Measuring How Much Work the Chaperone Groel Can Do

Measuring how much work the chaperone GroEL PNAS PLUS can do

Nicholas C. Corsepiusa,b,c and George H. Lorimera,b,c,d,1

aCenter for Biomolecular Structure and Organization, bBiochemistry PhD Program, cDepartment of Chemistry and Biochemistry, and dInstitute for Physical Science and Technology, University of Maryland, College Park, MD 20742

Contributed by George H. Lorimer, April 26, 2013 (sent for review April 1, 2013) SEE COMMENTARY Noncovalently “stacked” tetramethylrhodamine (TMR) dimers have rotation of the apical domains, the expansion of the central been used to both report and perturb the allosteric equilibrium in cavity, and the separation of the peptide binding sites (8). The R GroEL. A GroEL mutant (K242C) has been labeled with TMR, close to state has a high affinity for nucleotide, low affinity for SP, and is the peptide-binding site in the apical domain, such that TMR mole- the acceptor state for GroES. ATP binding is positively coopera- cules on adjacent subunits are able to form dimers in the T allosteric tive between subunits within a ring and negatively cooperative state. Addition of ATP induces the transition to the R state and the between rings within a 14mer. In the absence of GroES, GroEL separation of the peptide-binding sites, with concomitant unstacking can adopt three distinct allosteric states: TT, TR, and RR. of the TMR dimers. A statistical analysis of the spectra allowed us to In the presence of Mg2+ and K+, GroEL hydrolyzes ATP to compute the number and orientation of TMR dimers per ring as ADP and inorganic phosphate (9). In the absence of SP, the re- a function of the average number of TMR molecules per ring. The lease of ADP is the rate-limiting step in the catalytic cycle (10). TMR dimers thus serve as quantitative reporter of the allosteric state The addition of SP increases the rate of ATP consumption by of the system. The TMR dimers also serve as a surrogate for substrate GroEL by accelerating ADP/ATP exchange. A single SP binds to protein, substituting in a more homogeneous, quantifiable manner the apical domains of two or more GroEL subunits introducing a for the heterogeneous intersubunit, intraring, noncovalent cross- load on the ring in the form of noncovalent intersubunit cross- links provided by the substrate protein. The characteristic stimulation links that stabilize the T state. This constraint shifts the allosteric of the ATPase activity by substrate protein is also mimicked by the equilibrium in favor of the T state, whose weak affinity for nu- TMR dimers. Using an expanded version of the nested cooperativity cleotide leads to the dissociation of the product, ADP, effec- model, we determine values for the free energy of the TT to TR and tively increasing the rate of ATP consumption (11). TR to RR allosteric equilibria to be 27 ± 11 and 46 ± 2 kJ/mol, respectively. The free energy of unstacking of the TMR dimers was SP Binding Problem. Many GroEL SPs contain multiple GroES-like estimated at 2.6 ± 1.0 kJ/mol dimer. These results demonstrate that motifs of the generic sequence P-HHH-P-H, where P and H rep- GroEL can perform work during the T to R transition, supporting the resent polar and hydrophobic residues, respectively (12–14). The iterative annealing model of chaperonin function. association of these motifs with GroEL is difficult to quantitatively

analyze due to three levels of heterogeneity (Fig. 1). First, for BIOPHYSICS AND allostery | substrate protein binding problem every one native SP, there exist multiple misfolded states that form an ensemble of structures, all of which have the potential to COMPUTATIONAL BIOLOGY he GroEL/GroES nano-machine facilitates the folding of interact with GroEL differently. The second level of heterogeneity Ta large number of diverse substrate proteins (SPs), converting is topological. Any one of the misfolded states has several GroEL them from one of many misfolded states to unique native states, binding motifs, which can be arranged in multiple ways between which are no longer recognized by GroEL. This machine is ul- the seven SP binding sites of a ring. The third level occurs within the timately powered by the binding and hydrolysis of ATP, driving binding pocket itself. Although the seven SP binding pockets of GroEL through a series of allosteric states. Two views of GroEL GroEL are all identical, they bind the general sequence P-HHH-P-H, function have emerged: one as a passive antiaggregation cham- which, being degenerate, covers a wide range of structural sequen- ber and the other as an active folding device, performing work on ces. Thus, within a single SP–GroEL complex, the various SP SP (1, 2). Our experiments support the latter view, demonstrating that GroEL has the ability to perform work on its SPs via Significance domain movements that accompany the allosteric transitions. Noncovalently “stacked” tetramethylrhodamine dimers are Allostery. The chaperonin protein GroEL consists of 14 57-kDa used to report and perturb the allosteric equilibrium in GroEL. subunits, arranged in two back-to-back heptameric rings (3). A The spectroscopic differences between the TMR monomers and GroEL subunit contains three distinct domains: apical, interme- dimers allow for quantitative measurements of the population diate, and equatorial domains. The equatorial domain houses the of allosteric states. The noncovalent intersubunit stacking in- nucleotide-binding pocket, whereas the site for SP and GroES teraction within a dimer mimics the cross-linking constraint binding is found between helices H and I in the apical domain (4). that SP places on the structure of GroEL. This feature allows The SP binding sites, primarily composed of hydrophobic residues, TMR dimers to be used as SP surrogates to quantitate the impact ’ line the inner wall of the heptameric ring s central cavity and bind of SP on the chaperonin cycle of GroEL. GroEL overcomes a load “ the exposed hydrophobic regions of the misfolded SP. The mo- of 7.8 kJ/mol, demonstrating its ability to perform work on SP. bile loops” of GroES displace the SP from this site (5, 6). In the chaperonin cycle, SP first binds to, and then becomes encapsu- Author contributions: N.C.C. and G.H.L. designed research; N.C.C. performed research; lated inside, GroEL’s barrel-like structure. After a short time (a N.C.C. and G.H.L. analyzed data; and N.C.C. and G.H.L. wrote the paper. few seconds at 37 °C), the SP is released, whether folded or not. The authors declare no conflict of interest. The chaperonin cycle involves a series of allosteric transitions Freely available online through the PNAS open access option. within a heptameric ring (7). In the absence of ATP, the ring See Commentary on page 10884. adopts the T state, which has a high affinity for SP, low affinity 1To whom correspondence should be addressed. E-mail: [email protected]. for nucleotide, and cannot bind GroES. The binding of ATP This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. triggersatransitiontotheR state, which is accompanied by a 1073/pnas.1307837110/-/DCSupplemental.

