Exploring one-state downhill proteinfolding in single moleculesJianwei Liua,1,2, Luis A. Camposa,b,1, Michele Cerminarab, Xiang Wanga,3, Ravishankar Ramanathanb, Douglas S. Englisha,4,and Victor Muñoza,b,5

aDepartment of Chemistry and Biochemistry, University of Maryland, College Park, MD 20742; and bCentro de Investigaciones Biológicas, ConsejoSuperior de Investigaciones Científicas, Ramiro de Maeztu 9, Madrid 28040, Spain

Edited by Robert Baldwin, Stanford University, Stanford, CA, and approved November 16, 2011 (received for review July 12, 2011)

A one-state downhill protein folding process is barrierless at allconditions, resulting in gradual melting of native structure thatpermits resolving folding mechanisms step-by-step at atomic reso-lution. Experimental studies of one-state downhill folding havetypically focused on the thermal denaturation of proteins that foldnear the speed limit (ca. 106 s−1) at their unfolding temperature,thus being several orders of magnitude too fast for current sin-gle-molecule methods, such as single-molecule FRET. An importantopen question is whether one-state downhill folding kinetics canbe slowed down to make them accessible to single-molecule ap-proaches without turning the protein into a conventional activatedfolder. Here we address this question on the small helical proteinBBL, a paradigm of one-state downhill thermal (un)folding. Wedecreased 200-fold the BBL folding-unfolding rate by combiningchemical denaturation and low temperature, and carried out free-diffusion single-molecule FRET experiments with 50-μs resolutionand maximal photoprotection using a recently developed Trolox-cysteamine cocktail. These experiments revealed a single con-formational ensemble at all denaturing conditions. The chemicalunfolding of BBL was then manifested by the gradual change ofthis unique ensemble, which shifts from high to low FRETefficiencyand becomes broader at increasing denaturant. Furthermore, usingdetailed quantitative analysis, we could rule out the possibility thatthe BBL single-molecule data are produced by partly overlappingfolded and unfolded peaks. Thus, our results demonstrate the one-state downhill folding regime at the single-molecule level andhighlight that this folding scenario is not necessarily associatedwith ultrafast kinetics.

Protein folding is an ideal problem for single-molecule ap-proaches because the simple collective behavior that is fre-

quently observed in bulk experiments could hide an underlyingcomplexity of myriads of microscopic folding pathways (1). Thusprotein folding has been a major target for modern single-mole-cule experiments, including force-microscopy (2) and fluores-cence (3). Among these, single-molecule FRET (SM-FRET) hasthe advantage of recapitulating the conventional bulk chemicalunfolding experiments at the single-molecule level. SM-FRETmethods have already made important contributions to proteinfolding, such as demonstrating the conversion between native andunfolded populations of two-state-like folding (4), resolving thechemical-denaturant-induced expansion of the unfolded state (5)and its nanosecond conformational dynamics (6), and settingupper bounds for folding transition-path times (7).

Another important application is the characterization of thedownhill folding scenario predicted by energy landscape theory(1). Downhill folding proteins have a maximal free-energy barrier(i.e., at the denaturation midpoint) below 3RT. (RT is thermalenergy, where R is the gas constant and T is the temperaturein Kelvin.) The barrier top is thus significantly populated, andfolding may become truly downhill at conditions of very high,or low, stability (1). A populated barrier top allows experimentaldetection by differential scanning calorimetry (DSC) (8), which incombination with fast kinetic methods has led to the idea thatmost microsecond folding proteins fall within the downhill fold-

ing regime (9). This conclusion has been dramatically demon-strated with the recent advent of ultralong molecular dynamicssimulations of microsecond folding proteins, which resolve multi-ple folding-unfolding events and permit computing folding bar-riers accurately (10). Of particular relevance is the downhillextreme: the one-state (or global downhill) folding scenario (11).In this case, the free-energy landscape has only one minimum thatshifts along the reaction coordinate from native to unfolded va-lues as a function of denaturational stress, and the protein alwayspopulates a single conformational ensemble that becomes pro-gressively unfolded (12). Thus, at the denaturation midpoint, aone-state protein populates an ensemble of half-denatured con-formations rather than the 50–50 mix of folded and unfoldedmolecules.

