Microsecond barrier-limited chain collapse observed by time-resolved FRET and SAXS

Abstract

It is generally held that random coil polypeptide chains undergo a barrier-less continuous collapse when the solvent conditions are changed to favor the fully-folded native conformation. We test this hypothesis by probing intramolecular distance distributions during folding in one of the paradigms of folding reactions, that of cytochrome c. The Trp59 to heme distance was probed by time-resolved Förster resonance energy transfer (trFRET) in the microsecond time range of refolding. Contrary to expectation, a state with a Trp59-heme distance close to that of the GdnHCl denatured state is present after ~27 µs of folding. A concomitant decrease in the population of this state and an increase in the population of a compact high-FRET state (efficiency > 90%) show that the collapse is barrier-limited. Small-angle x-ray scattering measurements over a similar time range show that the radius of gyration under native favoring conditions is comparable to that of the GdnHCl denatured unfolded state. An independent comprehensive global thermodynamic analysis reveals that marginally stable partially folded structures are also present in the nominally unfolded GdnHCl denatured state. These observations suggest that specifically collapsed intermediate structures with low stability in rapid equilibrium with the unfolded state may contribute to the apparent chain contraction observed in previous fluorescence studies using steady state detection. In the absence of significant dynamic averaging of marginally stable partially folded states and with use of probes sensitive to distance distributions, barrier-limited chain contraction is observed upon transfer of the GdnHCl denatured state ensemble to native like conditions.

Introduction

The conformational and dynamic properties of the unfolded state of a globular protein under native conditions dictate the process by which the polypeptide begins the directed search for the native conformation.^1–5 In addition to its fundamental role in biology, the unfolded state has also received considerable attention recently with an increased appreciation of intrinsically disordered proteins^{6, 7} and the possible role of the unfolded ensemble in human diseases.^{8, 9}

Molar concentrations of urea or guanidine hydrochloride have typically been used to disrupt secondary and tertiary structures of proteins and the unfolded state achieved closely resembles a random coil.¹⁰ The unfolded state under native conditions is operationally achieved by rapid dilution of the chemical denaturant to concentrations where the native state is strongly favored.⁴ Consensus on the properties of the unfolded ensemble of single-domain globular proteins under native conditions has, however, been elusive. Single-molecule,^11–15 pulsed-field gradient NMR¹⁶ and kinetic folding^{17, 18} experiments have indicated that the earliest steps for a variety of motifs correspond to a global contraction of the unfolded ensemble, reflecting an adjustment to the solvent conditions. In this scenario, a negligible kinetic barrier, if any, exists between random-coil and compact conformations (Figure 1A). In contrast, small-angle x-ray scattering (SAXS) folding studies^{13, 19, 20} probing the earliest observable species in pressure jumps from the pressure denatured state²¹ and in dilution jumps from the chemically denatured state to native conditions have indicated that the initial dimensions of the polypeptide chain are comparable to the unfolded state (Figure 1B). The persistence of an extended chain and two-state behavior in the SAXS studies imply the presence of a kinetic barrier to compaction.

Figure 1.

Schematic of continuous and 2-state barrier-limited collapse scenarios. (A) In the continuous collapse model, the change in solvent conditions to low denaturant concentrations (low [D]) favoring the native state, N, also favors a contracted form of the unfolded state, U*, over the unfolded state with random-coil dimensions, U. (B) In the barrier-limited collapse model, the native-like conditions at low [D] result in stabilization of a collapsed partially folded intermediate state, I. The collapse transition in (A) and (B) is indicated by the arrow. (C) Expected Trp-heme distance distributions corresponding to the continuous collapse model show time-dependent distribution peak positions, reflecting adjustment of the polypeptide chain to the new solvent environment. This is modeled using g(r,t)=exp(−(r−r_ave(t))²/σ(t)², with r_ave(0)=42 Å, σ(0)=15 Å, r_ave(∞)=12.5 Å and σ(∞)=5 Å with r_ave(t)=r_ave(∞)+(r_ave(0)−r_ave(∞))·exp(−k·t), where k=(35 µs)⁻¹. (D) In the barrier-limited collapse model, there are two distance distributions, corresponding to U and I. During the collapse reaction, i.e. U→I, the peak positions are constant (42 Å and 12.5 Å) and only their relative populations change (indicated by arrows). The Trp59-heme distance distribution function is modeled using P(r)=a(t)*g_U(r_U)+(1−a(t))*g_I(r_I), where a(t)=exp(−k·t), k is the rate constant for the U→I transition, t is folding time and g_N(r) and g_I(r) are Gaussian distributions with peak positions corresponding to the average Trp59-heme distance in the U and I states. (E) For the continuous-collapse model, the peak of the lifetime distribution (solid line) is expected to change with refolding time. (F) In the barrier-limited collapse model, because only the populations of the distributions change, the lifetimes corresponding to each distribution, <τ>_U and <τ>_I, remain constant with folding time and only their amplitudes change. For clarity, the simulations assume a >2 kcal·mol⁻¹ stability for I. The simulations used a single Trp donor lifetime of 3 ns and R_o=34 Å.

