Identification of an on-pathway intermediate illuminates the kinetic competition between protein folding and misfolding

Significance

Protein folding occurs in a kinetic competition with misfolding. Although protein misfolding is the basis for many devastating human diseases, we know little about this competition. Here, we identify an on-pathway folding intermediate for P.69T pertactin, the largest protein known to refold reversibly from denaturant, that lies at the intersection between folding to the native structure and misfolding. The conformation of this intermediate reveals that the C-to-N-terminal vectorial folding observed during P.69T translocation across the bacterial outer membrane is preserved in vitro. These results show how folding information encoded within the amino acid sequence and the spatiotemporal constraints imposed by the cellular environment work in concert to support folding and suppress misfolding.

Abstract

Our current understanding of protein folding is based predominantly on studies of small (<150 aa) proteins that refold reversibly from a chemically denatured state. However, as protein length increases so does the competition between off-pathway misfolding and on-pathway folding, creating a more complex energy landscape ("folding funnel"). Little is known about how intermediates populated during the folding of larger proteins affect navigation of this more complex landscape. Previously, we reported extremely slow folding rates for the 539 aa β-helical passenger domain of pertactin (P.69T), including conditions that favor the formation of a kinetically trapped, off-pathway partially folded state (PFS). Existence of an on-pathway intermediate for P.69T folding was speculated but its characterization remained elusive. In this work, we exploited the extremely slow kinetics of PFS unfolding to develop a double-jump “denaturant challenge” assay. With this assay, we identified a transient unfolding intermediate, PFS*, that adopts a similar structure to PFS, including C-terminal folded structure and a disordered N terminus, yet unfolds much more quickly than PFS. Additional experiments revealed that PFS* also functions as an on-pathway intermediate for P.69T folding. Collectively, these results support a C-to-N-terminal model for P.69T folding, with folding initiated in the C-terminus with the rate-limiting formation of the transient on-pathway PFS* intermediate, which sits at the junction of the kinetic competition between folding and misfolding. Notably, processive folding from C-to-N terminus also occurs during C-to-N-terminal translocation of P.69T across the bacterial outer membrane. These results illuminate the crucial role of kinetics when navigating a complex energy landscape for protein folding.

Proper folding is required for protein function, yet it appears that every protein can alternatively misfold and aggregate, rather than form its native structure (1, 2). While stably folded proteins typically adopt only one native structure [or in some cases, two (3)], the total number of possible conformations that a polypeptide chain can adopt increases exponentially with chain length (4, 5). This higher ratio of nonnative to native conformations increases the likelihood that larger proteins will populate a misfolded state (6). Some signatures of the selective pressure to avoid stable, misfolded states are detectable in protein sequences, including selection against hydrophobic residues in large proteins (7), avoidance of long stretches of hydrophobic residues (8, 9), and, in multidomain proteins, low sequence conservation between consecutive domains of similar structure (10). Although it has been shown that larger, multidomain proteins can fold cotranslationally, concomitantly with vectorial appearance of the nascent chain (11, 12), little is known regarding the folding mechanisms of larger proteins, including the competing processes that determine whether a polypeptide chain will fold to its native state or instead lead to a misfolded and/or aggregated state. This knowledge gap exists due to both the more complicated folding mechanisms of larger proteins (13) and the technical challenges of structurally characterizing subtle differences between the short-lived intermediate states that lead to folding versus misfolding.

Although less prone to misfolding in general, studies of small proteins have identified strategies that may be relevant for the successful folding of larger proteins with more complex energy landscapes. For example, even the relatively simple folding mechanisms of small proteins can include nonnative interactions: Im9, an immunity protein from colicin-producing bacteria, folds by a two-state mechanism, yet its homolog, Im7, folds by a three-state mechanism with a nonnative yet on-pathway folding intermediate (14). The difference of a few amino acid residues between Im9 and Im7 is sufficient to alter the folding mechanism without affecting the thermodynamic stability of native state, via the stabilization of an intermediate conformation with nonnative, long-range contacts (15). Similarly, a recent study of influenza nucleoprotein discovered a single point mutation that can alter the folding pathway, leading to the population of an aggregation-prone intermediate (16). The energy landscapes of small proteins can also include unusually large energy barriers, leading to kinetic traps. A particularly extreme example of kinetic trapping is kinetic stability, where the folded state of a protein is less stable than its folded structure but remains folded by being trapped behind a high energy barrier and unfolds at a negligibly slow rate. A classic example of kinetic stability is α-lytic protease, which possesses a sufficiently high energy barrier for unfolding as to enable a native state lifetime of >1 y, despite having a native structure that is less stable than its unfolded state (17). “Bridge” interaction formed between the N- and C-terminal regions of α-lytic protease contributes to the unusually high energy of its transition state (18). Notably, another kinetically stable protease, SbtE, has a homolog, ISP1, that is instead thermodynamically stable, illustrating two distinct strategies used by Nature to maintain the native, functional protease structure (19). Currently, it remains unclear how nonnative interactions and/or kinetic trapped states constrain the folding of large proteins to favor the formation of productive (on-pathway) intermediate and/or avoid unproductive misfolded (off-pathway) conformations, and in particular what mechanisms enable large proteins to avoid kinetic traps that lead to misfolding.

Previously, we determined that the passenger domain of Bordetella pertussis pertactin (P.69T) can refold reversibly upon dilution from denaturant in vitro (20), despite its unusually large size (539 aa). Native P.69T consists of a single structural domain, a 16-rung right-handed parallel β-helix (21, 22). We previously showed that despite a continuous hydrogen bond network throughout the β-helix, native P.69T is composed of two segments with distinct stabilities and folding behaviors (Fig. 1A). For clarity, we refer to the N- and C-terminal segments within full-length P.69T as Nt and Ct, respectively, and to the isolated N- and C-terminal fragments as PNt and PCt, respectively. The N terminus (Nt; residues 1 to 334) of P.69T is significantly less stable than its C-terminus (Ct; residues 335 to 539), which enables P.69T to adopt a partially folded state (PFS) at equilibrium in intermediate concentrations of denaturant (e.g., 1 to 2 M guanidine hydrochloride, GdmCl) (20). However, although populated at equilibrium, PFS is not populated on the dominant kinetic pathway between U and N, as the rates for both folding of PFS→N and unfolding of PFS→U are orders of magnitude slower than U→N folding and N→U unfolding, respectively (23). Hence, PFS represents a misfolded state: a kinetically trapped, off-pathway conformation of P.69T (Fig. 1A).

Fig. 1.