The theoretical foundations of one-state folding are well estab-lished (12, 13), and its mechanistic features have been investi-gated on a variety of molecular simulations, including simple Go-like models (13, 14), more complex coarse-grained models (15),and atomistic molecular dynamics simulations in explicit solvent(10, 16). From the experimental side, one-state downhill foldingwas first described for the small α-helical protein BBL basedon the quantitative analysis of its probe-dependent equilibriumthermal unfolding process (17). This study was later complemen-ted at atomic resolution using NMR (18) and performing a globalanalysis of the atomic unfolding curves (19). Additional supporthas been obtained by DSC analysis (8), double perturbation ex-periments (20), and the multiprobe study of its microsecondfolding kinetics as function of temperature (21). Later on, similarprobe-dependent continuous unfolding has been reported formutants of monomeric λ-repressor (22) and for monellin (23).However, there still is open debate as to whether BBL (and byextension other proteins) is indeed an example of one-statedownhill folding, folds in the conventional activated fashion(24), or switches between one-state downhill and activated fold-ing (13). The debate has been mostly fueled by interpretationalissues rather than factual differences between experimental datafrom different BBL variants and/or groups (25). The notable ex-ception is the recently published SM-FRET data on BBL, whichshows a bimodal FRET efficiency histogram at the chemical-denaturation midpoint (26). This result raises an interesting ques-tion because these SM-FRETexperiments were performed under

Author contributions: D.S.E. and V.M. designed research; J.L., L.A.C., M.C., X.W., and R.R.performed research; D.S.E. contributed new reagents/analytic tools; J.L., L.A.C., and V.M.analyzed data; and V.M. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.1J.L. and L.A.C. contributed equally to this work.2Present address: Department of Pediatrics, Stanford University, Stanford, CA 94305.3Present address: Department of Chemistry, University of North Carolina, Chapel Hill,NC 27599.

4Present address: Department of Chemistry, Wichita State University, Wichita, KS 67260.5To whom correspondence should be addressed. E-mail: vmunoz@cib.csic.es.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1111164109/-/DCSupplemental.

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conditions at which the BBL relaxation time is over two orders ofmagnitude longer than the folding speed limit of approximately1 μs that is commonly used as reference for barrierless kinetics(27, 28). Thus, it is possible that BBL folds one-state downhillnear its unfolding temperature, where the kinetics are ultrafast(21, 29), but develops a barrier upon chemical denaturation atlow temperature. On the other hand, several technical issues,related to high levels of photodamage and discrepancies withcontrol experiments, have been noted in these SM-FRET studies(30).

Here we try to overcome such technical shortcomings andperform a detailed quantitative investigation of the folding beha-vior of BBL at the single-molecule level. The main issue is timeresolution. Current SM-FRET dyes saturate at photon emissionsof approximately 100 kHz (31), restricting the effective timeresolution to the 0.5–1 ms it takes to detect statistically signifi-cant numbers of photons. We optimized the time-resolution/photodamage trade-off by performing chemical-denaturation ex-periments at 279 K (which slows down BBL kinetics by approxi-mately 200-fold) in conjunction with a newly developedphotoprotection cocktail that affords emissions of approximatelyone photon per microsecond with little photodamage (32). Theother issue refers to the possible role of the protein tails in BBLfolding, which we address by studying a variant of BBL labeledwith single-molecule dyes at the ends of five-residue unstructuredN- and C-terminal tails.

Results and DiscussionOne-State Versus Two-State Folding at the Single-Molecule Level. Asa conceptual guide, it is useful to discuss the expected differ-ences between folding scenarios in the context of free-diffusionSM-FRETexperiments. The differences depend critically on theinterplay between the folding relaxation time, τf , and the binningtime, Tb. For a protein that folds over a significant free-energybarrier (>3RT) at all conditions (two-state folding scenario), in-dividual molecules populate either the native or the unfoldedstate with probabilities determined by the concentration of che-mical denaturant. For Tb ≪ τf , the FRET efficiency histogram(FEH) should show two peaks with amplitudes determined bythe folding equilibrium constant. Both peaks should have shot-noise limited widths because the conformational dynamics with-in each state are much faster than the overall folding relaxation(33). However, when Tb ≫ τf , molecules undergo multiple fold-ing-unfolding events during the observation time, and thus theFEH becomes a single, shot-noise limited peak at a position cor-responding to the population weighted average (Fig. 1, Leftcolumn). In the one-state folding scenario, the relaxation timereflects the conformational exchange within a unique ensemble.For Tb ≫ τf , the observed FEH is indistinguishable from that ofthe activated scenario. However, for short Tb, the FEH will showa single peak that is broader than shot noise because the under-lying unimodal FRETefficiency distribution is quasi-static (Fig. 1,Center column). A mixed scenario, in which there is a significant

