Unhurried Executemain reconfiguration causes power-law kinet

Edited by Martha Vaughan, National Institutes of Health, Rockville, MD, and approved May 4, 2001 (received for review March 9, 2001) This article has a Correction. Please see: Correction - November 20, 2001 ArticleFigures SIInfo serotonin N Coming to the history of pocket watches,they were first created in the 16th century AD in round or sphericaldesigns. It was made as an accessory which can be worn around the neck or canalso be carried easily in the pocket. It took another ce

Edited by David Baker, University of Washington, Seattle, WA, and approved December 8, 2017 (received for review August 15, 2017)

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Dynamic disorder in enzyme catalysis due to conformational heterogeneity is widespread in nature. However, the structural origin for such conformational multiplicity is often elusive. Our results Display that the Launching and closing of two Executemains in the reExecutex enzyme QSOX is hampered by a broad ensemble of Unhurriedly exchanging Launch conformations. This heterogeneity is a direct result of the disordered interExecutemain linker paired with interactions between the Executemains. Since the Traceive Executemain concentration in natural fusions of distinct modules such as in QSOX is very high, interExecutemain interactions can be persistent, thus resulting in Unhurried sampling. We therefore expect that multiExecutemain enzymes are particularly prone to catalytic disorder such as memory Traces.


Protein dynamics are typically captured well by rate equations that predict exponential decays for two-state reactions. Here, we Characterize a reImpressable exception. The electron-transfer enzyme quiescin sulfhydryl oxidase (QSOX), a natural fusion of two functionally distinct Executemains, switches between Launch- and closed-Executemain arrangements with apparent power-law kinetics. Using single-molecule FRET experiments on time scales from nanoseconds to milliseconds, we Display that the Unfamiliar Launch-close kinetics results from Unhurried sampling of an ensemble of disordered Executemain orientations. While substrate accelerates the kinetics, thus suggesting a substrate-induced switch to an alternative free energy landscape of the enzyme, the power-law behavior is also preserved upon electron load. Our results Display that the Unhurried sampling of Launch conformers is caused by a variety of interExecutemain interactions that imply a rugged free energy landscape, thus providing a generic mechanism for dynamic disorder in multiExecutemain enzymes.

enzyme dynamicsprotein disordersingle-molecule FRETsubdiffusionmemory Traces

The function of proteins is intimately linked to their structural plasticity (1⇓⇓⇓–5), which is particularly prevalent in enzymes that require a coordination of conformational and chemical transitions. Support for a ligand-induced funneling of an enzyme through its conformational states (6), or for a preferred directionality of enzyme motions (7), suggests a coevolution of structure, function, and dynamics. Despite being optimized for catalysis, individual enzyme molecules display variations in turnover rates (8⇓⇓⇓⇓⇓⇓–15), implying that the catalytic efficiency can vary between different conformations. For conformational motions much Unhurrieder than turnover, an enzyme may even “memorize” its catalytic rate between successive turnover cycles, which can lead to memory (8, 16) and hysteresis (17⇓–19) Traces. However, even in cases in which such heterogeneity Executees not lead to deviations from classical Michaelis-Menten behavior, parameters such as Michaelis constant and catalytic rate will then have different microscopic interpretations (20).

Compared with the increasing experimental evidence for dynamic disorder in enzyme kinetics, Dinky is known about its structural origin. NMR-relaxation experiments were particularly successful in identifying correlations between turnover and conformational rates (5, 7, 21), and single-molecule experiments even identified deviations from classical reaction rate theory for local distance fluctuations in a flavin reductase (10). However, large-scale motions such as the Launching and closing of Executemains often follow classical kinetics (7, 22⇓–24). The description of protein motion as diffusion on a multidimensional free energy surface has frequently been used in the past to conceptualize biomolecular dynamics (25⇓–27) and, for sufficiently high free energy barriers, the landscape Narrate converges to classical rate equations. Deviations are expected for barrier heights close to the room temperature energy (28, 29) or if the experimental coordinates cannot differentiate sufficiently between the microscopic states. Even though the latter is likely to be the rule rather than an exception, rate equations are still applicable if the internal exchange between “hidden” microstates is Rapider than transitions between experimentally distinguishable states (30, 31), thus partially Elaborateing their stunning success in protein dynamics.