www.pnas.org/cgi/doi/10.1073/pnas.1307837110 PNAS | Published online May 30, 2013 | E2451–E2459 Downloaded by guest on September 25, 2021 0 distribution of the surrogates across the subunits within a ring should be predictable. Finally, the surrogate should create an intersubunit load that is of uniform energetic value; i.e., the stabilization energy of each intersubunit cross-link should be identical. These qualities can be found by using noncovalently stacked tetramethylrhodamine (TMR) dimers as an SP surrogate. I Tetramethylrhodamine. TMR is commonly used in biochemical studies due to its high absorbance and fluorescence in the visible region. It is often covalently attached using a thiol- or amine- reactive linker group. As in previous studies (15–17), we took advantage of the dimer formation or stacking propensity of TMR. Dimer formation is accompanied by a change in the absorbance and fluorescence properties of the dye, a deviation that can be explained by Kasha’s exciton coupling model (18). Fluorescence is forbidden from this state, and large decreases in fluorescence are consistently observed under conditions that favor dimer formation. II A blue shift in the peak absorbance indicates that the xanthene planes housing the electronic transition are oriented parallel to one another. Various studies have demonstrated that the xanthenes of the two TMR molecules are stacked in the dimer (16, 19, 20). TMR has been used as a spectroscopic probe in other bio- III molecular experiments due to the spectroscopic difference between thedimericandmonomericdyespecies.HereweexploitTMRas both an allosteric probe and an SP surrogate. The fluorophore can be covalently attached to the protein at a cysteine residue using maleimide chemistry. The self-association of TMR is distance de- Fig. 1. The substrate protein binding problem: a schematic illustration of the pendent, and dimers only form when two labeled residues are in heterogeneous nature of SP binding. Level 0: SP’snativeconfirmation. Level I: every SP has multiple misfolded states. Level II: each misfolded state can bind close proximity. To use TMR dimers as an allosteric probe, the to GroEL with different topological arrangements. Level III: each SP binding residues to which TMR is attached were chosen such that in the T contact will differ because GroEL binds the general sequence P-HHH-P-H. state they are close enough to allow dimer formation and in the R state they are distant enough to prevent dimer formation.

binding site contacts differ from one another. This heterogeneity Results and Discussion fi ’ makes it dif cult to use GroEL s natural SPs to quantitatively TMR2-DTT as a Model System for Stacked TMR Dimers. The equilib- characterize their impact on the chaperonin cycle. rium of TMR dimer formation (stacking) can be shifted in favor We sought to address the SP binding problem by using an SP of dimers by lowering the entropic barrier to self-association. To surrogate with greatly reduced heterogeneity. The stimulatory accomplish this, TMR-maleimide was reacted with dithiothreitol effects of SP on the chaperonin cycle are rooted in the structural (DTT) (21) to yield TMR2-DTT to allow for the concentration- load that bound SP places on the movement of the apical domains independent formation of dimers. The stacking event is largely within a heptameric ring. Because a typical SP forms multiple (at driven by favorable van der Waals contacts and the entropy gain least two) noncovalent cross-links between the apical domains of associated with the expulsion of water. GroEL, an effective surrogate should impose similar noncovalent, The TMR dimer and monomer have distinct absorption and intersubunit cross-links. It should also be a single species that fluorescence spectra (Fig. 2). TMR alone has an absorbance interacts with each GroEL subunit in an identical fashion. Because spectrum that peaks at 551 nm with an extinction coefficient of −1 −1 there are seven GroEL subunits, there are numerous topological ∼75,000 cm ·M .Apurified sample of TMR2-DTT has a com- arrangements for such a probe, and therefore the number and paratively strong peak absorbance at 518 nm and a shoulder peak

A B C

Fig. 2. Comparison of TMR dimers and monomers. The model monomer sample is free TMR-5-maleimide (red), and the model dimer sample is a puriﬁed

sample of TMR2-DTT (blue). All measurements are taken at room temperature in 50 mM Tris-HCl, pH 7.5. In A and B, the displayed values are relative to the total amount of dye. (A) Relative molar absorptivity. (B) Relative steady-state ﬂuorescence emission; excitation at 540 nm. (C) Normalized steady-state excitation spectra of the monomer and dimer samples. The dimer is likely non- or weakly ﬂuorescent.

