• No results found

Folding and Domain Interactions of Three Orthologs of Hsp90 Studied by Single-Molecule Force Spectroscopy

N/A
N/A
Protected

Academic year: 2021

Share "Folding and Domain Interactions of Three Orthologs of Hsp90 Studied by Single-Molecule Force Spectroscopy"

Copied!
16
0
0

Bezig met laden.... (Bekijk nu de volledige tekst)

Hele tekst

(1)

University of Groningen

Folding and Domain Interactions of Three Orthologs of Hsp90 Studied by Single-Molecule

Force Spectroscopy

Jahn, Markus; Tych, Katarzyna; Girstmair, Hannah; Steinmaßl, Maximilian; Hugel, Thorsten;

Buchner, Johannes; Rief, Matthias

Published in:

Structure

DOI:

10.1016/j.str.2017.11.023

IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite from

it. Please check the document version below.

Document Version

Publisher's PDF, also known as Version of record

Publication date:

2018

Link to publication in University of Groningen/UMCG research database

Citation for published version (APA):

Jahn, M., Tych, K., Girstmair, H., Steinmaßl, M., Hugel, T., Buchner, J., & Rief, M. (2018). Folding and

Domain Interactions of Three Orthologs of Hsp90 Studied by Single-Molecule Force Spectroscopy.

Structure, 26(1), 96-105.e4. https://doi.org/10.1016/j.str.2017.11.023

Copyright

Other than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).

Take-down policy

If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim.

Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons the number of authors shown on this cover page is limited to 10 maximum.

(2)

Article

Folding and Domain Interactions of Three Orthologs

of Hsp90 Studied by Single-Molecule Force

Spectroscopy

Graphical Abstract

Highlights

d

Folding rates of

S. cerevisiae Hsp90 (Hsp82) and E. coli Hsp90

(HtpG) are similar

d

Folding of ER Hsp90 (Grp94) is slowed by misfolding of the

N-terminal domain

d

Domain interactions mediated by the charged linker are

stronger in Grp94 than Hsp82

d

ER Hsp90 differs from its cytosolic orthologs in basic

structural properties

Authors

Markus Jahn, Katarzyna Tych,

Hannah Girstmair,

Maximilian Steinmaßl, Thorsten Hugel,

Johannes Buchner, Matthias Rief

Correspondence

k.m.tych@tum.de (K.T.),

johannes.buchner@tum.de (J.B.),

matthias.rief@mytum.de (M.R.)

In Brief

Jahn and Tych et al. report high-precision

optical tweezers experiments to analyze

the structural and mechanical properties

of three orthologs of the heat-shock

protein 90 (Hsp90) molecular chaperone

family. Hsp90s are highly conserved

across species. They find differences in

folding rates, domain interactions, and

functionally relevant structural stabilities.

Jahn et al., 2018, Structure26, 96–105 January 2, 2018ª 2017 Elsevier Ltd. https://doi.org/10.1016/j.str.2017.11.023

(3)

Structure

Article

Folding and Domain Interactions

of Three Orthologs of Hsp90 Studied

by Single-Molecule Force Spectroscopy

Markus Jahn,1,4Katarzyna Tych,1,4,5,*Hannah Girstmair,2Maximilian Steinmaßl,1Thorsten Hugel,3Johannes Buchner,2,*

and Matthias Rief1,*

1Physics Department E22, Technical University of Munich, Garching, Bavaria 85748, Germany

2Chair of Biotechnology, Chemistry Department, Technical University of Munich, Garching, Bavaria 85748, Germany 3Institute of Physical Chemistry, University of Freiburg, Freiburg, Baden-W€urttemberg 79104, Germany

4These authors contributed equally 5Lead Contact

*Correspondence:k.m.tych@tum.de(K.T.),johannes.buchner@tum.de(J.B.),matthias.rief@mytum.de(M.R.) https://doi.org/10.1016/j.str.2017.11.023

SUMMARY

The heat-shock protein 90 (Hsp90) molecular

chap-erones are highly conserved across species.

How-ever, their dynamic properties can vary significantly

from organism to organism. Here we used

high-pre-cision optical tweezers to analyze the mechanical

properties and folding of different Hsp90 orthologs,

namely bacterial Hsp90 (HtpG) and Hsp90 from the

endoplasmic reticulum (ER) (Grp94), as well as from

the cytosol of the eukaryotic cell (Hsp82). We find

that the folding rates of Hsp82 and HtpG are similar,

while the folding of Grp94 is slowed down by

misfold-ing of the N-terminal domain. Furthermore, the

domain interactions mediated by the charged linker,

involved in the conformational cycles of all three

orthologs, are much stronger for Grp94 than for

Hsp82, keeping the N-terminal domain and the

mid-dle domain in close proximity. Thus, the ER resident

Hsp90 ortholog differs from the cytosolic

counter-parts in basic functionally relevant structural

prop-erties.

INTRODUCTION

The heat-shock protein 90 (Hsp90) family members, are highly conserved molecular chaperones that account for as much as 1%–2% of the proteome under non-stress conditions (Kruken-berg et al., 2011; Taipale et al., 2010). They are crucial for the final maturation of a diverse range of client proteins, and through stabilization and assistance in refolding after stress conditions (Mashaghi et al., 2014; Schopf et al., 2017). The exact roles of the different members of the Hsp90 family differ, depending on the organism and on where they are found in the cell, although the majority are involved in client stabilization (Johnson, 2012).

Cytosolic Hsp90 is essential in eukaryotes (Borkovich et al., 1989), and is also found in most bacteria. In E. coli, Hsp90, called HtpG, is not essential (Bardwell and Craig, 1988). Surprisingly, Hsp90 is not present in archaea (Chen et al., 2006). In

S. cerevisiae, there are two isoforms of Hsp90 in the cytosol,

Hsc82 and Hsp82, the latter of which is upregulated under heat stress conditions (Borkovich et al., 1989). In higher eukary-otes, besides the two cytosolic isoforms (Langer et al., 2003), an abundant Hsp90 isoform, the 94-kDa glucose-regulated protein (Grp94) is present in the endoplasmic reticulum (ER) (Johnson, 2012; Li and Buchner, 2012).

The domain architecture of Hsp90 is conserved (Figure 1). It consists of an N-terminal ATP-binding domain (N domain), a middle domain (M domain), known to interact with clients and, in the case of eukaryotic cytosolic Hsp90, also with co-chap-erone proteins, and a C-terminal domain (C domain), which mediates dimerization. In addition, Grp94 contains a pre-N domain, and a C-terminal KDEL sequence responsible for ER localization (Marzec et al., 2012). In Hsp82, there is a C-terminal MEEVD motif which is recognized by tetratricopeptide-contain-ing co-chaperones (Chen et al., 1998; Prodromou et al., 1999; Scheufler et al., 2000). The nucleotide-binding region in the N domain has been found to be the most conserved part of Hsp90 across species (Krukenberg et al., 2011). In Grp94 and Hsp82, the charged linker region between the N and M domains is extended compared with the bacterial species. It has been previously shown to be crucial for structural rearrangements of these domains during the functional cycle (Hainzl et al., 2009; Tsutsumi et al., 2012; Jahn et al., 2014).

All three Hsp90 orthologs are known to undergo large confor-mational changes between N-terminally open and closed states during their functional cycles. For HtpG, this conformational cycle is closely coupled to nucleotide binding and turnover (Ratzke et al., 2012), whereas, for Hsp82, co-chaperones are important in directing the conformational cycle (Hessling et al., 2009; Mickler et al., 2009; Ratzke et al., 2014). For Grp94, N domain dimerization has not been directly shown, and the dimer appears to remain largely in an open state, even in the presence of nucleotide (Frey et al., 2007; Krukenberg et al., 2009). Alongside these variations, there are also differences in the number of co-chaperones for each ortholog: over 20 Hsp82 co-chaperones have been discovered to date (Li et al., 2012; Taipale et al., 2010), whereas only a few seem to exist for Grp94 (Liu et al., 2010; Rosenbaum et al., 2014), and none have been identified so far for HtpG. Finally, owing to their local-ization in very different environments, the three Hsp90 orthologs 96 Structure 26, 96–105, January 2, 2018ª 2017 Elsevier Ltd.

(4)

interact with different sets of clients. In fact, while the clientele of Hsp82 is very large, with hundreds of client proteins known, few have been identified for HtpG (Honore´ et al., 2017; Sato et al., 2010) and Grp94 (Flach et al., 2010; Liu and Li, 2008; Rose-nbaum et al., 2014).

In this study, we set out to analyze the dynamics of cytosolic members of the Hsp90 family from bacteria and eukaryotes and of endoplasmic Hsp90 (structures shown inFigure 1A). We performed a detailed characterization of the folding behaviors of these three important representatives of the Hsp90 family, and find that these structurally highly similar molecular machines exhibit differences in charged linker dynamics and functionally relevant structural stabilities.

RESULTS

Comparison of Unfolding Signatures

To provide a detailed comparison of the mechanical signature of each ortholog, single-molecule force spectroscopy was per-formed in a custom-built optical trap setup (for details, see STAR Methods and Supplemental Information). The proteins were first attached via cysteines to 185-nm-long DNA handles, which were then bound to 1-mm-diameter silica beads via streptavidin/biotin and digoxigenin/antidigoxigenin binding. The beads were trapped by laser beams. As the distance between the two trapped beads is increased at a constant veloc-ity, by moving one of the laser beams, a force is applied to the protein molecule between them. This leads to the extension

and subsequent unfolding of the individual structural elements of the protein monomer. When the force is decreased, the pro-tein is allowed to relax and may refold. The resulting force-exten-sion traces can then be used to obtain the mechanical signature for the protein, by comparing the contour length increase after an unfolding peak to the number of amino acids in the domains or sub-domains and the forces at which each event occurs. Typical force-extension traces for Hsp82, HtpG, and Grp94 unfolding at a very slow speed of 10 nm/s are shown inFigure 2. The force-extension traces represent sequential stepwise transitions from a completely folded to a completely unfolded state. For each of the orthologs (Figures 2A, 2C, and 2E), we observe three main separate unfolding peaks corresponding to the three do-mains, as previously reported for Hsp82 (Jahn et al., 2014).