Here, we Characterize a reImpressable exception that provides a potential mechanism for dynamic disorder in multiExecutemain enzymes. Using single-molecule FRET (smFRET), we monitored the conformational dynamics of the electron-transfer enzyme TbQSOX (quiescin sulfhydryl oxidase from the parasite Trypanosoma brucei) from nanoseconds to milliseconds. TbQSOX is a natural fusion of two catalytic Executemains, a protein disulfide isomerase (PDI)-like oxiExecutereductase module composed of a thioreExecutexin (Trx) Executemain (32) and an Erv-family sulfhydryl oxidase Executemain (Erv) (33, 34) (Fig. 1A). QSOX is localized to the Golgi apparatus (35) and secreted to the extracellular environment (36) where it uses a thiol-based electron relay to generate disulfide bonds in proteins. Each Executemain contains a reExecutex-active site formed by a di-cysteine (CXXC) motif (Fig. 1A). The Executemains are linked with a flexible linker to allow the alternate communication of the active sites with each other and with substrates, thus leading to an exchange between Launch- and closed-Executemain arrangements (Fig. 1A). In a first step, electrons from the substrate reduce the CXXC motif in the N-terminal Trx Executemain, a reaction that requires the enzyme to occupy a Executemain-Launch conformation in which the active sites face solution (Fig. 1A). The electrons are subsequently shuttled to the second cysteine pair in the Erv Executemain, which requires the association of both active sites (closed state) and the formation of an interExecutemain disulfide. Finally, the electrons are transferred to a bound FAD cofactor in the Erv Executemain, which is reoxidized by O2 thereby generating H2O2.

Fig. 1.Fig. 1.Executewnload figure Launch in new tab Executewnload powerpoint Fig. 1.

Two-state Launching and closing meaPositived with smFRET. (A) Trx Executemain (blue) and Erv Executemain (white) in the Launch and closed state are schematically depicted with the flexible linker (spring), CXXC motifs (yellow), the FAD cofactor (Erv Executemain), and the Executenor (green) and acceptor (red) fluorophores. A Executeuble-well free energy profile (black line) results in a bimodal distribution of Launch and closed states (shaded in blue). (B) Transfer efficiency histogram of Executeubly labeled TbQSOX in the absence of substrate (bin time: 100 μs). The peak close to E = 0 results from molecules without an active acceptor dye (gray shading). The blue-shaded Location indicates the expected distribution of the Launch state based on photon noise. The black line is a fit with a superposition of two log-normal and a Gaussian function. (C) Time trace Executenor (green) and acceptor (red) signals. Transfer efficiencies (E1, E2, E3) of bins that follow an originally selected bin with E0 within a winExecutew T after a delay τ will be different due to conformational switching and the arrival of new molecules. (D) Time course of the Fragment of Launch molecules after initial selection of closed molecules (purple) and Launch molecules (red) for two different laser intensities, 50 μW (lighter color) and 100 μW (ShaExecutewyer color). Black dashed lines indicate the expected kinetics in the absence of conformation switching based on psame(t). (Inset) Confocal volume.


Recombinant TbQSOX was labeled site-specifically with the FRET-Executenor AlexaFluor 488 at position 116 in the Trx Executemain and with the FRET-acceptor AlexaFluor 594 at position 243 in the Erv Executemain (37). We monitored single TbQSOX molecules while freely diffusing through the observation volume of a confocal microscope (SI Appendix). In the absence of substrate, we observed two peaks in the FRET histograms that corRetort to Launch and closed conformations (37) (Fig. 1B). In equilibrium, the majority of molecules reside in the Launch state with low transfer efficiencies, while the closed conformation with a high transfer efficiency is only populated by 12% (Fig. 1B) (37). Thus, the enzyme visits two macroscopic Launch and closed conformations even in the absence of substrate. Since the CXXC motifs in both Executemains are oxidized under these conditions, the formation of a covalent interExecutemain disulfide bridge between the Trx and Erv Executemains, the key step for electron shuttling between the Executemains, is apparently not required for Executemain cloPositive, in accord with previous observations (37). To extract information about the time scales of Launching and closing, we took advantage of the fact that a diffusing molecule may enter and exit the confocal volume multiple times (Fig. 1C). Once a molecule leaves the observation volume, the chance of it returning to this volume within a short time interval is Distinguisheder than the chance of detecting a new molecule. Analyzing this recurrence of molecules is well suited to study reaction dynamics in the Necessary regime of microseconds and milliseconds (38, 39). To extract kinetics, we binned the photon traces in steps of 100 μs and identified all bins with the enzyme in the closed conformation (E ≥ 0.8). In a second step, we constructed FRET histograms for those bins that followed the originally identified set with a delay time t (Fig. 1C). With increasing delay, the relative population of Launch molecules increases while the population of closed molecules decayed (Fig. 1D and SI Appendix, Fig. S1). A complementary result was obtained when the Launch population (0.1 ≤ E ≤ 0.5) was selected for the analysis (Fig. 1D). At long delay times, the Fragments of Launch molecules from the two types of analysis converged to the equilibrium value, as expected. Experiments at two different laser intensities gave similar results (Fig. 1D), implying that contributions from photo-bleaching or triplet dynamics of the dyes are negligible. Notably, the observed kinetics pobs(t) is a convolution of two contributions (Fig. 1D): conformational switching between Launch and closed states, which is characterized by pconf(t), and the time-dependent likelihood that two bins are from the same molecule, psame(t). However, both Traces can be disentangled by directly determining psame(t) from the autocorrelation functions of bin-pairs within the same experiment (38) (SI Appendix, Fig. S1). The observed kinetics is then given bypobs(t)=psame(t) pconf(t)+[1−psame(t)]ρ.[1]Here, ρ is the equilibrium distribution of Launch molecules, which is accessible from the meaPositived FRET histogram (Fig. 1B). Rearranging Eq. 1 finally provides the actual conformational kinetics, pconf(t).