PCt, the isolated C-terminus of P.69T, closely resembles P.69T-Ct. (A) Schematic of P.69T folding and misfolding. PFS is off-pathway and has a much slower folding rate than full unfolded P.69T (U) and a much slower unfolding rate than native P.69T (N). An on-pathway intermediate (indicated by “?”) was previously predicted (20), but not detected. The structure of P.69T (PDB ID: 1dab) (21) is shown in blue (Nt; residues 1 to 333) and red (Ct; residues 334 to 539). (B) Far-ultraviolet (UV) circular dichroism (CD) spectra of P.69T (green), PCt (red), and PNt (blue). (C) Thermal denaturation of P.69T (green) and PCt (red) monitored by far-UV CD spectroscopy. Data were converted to fraction of the native state CD signal at 218 nm and fit to a sigmoidal model (Materials & Methods). Unfolding transitions for Nt and Ct segments are highlighted by blue and red shading, respectively.

In a past study, we added an exogenous fluorophore to either Nt or Ct to compare the folding rates for each segment of P.69T (23). Those experiments returned the same folding rates for both segments. However, we have since discovered that the isolated N terminus (PNt) is disordered (9, 24–26), suggesting that Nt and Ct are not equal partners in P.69T folding. In addition, an unresolved conundrum surrounding P.69T folding is the incompatibility between measured in vitro folding rates and relevant cellular timescales. Specifically, the fastest rate constant measured for P.69T folding in vitro [k = 5 × 10⁻⁴ s⁻¹; τ = 30 min (23)] is significantly slower than the time needed for bacterial replication (~20 min), which we use as a conservative upper bound for the in vivo folding rate (27). Notably, P.69T folding in vitro is much slower than the folding of many other proteins, including other large, processively wound (“solenoid”) proteins; e.g., the ankyrin domain of Notch (28, 29) and other proteins with β-helical structure (30, 31). For these reasons, we have long suspected that pertactin refolding in vitro may be slowed by the formation of transient off-pathway folding intermediates, which the cellular environment may help avoid, thereby accelerating the P.69T folding rate.

Here, we characterize the folding behavior of PCt, the isolated C-terminal segment of the pertactin passenger, and capitalize upon these results to identify an on-pathway intermediate populated during both the folding and unfolding of P.69T. This intermediate, which we call PFS*, is spectroscopically indistinguishable from PFS but thermodynamically less stable. Both PFS and PFS* consist of an unfolded, disordered Nt segment and a folded Ct. However, PFS* folds an order of magnitude faster to the native structure than to PFS, favoring the folding outcome in the kinetic competition between folding and misfolding. Strikingly, the in vitro P.69T folding pathway retains the C- to N-terminal folding mechanism used by the pertactin passenger domain upon its secretion across the outer membrane (OM) of B. pertussis (23). Collectively, these results advance our understanding of the interplay between intrinsic folding properties and the potential contributions of the cellular environment to avoiding misfolded, kinetically trapped states, particularly for large proteins with complex energy landscapes.

Results

P.69T C-Terminus (PCt) Is Stably Folded, in Contrast to PNt.

Previously, we showed that PNt adopts a highly expanded, disordered conformation (9, 24–26), suggesting that in P.69T the stability of Nt is dependent on Ct. Based solely on this finding, it is tempting to speculate that P.69T folds via a simple two-step model, with an on-pathway intermediate with a disordered Nt and a natively folded Ct, with Ct providing a template upon which Nt folds. However, while our past work identified PFS, which has a stably folded Ct that is populated at equilibrium at intermediate concentrations of denaturant (1 to 2 M GdmCl), the rates of PFS→N folding and PFS→U unfolding are orders of magnitude slower than complete refolding (U→N) or unfolding (N→U) of native P.69T (23), demonstrating that PFS is off-pathway. One resolution of this apparent paradox would be if Ct adopts two distinct (albeit structurally similar) intermediate states, one that is on-pathway and another (PFS) that is off-pathway, with different positions on the energy landscape for P.69T folding (Fig. 1A). A crucial hypothesis raised by this model is the existence of a previously undetected on-pathway intermediate with a Nt conformation that can rapidly fold/unfold, rather than a PFS-like slow folding/unfolding state.

As an initial approach to testing the hypothesis above, we first tested whether Ct is stably folded, independent of Nt. We cloned, expressed, and purified PCt (Materials & Methods) and found that, in stark contrast to the disorder of PNt, PCt adopts a stable, β-sheet-rich structure as measured by far-UV circular dichroism (CD) spectroscopy (Fig. 1B). Moreover, thermal denaturation of PCt resulted in a cooperative two-state transition with a melting temperature (T_m) that closely matches the T_m for unfolding the Ct segment of P.69T (Fig. 1C; T_m = 86.8 °C and 85.5 °C, respectively). These results demonstrate that, in direct contrast to the highly expanded, disordered structure of PNt (9, 24–26), PCt is stably folded.

As an orthogonal approach to assess the foldability of PCt, we turned to protease digestion. We have previously shown that native P.69T is largely resistant to degradation by proteinase K, except for one cleavage site within a loop that yields two fragments (apparent molecular weights of 27 and 28 kDa), which together constitute full-length P.69T (20). In contrast, under the same conditions PFS is rapidly degraded to one shorter fragment of 21 kDa, consisting of Ct, demonstrating that in the PFS Ct is stably folded and resistant to proteinase K, whereas Nt is unfolded and rapidly degraded (20). When PCt was subjected to proteinase K digestion under the same conditions used to digest native P.69T and PFS, PCt showed no evidence of degradation (SI Appendix, Fig. S1), consistent with the conclusion that PCt is stably folded.

PCt Unfolds Much More Slowly than P.69T.

We next tested whether PCt unfolds and refolds reversibly, and if so, whether PCt folds/unfolds rapidly (like native P.69T) or slowly (like PFS). We showed previously that it takes approximately 2 wk for P.69T unfolding/refolding titrations to reach equilibrium at intermediate concentrations of denaturant where PFS is populated (20). PCt folded status was adjusted by addition or dilution of GdmCl and monitored by tryptophan fluorescence emission spectroscopy as a function of time (Fig. 2). PCt refolding was complete after 24 h; however, in stark contrast to native P.69T, it took longer than 6 mo for the PCt unfolding titration to converge with the refolding titration, akin to the time necessary to unfold PFS (23). Although not explored in detail here, the denaturant-dependent PCt unfolding rates observed in Fig. 2B indicate a complex relationship between denaturant concentration and PCt unfolding kinetics. Ultimately, however, a standard two-state equilibrium between PCt folding and unfolding was established, consistent with the thermal denaturation results (Fig. 1C). The midpoint of the PCt unfolding transition (c_m, = 2.03 M) is indistinguishable from the unfolding midpoint for P.69T-Ct (c_m = 1.99 M) (20). The m-values for the PCt and P.69T-Ct equilibrium unfolding transitions are likewise indistinguishable (SI Appendix, Fig. S2), indicating that these folding transitions are similarly cooperative. Together, these results show that PCt adopts a conformation that is thermodynamically comparable to the Ct segment of native P.69T, but with a starkly different kinetic pathway for unfolding, more similar to the slow unfolding of Ct in PFS than the fast unfolding of the Ct region of native P.69T when unfolding from N→U. PCt and PFS both require >1 mo to unfold in 4 M GdmCl, whereas native P.69T unfolds completely in 10 s [Fig. 3 and (23)]. These results demonstrate that, in contrast to native P.69T, both PCt and PFS adopt a kinetically trapped conformation. Related to the paradox introduced above, the much slower unfolding rate of PCt than P.69T excludes the possibility of an on-pathway unfolding intermediate with a PCt-like Ct.