Worm-like chain (WLC) fits to the force-extension traces, shown as dashed lines, allow the determination of the contour length gains of the unfolded domains. The contour length gain and the associated unfolding force of multiple unfolding events of different molecules are collected in scatterplots (Figures 2B, 2D, and 2F). To increase statistical significance, the molecules are rapidly unfolded and refolded in cycles at 500 nm/s. The higher pulling velocity during the cycles (500 versus 10 nm/s) leads to higher unfolding forces compared with the sample traces ofFigures 2A, 2C, and 2E, but allows very precise deter-mination of contour length gains for every domain owing to the better statistics. Contour length gains are summarized inTable 1. To match the observed contour length gains to the exact num-ber of amino acids forming the individual domains, we use the

Figure 1. Crystal Structures of Three Hsp90 Orthologs

(A) Yeast Hsp82 (PDB: 2CG9), E. coli HtpG (PDB: 2IOP), and endoplasmic Grp94 (PDB: 2O1U) dimers are colored by domain, where the N domains are in blue, the charged linker regions are in purple, M domains are in orange, and C domains are in dark yellow. Only one monomer of each dimer is colored, for clarity. (B) Sequence conservation of the three Hsp90 orthologs, alignment created using CLC Sequence software (QIAGEN). Black regions indicate amino acids that are not resolved in the crystal structures. The sequence similarities between the three studied orthologs are as follows: Hsp82 to HtpG, 38% identity; Hsp82 to Grp94, 47% identity; HtpG to Grp94, 38% identity.

(5)

domains of the crystal structure and calculate the expected con-tour length gains. The procedure is described in more detail in the Supplemental Information. The expected values are compared with the measured ones in Table 1. All values of changes in contour length and unfolding forces are given as mean ± SD.

In an example unfolding trace for Hsp82 (Figure 2A), the first unfolding event with an associated contour length gain of

40.2 ± 1.5 nm (n = 76), is assigned to the unfolding of the C domain, the second unfolding event, 69.5 ± 2.5 nm (n = 76), corresponds well to the N domain, and the third, 85.0 ± 1.5 nm (n = 76), to the M domain. The M domain has an unfolding inter-mediate often visible in unfolding traces, resulting from its two structural sub-domains (Supplemental Information;Figure S1). The contour length assignments for Hsp82 are based on the number of amino acids in each domain resolved in the crystal

Figure 2. Mechanical Unfolding of Three Orthologs of Hsp90

(A, C, and E) Force-extension traces of Hsp82 (A), HtpG (C), and Grp94 (E) unfolded at a constant velocity of 10 nm/s. All constructs show three unfolding peaks representing the three domains (N, M, and C). Dashed lines are worm-like chain (WLC) fits describing the stretching behavior of the DNA handles and the unfolded protein and insets show the structure of the respective monomers. The first fit to each force-extension trace is placed to take into account the length contribution from unstructured regions of the proteins, as estimated from their respective crystal structures. The arrow in (A) indicates the flipping of the charged linker of Hsc82.

(B, D, and F) Unfolding forces plotted versus contour length gains for multiple native unfolding traces, 176 traces from 6 molecules for Hsp82 (B), 52 traces from 4 molecules for HtpG (D), and 21 traces from 13 molecules for Grp94 (F). Distinct clusters are observed and colored according to the domain that was unfolded. The unfolding event immediately preceding the N domain unfolding of Grp94 (gray population in the scatterplot, labeled ‘‘*’’), could correspond to either the 53-amino-acid-long stretch of the so-called ‘‘pre-N domain,’’ which is not resolved in the crystal structure (Dollins et al., 2005, 2007), or the 60-amino-acid-long charged linker region, which is also only partly resolved. This is investigated further, below. See alsoFigure S1.

(6)

structure (PDB: 2CG9;Ali et al., 2006), and have been previously determined by performing similar measurements using individ-ual domains (Jahn et al., 2016). It should be noted that the process of the unfolding of a given domain is stochastic, and therefore the order of unfolding of the domains will not be conserved in all unfolding traces.

The regions linking the M and C domains, and part of the region at the end of the C domain, are resolved in the crystal structure, but are likely to be flexible in solution, meaning that they do not contribute to the measured contour length gains of the domains. This is confirmed by the good agreement between the measured and expected gains in contour length, assuming these regions to be unstructured (seeTable 1; Sup-plemental Information;Figure S1A). The low force fluctuations, indicated by the black arrow inFigure 2A before the unfolding of the C domain, are attributed to the docking and undocking of the charged linker between the N and M domains (Jahn et al., 2014). This, in combination with the unstructured regions of the monomer, contributes a further 50 nm to the measured total change in contour length upon unfolding (shown as the first WLC fit in Figure 2A). The change in contour length of the C domain is smaller, by approximately 8.5 nm, than would be expected from the crystal structure (seeSupplemental Informa-tion;Table S1). This has been attributed to the fact that, in the

monomeric form of Hsp82, in addition to the unstructured region at the end of the C domain (residues 678–709), the final a helix of the C domain is also unstructured (residues 656–671), only being structured when Hsp82 is in the dimeric form (Jahn et al., 2016).

Compared with the Hsp82 signature, the unfolding pattern for HtpG (Figure 2C) is remarkably similar. Following the extension of an unstructured region (30 nm, seeSupplemental Information; Figure S1A), the C domain is seen to unfold with an associated contour length gain of 30.3 ± 1.3 nm (n = 52). If the finala helix is considered to be unstructured in the monomer of HtpG, as is the case for Hsp82, this value is in good agreement with the number of amino acids in this domain seen in the crystal struc-ture (PDB: 2IOP, 2IOQ;Shiau et al., 2006). This finala helix con-tributes to the 30 nm initial WLC fit to the unstructured regions of the protein (Figure 2C). The C domain of HtpG comprises fewer amino acids than that of Hsp82 (97 versus 120, seeFigure 1B), leading to a shorter expected change in contour length. The N domain of HtpG unfolds with a contour length change of 77.8 ± 2.6 nm (n = 52), approximately 6.6 nm longer than that observed for yeast Hsp82. This can only be explained by assuming that amino acids in the M domain closest to the N domain, some of which are attributed to the charged linker region in Hsp82 and Grp94, form a stable structure together with the N domain (colored purple in Figure 1B). Finally, the M domain of HtpG unfolds with a contour length gain of 81.4 ± 1.1 nm (n = 52). Both the size of this domain and the average unfolding force are very similar to those of Hsp82. How-ever, unlike the two sub-domains in Hsp82, the middle domain of HtpG has three structural or unfolding sub-domains, the interme-diate unfolding steps of which can be clearly identified, espe-cially in unfolding traces obtained at faster pulling speed (see Supplemental Information;Figure S1).

The mechanical signature of Grp94 can be seen inFigure 2E. As with the previously described unfolding patterns, three domi-nant features, corresponding to each of the three domains of the protein, can be seen. The unstructured regions of the protein contribute a contour length gain of 55 nm. The C domain exhibits a similar gain in contour length (39.5 ± 1.8 nm) (n = 14) to the Hsp82 C domain, as does the M domain. This domain, like that of Hsp82 and HtpG, also has a clear unfolding intermediate (Fig-ure 2E; Supplemental Information;Figure S1B), resulting from the sub-domains of the M domain unfolding sequentially. The key difference between Grp94 and the other two orthologs lies in the N domain signature. Before the main part of the N domain unfolds (labeled ‘‘N’’ inFigures 2E and 2F), there is an unfolding event immediately preceding it (labeled ‘‘*’’ inFigures 2E and 2F). The gain in contour length of this event is 21.8 ± 1.5 nm (n = 14). Structurally, this could correspond to either the 53-amino-acid-long stretch of the so-called ‘‘pre-N domain,’’ which is not resolved in the crystal structure (Dollins et al., 2005, 2007), or the 60-amino-acid-long charged linker region, which is also only partly resolved. Both are unexpected, as the existence of such a pronounced feature in the force-extension trace implies that this is a structured element with a significant mechanical stability in the monomer. To determine the nature of this feature, a deletion construct was made, comprising only the N-terminal domain and the charged linker, with the pre-N domain stretch and the M as well as the C domains removed (termed the

Table 1. Expected Contour Length Gains for the Individual Domains Domain (Amino Acids) Expected Gain in Contour Length (nm) Measured Gain in Contour Length (nm) Average Unfolding Force (pN) Yeast (Hsp82) N-Terminal domain (3–209) 71.8 69.5 ± 2.5 15.5 ± 1.6 Middle domain (280–528) 84.5 85.0 ± 1.5 19.2 ± 1.6 C-Terminal domain (535–654) 40.5 40.2 ± 1.5 11.1 ± 2.0 E. coli (HtpG) N-Terminal domain (4–228) 77.7 77.8 ± 2.6 11.9 ± 1.3 Middle domain (242–485) 83.0 81.4 ± 1.1 21.0 ± 1.9 C-Terminal domain (509–606) 32.4 30.3 ± 1.3 20.8 ± 4.1 Dog ER (Grp94) N-Terminal domain (73–275) 69.8 64.9 ± 1.8 18.1 ± 3.5 Middle domain (341–592) 86.0 85.9 ± 1.9 16.6 ± 3.1 C-Terminal domain (601–726) 42.5 39.5 ± 1.8 13.6 ± 2.5 Charged linker (*) (276–335) 21.1 21.8 ± 1.5 18.5 ± 5.1

Expected contour length gains were determined from the crystal struc-ture (see STAR Methods for details) and are Compared with the measured values shown inFigures 1B, 1D, and 1F. Errors are SD. See alsoTable S1.