E2452 | www.pnas.org/cgi/doi/10.1073/pnas.1307837110 Corsepius and Lorimer Downloaded by guest on September 25, 2021 formation of stacked TMR dimers between adjacent subunits in PNAS PLUS the T allosteric state and their disruption on addition of ATP. Moreover, as homogeneous noncovalent, intersubunit cross- links, the TMR dimers serve as SP surrogates.

TMR as an Allosteric Probe. TMR has been used to report the allosteric state of GroEL. Fig. 4 shows the absorption and fluorescence spectra of a sample of EL242C-TMR with an average of 4.3 dyes per ring. In the absence of ATP, GroEL adopts the T state, and the presence of a strong absorption peak at 518 nm indicates the presence of a population of TMR dimers. In the SEE COMMENTARY presence of ATP, the allosteric equilibrium is shifted in favor of the R state. As supported by both absorbance and fluorescence Fig. 3. Image of GroEL heptameric ring in the T (A) and R (B) state. Helices – H and I are highlighted in cyan. Residue 242 is highlighted in pink. T state measurements, the allosteric transition increases the Cα Cα dis- image from PDB 1OEL and R state image from PDB 2C7E. tance between 242C residues in adjacent subunits, leading to the dissociation of the TMR dimers into monomers. In the presence of ATP, the 518-nm dimer peak drops and the 551-nm monomer around 551 nm. The dimer sample is also only weakly fluorescent; peak rises. Likewise, addition of ATP is marked by a significant an equal concentration of monomer is 8–13 times more fluorescent. increase in fluorescence. Thus, qualitatively, TMR dimers are a Although the dominant population in a sample of TMR2-DTT suitable allosteric reporter. is the stacked form, it consists of molecules in equilibrium be- To use TMR dimers as quantifiable allosteric probes, we de- tween their stacked and nonstacked conformations. Thus, the termined the size of the population of the individual dye species fl uorescence observed from the TMR2-DTT sample may either in a given sample. To accomplish this, we first demonstrated that, be due to the intrinsic fluorescence of the stacked form or to the in a sample of EL242C-TMR, there exists only two spectrally residual population of nonstacked molecules. Evidence sug- distinct species. The two species model implies that, in every gesting that the stacked form is nonfluorescent can be found by sample, the entire population of dye molecules can be classified comparing the monomer and dimer fluorescence excitation spec- as either dimers or monomers. Mathematically, this can be stated fl fi tra. The uorescence excitation spectrum of puri ed TMR2-DTT as the sum of the mole fraction of monomer and dimer, αM and C is identical to the excitation spectrum of the monomer (Fig. 2 ), αD, respectively, is equal to unity i.e., the absorbance of the peak at 518 nm makes no contribution fl fl to the uorescence of the dimer. The uorescence of TMR2-DTT αM þ αD ¼ 1: [1] thus reflects the residual population of nonstacked molecules. Because the total concentration of dye molecules in a sample of A previous study has indicated that, in solution, concentration- TMR2-DTT is known from its absorbance in the presence of dependent self-association events proceed beyond dimer forma-

SDS, and the size of the nonstacked population is known from tion and higher-order aggregates are formed (24). The presence BIOPHYSICS AND ﬂ

the uorescence, the size of the population in the stacked form, of higher-order aggregates in the EL242C-TMR system would COMPUTATIONAL BIOLOGY and thus the equilibrium constant for stacking, can be calculated. preclude a simple two-species model. The equilibrium constant allows us to calculate the free energy of The validity of the two-species model was tested by analyzing a formation of the dimer ΔGdim. The average free energy of stacking series of relative absorption spectra (Fig. 5A). If the two-species is calculated to be −2.8 ± 0.3 kJ/mol dimer (±SEM). Although model is correct, then relative changes in the population of one the calculated free energy is unique to the TMR2-DTT system, it species will be compensated by an equal and opposite change in can be used as a reference for the formation of TMR dimers in theotherspecies.Plottingtherelativeabsorbanceofeachsampleat the EL242C-TMR system. 518 vs. 551 nm demonstrates a linear relationship (Fig. 5 B and C). Principal component analysis using singular value decomposition Criteria for Positioning the TMR Probe. If an enzyme is labeled with was also used to validate the two-species model (SI Materials TMR such that in one allosteric state, labeled residues are close and Methods). Thus, we conclude the total population of dye enough to form dimers and in another state, too far to associate, the dye can be used as a probe to report the allosteric state of the enzyme. Using simple ball and stick structures of TMR, the maximal Cα–Cα distance between residues that allows for A B the formation of dimers is ∼25 Å. In selecting a suitable residue for the placement of TMR, we used the crystal structure of apo GroEL (PDB 1OEL) (22) and the cryo-EM structure of the ATP bound GroEL (PDB 2C7E) (8). These structures were used to find a residue that (i) met the distance criteria for an allosteric probe, (ii) was near the peptide-binding site defined by the cleft between helices H and I, (iii) was solvent accessible and hence amenable to chemical modification, and (iv) whose mutation would not result in enzyme inactivation. Residue K242, which is located at the N-terminal end of helix H on the apical domain and is solvent accessible, was selected for mutation and labeling with TMR (Fig. 3). In the T state, the Cα–Cα distance between K242 residues in adjacent subunits is 24.5 Å. On ATP binding, Fig. 4. TMR dimers as allosteric probes. The absorbance (A) and steady-state fluorescence emission (B) of a sample of EL242C-TMR with 4.3 TMR per ring this distance increases to 25.4 Å. Mutagenesis was used to create is examined in the absence (green) and presence (orange) of 500 μM ATP. In the K242C mutation in the WT GroEL sequence (23). EL242C the absence of ATP, the enzyme is in the T state, indicated by the population can be purified using the same protocol as WT GroEL. The of dimers. On transition to the R state, the dimers dissociate into monomers, location of residue 242 near the SP binding pocket allowed causing a change in the peak absorbance and increase in the fluorescence.