Fig. 2.

The slow approach to equilibrium during folding (A) and unfolding (B) of PCt. The equilibrium midpoint (c_m) for PCt unfolding and refolding is 2.0 M GdmCl, but equilibrium is established extremely slowly. PCt was refolded from 8 M GdmCl (A, open symbols), or unfolded (B, filled symbols) to the indicated final GdmCl concentration, measured as the ratio of tryptophan emission intensities at 335 and 350 nm. Lines represent the fit to single or double sigmoidal models (Materials & Methods).

Fig. 3.

For native P.69T, unfolding of Nt accelerates the unfolding of Ct. (A) Unfolding kinetics of P.69T as a function of GdmCl concentration. Each dataset was fit to either a single- or double-exponential equation (Results and Materials & Methods). Rate constants for unfolding are summarized in SI Appendix, Table S1. (B) Unfolding of native P.69T (green), PFS (purple), and PCt (red) at two GdmCl concentrations (open circles: 2.8 M; filled circles: 7 M), showing that native P.69T unfolds orders of magnitude more rapidly than PFS or PCt.

Unfolding of Nt Accelerates Ct Unfolding.

The extremely slow PCt unfolding rate described above suggested that the presence of Nt and/or its unfolding may lead to a faster unfolding rate for the Ct region within native P.69T. To test this, we first used changes in tryptophan fluorescence emission to measure the denaturant-dependent unfolding rates of Nt and Ct within native P.69T, exploiting the distinct stabilities of Nt and Ct to make these measurements. Previously, we reported overall unfolding rate constants for native P.69T and PFS (23), but the unfolding rates for the individual Nt and Ct segments were not measured. Over a range of [GdmCl] from 1.1 to 2.1 M, the Nt region of native P.69T unfolds, leading to the PFS conformation (Fig. 3A) (20). Nt unfolding kinetics fit well to a single exponential model (Fig. 3A and SI Appendix, Table S1). As expected, as [GdmCl] increased, the rate constant for Nt unfolding increased, eventually occurring entirely within the dead time of our experimental setup (10 s). Nt unfolding corresponded to ~40% of the total fluorescence change upon unfolding, a percentage consistent with the number of tryptophan residues in each segment (Nt = 3/7 Trp residues; Ct = 4/7 Trp residues). Below 2.1 M GdmCl, Ct remained folded. Above 2.3 M GdmCl, both Nt and Ct unfolded. At these higher denaturant concentrations, the unfolding kinetics fit best to a double exponential model (Fig. 3A and SI Appendix, Table S1). The fast phase and slow phase consist of approximately 40 and 60%, respectively, of the total change in fluorescence upon unfolding. The fast phase was completed within the dead time of the experimental setup (10 s), consistent with the Nt unfolding rate constant extrapolated from measurements at lower GdmCl concentrations. The Ct unfolding rate constant also increased with increasing GdmCl concentration, and above 3.5 M GdmCl became too fast to accurately quantify using our experimental setup. These results are consistent with a model where the unfolding rate of Nt is faster than Ct under all conditions tested.

To determine whether the presence of Nt affects Ct unfolding—despite Nt unfolding more rapidly than Ct—we directly compared the rate constants for P.69T and PCt unfolding. Because the rates of these unfolding processes differ by orders of magnitude, it is difficult to compare them directly under identical conditions. Instead, we selected two denaturant concentrations, 2.8 M and 7 M GdmCl, as representative scenarios. As discussed above, in 2.8 M GdmCl native P.69T unfolding is best fit to a double exponential model, with an unfolding rate constant for native P.69T-Ct of 2.61 × 10⁻³ s⁻¹ (Fig. 3B). In contrast, no detectable unfolding of PCt occurred within 1 h at 2.8 M GdmCl (Fig. 3B and SI Appendix, Table S2). In 7 M GdmCl, native P.69T unfolded to U entirely within the dead time (<10 s), whereas PCt unfolding kinetics fit well to a single exponential with k = 2.29 × 10⁻³ s⁻¹ (Fig. 3B and SI Appendix, Table S2). Hence, native P.69T unfolds faster than PCt over a wide range of conditions, indicating that Nt accelerates the unfolding of the Ct segment of native P.69T.

To test whether the conformation of Nt—or just its presence, regardless of conformation—affects Ct unfolding, we compared the N→U unfolding rate constants measured above to the rate constant for PFS unfolding under identical conditions. To form PFS, native P.69T was incubated in 1.5 M GdmCl overnight. Subsequent unfolding of PFS in 2.8 M or 7 M GdmCl confirmed that the PFS unfolding rate constant is indistinguishable from the rate constant for PCt unfolding (Fig. 3B and SI Appendix, Table S2), indicating that the presence of an unfolded Nt (as in PFS) is insufficient to accelerate the unfolding rate of Ct in P.69T. In contrast, unfolding of Nt led to a 100 to 1,000-fold acceleration of Ct unfolding under the conditions tested here.

Identification of PFS*, an On-Pathway Unfolding Intermediate.

A potential model for how Nt unfolding could accelerate Ct unfolding is that Nt unfolding leads to the formation of an unfolding intermediate with a structure that resembles PFS spectroscopically but is not yet kinetically trapped as PFS. To test this hypothesis, we designed a double-jump “denaturant challenge” experiment (Fig. 4A), taking advantage of the extremely slow unfolding rate of the kinetically trapped PFS conformation. Native P.69T was first incubated in 1.5 M GdmCl, which is sufficient to rapidly unfold Nt (Fig. 3A). After 3 min, additional GdmCl was added, to 4.75 M. If the 3 min incubation in 1.5 M GdmCl was sufficient to not only unfold Nt but also form PFS, the subsequent transfer to 4.75 M GdmCl should lead to no observable unfolding to U within a few hours (23). Surprisingly, however, the brief incubation of P.69T in 1.5 M GdmCl led to rapid unfolding to U within the dead time of transfer to 4.75 M GdmCl (Fig. 4B). These results reveal that, upon unfolding of Nt, P.69T initially adopts a denaturant-sensitive, transient conformation that is spectroscopically indistinguishable from PFS, which we term PFS*, prior to forming PFS, which is kinetically trapped. Given the strikingly different kinetic behavior of PFS* and PFS, we performed an additional experiment to test whether PFS* unfolds to the same ensemble of U conformations populated during conventional N→U unfolding. Specifically, we performed a triple jump experiment, first unfolding N in 1.5 M GdmCl for 3 min to populate PFS*, followed by unfolding in 4 M GdmCl for 10 min to populate U, then diluting to 0.5 M GdmCl to observe refolding of this unfolded state. The refolding kinetics from this final jump from 4 to 0.5 M GdmCl were indistinguishable from the folding kinetics from a conventional U→N refolding experiment (SI Appendix, Fig. S3), indicating that PFS* unfolds to the same U ensemble as populated during more conventional unfolding experiments. Collectively, these results demonstrate that population of PFS* leads to rapid unfolding, supporting a model where PFS* serves as an on-pathway intermediate for unfolding.