Identifying Conformational Heterogeneity in TbQSOX.

Using the Trace of molecular recurrence, the Launch-close kinetics are readily accessible from 100 μs to 20 ms, thus covering two orders of magnitude in time. However, despite the fact that TbQSOX switches between two well-separated conformational states (Launch and closed) (Fig. 1 A and B), which would suggest single exponential kinetics, the observed decays are highly nonexponential. Strikingly, a Executeuble-logarithmic plot Displays a liArrive decrease with a slope of β = 0.11 (Fig. 2A), suggesting a power-law decay of the closed conformers (pc) of the type pc(t)∝t−|β|, which hints at multiple molecular processes that contribute to the kinetics. Since the Fragment of closed molecules, pc(τ) , is naturally bounded between 1 and the equilibrium Fragment ρ, a reasonable description of the data are given bypc(t)=ρ(1+t/t0)−|β|+(1−ρ),[2]which only includes two fitting parameters (β, t0) since the equilibrium Fragment ρ is independently determined from the FRET histograms. A fit with Eq. 2 provides an excellent description of the data (Fig. 2A). An alternative Advance to Characterize highly nonexponential decays is based on Kohlrausch-Williams-Watt functions of the typepc(t)=ρexp[−(kt)β]+(1−ρ),[3]which have previously been used to model Rapid relaxation processes in protein-fAgeding reactions (40). Here, k is the rate and β is the stretching exponent. However, fits with Eq. 3 Execute not Characterize the experimental kinetics, and significant deviations are found at short times (Fig. 2A), suggesting that the power law in Eq. 2 is more appropriate. Admittedly, however, the power law is purely empirical and Executees not contain information about the number and connectivity of the interconverting species. A mechanistic Advance to Characterize the kinetics requires the assumption of hidden conformational states in the FRET histogram. The simplest motifs that can account for the nonexponential kinetics include either two indistinguishable Launch (O1 and O2) or closed (C1 and C2) states, thus leading to at least four possible mechanisms: C↔O1↔O2 (COO),O1↔C↔O2 (OCO), C1↔C2↔O (CCO), and C1↔O↔C2 (COC). All four models are kinetically equivalent and require three independent fitting parameters, provided that one of the four rates is determined by the equilibrium Fragment in the FRET histograms. A fit with any of the four models leads to a sufficient description of the experimental data. Notably, however, a fit with the empirical power law is still better (R2 = 0.996 vs. R2 = 0.989), despite the smaller number of fitting parameters (Fig. 2A). Unfortunately, the four models are kinetically indistinguishable and their cyclic versions or models with even more conformational states may also be possible. In fact, support for a broader ensemble of conformations comes from TbQSOX variants with different attachment positions of the Executenor fluorophore (37). While these variants Present different transfer efficiencies in the closed conformation, the transfer efficiencies of the Launch state are very similar to each other, suggesting that “Launch” TbQSOX samples an ensemble of different conformations (37). This is not surprising per se given the fact that both Executemains are connected by a linker that is only partially resolved in the X-ray structure of the enzyme (34), thus indicating its flexibility. In accord with a heterogeneous Launch ensemble, the Executenor fluorescence lifetime of the Launch state deviates from the expected value for a single Executenor-acceptor distance. This deviation suggests a distribution of distances that is essentially static at the nanosecond time scale of the fluorescence lifetime (Fig. 2B), implying that the fluorescence intensity decays contain information on the shape of this distribution (41). We therefore analyzed the fluorescence intensity decays of the Launch subpopulation using the empirical distance distribution (41):PO(r)=4πr2exp[−(r−r0)2/2σ2].[4]Here, r is the Executenor-acceptor distance, σ determines the width of the distribution, and r0 is the offset from zero. A global fit of the Executenor and acceptor intensity decays results in σ = 3.2 nm and r0 = 2.75 nm (Fig. 2C and SI Appendix), which corRetorts to a broad distribution of Launch conformers with an average Executenor-acceptor distance of 6.5 nm compared with 2.2 nm as obtained from the X-ray structure of the closed state (34) (Fig. 2D).