free-energy barrier only near the denaturation midpoint, is alsopossible. In this case, the FEH measured with Tb ≪ τf shouldshow a single peak broader than shot noise in native and/or un-folding conditions, and two shot-noise limited peaks at the mid-point (Fig. 1, Right column).

Observation of a Unique, Gradually Unfolding, Single-Molecule Ensem-ble in BBL. BBL is a domain from the subunit 2 of the 2-oxo-glutarate reductase complex from Escherichia coli that is flankedby structurally flexible linkers (34). Given the marginal stabilityof BBL, the specific excision points in the sequence and the loca-tion of the cysteines for labeling with bulky SM-FRET dyes needto be considered carefully. Here we used a most conservativestrategy, extending the BBL sequence five residues on each endrelative to the consensus folded segment and placing the cysteinesat both ends (Fig. S1). We used A488–A594 as the SM-FRETpair. We have previously tested this same strategy on the slowtwo-state folder α-spectrin SH3 domain (55 residues), for whichwe could fully resolve the folded and unfolded states and foundexcellent quantitative agreement between bulk and SM-FRETexperiments (32). In addition, we performed all the experimentsat 279 K because at this temperature the BBL folding relaxationgreatly slows down (21), which should facilitate reaching Tb < τfconditions.

As a control, we measured the equilibrium chemical unfoldingof BBL by FRET in bulk. Bulk experiments produced a sigmoidalunfolding curve ranging from a FRET efficiency, E, of approxi-mately 0.8 to 0.4 (Fig. 2). Both urea and guanidinium chloride(GdmCl) denature BBL, but under our experimental conditions(i.e., 279 K) urea reaches its solubility maximum before the un-folding process is complete (Fig. 2). The bulk FRET unfoldingcurve is very similar to that of the unlabeled protein monitoredby CD (Fig. S2), indicating that (i) the dyes do not perturb BBLfolding, and (ii) the sample is nearly 100% labeled with one donorand one acceptor. Phenomenological fits to a two-state modelproduced the same thermodynamic parameters within experi-mental uncertainty. Furthermore, a combined two-state analysisof the unlabeled CD and labeled FRETcurves renders excellentfits (Fig. 2 and Fig. S2) with reasonable native and unfolded base-lines (e.g., red lines in Fig. 2). This global two-state analysissuggests that BBL is half-denatured at approximately 5.8 M urea(or ca. 2.1 M for GdmCl, which is 2.75 times a stronger denatur-ant in this case). The E of approximately 0.8 observed in nativeconditions translates onto a dye-to-dye distance of approximately

Fig. 1. Cartoon that compares folding scenarios at the single-molecule level.Blue indicates native, green midpoint, and red unfolding conditions.

Fig. 2. Equilibrium chemical denaturation of BBL measured by FRET. Blue(top scale), urea; green (bottom scale), GdmCl. The urea/GdmCl ratio is2.75. Circles represent the bulk data and the curve the global fit to thetwo-state model. The two red lines signify the native (linear) and unfolded(curved) baselines used for the global two-state fit. The dashed lines are thebaselines in the linear approximation. Inverted triangles show the position ofthe maximum on the single-molecule FEHs of Fig. 3.

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4.4 nm (assuming κ2 ¼ 2∕3; see SI Methods), which is in goodagreement with the native 3D structure (Fig. S3). Moreover, theoverall change in E upon BBL chemical unfolding is quite typicalfor single-domain proteins (3), indicating that there is ampledynamic range to resolve the putative folded and unfolded statesby SM-FRET.