Fig. 4.

Identification of PFS*, an on-pathway unfolding intermediate. (A) Kinetics of PFS formation (purple line) in the denaturant challenge experiment, monitored by tryptophan fluorescence emission spectroscopy. Incubating native P.69T in 1.5 M GdmCl for 3 min led to unfolding of Nt within 300 s (blue line; see also panel B and Fig. 3A). At various time points after the initiation of unfolding (indicated by orange arrows), the impact of the addition of 4.75 M GdmCl on P.69T unfolding was evaluated. The fraction of P.69T molecules in the PFS conformation, which unfolds extremely slowly in 4.75 M GdmCl (orange data points), increased as a function of time and fit to a single exponential model (purple line). The orange lines between the orange data points were added to guide the eye, to illustrate that even long after the jump to 4.75 M GdmCl there is no additional change to the fluorescence emission ratio. The hatched region between the blue and purple curves represents the fraction of P.69T molecules in an alternative conformation, PFS*, that resembles PFS but is more susceptible to unfolding. The population of molecules in the PFS* conformation decreased as a function of incubation time in 1.5 M GdmCl. Error bars represent the SD of three independent experiments; in several instances, the error bar is smaller than the height of the data point. (B) Examples of denaturant challenge experiments at 3 min and 63 min after the beginning of Nt unfolding. (C) PFS* unfolds in 2.8 M GdmCl at a rate similar to native P.69T, but much faster than PFS.

To track the fate of PFS*—specifically, its conversion to the kinetically trapped PFS—we incubated native P.69T in 1.5 M GdmCl for different amounts of time prior to the 4.75 M GdmCl denaturant challenge described above. We found that P.69T started to exhibit resistance to unfolding in 4.75 M GdmCl as soon as 8 min after addition of 1.5 M GdmCl (Fig. 4A). The fraction of P.69T resistant to rapid unfolding in 4.75 M GdmCl increased as a function of time and fit well to a single exponential model with a rate constant of 7.1 × 10⁻⁴ ± 6 × 10⁻⁵ s⁻¹. This result indicates that conversion of PFS* to PFS is spontaneous in 1.5 M GdmCl, albeit extremely slow, and represents the rate limiting step of converting native P.69T to PFS, which is kinetically trapped.

The distinct rates and large amplitudes of the fluorescence results reported above are consistent with a model where, in 1.5 M GdmCl, native P.69T initially unfolds to PFS* prior to forming PFS. These results do not, however, discern whether the PFS* intermediate is populated during the transition from N and U, or—like PFS—is an off-pathway misfolded state. To test the compatibility of PFS* to serve as an on-pathway intermediate populated during P.69T unfolding, we compared the unfolding kinetics of native P.69T, PFS and PFS* in 2.8 M GdmCl. P.69T was incubated in 1.5 M GdmCl for 3 min or overnight, to form PFS* or PFS, respectively. Given that Nt unfolds orders of magnitude faster than Ct and thus unfolding of PFS* will be the rate limiting step for unfolding, if PFS* is on-pathway when P.69T unfolds, the apparent unfolding rates of P.69T and PFS* are expected to be the same. Indeed, in 2.8 M GdmCl, the unfolding of P.69T from N overlapped with that of PFS*, whereas there was no detectable unfolding of PFS over 1 h (Fig. 4C and SI Appendix, Table S2). A similar experiment monitored by far-UV CD spectroscopy yielded comparable results (SI Appendix, Fig. S4). These results demonstrate that formation of PFS* is compatible with the unfolding of P.69T from N to U. Collectively, these results are consistent with a model where native P.69T unfolding proceeds in a stepwise fashion, initially by unfolding Nt to PFS*, followed by unfolded to U. In this model, PFS* serves as an on-pathway unfolding intermediate that, if populated for sufficient time (e.g., as in 1.5 M GdmCl), slowly converts to the kinetically trapped PFS.

PFS* Likely Also Represents the On-Pathway Intermediate for P.69T Folding.

The identification of PFS* and its compatibility as an on-pathway intermediate during P.69T unfolding raises the possibility that PFS* is also populated during P.69T folding from U. As a first test of whether a PFS*-like state lies between U and N, we determined the folding rate of PFS*→N. We previously showed that PFS→N folding is orders of magnitudes slower than U→N folding (23), and to date, we have not identified a P.69T intermediate that folds to the native P.69T structure faster than U. Building upon the double-jump denaturant challenge experiment described above, we incubated native P.69T in 1.5 M GdmCl for just 3 min to populate PFS*, before jumping back to 0.5 M GdmCl to observe refolding to N. Consistent with the model that PFS* is an on-pathway intermediate for U→N folding, refolding from PFS*→N fit well to a single exponential model and led to the fastest rate ever observed for refolding to native P.69T (5.3 × 10⁻³ ± 4 × 10⁻⁴ s⁻¹, Fig. 6 A and B and SI Appendix, Table S3), 10-fold faster than refolding from U→N (5.8 × 10⁻⁴ ± 3 × 10⁻⁵ s⁻¹, Fig. 6 A and B and SI Appendix, Table S3) and 100-fold faster than PFS→N (23). The folding acceleration when starting from PFS*, as opposed to U (or PFS), supports a model where the PFS* conformation serves as an on-pathway intermediate between U and N. Note that the burst phase change (completed within the dead time of our experimental setup; 10 s) was consistently observed during U→N refolding P.69T in this study (Fig. 6A) and past work (20, 23). Although we do not yet understand the precise nature of this burst phase conformational change, it occurs much faster than the folding rate of PFS* and thus may represent an initial collapse of the Ct conformational ensemble, given that we have no evidence of any folding within Nt prior to PFS* formation. This burst phase was not observed for refolding from PFS*→N (Fig. 6A).

Fig. 6.