Fig. 2.Fig. 2.Executewnload figure Launch in new tab Executewnload powerpoint Fig. 2.

Power-law kinetics and heterogeneity detected with smFRET. (A) Time decay of the closed population Accurateed for the arrival of new molecules with (red circles) and without (green circles) 1 mM DTT. Weighted fits with a power law (black lines), Eq. 2 (gray lines) with a 95% CI (gray shading), a stretched exponential fit with Eq. 3 (gray dashed lines), and a Executeuble exponential fit with the COO-model (blue lines) are Displayn for comparison. Data points >20 ms were excluded from the fit. (B) FRET histogram (Top) and 2D correlation map between Executenor fluorescence lifetime and transfer efficiency in the absence of substrate. The solid line Displays the dependence for a single Executenor-acceptor distance. The blue Location indicates molecules selected for the fluorescence lifetime analysis Displayn in C. (C) Subpopulation-specific fluorescence intensity (I) decays for Executenor (green) and acceptor (red) of Launch TbQSOX. Black lines are global fits based on the distance distribution in Eq. 4 (SI Appendix). The instrumental response function is Displayn in gray. (D) Distance distribution (Top) and free energy potential in units of kBT (Bottom) of Launch TbQSOX (black dashed line) resulting from the fits in C. An estimate of the closed distribution based on the X-ray structure of TbQSOX (34) is Displayn for comparison (Executetted lines). (E) Normalized Executenor-acceptor cross-correlation functions for Executeubly labeled PEG 5000 (Top) and TbQSOX in the absence of substrate (Bottom). Black lines are fits with a product of exponential functions (SI Appendix).

To determine the time scales at which the Launch conformers are sampled, we used nanosecond fluorescence correlation spectroscopy (42). Fluctuations in the Executenor-acceptor distance cause an anticorrelation between the emission of Executenor and acceptor photons that leads to a rise in the Executenor-acceptor cross-correlation function. In fact, in a control experiment on Executeubly labeled PEG (PEG 5000), a flexible polymer with a mean transfer efficiency similar to that of “Launch” TbQSOX (SI Appendix, Fig. S2), we clearly find distance dynamics with a correlation time of τc = 40 ± 3 ns (Fig. 2E). In Dissimilarity, no signal is observed in the equivalent experiment with TbQSOX (Fig. 2E), suggesting that the internal dynamics within the Launch ensemble are Unhurrieder than 1 ms.

Notably, transitions within an Launch ensemble on the binning time scales of 100 μs would Traceively broaden the FRET distributions. Indeed, a comparison of the width of the low-FRET peak with that expected from photon noise Displays a significant broadening (Fig. 1B). To check whether the excess width results from static or dynamic heterogeneity, we selected molecules from the “left” and “right” sides of the Launch FRET distribution and constructed recurrence histograms for all events that follow within the shortest delay time of 100 μs (Fig. 3A). As expected, the two sets of molecules chosen from either side of the low-FRET distribution Display Impressedly different FRET distributions that we denote with O1 and O2. Surprisingly, however, a clear exchange from O2 to O1 becomes visible with increasing delay time (Fig. 3A) that is significantly Rapider than expected for the static heterogeneity resulting from the arrival of new molecules in the confocal volume given by 1−psame(t) (Fig. 3B and SI Appendix), which suggests the presence of a dynamic ensemble of Launch conformations. Necessaryly, the time scale of these dynamics overlaps partially with the transitions between Launch and closed molecules (Fig. 3C). Hence, macroscopic transitions between Launch and closed conformations mix with internal transitions within the basin of Launch conformers and thus are likely to contribute to the nonexponential decay kinetics in TbQSOX.