Corsepius and Lorimer PNAS | Published online May 30, 2013 | E2453 Downloaded by guest on September 25, 2021 A B

Fig. 5. Two species model and extent of labeling. TMR bound to GroEL can be classiﬁed into two spectrally distinct species. The following experiment lends support to the idea that bound dye molecules can only exist as either monomers or dimers; no higher-order aggregates exist. (A) Relative absorbance of various samples of EL242C-TMR, ranging from 0.57 TMR per ring (dark red) to 5.9 TMR per ring (purple). (B) A plot of the absorbance at 551 vs. 518 nm for each curve. (C) The residuals calculated from a linear ﬁt. The straight line indicates that the change in the size of the population of one species is equally and oppositely accounted for by a change in the size of the other population.

molecules on EL-242C can be classified as either monomers or Methods; see also Fig. S2). Thus, in the T state, dye molecules dimers and there are no higher-order aggregates. bound in close proximity spontaneously associate, forming weakly It is also important to ensure that the spectral properties of fluorescent dimers, which absorb maximally at 518 nm. The ad- the population of monomers in the T state are equivalent to the dition of ATP triggers the T to R allosteric transition, causing population of dissociated dimers in the R state. The addition of dissociation of the dimers into monomers, marked by a fluores- ATP to a sample of EL242C-TMR shifts the allosteric equilibrium cence increase and exchange between the 518- and 551-nm in favor of the R state, causing the dissociation of dimers and in- absorbance peaks. creasing the population of monomers. As time elapses, the ATP is hydrolyzed to ADP, which slowly shifts the allosteric equilibrium Stochastic Binding Model. Each EL242C heptameric ring contains in favor of the T state, increasing the population of dimers. Fig. S1 seven possible TMR binding sites, such that a substochiometric shows the results of this experiment, and the validity of the two- addition of TMR creates an ensemble of different structures. In species model. A plot of the absorbance at 551 vs. 518 nm shows fact, there are 20 possible distinct orientations of dye molecules a strong linear relationship (R2 = 0.9998). For the purposes of on a ring (Fig. 6A). There is evidence that only cysteines at 242 subsequent analysis, we will assume the spectral properties of the are labeled (SI Materials and Methods; see also Fig. S3). We assume monomer in the T and R states are equivalent. Principal com- that the labeling process is stochastic: that all binding events are ponent analysis using singular value decomposition also lends independent and occur with equal probability. This assumption credibility to the simple two-species model (SI Materials and permits the development of the stochastic binding model (Fig. 6B)

Fig. 6. The stochastic binding model. The stochastic binding model allows us to quantify the distribution of labeled states. (A) An illustration of the 20 distinct labeled states in the system. (B) The probability of selecting any one labeled state from the total population is governed by a binomial distribution (Eqs. 2 and 3). Each column of labeled states in A corresponds to one of the eight curves in the binomial distribution. States within a column are all equally likely.

E2454 | www.pnas.org/cgi/doi/10.1073/pnas.1307837110 Corsepius and Lorimer Downloaded by guest on September 25, 2021 attach the fractional contribution to the monomer and dimer PNAS PLUS A populations to each of the 20 distinct labeled states (Fig. 7A). Mathematically, the fractional contribution of the two species d is accounted for in the matrix MF. The ﬁrst and second rows in d MF correspond to the fractional contribution to the monomer and dimer population, respectively. Taking the two assumptions together, one can predict the mole fraction of the population in the dimer, αDðρÞ, and monomer form, αM ðρÞ, given an average number of dye molecules per ring, ρ (Eq. 4; Fig. 7B)

2 3 SEE COMMENTARY

= = = = 6 2 = 7 6 1 1 7

d 6 01 3 15 20 5 0 7 7

MF≡4 5; = = = = 1 = 8 14 4 6 00 3 15 20 5 1 7

B d ⇀ αM ðρÞ MF • BðρÞ¼ : [4] αDðρÞ

The proposed model predicts the change in the mole fraction of monomers and dimers with the extent of labeling (Eq. 4). To test this model, we exploited the linear relationship between the mole fraction of dimer and the relative absorbance of the sample, found by combining the two species model (Eq. 1) with Beer’s law for two species (Eq. 5) to yield Eq. 6

Arel ¼ eM αM ðρÞþeD αDðρÞ; [5]

Arel ¼ ðeD − eM Þ αDðρÞþeM : [6]