Schematic illustrating features of the energy landscape and kinetic pathway consistent with P.69T folding and unfolding rates at different denaturant concentrations, with an analogy to Aesop’s fable The Tortoise and the Hare. An on-pathway intermediate state, PFS*, lies between the native (N) and fully unfolded (U) states. PFS* spontaneously converts to the more stable, off-pathway misfolded state, PFS, at a rate that is largely insensitive to denaturant. Conversion of PFS* to PFS slows down both folding to N and unfolding to U. Note that the energy of the unfolded state has been normalized to facilitate comparisons across the three panels. (A) Under native or near-native conditions, folding is favored. The Ct segment of P.69T first folds slowly to the on-pathway intermediate PFS*, after which rapid folding of Nt (illustrated as a running hare) kinetically outcompetes the conversion of PFS* to PFS (illustrated as a tortoise), leading to formation of the native P.69T β-helix structure. (B) In contrast, at intermediate denaturation conditions PFS* is more stable than either N or U, but PFS is even more stable. Moreover, while the energy barrier between PFS* and PFS remains steady (as a tortoise), the energy barriers that separate PFS* from either N or U are more sensitive to denaturation and now higher than the energy barrier to PFS (illustrated as sleeping hares), and thus the off-pathway misfolded state, PFS, predominates. (C) At high denaturation conditions (>2 M GdmCl), unfolding is favored. Native P.69T-Nt first unfolds to form PFS*, followed by rapid unfolding of P.69T-Ct (illustrated as a running hare), which occurs faster than the conversion of PFS* to PFS (illustrated as a tortoise), enabling unfolding to U to outcompete misfolding.

Because the folding of PFS*→N is 10-fold faster than U→N folding, PFS* does not accumulate during U→N refolding and is therefore difficult to study directly during refolding from U. As an alternative approach, we examined whether a PFS*-like structure is also populated during the folding of P.69T bearing a point mutation, L219E, that introduces a charged residue at a buried site in the Nt segment of native P.69T. Due to this mutation, P.69T-L219E adopts a PFS-like structure even under native conditions (SI Appendix, Figs. S1 and S5). We subjected this mutant construct to a double-jump denaturant challenge as described above: Denatured P.69T-L219E was first diluted to 0.5 M GdmCl to start refolding. At different time points, the refolding reaction was challenged with >4 M GdmCl. As with wild type P.69T, we found that the fraction of P.69T-L219E prone to rapid unfolding upon transfer to >4 M GdmCl was initially high but decreased gradually over time (Fig. 6C and SI Appendix, Fig. S6A), consistent with the initial formation of the PFS* intermediate during P.69T-L219E refolding, followed by its slow conversion to PFS. To check whether this unfolding-prone state is PFS*, we slowed down the PFS*→U unfolding rate to a measurable regime and repeated the experiment with a 2.8 M GdmCl challenge, instead of >4 M (SI Appendix, Fig. S6 B and C and Table S2). Consistent with a model where a PFS*-like conformation is populated during refolding of both P.69T-L219E and wild type P.69T, the unfolding rate constant for P.69T-L219E in the PFS* conformation was indistinguishable from wild type PFS* (SI Appendix, Fig. S6C).

Notably, the rate constant for conversion of PFS*→PFS appears largely insensitive to GdmCl concentration (3.3 × 10⁻⁴ ± 3 × 10⁻⁵ s⁻¹ for P.69T-L219E in 0.5 M GdmCl and 7.1 × 10⁻⁴ ± 6 × 10⁻⁵ s⁻¹ for wild type P.69T in 1.5 M GdmCl) (Fig. 4A and SI Appendix, Fig. S7). To test whether the conversion of PFS*→PFS is GdmCl concentration dependent, we repeated the double-jump denaturant challenge experiment using final GdmCl concentrations between 1.3 to 2 M. The conversion of PFS*→PFS was GdmCl insensitive (SI Appendix, Fig. S7), indicating that the conversion of PFS*→PFS does not involve a significant change in the solvent accessible surface area (SASA) (32). These results are consistent with the observation that the spectroscopic signatures of PFS* and PFS are indistinguishable.

Based on the findings above, we hypothesized that the dominant pathway for P.69T folding is processive folding from C-to-N terminus (Fig. 5A). Ct folds before Nt, forming the intermediate PFS*, which catalyzes the folding of Nt. Under this model, formation of PFS* is rate limiting; thus, the U→N rate constant should be comparable to the U→PFS* rate constant, and both rate constants should be at least 10-fold slower than folding of Nt from PFS*→N. To test this hypothesis, we compared the U→N folding rates of P.69T-L219E and P.69T. Each protein was fully unfolded in 7 M GdmCl before diluting to 0.5 M GdmCl to initiate folding. Because PFS* is spectroscopically indistinguishable from native P.69T-L219E, the folding kinetics of P.69T-L219E reflect the folding rate from fully unfolded state to PFS*. We found that in all cases, the folding kinetics fit well to a single exponential plus a burst phase completed within the dead time of our experimental setup (10 s) (SI Appendix, Fig. S8A). We used the rate constant of the measured exponential to represent the rate limiting step of folding. The P.69T-L219E folding rate constant was 7.2 × 10⁻⁴ ± 1 × 10⁻⁵ s⁻¹, similar to the P.69T folding rate constant (5.8 × 10⁻⁴ ± 3 × 10⁻⁵ s⁻¹) (Fig. 6B and SI Appendix, Fig. S8A and Table S3) and an order of magnitude slower than the PFS*→N folding rate. Collectively, these observations support the processive C-to-N terminus folding model described above. Notably, the rate difference between U→N folding of P.69T and P.69T-L219E was small, but statistically significant, suggesting that a foldable Nt slows down the folding of Ct, as compared to a construct with an Nt that is incapable of folding. To further elucidate the impact of Nt on the rate of Ct folding, we measured the folding rate of PCt U→N (SI Appendix, Fig. S8B) and found that PCt folding (9.5 × 10⁻⁴ ± 4 × 10⁻⁵ s⁻¹) was significantly faster than both P.69T and P.69T-L219E (Fig. 6B and SI Appendix, Table S3), indicating that both the presence of Nt and its foldability affect Ct folding. Collectively, these results indicate that both the presence and the foldability of Nt retards folding of the covalently linked Ct. In return, folding of Ct enables fast folding of Nt, which inhibits conversion of PFS* to the misfolded PFS.

Fig. 5.