(7)

Dpre-N DMC construct). The resulting unfolding traces of this Dpre-N DMC construct (Figure 3A) retain both features of the N domain unfolding peak, clearly demonstrating that the first event in this peak corresponds to the charged linker of Grp94. To account for unstructured regions, an additional WLC fit of 55 nm contour length gain is included (Figure 2E), as previously proposed for Hsp82 (Jahn et al., 2014).

Upon closer observation of the Hsp82 unfolding trace, it can be noted that there is a slight deviation in the N domain unfold-ing peak from the WLC fit at higher forces. This results from unfolding of a secondary element as clearly visible in faster pulled traces for the full-length construct (see also Supple-mental Information; Figure S1B) and in the N domain when measured alone (Supplemental Information; Figure S1C). In the case of Hsp82, it can be seen from the crystal structure (Fig-ure 1A) that, in the N-terminally closed dimer, the firstb strand of the N domain (amino acid residues 1–9) binds to the edge of

the mainb sheet in the N domain of the other monomer. This is reported to occur alongside with a concomitant movement of the first a helix (residues 13–22) (Ali et al., 2006). Since the deviation has a contour length of approximately 7 nm (deter-mined from Figure S1C), in agreement with the unfolding of 22 amino acids, we hypothesize that this region can unfold independent from the remaining part of the N domain. This hy-pothesis is further supported by the fact that Hsp82, without either the first 8 or the first 24 amino acids, is stably folded (Mickler et al., 2009; Richter et al., 2002). Thus, the mechanical stability of the N domain in the monomeric form of Hsp82 without the first b strand is not unexpected. A similar small deviation from the WLC fit can also be seen in the N domain signature for HtpG (see alsoSupplemental Information;Figures S1B and S1D) and in Grp94 (Supplemental Information; Fig-ure S1B), alongside a shorter measFig-ured gain in contour length versus expected gain in contour length for the latter.

Figure 3. The Charged Linker of Grp94

(A) A typical force-extension cycle trace of theDpre-N DMC construct (inset: schematic showing the construct comprising only the N domain and the charged linker). The unfolding traces are shown in black, refolding in purple. WLC fits are shown as gray dashed lines.

(B) Average contour length gains from WLC fits to repeated 500 nm/s force-extension cycles and the corresponding unfolding forces for each unfolding event. Full-length Grp94 unfolding events shown as dark gray circles,Dpre-N DMC construct unfolding events shown as red circles. For the N domain unfolding event, the average value of the unfolding force is 16.0 ± 3.8 pN (average ± SD) theDpre-N DMC construct and 18.1 ± 3.5 pN for the full-length construct. The average unfolding force of the charged linker is 15.5 ± 5.5 pN for theDpre-N DMC construct and 18.5 ± 5.1 pN for the full-length construct. These values are the same within error.

(C) Two 20 s excerpts from constant distance force versus time traces for Grp94Dpre-N DMC. The folded state of the charged linker is shown in purple and the unfolded state is in red.

(D) The corresponding probability plot, showing the likelihood of being in the unfolded (red) state or the folded (purple) state with increasing force. Error bars represent the error due to the finite measurement time (Stigler et al., 2011). If no error bars are shown, they are smaller than the symbol size.

(E) Plot of the transition rates versus force, going from the folded state to the unfolded state (purple) and from the unfolded state to the folded state (red). As expected, the rate of refolding (red) decreases with increasing force, while the rate of unfolding (purple) increases with increasing force. Rates were corrected for missed events as described in (Stigler and Rief, 2012). Rates and probabilities were calculated using hidden Markov analysis of traces collected from 7 individual molecules, from 21 constant distance traces between 20 and 80 s in length. See alsoFigure S2.

(8)

The Charged Linker

The most striking difference in the mechanical signatures of these three orthologs is the high mechanical stability of the charged linker region of Grp94, as demonstrated by the promi-nent unfolding peak seen immediately preceding the unfolding of the N domain (Figures 2E, 2F, and3A). This region was further characterized to obtain force-dependent kinetics and the free energy stabilizing the charged linker. These results are compared with those of the charged linker of Hsp82 (Jahn et al., 2014). As described above, a construct consisting of the charged linker and the N domain without the pre-domain was used to confirm the correct assignment of the Grp94 unfolding signature. The mechanical signature of this truncated construct is shown inFigure 3A. The clear overlap between the contour length versus unfolding force scatterplots for this construct and the full-length Grp94 monomer (Figure 3B) confirmed the assignment.

To assess the stability of the charged linker region in more detail, an assay was used where the optical traps are kept at a constant distance (passive mode). This applies a constant average force to the protein, and in our case enables the equilib-rium between the folded and the unfolded state of the charged linker to be measured at a given force. By varying the distance, and therefore the average force applied, the equilibrium between the two states is shifted. Two examples of force versus time traces for Grp94 are given inFigure 3C. It should be noted that short time traces are shown here for clarity, and that data were routinely collected for over 300 s per molecule, enabling large numbers of transitions between the folded and unfolded state to be observed. The states were assigned using a hidden Markov analysis (Stigler and Rief, 2012). Fluctuations between the folded state of the charged linker (purple) and the unfolded state (red) can be seen to occur repeatedly. At higher forces, the charged linker is more likely to be unfolded than at lower forces (Fig-ure 3D). It is obvious that the charged linker spends most of the time in the folded state between 4 and 5 pN. For comparison, the charged linker of Hsp82 is significantly less stable and, at forces of 4 pN, it is always in the unfolded (undocked) state (Sup-plemental Information;Figure S2).

The charged linker of Hsp82 is only thought to exhibit second-ary structure while it is in direct contact with the N domain (Jahn et al., 2014), which is why rather than referring to the folding and unfolding of the Hsp82 charged linker, we refer to its docking and undocking. The Hsp82 charged linker is in the stable, docked state 75% ± 8% of the time, when no force is applied to the mole-cule (Jahn et al., 2014), and the energy difference between the docked and the undocked state is very small, 1.1 ± 0.4 kBT, which explains the rapid oscillations between these two states, and the low overall force of the charged linker signature in the Hsp82 unfolding trace, seen as fluctuations before the unfolding of the C domain (Figure 2A). In contrast, the charged linker of Grp94 is mechanically more stable. At zero applied force, it is always found in the folded state (Figure 3D), with an energy dif-ference between the folded and the unfolded state of 8.7 kBT. Figure 3E shows the force-dependent folding/unfolding rate constants for all molecules measured. As the average force level is increased, the rate of unfolding increases and the rate of re-folding decreases. Fitting the data and extrapolating to zero force (fits inFigure 3E), using a previously described energetic

model (Gebhardt et al., 2010; Rognoni et al., 2012), gives a refolding rate of 260 ± 17 s 1 (±SD) and an unfolding rate of 0.19 ± 0.01 s 1(± SD). The calculated rate of unfolding at zero force implies that an unfolding event occurs once every 5 s compared with the charged linker of Hsp82, which undocks 65 times per second. This further illustrates the high stability of the charged linker of Grp94 compared with that of Hsp82.

The ER has reported resting calcium levels of around 250 to 600 mM (Demaurex and Frieden, 2003). A single molecule of Grp94 is predicted to bind between 16 and 28 molecules of Ca2+(Macer and Koch, 1988; Van et al., 1989), through both high-affinity (Kdof 1–5mM) and lower-affinity (Kdof600 mM) binding sites (Biswas et al., 2007). Of these calcium binding sites, at least one high-affinity binding site has been confirmed to be in the charged linker region (Biswas et al., 2007). To assess whether calcium affects the stability of the N domain and charged linker, the Dpre-N DMC construct was measured in the standard measurement buffer containing an additional 10 mM CaCl2(Supplemental Information;Figure S4). The result-ing energy difference between the folded and the unfolded state was found to be similar or even a little lower than that measured without CaCl2(7.5 kBT with CaCl2, 8.7 kBT without, seeFigure 3). An error of 10% in the calculated energy is estimated based on the uncertainty in the force calibration of the optical trap.

Comparison of Refolding Behaviors

The observation of successive force-extension cycles allows the quantification of the refolding process. Following the unfolding of the domains, the force is gradually reduced back to zero force. The subsequent re-extension of the molecule serves as a probe of whether or not it successfully refolded to its native state, confirmed by the observation of the native mechanical signature. Examples of refolding (purple) and unfolding (gray) traces for Hsp82, HtpG, and Grp94 are shown inFigures 4A, 4D, and 4G, respectively. The completely unfolded monomers refold through a series of events and the subsequent unfolding traces shown exhibit the fully native pattern. Where refolding transitions overlap with unfolding transitions, these can be attributed to the refolding of the same domains or sub-domains.