Fig. 7. Combining the stochastic binding model and the exclusive nearest The plot of the calculated mole fraction of dimer against the ob- neighbor assumption. (A) Each of the 20 distinct labeled states can be as- served absorbance at 518 and 551 nm was linear (Fig. 8A). How- signed a fractional contribution to the population of monomers (red) and c ever, the nonrandom nature of the residuals points to a small dimers (blue). These weights are collected into the matrix MF .(B) The matrix c ⇀ source of error of unknown origin (Fig. 8B). This error can be product MF ·BðρÞ yields two equations, the mole fraction of monomers (red)

and the mole fraction of dimers (blue), as a function of TMR per ring, ρ. explained by invoking positive cooperativity in the labeling pro- BIOPHYSICS AND cess; i.e., a dye molecule has a slight preference to react with a vacant subunit that is adjacent to an already labeled subunit as COMPUTATIONAL BIOLOGY that describes the distribution of labeling states in any sample from opposed to reacting in a strictly stochastic manner. the measured average number of dye molecules per ring, ρ. The distribution of states is described by a binomial distribution (Eqs. 2 and 3). Given the average number of dye molecules per ring, the stochastic binding model gives the fraction of the pop- A ulation containing k dye molecules per ring, where k =0–7in integer values. Each of the labeled states corresponding to k dye molecules per ring are equally likely 7! ρ k ρ 7−k bkðρÞ¼ 1 − ; [2] ð7 − kÞ!k! 7 7 2 3 b ðρÞ ⇀ 0 BðρÞ ≡4 ⋮ 5: [3]

b7ðρÞ

Exclusive Nearest Neighbor Assumption. The stochastic binding model allows us to convert a single measured value, the average B number of dye molecules per ring, to the fraction of the population in each of the 20 distinct labeled states. We further assume that only adjacent subunits are able to form dimers and that, at any given moment, a single TMR can only be associated with one other TMR: the exclusive nearest neighbor assumption. This assumption is justiﬁed considering the geometric constraints Fig. 8. Testing the stochastic binding model and the exclusive nearest imposed by the relatively rigid GroEL structure, and the distance neighbor assumption in the EL242C-TMR system. (A) Testing the model by exploiting the linear relationship (Eq. 6) between the predicted mole fraction constraint of dimer formation. The exclusivity in the assumption of dimer, αDðρÞ, and the relative absorbance (Fig. 5) of a samples of EL242C- is supported by the observation that no higher order aggregates TMR at 518 (blue) and 551 nm (red). (B)Theﬁtisrelativelygood,R2 > 0.98, but exist in the sample. The nearest neighbor assumption allows us to the residuals are not randomly distributed.

Corsepius and Lorimer PNAS | Published online May 30, 2013 | E2455 Downloaded by guest on September 25, 2021 The proportion of the bound TMR that is in the dimeric state can be A B computed with the exclusive nearest neighbor assumption. Finally, each noncovalent dimeric stacking bond is of identical strength. Because the T to R transition is concerted among the subunits within a ring, the energetic contribution to the stabilization of the T state is a simple sum of the number of dimers per ring. A ring can contain from zero to three dimers, and thus by increasing the number of dimers per ring, we can vary the cross-linking stabilization energy that shifts the allosteric equilibrium.

Expanded Nested Cooperativity Model of GroEL. The negative and positive cooperativity displayed by GroEL during nucleotide binding requires a hybrid MWC/KNF type allosteric model known as Fig. 9. ATPase activity of dye-labeled EL242C in 1 mM ATP. (A) Turnovers per the nested cooperativity model (NCM). As originally formulated + + minute plotted against TMR per ring at 10 mM K (blue) and 100 mM K (red). (25, 26), the NCM contained a simplifying assumption that ATP The ATPase activity of GroEL increases as the mole fraction of dimers increases. bound exclusively to the R state. Subsequent work, however, (B) Turnovers per minute plotted against dyes per ring for EL242C labeled with T TMR (pink) and F5M (yellow) in the presence of 100 mM K+. The increase in showed that the state could also bind and hydrolyze ATP (10, the turnover rate is not due to the mere presence of fluorophore, as indicated 26). An expanded version of the NCM, without the exclusive by the lack of ATPase stimulation observed in samples of EL242C-F5M. binding assumption was developed by Gresham (27) and was used to quantitatively analyze the turnover rate of GroEL (Eq. 7). The original formulation can be recovered from the expanded TMR as an SP Surrogate. SP binds to the T state of GroEL and form by setting c equal to zero. It contains seven independent stimulates its ATPase by placing a load on the apical domains of parameters that are to be fit for a given set of conditions. At its the ring. The bound SP serves as a noncovalent tether between two core, the NCM is an allosteric partition function of GroEL that adjacent subunits. This stabilizes the T state, which has weak af- accounts for the positive intraring cooperativity and negative finity for nucleotide, accelerating the rate of product release, and interring cooperativity. The equation gives the fraction of the increasing the rate of ATP consumption (10, 11). Likewise, the population with ATP bound, in each of the three allosteric states, apical domains of the EL242C-TMR are tethered by the non- as a function of ATP concentration. In its expanded form, this covalent stacking of the dye molecules. Similarly, an increase in the fraction is multiplied by the allosteric state’s Vmax, and the sum of steady-state turnover rate is observed with increasing number of these three terms gives the steady-state turnover rate. Two other dimers per ring (Fig. 9A). This results supports the assertion that parameters include the dissociation constants, kT and kR, of ATP