To resolve these contradictory views, we have reexamined the highly-helical heme containing protein, oxidized horse heart cytochrome c (Figure S1). Cytochrome c is ideal for a combined FRET and SAXS analysis of the earliest events in its folding reaction because it contains a single Trp donor and a covalently attached heme acceptor.^22–25 Although there is general agreement that a kinetic event occurs within the first 100 µs^{18, 23–25} of refolding, its interpretation has been the subject of debate.^{17, 22, 23} The only studies with sufficient time-resolution^{18, 24–26} to detect this rapid folding event in cytochrome c (<100 µs) have used steady-state detection methods that are not optimal for resolving compact and random-coil sub-populations. This has made it difficult to establish conclusively whether the initial events correspond to a folding event or simply barrier-less chain contraction.¹⁷ Studies using lifetime-resolved FRET, which overcomes these limitations, on the closely related yeast cytochrome c have suggested that a heterogeneous population with extended and compact forms is present on the millisecond timescale.²⁷

In this report, we detect co-existing sub-populations of compact and extended conformations of cytochrome c during the <100 µs collapse reaction by lifetime resolved Trp59 to heme FRET. The results, combined with corroborating sub-millisecond continuous-flow SAXS measurements and equilibrium data, provide definitive evidence for a barrier in the collapse reaction. The results also demonstrate the importance of marginally stable partially folded states that differentially bias SAXS and FRET studies of the unfolded ensemble. We also reexamine the folding mechanism of cytochrome c, allowing a reconciliation of various competing kinetic models.

Results

Fluorescence lifetime-resolved continuous-flow kinetics reveal timescale of compaction

To study the early folding kinetics of cytochrome c, we performed refolding experiments by denaturant dilution using a custom microchannel continuous-flow mixer.²⁸ This mixer can achieve complete mixing of denaturant solutions (e.g., 6 M GdnHCl or 8 M urea) and water in ~25–30 µs, making it capable of resolving at least part (~35–40%) of the early folding reaction of cytochrome c, comparable to previous studies.^{18, 25, 26} A major difference, however, is that the fluorescence lifetime of the FRET donor, Trp59, is resolved by time-correlated single photon counting (TCSPC). The clear separation in timescales between the excited-state decay (fluorescence lifetime< 10 ns) and the protein folding kinetics (> 100 ns), enables us to view the excited state decay as a snapshot at a particular time in folding. The key advantage of this experiment is that information concerning the donor-acceptor distance distribution (Figure 1C and 1D) is contained in the excited state decay of the donor and subsequently observable in the measured lifetimes and amplitudes (Figure 1E and 1F). The Förster distance, R_o, for the Trp59-heme pair (~35 Ų⁹) is well-suited for the Trp59-heme mean end-to-end distance expected from random-coil models.³⁰

The continuous-flow time-resolved FRET (CF-trFRET) raw data are shown in Figure S2 and several features are noteworthy. First, during the initial ~100 µs, an apparent loss of amplitude is observed. A decrease in the peak amplitude of a TCSPC trace is consistent with formation of an intermediate with an excited state Trp lifetime on the order of or shorter than the instrument response of the TCSPC detection system (~180 ps in this case) (Figure S3). Conformations in which the Trp59-heme distance is close to the native state (10–15 Å) would appear highly quenched and difficult to observe in a visual inspection of the kinetics except for the reduced peak height of the decay curves. These results indicate that during the ~30 µs kinetic step, a fraction of the unfolded population acquires a Trp59-heme distance that is compact (at most 15 Å), while the remainder of the population maintains an extended Trp59-heme distance. Although static quenching of Trp59 by nearby proximal amino acids can also give rise to an amplitude reduction in the raw data, the appearance of a fast (~45 ps) excited state decay component, discussed below, suggests that it is not a dominant contributing factor. This is further corroborated by the time-resolved SAXS results further below.

A second key feature, demonstrated by the Trp lifetime analysis (Figure 2), is that the four Trp59 excited state lifetimes do not change throughout the folding reaction, both during the ~30 µs kinetic phase and the longer ~650 µs phase leading to the native state. The three longer lifetimes, τ₂, τ₃ and τ₄, (Figure 2B) are also very similar, within measurement error, to those obtained in the unfolded baseline at high denaturant concentrations (Figures 2B and 2C). The close agreement between the values of τ_2–4 observed in equilibrium and kinetics demonstrates that the Trp-heme distances early in folding have not significantly changed relative those in the unfolded baseline ([GdnHCl]>4 M), as expected for a barrier-limited collapse (Figures 1B and 1F). If the compaction were continuous, a gradual shift of the lifetimes would have been observed (Figure 1E).