Performing repeated force-extension cycles at a faster veloc-ity, results in the force-extension traces shown inFigures 4B, 4E, and 4H for Hsp82, HtpG, and Grp94, respectively. Correspond-ing scatterplots are shown in Figures 4C, 4F, and 4I. Native mechanical signature data points are colored according to domain, and non-native unfolding events resulting from the unfolding of misfolded or intermediate structures are colored in red. In the scatterplot for Hsp82 (Figure 4C), all three domains are detected in the repeated unfolding/refolding cycles. A native unfolding pattern is seen in 36% of the collected unfolding traces (n = 56 force-extension cycles). This is in good agreement with previously published data (Jahn et al., 2016). While small proteins have been predicted and shown to refold very rapidly at zero force (Ainavarapu et al., 2007; Jackson, 1998; Plaxco et al., 1998), for larger proteins the likelihood of inter- and intra-domain misfolds resulting from non-native interactions stabilizing misfolded states increases with the number of amino acids. This slows down the folding rate, especially in large proteins with multiple homologous domains (Borgia et al., 2011; Peng et al., 2011; Xia et al., 2011) and in those with

(9)

non-homologous domains, such as Hsp82 (Jahn et al., 2016). Accordingly, the percentage of native unfolding patterns seen in HtpG is also only 25% (n = 59 force-extension cycles). This can clearly be seen in the eight successive 500 nm/s unfold-ing/refolding force-extension curves shown inSupplemental In-formation;Figure S3A. Strikingly, Grp94 does not refold, after the initial unfolding of the full monomer (plotted for reference in Figure 4I), to the native state over the course of the 46 force-extension cycles measured. As can be seen from the number of yellow-green-colored data points in the scatterplot for

Grp94 (Figure 4I), the C domain does refold regularly. This was also observed for Hsp82 and HtpG (Figures 4B, 4E, and Supple-mental Information; Figure S3A). The signature of the native M domain was also often seen (colored orange). However, the native states of the N domain and of the charged linker were not detected (colored blue and gray, respectively, in the initial unfolding of the full monomer). This finding implies that refolding of the N domain and charged linker are the most problematic. In addition, as discussed above, the addition of calcium did not increase the stability of the N domain or charged linker.

Figure 4. Refolding of Hsp82, HtpG, and Grp94

(A, D, and G) Two examples of representative force-extension traces at 10 nm/s showing the extension curve in gray (unfolding), and the relaxation curve in purple (refolding) for (A) Hsp82, (C) HtpG, and (E) Grp94.

(B, E, and H) Three repeated force-extension cycles at 500 nm/s with no waiting time at zero force for (B) Hsp82, (E) HtpG, and (H) Grp94. Native mechanical signatures of individual domains are colored according to domain (blue for the N domain, orange for the M domain, dark yellow for the C domain, and gray for the charged linker of Grp94).

(C, F, and I) Scatterplots of the unfolding forces and gains in contour length for repeated force-extension cycles at 500 nm/s with no waiting time at zero force, for (C) Hsp82, (F) HtpG, and (I) Grp94, illustrating the refolding capabilities of the three orthologs. Native mechanical signature data points are colored according to domain as in (B, E, and H). Non-native unfolding events resulting from the unfolding of misfolded or intermediate structures are colored in red. It should be noted that misfolds with contour length gains longer than those of natively folded individual domains are common and occur as a result of inter-domain misfolds. See alsoFigures S3andS4.

(10)

Interestingly, when slower velocities were used to unfold and refold Grp94, unfolding was completely reversible around 50% of the time (Figure 4G;Supplemental Information;Figure S3B). Slower force-extension velocities raise the refolding capability of HtpG to 100% (Figure 4D;Supplemental Information; Fig-ure S3B). This effect has previously been observed for Hsp82 (Jahn et al., 2016). It is assumed that the gradual reduction of force improves refolding by keeping the protein in an elongated state and thus prevents the occurrence of inter-domain misfolds (Jahn et al., 2016). Similar effects were observed for refolding at a small constant force, rather than at zero force (Jahn et al., 2016).

DISCUSSION

In this study, we determined the mechanical signatures of three orthologs of Hsp90 representing bacterial Hsp90, and cytosolic and endoplasmic eukaryotic Hsp90, using single-molecule opti-cal trap experiments with a view to assess the structure and dynamics of the protein monomers.

Here, the mechanical signatures of each of the orthologs resulting from forces applied along the selected pulling direc-tion have been established, with specific features in the force-extension traces being assigned to the unfolding and folding of their individual domains. Compared with the N domain of Hsp82, the N domain of HtpG unfolds with a larger contour length gain and a slightly lower average unfolding force. We attribute the larger contour length gain to the amino acids at the interface, with the M domain forming a stable structure together with the N domain. The Grp94 N domain unfolds with a similar unfolding force to that of Hsp82; however, the contour length gain is shorter. This is likely due to the pre-N domain region of Grp94 being unstructured in this monomeric construct. It therefore contributes to the 55 nm initial WLC fit and not to the N domain (Figure 2E). The M domains of all measured orthologs unfold in a very similar way, in both unfold-ing force and contour length gain. A prominent difference is that the Hsp82 M domain has two unfolding intermediates, resulting from the two sub-domains unfolding separately, while the HtpG M domain has three. The implications of this are discussed in detail below. The C domains of all three constructs exhibited very similar unfolding signatures (accounting for small differ-ences in sequence lengths), unfolding at similar forces and without any unfolding intermediates.

All three orthologs exhibited poor refolding in the absence of force, which was improved significantly when slow constant velocities of 10 or 20 nm/s were used (Figures 4A, 4D, 4G; Sup-plemental Information;Figure S2). This is attributed to the exis-tence of misfolding events, which can be prevented through the use of force as a ‘‘chaperone,’’ as was previously proposed for Hsp82 (Jahn et al., 2016). Misfolds are generally likely to occur in large proteins, and even inter-domain misfolds can be observed (Jahn et al., 2016). It is possible that the poor folding capability of Grp94 may be one of the reasons for the wide range of reported values for its ATPase activity, ranging from kcat = 0.02 ± 0.001 min 1 at 37C (Dollins et al., 2007) to 0.36 min 1at 30C (Frey et al., 2007), and our measured value of 0.47 ± 0.03 min 1at 30C (mean ± SD; seeSupplemental Information; Table S2). A significant amount of misfolded Grp94 might also explain the earlier controversy as to whether

Grp94 possesses ATPase activity at all (Li and Srivastava, 1993; Wassenberg et al., 2000; Wearsch and Nicchitta, 1997).

A deviation from the WLC fits to the high force range of the unfolding peaks of the N domains of each ortholog was noted. Such deviations occur as a result of conformationally flexible portions of protein domains being unraveled during the process of extending the protein domain under force. In Hsp82, this was attributed to the movement of the firstb strand and the first a helix of the N domain, known to occur during the N-terminal dimeriza-tion of Hsp82. The existence of such a deviadimeriza-tion in all three ortho-logs indicates that Grp94 and HtpG may also have similar ‘‘hand-shake’’ mechanisms for the stabilization of the N-terminally closed conformation of the dimer. No such conformation has yet been seen in crystal structures of either domain, although it should be noted that the crystal structures of Grp94 are trun-cated, starting at residue 73 or 69 (Dollins et al., 2005; Dollins et al., 2007).

The most striking feature of the unfolding signatures of the three proteins was the highly stable charged linker of Grp94. This was surprising, as the charged linker of Hsp82 only has a stabilizing energy of 1.1 kBT, docking and undocking hundreds of times per second. In contrast, the charged linker of Grp94 exhibits an energy difference between the folded and the unfolded state of 8.7 kBT and only unfolds approximately once every 5 s. Therefore, whereas the Hsp82 charged linker provides a flexible connection between the N and M domains, while also controlling the rotation of the N domain during the functional cycle of Hsp82 (Daturpalli et al., 2017; Hellenkamp et al., 2017; Li et al., 2012), the charged linker of Grp94 appears to play a significantly less dynamic role. Only the crystal struc-tures of the N domain of Grp94 include the residues involved in the charged linker as in the full-length crystal structure the majority of the residues involved in the charged linker have been deleted (Soldano et al., 2003). However, these crystal structures of the N domain of Grp94 lack electron density for the charged linker region, indicating that the charged linker is either locally disordered or conformationally variable if only the N domain is present. However, in both the Grp94 N domain crystal structure and the full-length Grp94 crystal structure there are twob strands, one at each end of the charged linker region, which form an antiparallel two-stranded b sheet ( Sol-dano et al., 2003). This stable b sheet, combined with the shorter length of the Grp94-charged linker compared with that of Hsp82, suggests a more rigid N/M domain interface in Grp94. This might provide a possible mechanism for conforma-tional coordination or even cooperation between the N and M domains during its functional cycle. HtpG only has an inter-domain linker of seven residues in length between the N and M domains (Shiau et al., 2006), which also results in a more rigid N/M domain interface (Shiau et al., 2006).

The length and the sequence of the charged linker of Hsp82 have both been shown to affect the rotational freedom of the N domain and the interaction with some client proteins (Daturpalli et al., 2017). The significantly different charged linker characteristics for Grp94 and HtpG are therefore likely to have im-plications for the ability of Grp94 and HtpG to interact with Hsp82 client proteins. Combined with the large surface area of the N/M domain interface in HtpG, and a more flexible, smaller interface between the M- and C-terminal domains (Shiau et al., 2006), it

(11)

appears to be the M/C domain interface that is primarily respon-sible for the conformational flexibility of the HtpG dimer during ATP hydrolysis and client maturation. This single interface could be responsible for the opening and closing of the dimer, as well as the rotation of the N and M domains (Richter et al., 2006; Street et al., 2011). In comparison, Hsp82 relies on both the N domain/M domain interface and the M/C domain interface to act as flexible hinges (Daturpalli et al., 2017; Hellenkamp et al., 2017).