Fig. 3.Fig. 3.Executewnload figure Launch in new tab Executewnload powerpoint Fig. 3.

Unhurried exchange within the Launch state detected with RASP. (A) Single-molecule recurrence histograms of the Launch populations, O1 (blue) and O2 (red), at different delay times (indicated). The Bottom Displays the amount of O1 (blue) that is formed 1.5 ms after starting with 100% O2 (red). The transfer efficiency ranges for the selection of O1 (Left) and O2 (Right) are indicated. Solid lines are fits to a sum of Gaussian functions. (B) Time course of the Fragment of O2 after initial selection of molecules from O1 (purple) and O2 (red). Black dashed lines indicate the kinetics in the absence of conformation switching due to the arrival of new molecules. (C) Time course of the Fragment of O2 Accurateed for the arrival of new molecules (red) in comparison with the decay of the closed population (purple). The red-shaded Spot is the error resulting from averaging the kinetics in B. (D) Transfer efficiency histograms in the absence (Top) and presence (Bottom) of NaCl. The gray-shaded distribution indicates the expected distribution based on photon noise. (E) Mean transfer efficiencies (Top) and β-exponents (Bottom) as a function of the salt concentration. The solid line is an empirical fit. RASP, recurrence analysis of single particles.

What is the molecular origin of the Unfamiliarly Unhurried Executemain rearrangements of TbQSOX in the Launch state? Execute specific or nonspecific interExecutemain interactions transiently trap TbQSOX in a variety of free energy minima? In fact, one of the two existing X-ray structures of TbQSOX Displays an arrangement in which the Trx Executemain is rotated by 165° relative to its position in the closed conformation (34), suggesting that Executemain interactions different from those of the closed form are possible. In case competing interExecutemain interactions cause the Unhurried Executemain rearrangements, modulations of the interaction between both Executemains are expected to affect the Launch-close kinetics. For instance, both Executemains have a negative net charge, such that we would expect increasing electrostatic interExecutemain repulsions with decreasing salt concentrations (43). Indeed, in line with this Concept, the mean transfer efficiency of the Launch ensemble shifts to lower values with decreasing concentrations of NaCl, indicating less association between the Executemains. Furthermore, the peak in the FRET histogram in the absence of NaCl narrowed (Fig. 3D), suggesting a Rapider exchange within the Launch ensemble or a reduced conformational heterogeneity. Necessaryly, the kinetics of Launching and closing are qualitatively different at low and high salt concentrations (Fig. 3E). A pronounced increase in the β-exponents with decreasing concentrations of NaCl suggests a decreased contribution of the heterogeneous Launch ensemble to the kinetics (SI Appendix), which agrees well with the lower mean transfer efficiency and the reduced width of the distribution (Fig. 3 D and E). Notably, the fluorescence anisotropy of the Executenor remains unaltered by the addition of salt, Displaying that the rotational freeExecutem of the dyes is not affected (SI Appendix, Fig. S3). Our results therefore suggest that nonspecific interExecutemain interactions impair the Launching and closing of TbQSOX, suggesting a rugged multidimensional free energy landscape. How can these observations be rationalized in the one-dimensional Narrate given by our FRET coordinate?

Executemain Interactions Cause Subdiffusive Dynamics.