Figure 2.

A “local” (non-global) analysis of cytochrome c CF-trFRET data. The results of a non-linear least squares fit of each excited state decay curve in Figure S2 using 4 exponentials plus a constant is shown. (A) The amplitudes, α_i, and (B) time constants, τ_i, as a function of refolding time, t, are shown with errors obtained from the fit. (C) The lifetime distribution of the unfolded state at 6 M GdnHCl obtained using the maximum entropy method. The dotted lines between panels B and C show the correspondence of the Trp excited state lifetimes during refolding with the peaks of the Trp excited state lifetime distribution of the unfolded ensemble in 6 M GdnHCl. The solid lines in (A) are global fits using a two exponential function with time constants of 30 µs and 650 µs.

Lastly, in contrast to the lifetimes, the amplitudes associated with the four Trp excited state decay lifetimes exhibit clear changes over the entire time course (Figure 2A), indicative of a change in the populations, but not in distances. Over the course of the first 100 µs of refolding, a decrease in the amplitudes of three Trp59 lifetimes (α₂, α₃ and α₄) is observed concomitant with an increase in the amplitude, α₁. This very fast lifetime component (τ₁~45 ps) is not observed in equilibrium measurements of the unfolded ensemble (Figure 2C). The fast lifetime component (α₁ and τ₁) represents a compact state with a very high FRET efficiency that forms during the ~30 µs folding kinetic phase. Its estimated average Trp-heme distance of ≤15 Å is only slightly greater than in the native state (~10 Å). The amplitude of the fast lifetime component (α₁, Figure 2A), however, does not extrapolate to zero at the initial time point for folding (t=0). The non-zero amplitude could reflect a faster compaction step to another marginally stable intermediate or, more likely, reflect the convolution of the finite mixing time of our mixer (~27 µs for complete mixing in these experiments) with the actual kinetics.

The concomitant decrease of the three longer lifetime amplitudes (α₂, α₃ and α₄) is consistent with these lifetimes originating from three dominant χ₁ Trp rotamers, also observed in model peptides.^{31, 32} The rotamers of Trp59 interconvert on a timescale longer than the Trp excited state lifetime (several ns) but faster than the collapse time of ~30 µs. The source of the three lifetimes is therefore most likely heterogeneity at a local level rather than very separate Trp-heme distances. This conclusion is corroborated by equilibrium lifetime measurements and by SAXS studies, as discussed below.

A model independent description of the data can also be obtained from singular value decomposition (SVD) analysis of the data, as shown in Figure 3. An excellent approximation to the raw data (Figure S2) can be obtained using only the first two sets of basis vectors (Figure 3A,B and 3C,D). Consistent with the lifetime analysis in Figure 2, the depopulation of the first state (primarily basis vector u₁ in Figure 3A having a long lifetime) leads to the concomitant increase in population of a second state (primarily basis vector u₂ in Figure 3C dominated by a short lifetime component) during the ~30 µs kinetic phase. The positive amplitude for vector v₁ (Figure 3B) and negative amplitude for vector v₂ (Figure 3D) are consistent with this scenario. Population of Trp59-heme distances intermediate between those in the compact state and the nearly unfolded state are negligible as indicated by the very low statistical weight and random pattern of the third (u₃ and v₃ in Figures 3E and 3F, respectively) and subsequent basis vectors (not shown). Similar results are obtained in jumps to 0.225M GdnHCl and when longer times are included, as shown in Figure S4. A simulation illustrating that a series of TCSPC traces for the barrier-less approach cannot be described in this simple way is shown in Figure S5, where a minimum of five basis vectors are necessary with the same signal-to-noise ratio and amplitudes.

Figure 3.

Singular value decomposition (SVD) of the raw CF-trFRET data. The first (A,B), second (C,D) and third (E,F) basis vectors from the SVD of the raw data are shown. The panels on the left (u₁, u₂, and u₃) correspond to the basis vectors along the tryptophan excited state decay axis (ns timescale). Their corresponding basis vectors along the folding time axis (µs timescale) are shown in the right panels (v₁, v₂ and v₃). The singular values, w₁,w₂ and w₃, are indicated in the right panels. The remaining vectors, similar to the third vectors (u₃ and v₃), are random noise and not shown. The vectors v₁ and v₂ are fit globally to a two-exponential decay with time constants of 30±3 µs and 650 µs. The value of the slower time constant was determined from similar but independent experiments extending out to 1 ms (Figure S4). Refolding was initiated from 4.5M GdnHCl by a ten-fold dilution to 0.45M GdnHCl and protein concentration of 30 µM, at pH 7.0 and 21 °C. All data were acquired in the presence of 0.2 M imidazole to prevent misligation to the heme.