Overall, we have identified a number of similarities and signif-icant differences in the folding and domain interactions of these three orthologs. We have discussed the functional implications of these in the context of their conformational cycles, structures, and dynamics. Our results will inform future studies of the impor-tant Hsp90 family.

STAR+METHODS

Detailed methods are provided in the online version of this paper and include the following:

d KEY RESOURCES TABLE

d CONTACT FOR REAGENT AND RESOURCE SHARING d METHOD DETAILS

B Molecular Cloning, Protein Expression and Purification

B ATPase Measurement

d QUANTIFICATION AND STATISTICAL ANALYSIS

B Constant Velocity Optical Tweezers Experiments

B WLC Fitting of Multi-Domain Proteins

B Assignment of Contour Length Gains to Structure

B Constant Distance Optical Tweezers Experiments d DATA AND SOFTWARE AVAILABILITY

SUPPLEMENTAL INFORMATION

Supplemental Information includes four figures and two tables and can be found with this article online athttps://doi.org/10.1016/j.str.2017.11.023.

ACKNOWLEDGMENTS

The authors thank the German Research Foundation for financial support (SFB863 A4). K.T. gratefully acknowledges funding from an HFSP Cross-Disci-plinary Fellowship LT000150/2015-C.

AUTHOR CONTRIBUTIONS

M.J., K.T., T.H., J.B., and M.R. designed the research. M.J., K.T., H.G., and M.S. performed the research. M.J., K.T., T.H., J.B., and M.R. wrote the paper. M.J. and K.T. analyzed the data.

Received: August 2, 2017 Revised: October 16, 2017 Accepted: October 27, 2017 Published: December 21, 2017

REFERENCES

Ainavarapu, S.R.K., Brujic, J., Huang, H.H., Wiita, A.P., Lu, H., Li, L., Walther, K.A., Carrion-Vazquez, M., Li, H., and Fernandez, J.M. (2007). Contour length and refolding rate of a small protein controlled by engineered disulfide bonds. Biophys. J. 92, 225–233.

Ali, M.M.U., Roe, S.M., Vaughan, C.K., Meyer, P., Panaretou, B., Piper, P.W., Prodromou, C., and Pearl, L.H. (2006). Crystal structure of an Hsp90-nucleo-tide-p23/Sba1 closed chaperone complex. Nature 440, 1013–1017.

Altschul, S., Madden, T.L., Sch€affer, A.A., Zhang, J., Zhang, Z., Miller, W., and Lipman, D.J. (1997). Gapped BLAST and PSI-BLAST: a new generation of pro-tein database search programs. Nucleic Acids Res. 25, 3389–3402.

Altschul, S.F., Gish, W., Miller, W., Myers, E.W., and Lipman, D.J. (1990). Basic local alignment search tool. J. Mol. Biol. 215, 403–410.

Bardwell, J.C., and Craig, E.A. (1988). Ancient heat shock gene is dispensable. J. Bacteriol. 170, 2977–2983.

Biswas, C., Ostrovsky, O., Makarewich, C.A., Wanderling, S., Gidalevitz, T., and Argon, Y. (2007). The peptide-binding activity of GRP94 is regulated by calcium. Biochem. J. 405, 233–241.

Borgia, M.B., Borgia, A., Best, R.B., Steward, A., Nettels, D., Wunderlich, B., Schuler, B., and Clarke, J. (2011). Single-molecule fluorescence reveals sequence-specific misfolding in multidomain proteins. Nature 474, 662–665.

Borkovich, K.A., Farrelly, F.W., Finkelstein, D.B., Taulien, J., and Lindquist, S. (1989). hsp82 is an essential protein that is required in higher concentrations for growth of cells at higher temperatures. Mol. Cell. Biol. 9, 3919–3930.

Chen, B., Zhong, D., and Monteiro, A. (2006). Comparative genomics and evo-lution of the HSP90 family of genes across all kingdoms of organisms. BMC Genomics 7, 156.

Chen, S., Sullivan, W.P., Toft, D.O., and Smith, D.F. (1998). Differential interac-tions of p23 and the TPR-containing proteins Hop, Cyp40, FKBP52 and FKBP51 with Hsp90 mutants. Cell Stress Chaperones 3, 118–129.

Daturpalli, S., Knieß, R.A., Lee, C.-T., and Mayer, M.P. (2017). Large rotation of the N-terminal domain of hsp90 is important for interaction with some but not all client proteins. J. Mol. Biol. 429, 1406–1423.

Demaurex, N., and Frieden, M. (2003). Measurements of the free luminal ER Ca2+ concentration with targeted ‘‘cameleon’’ fluorescent proteins. Cell Calcium 34, 109–119.

Dollins, D.E., Immormino, R.M., and Gewirth, D.T. (2005). Structure of unli-ganded GRP94, the endoplasmic reticulum Hsp90. Basis for nucleotide-induced conformational change. J. Biol. Chem. 280, 30438–30447.

Dollins, D.E., Warren, J.J., Immormino, R.M., and Gewirth, D.T. (2007). Structures of GRP94-nucleotide complexes reveal mechanistic differences between the hsp90 chaperones. Mol. Cell 28, 41–56.

Flach, H., Rosenbaum, M., Duchniewicz, M., Kim, S., Zhang, S.L., Cahalan, M.D., Mittler, G., and Grosschedl, R. (2010). Mzb1 protein regulates calcium homeostasis, antibody secretion, and integrin activation in innate-like B cells. Immunity 33, 723–735.

Frey, S., Leskovar, A., Reinstein, J., and Buchner, J. (2007). The ATPase cycle of the endoplasmic chaperone Grp94. J. Biol. Chem. 282, 35612–35620.

Gebhardt, J.C.M., Bornschlo¨gl, T., and Rief, M. (2010). Full distance-resolved folding energy landscape of one single protein molecule. Proc. Natl. Acad. Sci. USA 107, 2013–2018.

Hainzl, O., Lapina, M.C., Buchner, J., and Richter, K. (2009). The charged linker region is an important regulator of Hsp90 function. J. Biol. Chem. 284, 22559–22567.

Hellenkamp, B., Wortmann, P., Kandzia, F., Zacharias, M., and Hugel, T. (2017). Multidomain structure and correlated dynamics determined by self-consistent FRET networks. Nat. Methods 14, 174–180.

Hessling, M., Richter, K., and Buchner, J. (2009). Dissection of the ATP-induced conformational cycle of the molecular chaperone Hsp90. Nat. Struct. Mol. Biol. 16, 287–293.

Honore´, F.A., Me´jean, V., and Genest, O. (2017). Hsp90 is essential under heat stress in the bacterium Shewanella oneidensis. Cell Rep. 19, 680–687.

Jackson, S.E. (1998). How do small single-domain proteins fold? Fold. Des. 3, R81–R91.

Jahn, M., Rehn, A., Pelz, B., Hellenkamp, B., Richter, K., Rief, M., Buchner, J., and Hugel, T. (2014). The charged linker of the molecular chaperone Hsp90 modulates domain contacts and biological function. Proc. Natl. Acad. Sci. USA 111, 17881–17886.

Jahn, M., Buchner, J., Hugel, T., and Rief, M. (2016). Folding and assembly of the large molecular machine Hsp90 studied in single-molecule experiments. Proc. Natl. Acad. Sci. USA 113, 1232–1237.

(12)

Johnson, J.L. (2012). Evolution and function of diverse Hsp90 homologs and cochaperone proteins. Biochim. Biophys. Acta 1823, 607–613.

Krukenberg, K.A., Bo¨ttcher, U.M.K., Southworth, D.R., and Agard, D.A. (2009). Grp94, the endoplasmic reticulum Hsp90, has a similar solution conformation to cytosolic Hsp90 in the absence of nucleotide. Protein Sci. 18, 1815–1827.

Krukenberg, K.A., Street, T.O., Lavery, L.A., and Agard, D.A. (2011). Conformational dynamics of the molecular chaperone Hsp90. Q. Rev. Biophys. 44, 229–255.

Langer, T., Rosmus, S., and Fasold, H. (2003). Intracellular localization of the 90 kDA heat shock protein (HSP90alpha) determined by expression of a EGFP-HSP90alpha-fusion protein in unstressed and heat stressed 3T3 cells. Cell Biol. Int. 27, 47–52.

Li, J., and Buchner, J. (2012). Structure, function and regulation of the hsp90 machinery. Biomed. J. 36, 106–117.

Li, Z., and Srivastava, P.K. (1993). Tumor rejection antigen gp96/grp94 is an ATPase: implications for protein folding and antigen presentation. EMBO J.

12, 3143–3151.

Li, J., Soroka, J., and Buchner, J. (2012). The Hsp90 chaperone machinery: conformational dynamics and regulation by co-chaperones. Biochim. Biophys. Acta 1823, 624–635.

Liu, B., and Li, Z. (2008). Endoplasmic reticulum HSP90b1 (gp96, grp94) opti-mizes B-cell function via chaperoning integrin and TLR but not immunoglob-ulin. Blood 112, 1223–1230.

Liu, B., Yang, Y., Qiu, Z., Staron, M., Hong, F., Li, Y., Wu, S., Li, Y., Hao, B., Bona, R., et al. (2010). Folding of Toll-like receptors by the HSP90 paralogue gp96 requires a substrate-specific cochaperone. Nat. Commun. 1, 1–10.