In free-diffusing SM-FRETexperiments, we managed to mea-sure FEH from individual BBL molecules with 50-μs resolutionacross the entire chemical-denaturation curve thanks to a re-cently developed photoprotection cocktail (32). The results areshown in Fig. 3, where we include data up to 8.1 M urea (blue),and, beyond this point, using GdmCl in proportionate concentra-tions (i.e., 2.75 times lower; green) to access fully denatured con-ditions. The FEH under native conditions showed a singleprotein-peak at E of approximately 0.8 together with a very smallpeak at E of approximately zero, indicating there is a very smallfraction of molecules in which the acceptor is turned off. Ingeneral, the data in urea were of higher quality. Fig. 3 also showsthat the single-molecule folding behavior of BBL is quite differ-ent from that of other proteins (3). For BBL, the increase inchemical denaturant shifts the single peak gradually from high tolow E values. At the chemical-denaturation midpoint (ca. 6 Murea as judged by the halfway position of the peak maximum), theFEH still shows only one nonzero peak. Remarkably, the hEi ob-tained from the single-molecule FEHs is in excellent agreementwith the bulk FRETcurve (triangles in Fig. 2). Furthermore, thedenaturation midpoint estimated from the position of the FEHpeak is similar to that estimated from bulk. Altogether, the quan-titative agreement confirms that the single-molecule experimentsfaithfully report on the folding behavior of BBL.

Contributions to the FEH Width. For a process that interconvertswith slow dynamics relative to Tb (here 50 μs), the FEH widthis determined by a combination of shot noise and the underlyingFRET efficiency distribution (hE2i − hEi2 or conformationalvariance) (33), but it is also affected by experimental factors suchas sample heterogeneity and dye photochemistry. In Fig. 4, weplot the experimental variance (σ2) of the nonzero FEH peakversus the progress of the unfolding reaction as signaled by thedecrease in hEi. Fig. 4 highlights that the FEHs are broader thanexpected from shot noise (cyan curve) at all conditions. More-over, the total variance increases in sigmoidal fashion as unfold-ing progresses. This pattern is different from the expectation fora two-state scenario under Tb < τf conditions, in which the con-formational variance has a distinct maximum at the denaturationmidpoint that dominates over the shot-noise dependence on E

(e.g., the red curve in Fig. 4, which shows the variance expectedfrom the two-state fit to the BBL bulk FRET curve).

To investigate the actual contribution from conformationalvariance, we measured the FEH near the denaturation midpointwith Tb varying from 50 μs to 1 ms, while keeping the photonthreshold over background constant. This exercise shows thatthe FEH sharpens significantly as Tb is extended, starting froman extra variance over shot noise of 0.0096 at 50 μs and decreasingdown to 0.0029 at 1 ms (Fig. S4). This result confirms that BBLundergoes conformational dynamics in the submillisecond time-scale. However, it also shows that there is residual variance at thelongest Tb, which could be caused by either chemical heteroge-neity and/or photochemical artifacts. An analysis of the photonemission fluctuations undergone by free-diffusing single mole-cules of BBL provides additional clues of the source of such re-sidual variance. From this analysis, we discovered that the majorcontribution to the residual variance seems to arise from the spe-cific time bins along free-diffusing trajectories in which an accep-tor deactivation-reactivation event takes place (Fig. S5). On theother hand, we did not find apparent signs of sample heteroge-neity (entire single-molecule diffusive trajectories with strange Evalues).

Conformational Dynamics from Single Molecules. The ability to re-solve microsecond FRET fluctuations gives us the opportunityto measure the conformational dynamics of BBL from the auto-correlation function (R) of E fluctuations along free-diffusingsingle-molecule trajectories (35). Practically, we achieve this cal-culation by computing the average autocorrelation function over

Fig. 3. Single-molecule FRET-efficiency histograms of BBL as a function of urea (blue) and GdmCl (green). The histograms were obtained from 50-μs bins withNT ¼ 40 (urea) orNT ¼ 30 (GdmCl). The red curves are fits to a lognormal distribution, and the black vertical lines signal the extreme FRETefficiency values. Thered star signals the FEH closest to the denaturation midpoint.

Fig. 4. The width of the FEH versus the position of its maximum. The width isrepresented by the variance (σ2) from fits of the histograms to a lognormaldistribution (red curves shown in Fig. 3). The abscissa shows the position ofthe FRET efficiency maximum in the FEH. Blue, urea; green, GdmCl; cyan,shot-noise width for NT ¼ 40; red, simulation for a two-state model basedon the fit to the bulk unfolding curve assuming NT ¼ 40 and no conforma-tional exchange. For the data in GdmCl, the shot-noise variance is slightlyhigher (e.g., 0.008 at E ¼ 0.4).