TMR dimers behave as surrogates for SP in the chaperonin cycle. from a T ring and an R ring, respectively. The two terms appear

= kR = ½ATP The stimulation is due to the cross-linking effect of TMR dimers and in the NCM as c ¼ kT and α ¼ kR. Last, the NCM contains ﬂ not merely to the presence of a hydrophobic uorophore close the two allosteric equilibrium terms, L1 for the TT to TR transition ﬂ SP binding site. To address this, EL242C was labeled with uo- and L2 for the TR to RR transition

h i 13 1 6 7 7 6 13 VTT c α ð1 þ c αÞ þ VTR L1 c α ð1 þ c αÞ ð1 þ αÞ þ α ð1 þ c αÞ ð1 þ αÞ þ VRR L1 L2 α ð1 þ αÞ v ¼ 2 : [7] 14 7 7 14 ð1 þ c αÞ þ L1 ð1 þ c αÞ ð1 þ αÞ þ L1L2ð1 þ αÞ

resceine-5-maleimide (F5M), a compound structurally similar to In our analysis, the NCM (Eq. 7) is modified to predict the distri- TMR. However, it neither forms dimers nor stimulates ATPase bution of allosteric states as a function of ATP concentration. Doing activity (Fig. 9B). The TMR dimers are thus behaving as molecular so decreases the number of independent parameters, replacing the latches, perturbing the allosteric equilibrium to favor the T state. three Vmax terms in the expanded derivation, with a single pro- In addition to being an allosteric probe, TMR dimers act as an portionality constant, A. This constant converts the instrument’s SP surrogate because they serve as noncovalent cross-links, be- arbitrary fluorescence readout value to the fluorescence increase tween subunits within a ring, that place a load on the apical observed from the dissociation of a dimer, on transition of a ring domains in the same way as SP. TMR serves as an ideal SP to the R state. Given a single GroEL 14mer with m TMR dimers surrogate because it circumvents the problems of heterogeneity on one ring and n TMR dimers on the other, there will be inherent in the SP binding problem (Fig. 1). As opposed to SP, a fluorescence increase proportional to m on the TT to TR and TMR is a small molecule that covalently binds to a single posi- an increase proportional to n on the TR to RR transition. The tion near the SP binding site. In demonstrating the use of TMR modified NCM (Eq. 8) predicts the observed fluorescence in- as an allosteric probe, we showed that the topological arrange- crease in a labeled species with m dimers on the first ring and n ment is readily predictable using the stochastic binding model. on the second

h i 1 6 7 7 6 13 m A L1 c α ð1 þ c αÞ ð1 þ αÞ þ α ð1 þ c αÞ ð1 þ αÞ þðm þ nÞA L1 L2 α ð1 þ αÞ F′ ¼ 2 : [8] 14 7 7 14 ð1 þ c αÞ þ L1 ð1 þ c αÞ ð1 þ αÞ þ L1 L2 ð1 þ αÞ

E2456 | www.pnas.org/cgi/doi/10.1073/pnas.1307837110 Corsepius and Lorimer Downloaded by guest on September 25, 2021 PNAS PLUS A B SEE COMMENTARY

Fig. 10. Distribution of cross-linked states. (A) Illustration of how the 20 distinct labeled states can be assigned to one of the four cross-linked states: 0 dimers per ring (green), 1 dimer per ring (blue), 2 dimers per ring (red), and 3 dimers per ring (purple). These weights are collected in the matrix C.^ (B) The matrix product ^ ⇀ C· BðρÞ yields four equations, cmðρÞ where m is an integer between 0 and 3 that corresponds to the size of the population of heptameric rings with m dimers.

As pointed out above, each sample consists of an ensemble of stacked dye molecules to the stabilization of the T state can be labeled states. The stochastic binding model and the exclusive assumed to be additive across a ring. The stabilization of an allo- nearest neighbor assumption were used to calculate the size of steric state quantitatively enters into the NCM as a modification each labeled state, in a given sample, as a function of the average to the allosteric equilibrium terms L1 and L2 (Fig. 11B). The end number of dye molecules per ring. Each state can be binned result is a modified form of the NCM that predicts the biphasic corresponding to the number of dimers it contains (Fig. 10A). fluorescence increase observed for a given labeled state, taking ^ Mathematically, this function is performed by the matrix C. The into account the perturbation placed on the allosteric equilibrium ^ ⇀ matrix product of C and BðρÞ (Eq. 3) produces four functions, by the presence of the dimers (Eq. 10)

h i m1 6 7 7 6 mþn 13 m A L1 D c α ð1 þ c αÞ ð1 þ αÞ þ α ð1 þ c αÞ ð1 þ αÞ þðm þ nÞ A L1 L2 D α ð1 þ αÞ Fmn ¼ 2 ; [10] 14 m 7 7 mþn 14 ð1 þ c αÞ þ L1 D ð1 þ c αÞ ð1 þ αÞ þ L1 L2 D ð1 þ αÞ

cmðρÞ, where m is an integer between 0 and 3 (Fig. 10B; Eq. 9). BIOPHYSICS AND

These functions give the size of the population of the four cross- COMPUTATIONAL BIOLOGY linked states (m =0–3 per ring) as a function of the average 3 3 F ¼ ∑ ∑ C C F : [11] number of dye molecules per ring m n mn n¼0 m¼0 2 3