PFS* is an on-pathway folding intermediate for P.69T folding from U→N. (A) Faster kinetics for folding to the P.69T native structure when starting from PFS* (orange; k_f = 5.3 × 10⁻³ ± 4 × 10⁻⁴ s⁻¹ SEM) versus U (green; k_f = 5.8 × 10⁻⁴ ± 3 × 10⁻⁵ s⁻¹ SEM). (B) Comparison of folding rate constants in 0.5 M GdmCl for PFS* (orange), fully unfolded P.69T (green), P.69T-L219E (blue) (SI Appendix, Fig. S8A), and PCt (red) (SI Appendix, Fig. S8B). Error bars represent the SD of independent experiments. Student’s t test: **P < 0.01; ***P < 0.001; ****P < 0.0001. (C) Kinetics of PFS* formation during refolding of P.69T-L219E. P.69T-L219E was fully unfolded in 7 M GdmCl. Refolding was initiated by dilution into 0.5 M GdmCl; this corresponds to t = 0 s. The overall progress of refolding, as measured by the 335/350 nm fluorescence emission ratio, is shown in blue. Alternatively, at each indicated time point, an aliquot of the refolding sample was transferred to 4.25 M GdmCl. Orange points indicate the impact of this “denaturant challenge” on P.69T-L219E fluorescence ratio at different refolding timepoints. The fraction of P.69T-L219E molecules in the PFS conformation, which unfolds extremely slowly in 4.25 M GdmCl, increased as a function of time and fit well to a single exponential model (purple line). The hatched region between the blue and purple curves represents the fraction of P.69T-L219E molecules in the PFS* conformation (SI Appendix, Fig. S8). Error bars represent SEM of three independent experiments. The height of some error bars is smaller than the size of the datapoints.

Discussion

Protein folding is a cooperative process, requiring coordinated interactions between hundreds to thousands of atoms. The rapidity and cooperativity of protein folding makes it challenging to analyze folding intermediates, a challenge exacerbated when folding and misfolding occur simultaneously. Historically, the complications of competing, off-pathway misfolding reactions have led to a strong focus on model proteins with simple folding pathways and negligible competition from misfolding (33). Yet this focus has led to relatively little insight into how larger proteins successfully navigate the regions of their folding energy landscapes that lie close to the intersection between folding and misfolding.

Here, we show that the folding pathway of P.69T, the 539 aa β-helical passenger domain of the B. pertussis autotransporter protein pertactin, includes a previously uncharacterized intermediate, PFS* (Fig. 5). Nt is less stable than Ct, and under denaturing conditions unfolds more rapidly than Ct, populating PFS*, which rapidly unfolds to U (Fig. 5C). However, conditions that prolong the lifetime of PFS* (for example, destabilizing the native structure, Fig. 5B) increase the likelihood of PFS* converting to PFS, demonstrating that PFS* lies at the junction between folding and misfolding. PFS and PFS* both possess a folded C-terminus and disordered N terminus and are indistinguishable using standard spectroscopic approaches, which for years has complicated the untangling of the P.69T folding and misfolding pathways (20, 23). However, the double-jump results reported here revealed that upon dilution from denaturant, PFS* forms more rapidly than PFS and is converted to the native structure many orders of magnitude more quickly than the conversion of PFS→N, highlighting the kinetic competition between proper folding and misfolding pathways (Fig. 5A).

Although the specific differences between PFS* and PFS remain to be determined, some possibilities can be considered. The conversion of PFS* to PFS is insensitive to denaturant concentration (SI Appendix, Fig. S7) and thus is unlikely to include a large change in SASA, indicating that the PFS*→PFS conversion is not associated with a global conformational change. Other possibilities can also be excluded. For example, it was previously demonstrated that proline isomerization is not the rate-limiting step for P.69T folding (23), and the reported rate constants of proline isomerization (34) are not sufficient to explain the kinetics reported here. We did not observe aggregation of any form of P.69T, including different conformations, mutants, or truncations in our experiments. Specifically, we did not observe any pelletable fraction nor loss of fluorescence during refolding that would be consistent with aggregation. One possibility that remains to be tested is whether PFS*→PFS represents the formation of a dimer or other small oligomer, potentially via an exposed interface or domain swapping.

Regardless of the specific origin of the subtle PFS*→PFS structural change, this conversion leads to a high energy barrier and thus kinetic trapping of PFS. We took advantage of the denaturant concentration insensitivity of the PFS*→PFS conversion (SI Appendix, Fig. S7) to estimate the equilibrium constant for this conversion. Specifically, it was previously shown that the rate constants for folding (PFS→N) and unfolding (PFS→U) were quite similar (~1 × 10⁻⁶ s⁻¹) and largely insensitive to denaturant concentration from 0 to 3 M GdmCl (23), suggesting that folding of PFS→N and unfolding of PFS→U likely share the same rate-limiting step; namely, the conversion from PFS to PFS*. The PFS*→N and PFS*→U rate constants are orders of magnitude faster than PFS→N and PFS→U, hence a two-step model with a denaturant-insensitive rate-limiting step and a subsequent faster step are sufficient to explain both PFS→N and PFS→U. In this work, we measured the PFS*→PFS rate constant (k_PFS*→PFS) as ~5 × 10⁻⁴ s⁻¹ (Figs. 4A and 6C and SI Appendix, Fig. S7). We can thus estimate the equilibrium constant between PFS* and PFS (K_eq = k_PFS*→PFS/k_PFS→PFS*) to be on the order of hundreds and thus estimate the stability of PFS as ~15 kJ/mol lower than PFS*.

A P.69T folding pathway that begins with the rate-limiting folding of the C-terminus to PFS* followed by rapid folding of Nt stands in contrast to a previous model for P.69T folding, drawn from site-specific fluorescent labeling measurements, that the N and C termini fold in a concerted mechanism (23). Our finding that Nt folding is dependent on Ct folding, yet orders of magnitude faster, enabled this update. Crucially, C-to-N-terminal folding of P.69T is also observed in vivo, during C-to-N-terminal translocation of P.69T across the OM of B. pertussis (35). It is striking that, even without the spatial constraints of membrane translocation, P.69T folding in vitro retains this C-to-N-terminal folding vector. A similar result was predicted by steered molecular dynamics simulations (36). Nevertheless, the rate constant for folding of P.69T in vitro reported here (5.8 × 10⁻⁴ ± 3 × 10⁻⁵ s⁻¹, Fig. 6 A and B and SI Appendix, Table S3) is still much slower than the expected folding rate in vivo (27), suggesting that the cellular environment further accelerates P.69T folding. Folding vectorially from C-to-N terminus during translocation across the OM may suppress the formation of unproductive long-range interactions between Nt and Ct during folding. The observation that the presence of Nt slows down the folding of Ct (Fig. 6B) supports this model.