Macer, D.R., and Koch, G.L. (1988). Identification of a set of calcium-binding proteins in reticuloplasm, the luminal content of the endoplasmic reticulum. J. Cell Sci. 91 (Pt 1), 61–70.

Marzec, M., Eletto, D., and Argon, Y. (2012). GRP94: an HSP90-like protein specialized for protein folding and quality control in the endoplasmic reticulum. Biochim. Biophys. Acta 1823, 774–787.

Mashaghi, A., Kramer, G., Lamb, D.C., Mayer, M.P., and Tans, S.J. (2014). Chaperone action at the single-molecule level. Chem. Rev. 114, 660–676.

Mickler, M., Hessling, M., Ratzke, C., Buchner, J., and Hugel, T. (2009). The large conformational changes of Hsp90 are only weakly coupled to ATP hydro-lysis. Nat. Struct. Mol. Biol. 16, 281–286.

Peng, Q., Fang, J., Wang, M., and Li, H. (2011). Kinetic partitioning mechanism governs the folding of the third FnIII domain of tenascin-C: evidence at the sin-gle-molecule level. J. Mol. Biol. 412, 698–709.

Peterman, E.J.G., Gittes, F., and Schmidt, C.F. (2003). Laser-induced heating in optical traps. Biophys. J. 84, 1308–1316.

Plaxco, K.W., Simons, K.T., and Baker, D. (1998). Contact order, transition state placement and the refolding rates of single domain proteins. J. Mol. Biol. 277, 985–994.

Prodromou, C., Siligardi, G., O’Brien, R., Woolfson, D.N., Regan, L., Panaretou, B., Ladbury, J.E., Piper, P.W., and Pearl, L.H. (1999). Regulation of Hsp90 ATPase activity by tetratricopeptide repeat (TPR)-domain co-chap-erones. EMBO J. 18, 754–762.

Ratzke, C., Nguyen, M.N.T., Mayer, M.P., and Hugel, T. (2012). From a ratchet mechanism to random fluctuations evolution of Hsp90’s mechanochemical cycle. J. Mol. Biol. 423, 462–471.

Ratzke, C., Hellenkamp, B., and Hugel, T. (2014). Four-colour FRET reveals directionality in the Hsp90 multicomponent machinery. Nat. Commun. 5, 4192.

Richter, K., Reinstein, J., and Buchner, J. (2002). N-terminal residues regulate the catalytic efficiency of the Hsp90 ATPase cycle. J. Biol. Chem. 277, 44905–44910.

Richter, K., Buchner, J., Sobott, F., Good, V.M., Ali, M.M., Prodromou, C., Robinson, C.V., Saibil, H.R., Pearl, L.H., and Buchner, J. (2006). hsp90: twist and fold. Cell 127, 251–253.

Rognoni, L., Stigler, J., Pelz, B., Ylanne, J., and Rief, M. (2012). Dynamic force sensing of filamin revealed in single-molecule experiments. Proc. Natl. Acad. Sci. USA 109, 19679–19684.

Rosenbaum, M., Andreani, V., Kapoor, T., Herp, S., Flach, H., Duchniewicz, M., and Grosschedl, R. (2014). MZB1 is a GRP94 cochaperone that enables proper immunoglobulin heavy chain biosynthesis upon ER stress. Genes Dev. 28, 1165–1178.

Sato, T., Minagawa, S., Kojima, E., Okamoto, N., and Nakamoto, H. (2010). HtpG, the prokaryotic homologue of Hsp90, stabilizes a phycobilisome protein in the cyanobacterium Synechococcus elongatus PCC 7942. Mol. Microbiol.

76, 576–589.

Scheufler, C., Brinker, A., Bourenkov, G., Pegoraro, S., Moroder, L., Bartunik, H., Hartl, F.U., and Moarefi, I. (2000). Structure of TPR domain-peptide com-plexes: critical elements in the assembly of the Hsp70-Hsp90 multichaperone machine. Cell 101, 199–210.

Schopf, F.H., Biebl, M.M., and Buchner, J. (2017). The HSP90 chaperone ma-chinery. Nat. Rev. Mol. Cell Biol. 18, 345–360.

Shiau, A.K., Harris, S.F., Southworth, D.R., and Agard, D.A. (2006). Structural analysis of E. coli hsp90 reveals dramatic nucleotide-dependent conforma-tional rearrangements. Cell 127, 329–340.

Soldano, K.L., Jivan, A., Nicchitta, C.V., and Gewirth, D.T. (2003). Structure of the N-terminal domain of GRP94. Basis for ligand specificity and regulation. J. Biol. Chem. 278, 48330–48338.

Stigler, J., and Rief, M. (2012). Hidden Markov analysis of trajectories in single-molecule experiments and the effects of missed events. ChemPhysChem 13, 1079–1086.

Stigler, J., Ziegler, F., Gieseke, A., Gebhardt, J.C.M., and Rief, M. (2011). The complex folding network of single calmodulin molecules. Science 334, 512–516.

Street, T.O., Lavery, L.A., and Agard, D.A. (2011). Substrate binding drives large-scale conformational changes in the Hsp90 molecular chaperone. Mol. Cell 42, 96–105.

Taipale, M., Jarosz, D.F., and Lindquist, S. (2010). HSP90 at the hub of protein homeostasis: emerging mechanistic insights. Nat. Rev. Mol. Cell Biol. 11, 515–528.

Tsutsumi, S., Mollapour, M., Prodromou, C., Lee, C.-T., Panaretou, B., Yoshida, S., Mayer, M.P., and Neckers, L.M. (2012). Charged linker sequence modulates eukaryotic heat shock protein 90 (Hsp90) chaperone activity. Proc. Natl. Acad. Sci. USA 109, 2937–2942.

Van, P.N., Peter, F., and So¨ling, H.D. (1989). Four intracisternal calcium-bind-ing glycoproteins from rat liver microsomes with high affinity for calcium. No indication for calsequestrin-like proteins in inositol 1,4,5-trisphosphate-sensi-tive calcium sequestering rat liver vesicles. J. Biol. Chem. 264, 17494–17501.

von Hansen, Y., Mehlich, A., Pelz, B., Rief, M., and Netz, R.R. (2012). Auto- and cross-power spectral analysis of dual trap optical tweezer experiments using Bayesian inference. Rev. Sci. Instrum. 83, 95116.

Wassenberg, J.J., Reed, R.C., and Nicchitta, C.V. (2000). Ligand interactions in the adenosine nucleotide-binding domain of the Hsp90 chaperone, GRP94. II. Ligand-mediated activation of GRP94 molecular chaperone and peptide binding activity. J. Biol. Chem. 275, 22806–22814.

Wearsch, P.A., and Nicchitta, C.V. (1997). Interaction of endoplasmic reticu-lum chaperone GRP94 with peptide substrates is adenine nucleotide-indepen-dent. J. Biol. Chem. 272, 5152–5156.

Xia, F., Thirumalai, D., and Gr€ater, F. (2011). Minimum energy compact struc-tures in force-quench polyubiquitin folding are domain swapped. Proc. Natl. Acad. Sci. USA 108, 6963–6968.

(13)

STAR

+METHODS

KEY RESOURCES TABLE

CONTACT FOR REAGENT AND RESOURCE SHARING

Further information and requests for resources and reagents should be directed to and will be fulfilled by the Lead Contact, Katarzyna Tych (k.m.tych@tum.de).

METHOD DETAILS

Sequence similarities were calculated using BLASTP 2.6.1 (Altschul et al., 1997, 1990) (Swiss-Prot/TrEMBL accession codes for Grp94, Hsp82 and HtpG are P41148, P02829 and P0A6Z3, respectively). Sequence conservation of the three Hsp90 orthologues was assessed through an alignment created using CLC Sequence software (Qiagen). Monomers of Hsp82, HtpG and Grp94 were expressed and purified according to methods detailed below. For use in the optical trapping experiment, maleimide-functionalized DNA oligonucleotides were reacted with the free cysteines in the protein constructs (see ‘Molecular cloning, protein expression and purification’ below). These were then hybridized with long DNA handles, which were functionalized with either biotin or digoxigenin. These functionalized handles enable the protein constructs to bind to streptavidin- or anti-digoxigenin-coated silica beads (1mm diameter). By trapping one bead of each type in the foci of each of the two laser beams in the custom-built optical tweezers setup (described previously (von Hansen et al., 2012)), a dumbbell geometry is established with a protein construct between the two beads.