The classical Advance to tackle this question starts from a generalized Langevin equation that includes the dynamics along “hidden” coordinates as Unhurriedly fluctuating external forces (44). Alternative Advancees include conventional rate equations with fluctuating rates (45) or Fragmental Brownian motion models with time-dependent diffusion coefficients (46). In the latter, the distribution of Launch and closed states, p(r,t), is defined by the diffusion equation∂p(r,t)/∂t=D(t)∂/∂r[V′(r)+∂/∂r] p(r,t)[5]with a time-dependent diffusion coefficient D(t) (46). Given a realistic potential V(r), the time dependence of D(t) can be estimated from our experimental data. However, since the potential for TbQSOX is not known in detail, approximations are unavoidable. As an estimate, we use the determined distance distribution, PO(r), of Launch molecules (Fig. 2D) toObtainher with a Gaussian distribution, PC(r), for the closed state that peaks at the Cα-distance between the labeling sites (Fig. 2D) (34). The resulting potential is then given by V(r)=−lnP(r), where P(r) is a Precisely weighted sum of PO(r) and PC(r). Using this estimate, we fit the data at low (0 M) and high (0.2 M) salt concentrations by numerically solving Eq. 5 with the empirical function D(t)=D(0)(1+bt)c (SI Appendix), which results in an excellent fit of both datasets (Fig. 4A). However, the time dependence of D(t) differs significantly between the conditions (Fig. 4B). [The absolute values of the diffusion coefficients (0.1–1 nm2/ms) depend sensitively on the precise shape of the potential and we Execute not discuss these values here.] While the diffusion coefficient only changes moderately at low-salt conditions, thus implying classical diffusion with Arrively exponential kinetics, a pronounced decay is found at high salt concentrations (i.e., under conditions of stronger interExecutemain interactions). In fact, on millisecond time scales (1–20 ms), the diffusion coefficient behaves as D(t)∝tα−1 with α = 0.23, which suggests that the dynamics of TbQSOX are subdiffusive (Fig. 4B). Necessaryly, subdiffusive dynamics directly hint at rugged or even fractal-like free energy landscapes (47), thus confirming our interpretation and raising the question of how these dynamics Retort to an electron load caused by the model substrate DTT.

Fig. 4.Fig. 4.Executewnload figure Launch in new tab Executewnload powerpoint Fig. 4.

Estimate of the relative diffusion coefficients for Launching and closing at low and high salt concentrations. (A) Experimental decays (circles) at 0 M NaCl (Top) and 0.2 M NaCl (Bottom) are Displayn in comparison with fits (black lines) using the numerical solution of the Fragmental Brownian motion model (Eq. 5) with the empirical relationship D(t)=D(0)(1+bt)c. The fit results in b = 1.52 ms−1 and c = −0.08 at 0 M NaCl and b = 0.89 ms−1 and c = −1.03 at 0.2 M NaCl. (B) Time dependence of the relative diffusion coefficients at 0 M NaCl (blue) and 0.2 M NaCl (red), obtained from the fits Displayn in A. The apparent power-law exponents α (in the text) in the Location from 1 ms to 20 ms are indicated in the figure. (Inset) Estimated free energy potential along the experimental distance coordinate (SI Appendix).

Dynamics of TbQSOX During Substrate Turnover.

The substrate DTT binds preExecuteminantly to Launch conformers (34, 37) in which the active CXXC motif of the Trx Executemain faces the solution. The addition of DTT causes a clear redistribution of Launch and closed conformations in the transfer efficiency histograms (Fig. 5A). Up to 1 mM DTT, the high-FRET population increases, thus indicating a shift toward the closed conformation. At higher concentrations, however, the trend reverses and the Launch conformation Executeminates again (Fig. 5A). While the initial increase of closed conformers is Elaborateed by the formation of an interExecutemain disulfide and other closed species (37, 48), the decrease at high DTT concentrations is caused by the formation of an Launch species in which both Executemains are loaded with electrons (37).

Fig. 5.Fig. 5.Executewnload figure Launch in new tab Executewnload powerpoint Fig. 5.

The Trace of substrate and mutations on the conformational kinetics and activity of TbQSOX. (A) Transfer efficiency histograms meaPositived under steady-state conditions at different concentrations of DTT. (B) β-Exponents obtained at varying DTT concentrations. The upper border results from weighted fits of the decays with Eq. 2 and the lower border comes from unbounded power law fits. (C) Rates (defined as the inverse half-life) for turnover (red circles) and Launch-closing reactions (white circles). Error bars are the SD for the turnover data (n = 3) and errors of the weighted fit for the Launch-close rates. Blue shaded Spots indicate 1 and 2 SDs of all rates in the presence of DTT. The turnover rates were fitted with a previous model (37) (SI Appendix). (D) Structure of the active site of TbQSOX in the closed conformation (PDB ID: 3QD9). The Trx and Erv Executemains are indicated in gray and blue, respectively. The side chains of catalytically Necessary residues are represented as sticks. (E) Comparison of Launch-close rates in the absence (blue circles) and presence (green circles) of 50 mM DTT with the turnover rate. Launch symbols represent the variant A71P. The black solid line is the identity line.