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a “supertrajectory” obtained by concatenating hundreds of indi-vidual trajectories selected to be significantly longer than theexpected dynamics (32). For BBL, the autocorrelation func-tion near the chemical-denaturation midpoint obtained from tra-jectories >0.5 ms results in an exponential decay with τ approxi-mately 200 μs (Fig. 5A). The analysis performed on trajectories>0.75 and even >1 ms produces essentially the same relaxationtime in spite of the noisier decays (Fig. S6). Moreover, the bulkconformational dynamics measured with an infrared laser-in-duced T-jump instrument on the protein without fluorescent la-bels are nearly identical (Fig. 5B). Such agreement demonstratesthat the fluorescent labels do not perturb the folding dynamics ofBBL. Moreover, it confirms the BBL midpoint folding-unfoldingrate of approximately 5;000 s−1 obtained with SM-FRET, a para-meter that is critical for the quantitative analysis of the FEHs.

The relaxation rate (1∕τ) obtained from the E autocorrelationfunction of single-molecule trajectories as a function of urea con-centration is almost constant (Fig. S7), indicating that the fold-ing dynamics of BBL at 279 K have extremely weak chemical-denaturant dependence (Fig. S7, blue). In conditions of completeunfolding (e.g., 3 M GdmCl), however, the autocorrelation func-tion immediately drops to zero, signaling the disappearance ofsubmillisecond dynamics. To confirm these results, we also per-formed infrared laser T-jump experiments. With the T-jumpmethod, we could not reach 279 K because around this tempera-ture BBL is maximally stable against cold-heat denaturation(SI Methods). However, we could measure the bulk dynamics ofunlabeled long-BBL over a similar range of chemical denaturantat 287 K, which is intermediate between those of the SM-FRETexperiments and of previous T-jump experiments on other BBLvariants (i.e., 298 K) (21). The comparison reveals a clear de-creasing trend in the always weak chemical-denaturant depen-dence of BBL folding dynamics as temperature lowers, leading tovirtually no dependence at approximately 280 K (Fig. S7). Nearlyflat chevron plots are consistent with downhill folding accordingto computer simulations (14) and theoretical 1D free-energy sur-face models (9). However, the completely flat chevron of BBL at279 K points to compensating dynamical effects. On the onehand, chemical denaturant could speed up the conformationaldynamics of partially unfolded BBL (i.e., <3 M GuHCl), ashas been recently shown for the dynamics of expanded versuscollapsed unfolded states (6, 36). On the other hand, the relaxa-tion rate for one-state downhill folding should be approximatelyproportional to the squared curvature of the single free-energysurface well (21), which for BBL seems to become broader at highdenaturant (see FEH variance in Fig. 4).

Quantitative Analysis of the BBL Single-Molecule Data. The data inFig. 3 strongly point to the one-state downhill folding scenario.However, the FEH width and how it depends on chemical dena-turant, binning time, and photon threshold are key for determin-ing whether the presence of a folding barrier can be entirely ruledout. To explore this issue, we analyzed the BBL FEHs using theGopich–Szabo theory for single-molecule FRET experiments(33, 37).

As a first test, we investigated the changes in FEH width andposition with chemical denaturant. The effects of conformationalexchange and shot noise in the FEH of a protein interconvertingbetween two states can be described quantitatively by the analy-tical three-Gaussian (3G) expression developed by Gopich andSzabo (SI Methods). We thus applied the 3GGopich–Szabo treat-ment by performing an integrated fit to the BBL FEHs at differ-ent denaturant concentrations (i.e., data of Fig. 3). In this fit, thenative and unfolded populations are determined by global para-meters (Cm and m value), whereas the native and unfolded Evalues (E1 and E2) are floated freely for each FEH to allow max-imal flexibility. The results from this exercise are illuminating.Such fit imposes that the native and unfolded populations arekept nearly constant over the entire denaturant range (pN from<0.7 at 0 M GdmCl down to >0.4 at 7 M GdmCl; Fig. 6, Inset).Because pN is predicted to be close to 0.5 at all conditions, andthe experimental hEi changes sigmoidally with denaturant (inagreement with the bulk unfolding curve, Fig. 2), the fit ascribesthe entire change in hEi to E1 and E2. This fit results in baselinesthat closely track the overall FRETcurve slightly above or below(Fig. 6). Such baselines and changes in pN are physically implau-sible because we know from bulk FRET, CD, and infrared laser Tjump that BBL is already fully denatured at 3.5 M GdmCl. Thereason is that the fit is in fact assigning the theoretical “unfolded”state to the FEH tail at low E that results from transient acceptorphotodeactivations rather than to a true state. The implication isthat the SM-FRET data of BBL is quantitatively incompatiblewith an activated folding scenario.