Combining the modiﬁed NCM in Eq. 10 with the statistical = 6 2 = 1 7

6 11 3 5 00007 distribution of cross-linked states (Eq. 9)yieldsanequation

6 7

= = = ﬂ 6 1 4 3 7 that predicts the uorescence increase associated with the al- ^ 6 00 3 5 5 0007

C ≡ 6 7; losteric transitions in a sample with a known average number of 6 2 = 7 6 00 0 0 5 1007 dye molecules per ring, as a function of ATP concentration (Eq. 6 7 4 5 11). The solution to Eq. 11 depends on the value of the various 00 0 0 0 011 independent parameters in the equation: A, c, kR, L1, L2,and,D. The large number of parameters gives the equation a great deal of fl fi 2 3 exibility when being t to a particular data set. However, we have c ðρÞ collected data sets for multiple samples, with varying numbers of 0 fi ⇀ 6 c ðρÞ 7 average dye molecules per ring. These data sets were t globally ^ × BðρÞ¼6 1 7: [9] 11 C 4 c ðρÞ 5 with Eq. (Fig. 12). Varying any one parameter will change the 2 fi fi c ðρÞ t for all data sets, allowing for increased con dence in the 3 fitted values. The results of the global fittoEq.11 are summarized in It is known that SP places a load on the apical domains of a ring Tables 1 and 2. The indicated range of each parameter falls and that the presence of SP leads to a stimulation in ATPase within the 95% CI of the fit.ThefreeenergyoftheTT to TR activity. To arrive at a quantitative impact of SP on the chaperonin and TR to RR transitions were found to be 27 ± 11 and 46 ± 2 cycle, we view the load that SP places on the ring to result in the T kJ/mol, respectively. TMR dimers acting as an SP surrogate stabilization of the state and thus an increase in the free energy ± of the T to R allosteric transition (Fig. 11A). Likewise, the cross- increase this free energy gap by 2.6 1.0 kJ/mol dimer, linking effect of the stacking interaction in TMR dimers stabil- a value that is similar to that for the dissociation of TMR2- izes the T state of GroEL. The advantage of the TMR dimer is DTT. These experiments demonstrate that the GroEL nano- that it is of uniform energetic value and likely to be of a compa- machineisabletoperformworkandovercomealoadofat rable magnitude to the TMR2-DTT stacking free energy: −2.7 ± least 7.8 kJ/mol ring. This result supports the idea of GroEL 0.3 kJ/mol dimer. Furthermore, a ring can have from zero to three function that relies on forced unfolding of bound substrate TMR dimers. Because of the concerted nature of the allosteric protein to free it from a kinetic folding trap, affording it an- transitions exhibited by GroEL, the energetic contribution of the other opportunity to reach its native state.

Corsepius and Lorimer PNAS | Published online May 30, 2013 | E2457 Downloaded by guest on September 25, 2021 The cross-linking force of the dimer increases the free energy A B gap in the T to R allosteric transition by an amount equal to the free energy of dimer formation. The effect of this stabilization can be factored into the NCM as a modification to the allosteric equilibrium terms L1 and L2. The NCM can also be modified for use as an allosteric partition function to predict fluorescence increases that correlate with allosteric population changes instead of turnover rates. When the modified NCM is paired with the predicted distribution of labeled states, the parameters in the equation can be globally fit to a series of data sets allowing for increased confidence in the fitted parameters. The proposed model highlights the importance of the SP cross- linking energy within the allosteric cycling of GroEL. The load placed on the apical domain stabilizes the T state, increasing the free energy gap and shifting the allosteric equilibrium in favor of the T state. Because of negative cooperativity, this effect is more significant for the TR to RR transition than the TT to TR transition.

Fig. 11. Quantifying the effect of SP on the allosteric equilibrium. (A) A free energy diagram of GroEL’s ﬁrst allosteric transition: TT to TR. The diagram indicates how the presence of a TMR dimer on a ring stabilizes the T state and increases the free energy gap between the TT and TR states. Because the allosteric transition is concerted, the effect of multiple dimers is additive. (B) Mathematically, this interpretation leads us to quantitatively account for the presence of TMR as a perturbation to the allosteric equilibrium.

Concluding Remarks TMR as an Allosteric Probe for GroEL. TMR, covalently bound near the SP binding site of GroEL’s subunits, forms populations of B monomers and dimers depending on nearest neighbor occu- pancy. Combining the stochastic binding model and the exclusive nearest neighbor assumptions allows us to predict the distribution of labeled states from the average number of TMR molecules per ring. Introducing ATP induces an allosteric conformational change that causes dimers to dissociate into monomers. Because the monomers and dimers have different spectroscopic signatures, the transition can be monitored using either absorbance or ﬂuo- rescence spectroscopy. The change in the observed ﬂuorescence or absorbance, on the addition of ATP, can be directly correlated with a change in the population of the T and R allosteric states, providing a quantitative measure of the allosteric activity.