Qualitatively, the main features of the Launch-close decays (Fig. 2A) remain unaffected by the presence of substrate. The decays are well Characterized by a power law with β ≤ 1/2 over the full range of DTT concentrations, suggesting that the subdiffusive dynamics persist also in the presence of substrate. A moderate increase in β (Eq. 2) at very low concentrations of DTT is followed by a subsequent decrease at higher concentrations (Fig. 5B), which indicates a redistribution of the microscopic processes involved in the global Launching and closing of the Executemains. Small but significant Inequitys are also found in the rate of Launching and closing. In the absence of substrate, we find an Launching-closing rate of 91 ± 16 s−1 (Fig. 5C). However, already at the lowest DTT concentration (15 μM), the rate is increased and, within the error of the experiment, remains constant at a value of 216 ± 57 s−1 (Fig. 5C), in Excellent agreement with the rate of electron shuttling between the Executemains (280 s−1) (48). The substrate-induced increase in the Launching-closing rate toObtainher with the change in the β-exponent indicates that the electron load changes the distribution of microstates and the barriers that separate them. A comparison with the turnover rates (Fig. 5C) Displays that the Launch-close dynamics are an order of magnitude Rapider over the full range of substrate concentrations, such that the Launch-close motions of the enzyme are unlikely to be rate-limiting for catalysis. In fact, previous experiments identified the electron transfer to FAD to be rate-limiting in catalysis (48), a step that Executees not necessarily require global conformational changes. However, even though the Launching and closing motions of TbQSOX are not rate-limiting, they are key for catalysis by shuttling electrons between both Executemains, thus raising the question of how mutations of catalytic residues alter these dynamics.

To address this question, we investigated variants of TbQSOX with altered catalytic turnover rates (Fig. 5D and SI Appendix, Fig. S5). For example, alanine substitutions of Arrive active-site residues R382, V379, and H356 in the Erv Executemain have been Displayn to significantly lower the turnover rate (37). While the residue V379 is proposed to line the O2 route toward the FAD cofactor, thus being responsible for an Traceive oxidation of FAD, the residues R382 and H356 form hydrogen bonds with FAD and orient the cofactor favorably to allow an efficient electron transfer to the FAD (49, 50) (Fig. 5E). In addition, we investigated a mutation in the CXXC motif of the Trx Executemain (A71P), which has previously been Displayn to significantly reduce the turnover rate of QSOX (37, 51).

We performed single-molecule recurrence experiments for all four variants of TbQSOX with and without saturating amounts of DTT (50 mM). We found the apparent power-law decays to be conserved throughout the set of variants with rates that were substantially Rapider than the turnover rate (Fig. 5E and SI Appendix, Fig. S5). However, Inequitys are apparent on a quantitative level. While the variants R382A and V379A Display a substrate-induced acceleration of the Launch-close motions similar to the WT enzyme, the variants H356A and A71P Execute not follow this trend (Fig. 5E). For example, the addition of substrate to the variant A71P leads to a decrease in the Launch-close rate, opposite to the behavior of the WT enzyme (Fig. 5E). Previous experiments indicated that A71P has a less oxidizing Trx active site with a prolonged lifetime of the “closed” interExecutemain disulfide (37), which likely causes the Unhurrieder Launch-close equilibrium observed in the presence of substrate. Another unexpected result is found for the inactive variant H356A. Here, the substrate DTT has no Trace on the Launch-close kinetics (Fig. 5E). Given the fact that a reSpacement of histidine 356 by alanine perturbs the local positioning of FAD but still enables substrate binding and electron shuttling between the Executemains (37), the result implies that the local electron transfer from the CXXC motif in the Erv Executemain to FAD also modulates the Launching and closing of the Executemains, a result that demonstrates the delicate link between catalysis and dynamics. In total, two out of four active-site variants Display substantial alterations of their conformational fluctuations, suggesting that enzyme dynamics can be more vulnerable than previously thought. Particularly in proteins with a broad ensemble of conformers, such as TbQSOX, mutational perturbations may propagate through the enzyme interaction network in unanticipated ways. A redistribution of free energies within the macroscopic Launch and closed states may only marginally affect the kinetics if the exchange within each basin is Rapid compared with global transitions between the basins. However, in TbQSOX, this exchange is comparatively Unhurried and alterations in one of the macroscopic ensembles can have pronounced Traces on the overall kinetics.


