and ATP-bound states are nearly identical and show reduced variances. (Right) Boxplot of the bending (angle I30-D41-S52) of helix H3 for the apo, ADP-bound, and ATP-bound states. The apo and ADP-bound states show a stronger bending of H3 and a higher variance compared to the ATP-bound state. Box parameters are as in a.

The alterations in H3 conformation in terms of bending and torsion are also evident from the FDA, where H3 features high forces in intrahelix hydrogen bonding. The H3 forces propagate into a network of residues at the interface of the NTD with the middle domain. The distances between the involved residue pairs at the interface were monitored and their correlation analyzed to establish a link between the observed force network and the opening/closing transition in HtpG. Correlations between three specific distances, R47–D329, Y57–D329, and D55–K271, and the aforementioned H3 torsion and bending are shown in Fig. 6 a. These distances in turn were found to correlate with the angle between H3 and α-helix 18 of the middle domain (H18, T343–D366), an angle crucial for the hinge motion involved in opening and closing the HtpG dimer. For the ATP-bound state, the correlation between the monitored observables is much stronger than it is for the ADP-bound or apo state. Even though the correlation factor of the torsion of α-helix 3 is not high, the values are still significantly different from zero (Stat3 in the Supporting Material). The two complementary analysis techniques, FDA and structural correlations, revealed a consistent pattern of an allosteric mechanism in HtpG, in which H3 plays a pivotal role.

Figure 6.

Structural correlations in HtpG and model for the signaling pathway. (a) Correlation matrix of structural observations chosen according to the analysis of the force distribution. A high/low (absolute) value of the correlation coefficient is represented by a dark/light color. In each cell, the green, yellow and red (left, middle, and right) bars represent coefficients for the apo, ADP-bound, and ATP-bound states. (b) For clarification, the icons above each column in a are depicted in the interface and ligand-binding area of HtpG. The NTD is green, the middle domain is orange, ATP is red, and magnesium is gold. Residues for which distance correlations were calculated in a are shown as sticks. (c) Proposed model for HtpG allosteric communication based on FDA, structural observations, and correlations between the two. Red and yellow arrows indicate correlations between the observables in simulations of ATP- and ADP-bound HtpG, whereas red/yellow dashed arrows indicate correlations for both nucleotides. The analysis results in a bending pathway influenced by ADP and ATP, whereas the torsion pathway is also influenced, but only by ATP. Both pathways influence the H3-H18 angle (bottom) and thereby the opening and closing transition of the HtpG dimer at the NTD.

Discussion

Consistency with experimental results

Hydrogen-deuterium exchange (HX) experiments were able to quantify the relative flexibility of segments of HtpG dependent on the nucleotide bound to the NTD (6). To compare this theoretical work with the HX data, we mapped the HX data measured for the apo and AMPPNP states on a representative apo and ATP trajectory from our MD simulations (Movie S2 and Movie S3) and observe an overall agreement. The root-mean-square fluctuations (RMSFs) of the amino acids were calculated, showing a much higher fluctuation for amino acids 105–122 in the apo state than in the ADP- or ATP-bound state. This region corresponds to the lid in the NTD, which represents the interaction site between the two protomers. The HX experiments also mark this region (apo state amino acids 108–119) as a particularly mobile area. The apo state has a higher HX compared to the ADP- and AMPPNP-state in that region than in any other region (6).

Electron microscopy analysis of HtpG made by Southworth et al. allowed additional insight into nucleotide-dependent conformational changes (28). They found that 68% of HtpG in the apo state adopts an open conformation, whereas only 33% of the AMPPNP-bound structures are open. At the end of our simulations, 56% of the apo state, 45% of the ADP-bound state, and 22% of the ATP-bound state adopt the open conformation, which is in good qualitative agreement, given that there are only nine independent trajectories of limited timescale. The opening and closing transition of HtpG and other Hsp90s is believed to occur on timescales of milliseconds to minutes, which are the typical timescales of HX or fluorescence energy transfer (6,29). We here find this transition to occur on the submicrosecond timescale.

As suggested by both our simulations and the electron microscopy results, HtpG can visit closed and open conformations in any of the three states, and nucleotide binding shifts the equilibrium toward more closed states. Therefore, the opening transition is a stochastic process that requires extensive sampling in both simulations and experiments. Individual molecular nanosecond-timescale trajectories can represent only part of the conformational ensemble and thus have not been the focus of our analysis here.

We here identified an area of signal propagation, namely, the nucleotide-binding niche, H3 (I30–A50) and H18 (T343–D366), a region with comparably small conformational fluctuations. Apparently, force propagation is efficient through such stiff regions. In line, the underlying crystal structures (see Materials and Methods for details) here have a low mean B-factor of 62 ± 6 (Cα only) compared to the overall mean of 106 ± 35 (Cα only), indicating a stiff regime in the crystal structure.