As a second test, we investigated the interplay between Tb andphoton threshold (NT) in determining the FEH shape. These twofactors affect the FEH width in different ways, providing criticalquantitative information about the underlying E distribution.Here, we focused on the FEH near the denaturation midpoint(6.1 M urea) where the sensitivity to two overlapping peaks ismaximal. In numerical simulations using the 3G Gopich–Szabotheory, we observed that Tb < 200 μs is still short enough to

Fig. 5. BBL conformational dynamics near the chemical-denaturation mid-point. Data are shown in blue and the fits to a single exponential decay inred. (A) Autocorrelation function of the FRET efficiency fluctuations under-gone by individual free-diffusing BBL molecules (labeled with A488–A594) at6.1 M urea and 279 K. (B) BBL relaxation decay measured in unlabeled BBL byinfrared absorption at 1;649 cm−1 after a nanosecond laser-induced T jumpfrom 278 to 282 K in the presence of 2.2M 13C-GdmCl (equivalent to ca. 6.1 Murea). Because BBL has maximum stability against cold-heat denaturationat approximately 280 K, the change in native signal upon this 4 K jump isonly approximately 0.5% (measured by Fourier transform infrared spectro-scopy and CD).

Fig. 6. Global fitting of the FEH as function of chemical denaturant to thetwo-state model. The position of the native (green circles) and unfolded (redcircles) states obtained from the global fit of the FEHs to the 3G Gopich–Sza-bo theory for a two-state system parameterized with the BBL rate data fromFig. S7 are shown. Filled circles are for urea (top scale) and open circles forGdmCl (bottom scale). The scales correspond to urea/GdmCl ratio of 2.75. Thethin continuous lines are polynomial fits to guide the eye. The fit to the bulkdata (gray curve) and the hEi obtained from the FEH (blue small circles) arealso shown for reference. (Inset) Changes in native probability as function ofdenaturant concentration obtained from the fit.

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avoid a dominant contribution from conformational exchange inthe midpoint FEH of BBL. We thus obtained the experimentalFEH of BBL at 6.1 M urea with different Tb pushing NT to thehighest possible values. We managed to reach NT ¼ 60 for 50-μsbins, and maintain proportionally high thresholds for 100 and150 μs bins (NT of 110 and 145, respectively). Interestingly, asTb and NT increase, the FEH becomes narrower, but alwaysmaintains a single peak with a decaying tail at low E (Fig. 7, Left,for Tb ¼ 100 μs, and Fig. S8).

The FEH tail, however, cannot be explained as an incipientunfolded state because, at the very high photon counts obtainedfor these data, the unfolded state should produce a distinct sec-ond peak. Indeed, calculations with the 3G Gopich–Szabo theoryusing the global fit parameters (E1 ¼ 0.63, E2 ¼ 0.47, andpN ¼ 0.63), the BBL folding relaxation rate of k ¼ 5;000 s−1,the experimental Tb, and reciprocal of the average number ofphotons (SI Methods) produce histograms with two perfectly dis-tinguishable peaks that are in stark contrast with the experiment(Fig. 7, Center, and Fig. S8). Moreover, this result is invariantwhether pN is fixed to the global fit value or allowed to float freely(it converges to 0.61 vs. the global 0.63).