REAGENT or RESOURCE SOURCE IDENTIFIER

Bacterial and Virus Strains

BL21-Gold(DE3) strain Agilent Technologies, USA Catalog #230132

Critical Commercial Assays

Quikchange Lighting Agilent Technologies, USA Catalog #210519

Anion Exchange Mono Q column GE Healthcare, USA Product code 17516601

Size exclusion column, Superdex 200 GE Healthcare, USA Product code 17517501

Deposited Data

Sequences for all protein constructs Mendeley data https://doi.org/10.17632/b7nfbz4xfp.1

Oligonucleotides

Protein to DNA handle coupling oligo:

GGCAGGGCTGACGTTCAACCAGACCAGCGAGTCG-Thiol

IBA GmbH, Germany Custom order for this paper

Biotin-modified primer for DNA handles 5’-GGCGA5CTGG5CGTTGATTTG-3’ 5: dT-Biotin (total: 3)

IBA GmbH, Germany Custom order for this paper

Digoxygenin-modified primer for DNA handles 5’-GGCGA5CTGG5CGTTGATTTG-3’ 5: dT-Digoxigenin modification (total: 3)

IBA GmbH, Germany Custom order for this paper

Linker primer for DNA handles

5’-CGACTCGCTGGTCTGGTTGAACGTCAGCCCTGCCXCC TGCCCGGCTCTGGACAGG-3’

X: stable abasic site

IBA GmbH, Germany Custom order for this paper

Recombinant DNA

Grp94Dpre-N DMC construct Genscript, USA Custom order for this paper

Grp94 (C. lupus Hsp90) construct (ubi – Grp94 – ubi – His) Genscript, USA Custom order for this paper Hsp82 (S. cerevisiae Hsp90) construct (ubi – Hsp82 – ubi – His) Genscript, USA Custom order for this paper

Hsp82DMDC deletion construct Genscript, USA Custom order for this paper

HtpG (E. coli Hsp90) construct (ubi – HtpG – ubi – His) Genscript, USA Custom order for this paper

HtpGDC construct Genscript, USA Custom order for this paper

Software and Algorithms

(14)

The protein can then be subjected to multiple stretch-and-relax cycles or can be held at a constant trap distance, such that a constant average force is applied. The trap stiffness of the optical traps is set to 0.3 – 0.4 pN/nm and data are collected at an acquisition frequency of 20 or 30 kHz. All measurements were carried out in 40 mM HEPES, 150 mM KCl, and 10 mM MgCl2, pH 7.4 with the addition of a scavenger system comprising glucose, glucose oxidase and glucose catalase to reduce photo damage. Measurements are conducted at a controlled room temperature of 23C, and because of laser heating the temperature inside the measurement chamber is 30C (Peterman et al., 2003).

Molecular Cloning, Protein Expression and Purification

The Hsp82, HtpG and Grp94 monomer constructs were genetically inserted between two ubiquitin domains with cysteine mutations for DNA coupling. Ubiquitin domains are mechanically stable and are often used as spacers in such constructs. The molecular cloning and protein expression and purification steps for these constructs are described in detail in (Jahn et al., 2014). Briefly, DNA constructs were synthesized (Genscript, USA) and sub-cloned into the pET28 vector (Novagen, Germany). Plasmids were transformed into BL21DE3 cod+ (Stratagene, USA). Proteins were then expressed overnight at 20C and cells harvested by centrifugation before being lysed in a French Press (Constant Systems, UK). His-tagged proteins were purified by Ni-NTA column (GE Healthcare, USA). SUMO tags were removed by digestion overnight with SENP during dial-ysis at 4C then purified further on the Ni-NTA column. Proteins were further purified by Anion Exchange on a Mono Q column (GE Healthcare, USA).

The sequences for the constructs are given below (this data has been deposited online and can be found here:https://doi.org/10. 17632/b7nfbz4xfp.1). Hsp82 MACKMQIFVKTLTGKTITLEVEPSDTIENVKAKIQDKEGIPPDQQRLIFAGKQLEDGRTLSDYNIQKESTLHLVLRLRGGELMASETFEFQA EITQLMSLIINTVYSNKEIFLRELISNASDALDKIRYKSLSDPKQLETEPDLFIRITPKPEQKVLEIRDSGIGMTKAELINNLGTIAKSGTKAFME ALSAGADVSMIGQFGVGFYSLFLVADRVQVISKSNDDEQYIWESNAGGSFTVTLDEVNERIGRGTILRLFLKDDQLEYLEEKRIKEVIKRHS EFVAYPIQLVVTKEVEKEVPIPEEEKKDEEKKDEEKKDEDDKKPKLEEVDEEEEKKPKTKKVKEEVQEIEELNKTKPLWTRNPSDITQEEYN AFYKSISNDWEDPLYVKHFSVEGQLEFRAILFIPKRAPFDLFESKKKKNNIKLYVRRVFITDEAEDLIPEWLSFVKGVVDSEDLPLNLSREM LQQNKIMKVIRKNIVKKLIEAFNEIAEDSEQFEKFYSAFSKNIKLGVHEDTQNRAALAKLLRYNSTKSVDELTSLTDYVTRMPEHQKNIYYIT GESLKAVEKSPFLDALKAKNFEVLFLTDPIDEYAFTQLKEFEGKTLVDITKDFELEETDEEKAEREKEIKEYEPLTKALKEILGDQVEKVVVS YKLLDAPAAIRTGQFGWSANMERIMKAQALRDSSMSSYMSSKKTFEISPKSPIIKELKKRVDEGGAQDKTVKDLTKLLYETALLTSGFSL DEPTSFASRINRLISLGLNIDEDEETETAPEASTAAPVEEVPADTEMEEVDKLMQIFVKTLTGKTITLEVEPSDTIENVKAKIQDKEGIPPDQQ RLIFAGKQLEDGRTLSDYNIQKESTLHLVLRLRGGKCLEHHHHHH Hsp82 Delta M, Delta C MACKMQIFVKTLTGKTITLEVEPSDTIENVKAKIQDKEGIPPDQQRLIFAGKQLEDGRTLSDYNIQKESTLHLVLRLRGGSMASETFEFQAE ITQLMSLIINTVYSNKEIFLRELISNASDALDKIRYKSLSDPKQLETEPDLFIRITPKPEQKVLEIRDSGIGMTKAELINNLGTIAKSGTKAFMEA LSAGADVSMIGQFGVGFYSLFLVADRVQVISKSNDDEQYIWESNAGGSFTVTLDEVNERIGRGTILRLFLKDDQLEYLEEKRIKEVIKRHSE FVAYPIQLVVTGGSMQIFVKTLTGKTITLEVEPSDTIENVKAKIQDKEGIPPDQQRLIFAGKQLEDGRTLSDYNIQKESTLHLVLRLRGGKCL EHHHHHH HtpG MACKMQIFVKTLTGKTITLEVEPSDTIENVKAKIQDKEGIPPDQQRLIFAGKQLEDGRTLSDYNIQKESTLHLVLRLRGGSMKGQETRGFQ SEVKQLLHLMIHSLYSNKEIFLRELISNASDAADKLRFRALSNPDLYEGDGELRVRVSFDKDKRTLTISDNGVGMTRDEVIDHLGTIAKSG TKSFLESLGSDQAKDSQLIGQFGVGFYSAFIVADKVTVRTRAAGEKPENGVFWESAGEGEYTVADITKEDRGTEITLHLREGEDEFLDDW RVRSIISKYSDHIALPVEIEKREEKDGETVISWEKINKAQALWTRNKSEITDEEYKEFYKHIAHDFNDPLTWSHNRVEGKQEYTSLLYIPSQA PWDMWNRDHKHGLKLYVQRVFIMDDAEQFMPNYLRFVRGLIDSSDLPLNVSREILQDSTVTRNLRNALTKRVLQMLEKLAKDDAEKYQ TFWQQFGLVLKEGPAEDFANQEAIAKLLRFASTHTDSSAQTVSLEDYVSRMKEGQEKIYYITADSYAAAKSSPHLELLRKKGIEVLLLSDRI DEWMMNYLTEFDGKPFQSVSKVDESLEKLADEVDESAKEAEKALTPFIDRVKALLGERVKDVRLTHRLTDTPAIVSTDADEMSTQMAKL FAAAGQKVPEVKYIFELNPDHVLVKRAADTEDEAKFSEWVELLLDQALLAERGTLEDPNLFIRRMNQLLVSGGSMQIFVKTLTGKTITLEV EPSDTIENVKAKIQDKEGIPPDQQRLIFAGKQLEDGRTLSDYNIQKESTLHLVLRLRGGKCLEHHHHHH HtpG Delta C MACKMQIFVKTLTGKTITLEVEPSDTIENVKAKIQDKEGIPPDQQRLIFAGKQLEDGRTLSDYNIQKESTLHLVLRLRGGSMKGQETRGFQ SEVKQLLHLMIHSLYSNKEIFLRELISNASDAADKLRFRALSNPDLYEGDGELRVRVSFDKDKRTLTISDNGVGMTRDEVIDHLGTIAKSGT KSFLESLGSDQAKDSQLIGQFGVGFYSAFIVADKVTVRTRAAGEKPENGVFWESAGEGEYTVADITKEDRGTEITLHLREGEDEFLDDWR VRSIISKYSDHIALPVEIEKREEKDGETVISWEKINKAQALWTRNKSEITDEEYKEFYKHIAHDFNDPLTWSHNRVEGKQEYTSLLYIPSQAP WDMWNRDHKHGLKLYVQRVFIMDDAEQFMPNYLRFVRGLIDSSDLPLNVSREILQDSTVTRNLRNALTKRVLQMLEKLAKDDAEKYQT FWQQFGLVLKEGPAEDFANQEAIAKLLRFASTHTDSSAQTVSLEDYVSRMKEGQEKIYYITADSYAAAKSSPHLELLRKKGIEVLLLSDRI DEWMMNYLTEFDGKPFQSVSGGSMQIFVKTLTGKTITLEVEPSDTIENVKAKIQDKEGIPPDQQRLIFAGKQLEDGRTLSDYNIQKESTLH LVLRLRGGKCLEHHHHHH

(15)