TMR Dimers as Surrogates for SP. In the T state, TMR-labeled 242C residues are close enough to self-associate into dimers. These dimers act as noncovalent intraring, intersubunit cross-links that place a load on the apical domain, mimicking the effects of the cross-linking force provided by SP. Consequently, SP and the TMR dimers stimulate the ATPase activity of GroEL by stabi- Fig. 12. Fluorescence increase vs. [ATP]. The ﬂuorescence increase observed lizing the T state with this cross-linking force. However, TMR in the presence of various concentrations of ATP is plotted for samples of dimers avoid the problems associated with the heterogeneous EL242C-TMR with an average of 1.8 (red), 2.8 (orange), 3.8 (green), 4.7 μ nature of SP binding to GroEL. The predictable distribution of (blue), and 5.6 (purple) TMR per ring. (A) [ATP] range from 0 to 100 M. (B) [ATP] range from 0 to 1 mM. Two of the data sets, 1.8 and 5.6 TMR per ring, dimers and the uniformity of the cross-linking force make TMR were collected over an [ATP] range of 0–100 μM and the remaining three dimers a suitable surrogate for quantifying the role of SP in the sets over an [ATP] range of 0–1 mM. Solid lines are the results of the global catalytic cycle of GroEL. ﬁt of the data sets to the expanded NCM (Eq. 11).

E2458 | www.pnas.org/cgi/doi/10.1073/pnas.1307837110 Corsepius and Lorimer Downloaded by guest on September 25, 2021 Table 1. Results of the global fit of the expanded NCM (Eq. 11) Table 2. R2 value of each curve in the global fitoffluorescence PNAS PLUS to the fluorescence vs. [ATP] data vs. [ATP] data to the expanded NCM (Eq. 11) Parameter Value TMR/ring R2 value

A 0.98 ± 0.10 1.79 0.9115

kR (μM) 0.9 ± 0.3 2.78 0.9776 c 0.042 ± 0.008 3.78 0.9909

ΔGL1 (kJ/mol) 26 ± 11 4.68 0.9828

ΔGL2 (kJ/mol) 46 ± 2 5.49 0.9966 ΔGD (kJ/mol) 2.6 ± 1.0 SEE COMMENTARY See text for explanation of fitted parameters. The range of each parameter that falls within the 95% CI of the global fit is given. GroEL14; i.e., <10% of the rings may be contaminated with an ensemble of SPs. The concentration of purified EL242C was calculated by measuring the − absorbance at 280 nm and using the extinction coefficient of 9,600 cm-1·M 1. The model also supports the iterative annealing model of GroEL function. GroEL performed work on the TMR dimers, over- Steady-State ATP Hydrolysis. The steady-state hydrolysis of ATP was measured coming the free energy of dimer formation while transitioning at 37 °C as previously described (10). from the T to R state. Likewise, the iterative annealing model suggests that GroEL can perform work on SPs by forcibly un- Data Analysis. Data from all instruments was saved in ASCII format and folding the bound SP on its release into the central cavity, res- imported into Microsoft Excel 2010. All data analysis, except singular value cuing it from its kinetic folding trap and affording it another decomposition (SI Materials and Methods) was performed in Excel. Globally fi fl opportunity to reach its native state. tting the uorescence vs. [ATP] experimental data to Eq. 11 was performed by nonlinear least-squares analysis. The least-squares value for each curve fi Materials and Methods was summed and minimized using Excel solver. The 95% CI of the twas taken to be ±1.65 SDs from the mean of the residuals. Error in fitted Additional information on instrumentation, synthesis and purification of parameters was calculated as the largest deviation from the fitted least- TMR -DTT, labeling GroEL K242C, and fluorescence vs. [ATP] is provided in SI 2 squares value that falls within the 95% CI. R2 values for each curve were Materials and Methods. calculated as detailed in DeVore (28). Singular value decomposition, performed in MATLAB, was used in a principle component analysis of the Construction of GroEL K242C. The mutant K242C was prepared as described spectra of EL242C-TMR in support of the two-species model. More than 98% in ref. 23 and in SI Materials and Methods. We inserted the K242C muta- of the variance was accounted by this model (29). tion into a WT background rather than into a cysteine-free background because cysteine-free GroEL is much less stable than the WT. ACKNOWLEDGMENTS. We thank Ms. Yu Yang for constructing the GroEL mutant K242C, Dr. Edward Eisenstein (Institute for Bioscience and Bio- fi Puri cation of GroEL. WT GroEL and the mutant GroEL K242C, free of technology Research, University of Maryland Biotechnology Institute) for the tryptophan-containing contaminants, were purified as previously described gift of the plasmid pGEL1, and Dr. Dorothy Beckett and Dr. Dave Thirumalai (11). Typically, GroEL preparations contained <0.2 mol of contaminating SP/ for constructive criticism. BIOPHYSICS AND COMPUTATIONAL BIOLOGY 1. Thirumalai D, Lorimer GH (2001) Chaperonin-mediated protein folding. Annu Rev 16. Blackman MJ, et al. (2002) Structural and biochemical characterization of a fluorogenic Biophys Biomol Struct 30:245–269. rhodamine-labeled malarial protease substrate. Biochemistry 41(40):12244–12252. 2. Horwich AL, Fenton WA (2009) Chaperonin-mediated protein folding: Using a central 17. Okoh MP, Hunter JL, Corrie JE, Webb MR (2006) A biosensor for inorganic phosphate – cavity to kinetically assist polypeptide chain folding. 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Corsepius and Lorimer PNAS | Published online May 30, 2013 | E2459 Downloaded by guest on September 25, 2021