A similar quantitative test can be performed for the one-statedownhill scenario. In this case, the FEH width would be deter-mined by the underlying single conformational ensemble andmodulated by Tb and NT . For this purpose, we used an extremelysimple model in which the folding dynamics of BBL are describedas diffusion on a quasi-harmonic one-dimensional free-energysurface with E as order parameter (32). To calculate the FEHs,we performed stochastic dynamic simulations with a diffusioncoefficient that reproduces the experimental rate of 5;000 s−1and photon fluxes that mimic the experimental conditions (SIMethods). In this case, the only parameters required to reproducethe three FEHs simultaneously are the mean and variance ofthe one-state E distribution. Remarkably, the FEHs predictedby this simplistic model reproduce the overall FEH shape andits changes with Tb and NT quite well (Fig. 7, Right, and Fig. S8).The only exception is the low E region of the histogram, whichis expected given that it appears to be caused by photochemicalartifacts (acceptor deactivations). Therefore, we can concludethat the BBL SM-FRET data is quantitatively consistent withthe one-state downhill folding scenario.

ConclusionsIn this work, we have embarked in the experimental analysisof downhill folding at the single-molecule level. This analysis ischallenging because candidate proteins have intrinsically malle-

able conformational ensembles. There are two potential sourcesof perturbation: the excision points for extracting the BBL do-main and the chemical labeling with fluorescent probes. Here wehave used a very conservative strategy that placed the labelingsites at the ends of five-residue unstructured tails flanking thefolded structure (Fig. S1). The success of our general strategy isdemonstrated by the equivalent unfolding curves (Fig. 2 andFig. S2) and identical folding relaxation rates (Fig. 5) obtained bySM-FRETand bulk experiments on the unlabeled protein, as wellas by the consistency with previous bulk measurements on otherBBL variants (25) (Fig. S7). Another challenge is to reach thestringent time-resolution requirements for SM-FRET experi-ments without inducing serious photochemical artifacts. Combin-ing low temperature (279 K) and a purposely developed cocktail(32), we have reached Tb < τf conditions with very low (althoughstill detectable) photodamage.

These SM-FRET experiments revealed a unimodal FRETefficiency distribution that gradually shifts toward lower E andbecomes broader as denaturational stress increases, exactly asexpected for one-state downhill folding (see Fig. 1). Our results,however, are in stark contrast with a previous SM-FRET studyperformed at 279 K on the QNND-BBL variant (Fig. S1), andwhich showed bimodal FEHs (26). The discrepancy in this caseis in the experimental data themselves, and not just in the inter-pretation, as it happened previously with bulk data (25). Directcomparison, however, demonstrates that our SM-FRET data areof far superior quality on all fronts: more conservative labelingscheme (they used much larger probes, ref. 30, and placed a la-beling site in direct contact with helix 2; Fig. S1), much reducedphotodamage, and higher resolution (at least 1.7 times higherphoton counts). Moreover, our SM-FRET experiments agreequantitatively with bulk equilibrium and kinetic experimentson the unlabeled variants, whereas the previous study is inclear disagreement (30). It is also interesting that a just-publishedultra-large-scale molecular dynamics study of 10 fast-foldingproteins shows distinctive one-state downhill folding for theQNND-BBL variant (10). We have investigated the source of thediscrepancy by replicating the BBL variant and experiments ofthe previous study. However, we were unable to reproduce theirresults even at the most basic level. For instance, the equilibriumchemical unfolding curve of QNND-BBL at 279 K has Cm ofapproximately 2.4 M GdmCl and not 4 M GdmCl as reportedbefore (Fig. S9A). In fact, in our hands, QNND-BBL and longBBL show very similar unfolding curves (Fig. S9B). Moreover,we have been unable to get high photon fluxes with the A564–A647 pair they used because A647 undergoes the characteristicphotoisomerization blinking of carbocyanine dyes. We couldmeasure the FEH at the midpoint with 50-μs resolution whenwe labeled QNND-BBL with the A488-A594 pair, but wefound no traces of a double-peaked histogram (Fig. S9C). Sortingout such serious discrepancies on the QNND-BBL results mayrequire involvement of a third independent lab.

In addition, we also deemed it important to perform a quan-titative theoretical analysis because the lack of a bimodal FEH isafter all a negative observation. The objective was to determinewhether the unimodal FEHs of BBL could be explained at all astwo unresolved peaks for native and unfolded states. Such quan-titative analysis indicates that it is impossible to obtain a physi-cally reasonable two-state fit to the BBL SM-FRET data as afunction of chemical denaturant (Fig. 6). Furthermore, we havemeasured the FEH near the denaturation midpoint with unpre-cedentedly high NT and saw no signs of a double peak, whereasquantitative theory indicates that under those conditions a bimo-dal distribution should be readily apparent on a barrier-crossingscenario (Fig. 7 and Fig. S8). On the other hand, a simple modelof one-state downhill folding dynamics at the single-moleculelevel describes reasonably well the effects of varying Tb and NTin the midpoint FEH.