Another distinctive aspect of P.69T folding in vivo is the lack of folding that occurs immediately after P.69T synthesis, when pertactin is translocated through the inner membrane (IM) into the periplasm (37). During IM translocation, the first portion of P.69T to enter the periplasm is the disordered Nt, positioning it to retard the folding of Ct when it appears in the periplasm, as we show here also occurs during refolding in vitro (Fig. 6B). In contrast, during translocation across the OM, P.69T-Ct appears first, which could enable Ct to fold at a much faster rate. Although P.69T is a large protein of 539 aa, its native β-helix structure is dominated by local contact order (CO; absolute CO = 17.6, relative CO = 0.0327), leading to a predicted folding rate many orders of magnitude faster than the measured in vitro folding rate observed (38, 39). The folding mechanism proposed here highlights the distinct contributions of the N- and C-terminus to P.69T folding, contributions that are retained even in the absence of vectorial translocation across cell membranes. Collectively, these results demonstrate that both the innate protein-folding properties observed in the test tube and the spatiotemporal constraints of the cellular environment contribute to efficient folding of a large protein to its native structure, including the avoidance of off-pathway misfolded structures. Similar strategies may help suppress misfolding and aggregation during cotranslational folding and the secretion of proteins from one subcellular compartment to another.

Materials and Methods

Cloning.

A plasmid constructed previously (9) was used for expression of the pertactin passenger domain (P.69T) in the cytoplasm of Escherichia coli. Truncations and point mutants were generated by site-directed mutagenesis and subcloning of this plasmid. The sequence of each expression plasmid was confirmed by Sanger sequencing. Amino acid residue numbers are consistent with the pertactin crystal structure (PDBID 1DAB) (21). A335 was previously determined as the N-terminal residue of Ct (20), however, H334 was included in the PCt construct to provide a spacer between A335 and the N-terminal methionine residue introduced by the start codon.

Protein Purification.

Wild type and mutant pertactin constructs were expressed in E. coli BL21(DE3) pLysS and proteins were purified from inclusion bodies as described previously (20). Briefly, a single colony of transformed E. coli BL21(DE3) pLysS was used to inoculate an overnight culture in LB medium with 50 mg/L ampicillin (LB-Amp). One milliliter of this overnight culture was used to inoculate 100 mL LB-Amp, followed by incubation at 37 °C with shaking to OD₆₀₀ = 1. A portion (40 mL) of this culture was then used to inoculate 2 L LB-Amp, which was incubated at 37 °C with shaking until OD₆₀₀ = 0.6 to 0.8. Expression was induced by addition of 500 µM isopropyl β-D-1-thiogalactopyranoside. Cells were incubated at 37 °C with shaking for an additional 2 h, at which point 2 mM ethylenediaminetetraacetic acid and 0.5 mM phenylmethylsulfonyl fluoride were added and cells were harvested by centrifugation at 3,750× g. Cell pellets were stored −80 °C. Cell pellets were thawed and resuspended in cell lysis buffer (50 mM TrisHCl pH7.5, 100 mM NaCl) with protease inhibitors and 1 mg/mL lysozyme, then lysed by sonication. The cell lysate was centrifuged at 12,000× g for 20 min, and the insoluble fraction from the centrifugation was washed with 1% Triton X-100 in cell lysis buffer and solubilized with 25 mL 6 M GdmCl in cell lysis buffer by shaking at 4 °C overnight. Solubilized inclusion bodies were diluted with dialysis buffer (50 mM TrisHCl pH8.0) at a 1:2 ratio and dialyzed against 10 L dialysis buffer for 2 d to remove denaturant. Dialysis buffer was refreshed once after 1 d to further lower the residual denaturant concentration to <0.03 mM. The dialysate was clarified by centrifuging at 12,000× g for 20 min and purified by chromatography, as described below.

P.69T and P.69T-L219E was first purified by anion exchange chromatography (Source 15Q, Cytiva), by loading onto the column in 50 mM TrisHCl pH8 and eluting with a gradient of 0 to 150 mM NaCl in 50 mM TrisHCl pH8. Native P.69T eluted at 6 to 8 mS/cm and P.69T-L219E eluted at 12 to 14 mS/cm. Ion exchange chromatography fractions enriched in pertactin constructs were pooled and purified further using size exclusion chromatography (SEC; Superdex 200, Cytiva) equilibrated with SEC buffer (50 mM TrisHCl pH7.5, 100 mM NaCl). PCt was purified using only size exclusion chromatography, in SEC buffer. Final purity of the protein (>99%) was verified by Coomassie stained sodium dodecyl sulfate polyacrylamide gel electrophoresis (SDS-PAGE). Purified proteins were concentrated using centrifugal filters (Sartorius Vivaspin Turbo 15, 10 K MWCO) in storage buffer (25 mM TrisHCl pH7.5, 50 mM NaCl) followed by aliquoting, flash freezing, and storage at −80 °C.

Far-UV CD Spectrometry.

Far-UV CD spectra, thermal denaturation curves, and kinetic traces were collected using a J-815 or J-1500 CD spectropolarimeter (Jasco) as previously described (24). For each spectrum, 5 μM protein in 25 mM sodium phosphate pH7.5 buffer was measured in 1 mm quartz cuvette (Starna). Data were obtained with a bandwidth step of 1 nm and data integration time of 1 s and represented as the average of a triplicated measurement of the same sample. Thermal denaturation data and kinetic traces were monitored at 218 nm and measured in 2 mm quartz cuvette (Starna). Thermal denaturation curves were collected using 5 µM P.69T and P.69T-L219E or 10 µM PCt in 25 mM sodium phosphate pH7.5 buffer. The temperature ramp rate was 2.5 min/°C and data integration time was 4 s. Thermal denaturation curves were fit to a single or double sigmoidal model and the melting temperature (T_m) was defined as the inflection point of the sigmoidal curve (see Data Analysis and Statistics, below). Kinetic traces were collected using 2.5 µM protein. Data acquisition interval was 5 s and integration time was 4 s.

Proteolytic Digestion.

P.69T and variants (5 µM each) were digested with 2 µg/mL proteinase K (Sigma) for 24 h at room temperature in 50 mM TrisHCl pH8.8, 7.5 mM CaCl₂. For PFS, P.69T was incubated in 1 M GdmCl at room temperature overnight before addition of protease supplemented with 1 M GdmCl. Proteolysis reactions were quenched by boiling. Digested fragments were resolved by Coomassie stained SDS-PAGE. Images were processed using Fiji (40).

Fluorescence Spectroscopy and Equilibrium Denaturation Titrations.