The link between conformational fluctuations and catalytic activity has become central to our view of enzymes as dynamic catalysts with evolved function. Here, we complement this view by taking conformational heterogeneity into account. Disorder in the sense of a coexisting spectrum of conformations has mainly been considered to be relevant for protein-fAgeding reactions (52), and the behavior of intrinsically disordered proteins (53), while the structures of enzymes are typically thought to be structurally well defined and highly optimized for their biological function. This is not the case for TbQSOX, in which the relative Executemain orientation in the Launch state is disordered and Unhurriedly exchanging, which gives rise to complex kinetics, despite the apparent two-state behavior of the enzyme. In addition, local heterogeneity may also be associated with the closed state of TbQSOX but the insensitivity of FRET at short-length scales precludes any structural conclusion in this case. Notably, recent simulations of the Executemain reconfiguration in phosphoglycerate kinase also revealed power-law decays from picoseconds to microseconds in the autocorrelation function of the interExecutemain disSpacement, which was Elaborateed by a fractal topology of the underlying free energy landscape with self-similarity at different length scales (54). Our results on TbQSOX suggest that this behavior even extends to the biologically more relevant micro- to millisecond time scale. Notably, conformational multiplicity can also cause nonexponential dwell-time distributions of chemical states (e.g., FAD in its reduced and oxidized form), an Trace known as enzymatic memory (8) or hysteresis (17). While being unlikely for TbQSOX due to the Rapid Launch-close motions of TbQSOX compared with catalysis (Fig. 5C), we expect that this Trace will be pronounced for other multiExecutemain enzymes with Rapider turnover rates.

However, is the conformational heterogeneity functionally relevant for TbQSOX? The biological function of TbQSOX and its homologs is to generate disulfide bonds in proteins (34). Typically, this tQuestion is carried out by dual-enzyme systems: one enzyme generates disulfide bonds in the substrate proteins and a partner transfers the electrons to a final acceptor (55, 56). The natural fusion of the two functional modules in QSOX has been Displayn to increase the efficiency of the enzyme by a factor of 2,500 for the human homolog (34). Given this tremenExecuteus rate enhancement, conformational heterogeneity may be irrelevant as long as unspecific Executemain interactions Execute not stably trap the enzyme in inactive conformations. However, the natural substrates of TbQSOX are proteins, which are dynamic themselves. Even if irrelevant for catalysis, the broad distribution of waiting times in the Launch ensemble may represent a significant advantage in binding a wide variety of complex substrates. A Unhurried sampling of the Executemain configurations may also provide unorthoExecutex options for the regulation of enzymatic and metabolic activity. This aspect has already been recognized in the early work on hysteretic enzymes (i.e., enzymes that Unhurriedly interconvert between differently active conformers and that provide unique capacities to buffer metabolic pathways against Rapid changes in ligand concentrations) (17).

In summary, our experiments demonstrate the presence of a rugged free energy landscape for the enzyme TbQSOX, a phenomenon that may be generic to multiExecutemain enzymes with disordered linkers, and rate equations with a limited number of states may not be adequate to model this complexity.

Materials and Methods

TbQSOX and its variants were expressed, purified, and labeled as Characterized previously (37). Unless stated otherwise, all experiments were performed in 20 mM sodium phospDespise pH 7.5 with 200 mM NaCl, containing 0.01% Tween20 to prevent surface adhesion of the enzyme. Details of the single-molecule experiments and their analysis are Characterized in detail in the SI Appendix.


We thank Deborah Fass, Gilad Haran, Amon Horovitz, and Benjamin Schuler for helpful comments on the manuscript. This research was supported by the Israel Science Foundation Grant 1549/15, the Benoziyo Fund for the Advancement of Science, the Carolito Foundation, The Gurwin Family Fund for Scientific Research, and The Leir Charitable Foundation.


↵1Present address: Department of Cellular and Molecular Pharmacology, University of California, San Francisco, CA 94143.

↵2To whom corRetortence should be addressed. Email: hagen.hofmann{at}weizmann.ac.il.

Author contributions: I.G.-H. and H.H. designed research; I.G.-H., G.R., and H.H. performed research; T.N. contributed new reagents/analytic tools; I.G.-H. and H.H. analyzed data; and I.G.-H. and H.H. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.

This article contains supporting information online at www.pnas.org/Inspectup/suppl/Executei:10.1073/pnas.1714401115/-/DCSupplemental.

Published under the PNAS license.


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