Fig. 7. Quantitative analysis of the FEH near the denaturation midpoint.(Left) FEH of BBL measured at 6.1 M urea using Tb ¼ 100 μs andNT ¼ 110. (Center) Fit of the FEH to a two-state model using the 3G Go-pich–Szabo theory (dark blue). The 3G curves representing the native state(green), unfolded state (red), and conformational exchange (black) are alsoshown. (Right) Prediction for the one-state downhill folding scenario ob-tained from stochastic dynamic simulations (dark blue). (Center and Right)The experimental histogram is shown for reference as a shaded area inthe background. The residuals from the fits are shown on top.

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We thus conclude that the single-molecule data and analysispresented here strongly support the one-state downhill foldingscenario for the chemical denaturation of BBL at low tempera-ture. Our SM-FRET data on BBL buttress all prior analyses ofone-state downhill folding based on bulk thermal denaturation(8, 17, 18, 20, 21). The single-molecule results have farther-reach-ing implications. Previous bulk studies have focused on tempera-ture, and thus have been carried out under conditions at whichBBL reaches the folding speed limit. In this case, BBL folds-un-folds two orders of magnitude more slowly. Assuming a classicalrate expression, such difference converts onto a 4RT barrier,which would place BBL within the barrier-crossing scenarioat the SM-FRET conditions even if it folded downhill at themidpoint temperature. Still, in our experiments, we see a unique,gradually shifting, conformational ensemble. The most plausibleinterpretation is that folding-unfolding rates are largely con-trolled by dynamic factors (conformational motions) in additionto energetic differences in the overall free-energy barrier. Ac-cording to analytical theory, complex dynamical factors are in-trinsic to the folding process (1), but their specific role has tra-ditionally eluded experimental scrutiny (11). Evidence supportinga major role of conformational dynamics in folding has accumu-lated recently. The analysis of fast-folding kinetics with theoreti-cal free-energy surface models led to the proposal of an intrinsictemperature dependence of the preexponential term of the fold-ing rate equation equivalent to approximately 1 kJ∕mol perresidue (9). Hence, for a 60-residue protein, a speed limit of1 μs at 350 K would convert to approximately 190 μs at 279 K.The timescale and amplitude of protein conformational motionscan also strongly depend on the compactness and structural prop-erties of the conformational ensemble, something that has been

dramatically demonstrated in recent measurements of the intra-chain dynamics of unfolded protein L (36). Our results advocatefor such a critical role of conformational dynamic factors indetermining folding rates, and they shed light onto the reasonswhy some previous experimental results seemed inconsistent withthe traditional rate-barrier paradigm. For instance, this idea ex-plains why small all-beta proteins, such as WW domains, exhibitdownhill folding features, whereas they fold significantly moreslowly than their α-helical counterparts (38), or why monellin be-haves thermodynamically as a one-state downhill folder, but foldsslowly (23).

MethodsBulk Experiments. Bulk equilibrium experiments were performed at 279 K in20 mM acetate buffer pH 6.

Single-Molecule FRET Experiments. Single-molecule experiments were per-formed at 279 K and at a protein concentration of 75 pM on the same buffer.All measurements were carried out on a custom-made single-moleculefluorescence microscope system (39) with time resolution of 50 μs in samplescontaining 1 mM (S)-Trolox methyl ether and 10 mM 2-mercaptoethylamine.SM-FRET efficiency histograms were corrected using a 0.13 probability ofdonor leak-through to the acceptor channel, or by a detailed treatmentthat takes into account leak-through, cross-talking, and quantum yields. SeeSI Methods for detailed description of SM-FRET controls, SM-FRET and infra-red T -jump kinetic experiments, quantitative analysis with the 3G Gopich–Szabo theory, and stochastic dynamic simulations of one-state downhillfolding.

ACKNOWLEDGMENTS. This work was supported in part by the Marie CurieExcellence Award MEXT-CT-2006-042334, and Grants BFU2008-03237 andCONSOLIDER CSD2009-00088 from the Spanish Ministry of Science andInnovation.

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