Consistency with other theoretical methods

Our major result is a force-transduction pathway from the nucleotide-binding site into the NTD's lid and the middle domain, depending on the nucleotide-binding state of HtpG. The question arises, how this result compares to other theoretical studies on HtpG (15–17,30), which were based on the analysis of structural changes and correlated dynamics. We observe in our comparably extensive simulations very similar dynamics of HtpG in the three different states. More specifically, the first eigenvector of the apo, ADP-bound, and ATP-bound states obtained from PCA on our simulation data shows a correlated motion between the NTD and the CTD, as detected previously.

The FDA performed here, however, being based on forces instead of coordinates, reveals a pattern of allosteric communication different from the pathway observed by PCA. Fig. S4 shows the change in structural fluctuations along the first eigenvector between the ADP- and ATP-bound states as compared to the corresponding force differences between the two states. The results of the FDA are in line with the results of the PCA, yet with a much higher sensitivity for the allosteric network connecting the NTD and middle domain. In fact, PCA is based on large-amplitude correlated motion and therefore might overlook smaller structural alterations within the protein core, which FDA is able to pick up. On the other hand, FDA was not able to dissect the allosteric network to the CTD within the limited simulation time.

Signal pathway model

Given the results from the FDA of the different ligand bound states and the structural correlations in the protein, the following model arises (Fig. 6, b and c). A bound ligand has an impact on the torsion and the bending of helix H3 (I30–A50) via the magnesium ion in the binding niche. The bending pathway is influenced by ADP (bending of H3) and ATP (unbending of H3) (Fig. 3 b. For both ligands, the bending is correlated with distances in the interface between the N-terminal and middle domains. More specifically, a clamplike structure (Y57 and D329) at the end of H3 is locked in the hinge region of the interface. The torsion pathway is also influenced by both ligands, but only for ATP does the torsion propagate into the interface in terms of correlated interresidue distances (clamp R47, Y57, and D329). Both pathways ultimately alter the angle between helices H3 (N-terminal domain) and H18 (middle domain), which influences the opening and closing of the HtpG dimer. ADP uses the bending pathway, whereas ATP uses the bending and torsion pathways and has, therefore, a stronger effect on the opening/closing mechanism. If no ligand is bound and H3 is flexible and bent, the end of H3 binds to D55 more strongly than to K271, which acts as a hinge joint that allows the N-terminal domain to tilt and rotate.

A current model of HtpG allostery includes a reorientation of the N-terminal domain, resulting in, for example, a compact dimer in the ADP-bound state (22). We could not observe such a reorientation within the restricted timescale of our simulations but detected a faster closing of the lid in the case of ADP binding, introduced by a shortening of the distance between Lys-99 and helix H3 (Fig. S5). This might lead to a more compact structure. However, since the ADP bound structures are more flexible than the ATP bound structures, further reorientation (e.g. to a compact ADP conformation) is possible and at least more likely than for the apo or the ATP bound state. In agreement with recent findings from SAXS measurements (7), we find that the NTD features an intrinsic flexibility such that the apo state reversibly opens and closes on the nanosecond timescale. ATP binding shifts this dynamic equilibrium toward the closed state by stiffening the hinge, an allosteric scenario best described by conformational selection, in contrast to the Monod-Wyman-Changeux (MWC) model (31). Here, we were able to underpin a conformational-selection mechanism by a signal pathway coupling the distant regions involved.

Putative binding sites for client proteins are located in the middle domain of HtpG and similarly in other Hsp90s (32). Interestingly, our analysis suggests that only the binding of ATP causes the allosteric signal to reach these putative binding regions. As such, our computational model supports the view of client protein binding to the middle domain. This region specifically senses ATP binding, though without being able to distinguish the apo from the ADP-bound state.

FDA proved successful in detecting signal propagation with high sensitivity, even through minute structural adaptations such as slight helix straightening by ATP. This underlines the power of FDA to reveal allosteric networks through rigid regions such as the protein core or well-defined secondary-structure elements. In contrast, structure-based methods analyze (collective) motions in structural models or molecular simulations. FDA does not rely on large-amplitude conformational fluctuations but instead tracks the signal, i.e., the forces, itself. Also, allosteric transitions can occur at timescales as slow as milliseconds to seconds, whereas atomistic simulations cover femtoseconds to microseconds. As forces within a protein upon perturbation equilibrate relatively fast compared to the conformational change they trigger (18), FDA is capable of recognizing those mechanisms before structural changes lead to allostery. As a result, FDA can reveal allosteric networks without either observation of large-amplitude motions or an underlying mechanism such as induced fit or population shift.

Our model can be directly tested by functional assays of HtpG mutants. We predict that an Asp-329 mutant will behave in an apo-like way, even in the presence of ATP or ADP. Drastic changes in the allosteric pathway can also be expected for Asp-55 or Lys-271 mutants. It remains to be elucidated how generally the bending and torsion pathways obtained from this analysis describe signal propagation in other Hsp90 homologs.