All fluorescence measurements were collected using a Fluorolog-QM spectrofluorometer (Horiba). Samples were measured in a 10 mm quartz cuvette (Starna) at 20 °C. Data were collected using the instrument’s Felix-GX software and corrected for excitation fluctuations and emission offset using the built-in quanta lookup table provided by the manufacturer. Equilibrium fluorescence spectra of P.69T in different concentrations of GdmCl have been previously reported (20); the corresponding spectra for PCt are shown in SI Appendix, Fig. S9. For unfolding, 200 nM PCt was incubated in 0 to 8 M GdmCl, 25 mM TrisHCl pH7.5, 50 mM NaCl in 5 mL Protein LoBind tubes (Eppendorf). For refolding, PCt were first fully unfolded in 8 M GdmCl, 25 mM TrisHCl pH7.5, 50 mM NaCl, then diluted with 25 mM TrisHCl pH7.5, 50 mM NaCl to 4,800 μL, to a final concentration of 200 nM PCt and 0.1 to 8 M GdmCl in 5 mL Protein LoBind tubes (Eppendorf). To avoid time-dependent photobleaching, three strategies were employed: i) samples were stored in the dark, ii) at each indicated time point, the fluorescence emission of a fresh aliquot at each concentration was measured, and iii) fluorescence emission changes were calculated as a ratio of two values, rather than relying on changes in absolute intensity (20, 23).

At various time points (unfolding: 1 h, 1 d, 5 d, 1 mo, 5 mo, 26 mo; refolding: 1 h, 4 h, 1 d, 2 d, 6 d), the tryptophan emission spectrum was collected, with excitation at 280 nm (slit width 2 nm) and emission measured from 315 to 380 nm (slit width 5 nm), with 0.2 s exposure at a wavelength scan step of 1 nm. The same corrected fluorescence values were collected as described above, and the ratio between fluorescence emission intensities at 335 nm and 350 nm (referred to as 335/350) was calculated at each time point for each GdmCl concentration. The resulting titration curves were fit to a single or double sigmoidal model and the denaturation midpoint, c_m, was defined as the inflection point of the individual sigmoidal curve (see Data Analysis and Statistics, below). The rate constants calculated based on the change of fluorescence calculated based on the 335/350 change were consistent with the rate constants calculated directly from the intensity change at 335 nm.

Ensemble Kinetic Measurements.

Protein was preincubated in the desired buffer in a 1.5 mL Protein LoBind tube (Eppendorf). Buffer that would be added to the protein was premixed in a 1.5 mL microcentrifuge tube. Refolding (or unfolding) was initiated by manually mixing the buffer with the protein and transferring the resulting mixture to the cuvette inside of the fluorometer, resulting in a 10 s dead time. Data collection started precisely 10 s after initial mixing of buffer and protein. Data were collected by excitation at 280 nm (slit widths 2 nm) and acquiring emission at 335 nm and 350 nm (slit widths 5 nm) simultaneously using two photomultiplier detectors. The fluorescence emission ratio at 335 and 350 nm reflects the folding states of P.69T variants (20). Interpretations of ensemble kinetic measurements are based on the theory that observed fluorescence represents the average fluorescence of molecules converting between two states (41).

An inconsistency between the kinetics measured in this work and previous work (20, 23) was determined to arise due to a difference in the protein storage condition used in previous work, which did not completely preserve the native conformation of P.69T, leading to a small subpopulation of PFS in the starting sample. Because of the extremely slow unfolding kinetics of PFS relative to N, the unfolding time used to prepare samples for folding experiments was insufficient to unfold this subpopulation of PFS to U. Note that these differences do not alter the conclusions drawn from past studies (20, 23).

Data Analysis and Statistics.

Data were fit to a single exponential model using the following equation:

$$\mathrm{F}={\mathrm{F}}_{\mathrm{S}}+\left({\mathrm{F}}_{\mathrm{E}}-{\mathrm{F}}_{\mathrm{S}}\right)*\left(1-e^{k*t}\right),$$ [1]

where F represents the measured fluorescence at each time point, F_S and F_E represent the fluorescence of the start and end state, k represents the rate constant and t represents time. Only measurable changes were included in the analysis. Fluorescent changes from the start state within the dead time (burst phase) were not included in the analysis. Such burst phase was only observed with refolding from U (Fig. 6A and SI Appendix, Fig. S8) and was consistently observed in previous studies (20, 23).

Data were fit to a double exponential model using the following equation:

$$\mathrm{F}={\mathrm{F}}_{\mathrm{S}}+\left({\mathrm{F}}_{\mathrm{E}}-{\mathrm{F}}_{\mathrm{S}}\right)\left({\mathrm{P}}_{\text{fast}}*\left(1-e^{kfast*t}\right)+{\mathrm{P}}_{\text{slow}}*\left(1-e^{kslow*t}\right)\right),$$ [2]

where P_fast, P_slow, k_fast, and k_slow represent the fractional amplitude and rate constants of the fast and slow phases, respectively.

Sigmoidal models were fit to the following equation:

$$\mathrm{F}={\mathrm{F}}_{\mathrm{U}}+\left({\mathrm{F}}_{\mathrm{N}}-{\mathrm{F}}_{\mathrm{U}}\right)/\left(1+{10}^{\left(\text{Cm}-\left[\text{GdmCl}\right]*\text{slope}\right)}\right),$$ [3]

where c_m represents the GdmCl concentration at the denaturation midpoint and slope was determined by the fitting software (GraphPad Prism). For thermal denaturation experiments, c_m and [GdmCl] are replaced with melting temperature (T_m) and temperature (T).

Double sigmoidal models were fit to the following equation:

$$\begin{array}{c}\mathrm{F}={\mathrm{F}}_{\mathrm{U}}+\raisebox{1ex}{$\left({\mathrm{F}}_{\mathrm{I}}-{\mathrm{F}}_{\mathrm{U}}\right)$}\!\left/ \!\raisebox{-1ex}{$\left(1+{10}^{\left(\text{Cm}1-\left[\text{GdmCl}\right]*\right)\text{slope}1}\right)$}\right. \\ + \raisebox{1ex}{$\left({\mathrm{F}}_{\mathrm{N}}-{\mathrm{F}}_{\mathrm{I}}\right)$}\!\left/ \!\raisebox{-1ex}{$\left(1+{10}^{\left(\text{Cm}2-\left[\text{GdmCl}\right])*\right)\text{slope}2}\right)$}\right.,\end{array}$$ [4]

where F_I represents the fluorescent intensity of the plateau between the two unfolding transitions (I), c_m1 and c_m2 represent the GdmCl concentrations at the denaturation midpoint of transitions at lower and higher concentrations of denaturant, respectively.

Fraction native was defined by the following equation:

$$\mathrm{Fraction} \mathrm{native}=\raisebox{1ex}{$\left(\mathrm{F}-{\mathrm{F}}_{\mathrm{U}}\right)$}\!\left/ \!\raisebox{-1ex}{$\left(\mathrm{F}\mathrm{U}-{\mathrm{F}}_{\mathrm{U}}\right)$}\right..$$ [5]

Supplementary Material

Appendix 01 (PDF)

Data, Materials, and Software Availability

Raw data (spectra and kinetic traces) are available at https://github.com/plclark1/ProteinFolding/tree/main/Identification_of_an_on-pathway_intermediate_illuminates_the_kinetic_competition_between_protein_folding_and_misfolding (42).