Grp94 MACKMQIFVKTLTGKTITLEVEPSDTIENVKAKIQDKEGIPPDQQRLIFAGKQLEDGRTLSDYNIQKESTLHLVLRLRGGELDDEVDVDGTV EEDLGKSREGSRTDDEVVQREEEAIQLDGLNQIRELREKSEKFAFQAEVNRMMKLIINSLYKNKEIFLRELISNASDALDKIRLISLTDENALA GNEELTVKIKCDKEKNLLHVTDTGVGMTREELVKNLGTIAKSGTSEFLNKMTEAQEDGQSTSELIGQFGVGFYSAFLVADKVIVTSKHNND TQHIWESDSNEFSVIADPRGNTLGRGTTITLVLKEEASDYLELDTIKNLVKKYSQFINFPIYVWSSKTETVEEPMEEEEAAKEEKEDSDDEAA VEEEEEEKKPKTKKVEKTVWDWELMNDIKPIWQRPSKEVEDDEYKAFYKSFSKESDDPMAYIHFTAEGEVTFKSILFVPTSAPRGLFDEYG SKKSDYIKLYVRRVFITDDFHDMMPKYLNFVKGVVDSDDLPLNVSRETLQQHKLLKVIRKKLVRKTLDMIKKIADEKYNDTFWKEFGTNIKL GVIEDHSNRTRAKLLRFQSSHHPSDITSLDQYVERMKEKQDKIYFMAGSSRKEAESSPFVERLLKKGYEVIYLTEPVDEYCIQALPEFDGK RFQNVAKEGVKFDESEKTKESREAIEKEFEPLLNWMKDKALKDKIEKAVVSQRLTESPCALVASQYGWSGNMERIMKAQAYQTGKDIST NYYASQKKTFEINPRHPLIKDMLRRVKEDEDDKTVSDLAVVLFETATLRSGYLLPDTKAYGDRIERMLRLSLNIDPDAKVEEEPEEEPEETT EDTTEDTEQDDEEEMDAGTDDEEQETVKKSTAEKDELKLMQIFVKTLTGKTITLEVEPSDTIENVKAKIQDKEGIPPDQQRLIFAGKQLEDG RTLSDYNIQKESTLHLVLRLRGGKCLEHHHHHH

Grp94 Delta M Delta C Delta pre-N

MACKMQIFVKTLTGKTITLEVEPSDTIENVKAKIQDKEGIPPDQQRLIFAGKQLEDGRTLSDYNIQKESTLHLVLRLRSSSEKFAFQAEVNR MTEAQEDGQSTSELIGQFGVGFYSAFLVADKVIVTSKHNNDTQHIWESDSNEFSVIADPRGNTLGRGTTITLVLKEEASDYLELDTIKNLVK KYSQFINFPIYVWSSKTETVEEPMEEEEAAKEEKEDSDDEAAVEEEEEEKKPKTKKVEKTVWDWELMNDIGGSMQIFVKTLTGKTITLEVE PSDTIENVKAKIQDKEGIPPDQQRLIFAGKQLEDGRTLSDYNIQKESTLHLVLRLRGGKCLEHHHHHH

ATPase Measurement

ATPase was determined using a coupled colorimetric assay as previously described (Frey et al., 2007).

QUANTIFICATION AND STATISTICAL ANALYSIS

The data from the optical trapping experiments were analyzed to collect the unfolding forces and increases in contour length from the constant velocity curves, and to measure the rates of transitions between states from the constant distance traces. The expected contour length gain by unfolding is the number of amino acids unfolded times the contour length of an individual amino acid minus the initial distance between the force exertion points, which can be determined by the crystal structure. These methods are outlined below.

Constant Velocity Optical Tweezers Experiments

Displayed force-extension traces recorded at 20 kHz or 30 kHz are filtered by a sliding average of 201 points for a pulling velocity of 10 nm/s, 101 points for 20 and 100 nm/s and 51 points for 500 nm/s.

WLC Fitting of Multi-Domain Proteins

To describe the elastic response to force of the DNA handles and the unfolded protein worm like chain models (WLC) are employed. DNA is described by an extensible WLC with a fixed Hookean contribution of 300 to 700 pN (K-value), while unfolded protein is modelled with a standard WLC fit with a fixed protein persistence length of 0.7 nm. Using a global fitting routine fitting simultaneously all unfolding regions of the protein with an extensible WLC in series with multiple WLC fits allows the determination of the contour length of the unfolded regions. DNA persistence length and DNA contour length are free fitting parameters and yield expected values of approximately 20 nm and 370 nm respectively. For formulas see (Jahn et al., 2014).

To minimize the errors by the DNA parameters while determining the contour length of the unfolded protein, it is necessary to choose fit regions at similar forces. However, as described in the main text, some secondary structure in the N domain already unfolds before the core of the N domains unfold. Therefore, choosing different fitting regions can lead to errors in all domain contour length gains determined (depending on the unfolding sequence). To avoid this Hsp82 and Grp94 are fitted at regions where parts of the N-terminal domain are already unfolded (seeFigure S1). This leads to a slight underestimation of the measured contour length of the N domain. In the case of HtpG the N domain unfolds at significantly lower forces than the M and C domain. Therefore this approach is not feasible and the fitting region for the folded domain was chosen at lower forces, leading to a higher error and no underestimation of the contour length gain (seeTable 1).

To determine meaningful contour length gains for proteins with unstructured regions it is also important to incorporate them in the WLC model. Therefore, the first WLC fit was fixed to a contour length with an estimate of the unstructured length of the protein, as described in the main text. Notably, this approach helps to partially compensate for the small error resulting from not considering the folded domains.

The differences in loading rates between the three full-length chaperones, defined as the rate of change in force over time, are negligible. The loading rate depends on the pulling velocity, the Worm-Like-Chain parameters of the DNA handles and of the parts of the protein which have already unfolded. The dominant parameter is the DNA as this is the most compliant element of the construct. The only parameter that will be different between the orthologues will therefore be the length of the unstructured region before the first unfolding peak of each protein, as the same pulling velocities were applied to each chaperone. This was found to have

(16)

a minimal influence on the loading rate (the loading rates are the same within 5% between the three co-chaperones, calculated at 10 pN for WLC fits with the same fitting parameters as those used to fit the 500 nm/s data for each chaperone). Therefore, this effect is smaller than the error given for the measured forces.

Assignment of Contour Length Gains to Structure

To assign the measured contour length gains resulting from domain unfolding to the crystal structure, we calculate the number of amino acids nijbetween amino acid i and amino acid j using:

lij= nij 0:35 dij

Where lijis the measured contour length, 0.35 is the length per amino acid and dijis the initial distance between the amino acids in the native structure between amino acid i and amino acid j, which is taken from the respective crystal structure.

Table S1shows an assignment without further assumptions taking all resolved amino acids as individual domains. We observe that the measured contour length of the C domains is much shorter than the expected ones. This is accounted for by the fact that the last C-terminal alpha helix is not structured in all monomeric orthologues as explained by the main text. In general, the expected domain size seems to be a little bit larger than the measured ones. This can be explained by the fact that linkers are resolved in the crystal structure, but are flexible in solution. Taking these two considerations into account we optimize the model using only the cores of the domains (excluding the linkers) and assume that the last alpha helix is unstructured. This optimized assignment is presented inTable 1 and shows good agreement with the data. Unstructured regions are illustrated as red inFigure S1A.

Two minor details should be mentioned. First, the expected contour length gain of the N domain in Hsp82 is determined using amino acid 2 of the other monomer for initial distance calculation, since we showed that the first beta sheet binds to the N domain in the monomeric form. Second, the N domain of Grp94 is not completely resolved in the crystal structure. Therefore, we estimated the initial length assuming a similar fold as the Hsp82.

Constant Distance Optical Tweezers Experiments

The data evaluation was performed as described in (Jahn et al., 2014). Briefly, equilibrium constant distance measurements were performed by keeping the optical traps separated by a fixed distance, and monitoring the resulting folding and unfolding transitions of the charged linker of Grp94. Data were coarse grained into 100 force bins. Transitions between the folded and unfolded states of the charged linker were detected using Hidden Markov modelling. Analysis was performed using custom-written software in Igor Pro (Wavemetrics, USA)

The energies at a given force were calculated using an equilibrium statistical mechanics approach, where the free energy is calcu-lated from the contributions of the protein in a given state, the bead displacement, the DNA linker and the unfolded peptide (Jahn et al., 2014). The force-dependent probabilities depend on the energy difference between the states measured, in this case between the folded and the unfolded state of the charged linker of Grp94. The energy difference was therefore derived from a global fit to the force-dependent probabilities, using the model and error assumptions given in (Jahn et al., 2014).

Force-dependent transition rates between the folded and unfolded state of the charged linker were extracted from dwell time histo-grams for each constant distance trace, by fitting these with single exponentials, and corrected for missed transitions that were too rapid to detect, according to the method described in (Jahn et al., 2014). The rates for folding and unfolding at zero force were fitted using the model described in (Rognoni et al., 2012), as before (Jahn et al., 2014).

DATA AND SOFTWARE AVAILABILITY

Referenties

GERELATEERDE DOCUMENTEN

Each person played a round with each other person (i.e. fair confederate; participant vs. unfair confederate; fair confederate vs. unfair confederate) on each payout matrix, for

Alice and Bob set their threshold to detect eavesdropping to a bit error rate of Q + σ, where Q is the averaged quantum bit error rate.. Basis

Forces exerted on the trapped microsphere were calculated as described in the previous section. In the next chapters, measurements will be shown with on the horizontal axis the

FOM Institute for Atomic and Molecular Physics (AMOLF), Faculty of Mathematics and Natural Sciences, Leiden University.

Ik wil verder Astrid van der Horst op amolf, en Christoph Schmidt en Gijs Wuite van de Vrije Universiteit Amsterdam bedanken voor de vele praktische tips voor het bouwen van

Finally, during the testing and simulation phase, the conceptual model and operational system are used to both test and validate the operational performance of the system.. The

Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of

Ga eerst zelf eens na wat jouw rituelen zijn voor, tijdens en na de warme maaltijd.. Bespreek deze ongeveer vijf minuten met