The seeming incongruity in the amplitude of the second vector in the SVD analysis (Figure 3C and D) and the large amplitude of its most closely corresponding phase (the fast ~45 ps lifetime phase) in the lifetime analysis (Figure 2A) is due to the incorporation of the instrument response in the lifetime analysis, which extrapolates the amplitude of the fast lifetime to the pulse arrival time. As illustrated in the simulation in Figure S3, the apparent amplitude for a ~45 ps component will appear small if the instrument response full-width half-maximum is several times greater, ~180 ps for the data shown in Figures 2 and 3. A substantial fraction of excited Trp59 molecules have returned to their electronic ground state during the instrument response time.

Time-resolved small-angle x-ray scattering corroborates FRET results

To address whether the collapse suggested by the CF-trFRET experiment is a global phenomenon, we performed small-angle x-ray scattering (SAXS) measurements during the sub-millisecond folding of cytochrome c. The radius of gyration (R_g) and scattering profiles obtained from SAXS are sensitive to all interatomic distances. Although the R_g measurements will be biased toward larger distances,³⁰ the overall scattering pattern will be proportional to relative populations. Folding kinetics initiated from the GdnHCl unfolded state were pursued because this state more closely resembles a random coil polypeptide^{10, 33} than the pH-unfolded state of cytochrome c used in previous continuous-flow SAXS studies.³⁴

Small-angle scattering curves obtained from 100 µs to 4 ms corroborate the main findings of the CF-trFRET measurements: the earliest observed contraction of the Trp-heme distance is concerted with the global compaction of the unfolded ensemble. A plot of the R_g (Figure 4A) shows that the tail of the collapse reaction is observed over the first ~150 µs, leading to an R_g that is ~24 Å. Extrapolation of the biexponential decay to t=0 reveals that the R_g of the initial species, 30.4 Å, is very similar to the value for the unfolded ensemble measured at a large series of GdnHCl concentrations and extrapolated to low [GdnHCl], 31.2 Å (Figure S6). Although local structural events are likely to have occurred, the global dimensions are, on average, very similar to those of the unfolded ensemble.

Figure 4.

Small-angle x-ray scattering (SAXS) of cytochrome c during sub-millisecond refolding. (A) The radius of gyration, R_g, (circles) during refolding from 4.5M GdnHCl to 0.45 M GdnHCl at pH 7.0 in the presence of 0.2M imidazole and modeling of R_g² vs. time (solid line) to a double exponential with fixed time constants of 45 µs and 650 µs are shown. The final protein concentration was 2 mg·mL⁻¹ and the total flow rate was 20 mL·min⁻¹. (B) The zero-angle scattering intensity obtained from the Guinier analysis in (A) shows that cytochrome c is monomeric throughout folding.

The peak in the Kratky spectrum at 300 µs (Figure S7, panel B) suggests that the ~30 µs kinetic phase leads to the population of compact species as expected from the CF-trFRET experiment. A peak is evident in the Kratky plot also after accounting for the population of all kinetic species as discussed below. The R_g decreases to the native value (~15 Å) with a 600±200 µs time constant (obtained by fitting R_g²), consistent with the time constant of the slower folding kinetic phase in fluorescence studies (Figures 2A, 3B and S4).^{17, 18, 26} The uniform zero-angle scattering intensity (Figure 4B) rules out the presence of dimeric species that are known to form at much higher protein concentrations and in the absence of imidazole.³⁵ At protein concentrations of 1 to 3.5 mg·mL⁻¹, interparticle interference effects are also negligible.^{33, 36}

High denaturant equilibrium intermediate is revealed by fluorescence lifetime and SAXS

As part of a comprehensive approach to map the free energy landscape of cytochrome c, we performed equilibrium unfolding titrations monitored by trFRET and SAXS. These studies play a significant complementary role in identifying and accurately characterizing partially folded states because denaturants can populate these states under equilibrium conditions. Furthermore, because dynamic averaging of trFRET and SAXS measurements are on the several ns and faster timescale, partially folded states populated in equilibrium studies may be readily observed even if their inter-conversion occurs beyond the time resolution of our kinetic experiments. Robust equilibrium data and global analysis also allows a test of the correspondence between thermodynamic parameters (ΔG and m-values) extracted from equilibrium and kinetic measurements, an important part of assessing the validity of a kinetic model. Because both SAXS and trFRET are complementary dimensional probes, yielding global and pairwise distance distributions, respectively, they can be used to monitor the denaturant dependence of the dimensions of the unfolded state.

trFRET and SAXS detected equilibrium titrations (Figures 5 and S6, respectively) reveal several key features of the energy landscape of cytochrome c: 1) the presence of a high denaturant equilibrium intermediate state with a mid-point of 3.6 M, 2) absence of any significant change in the dimensions of the unfolded ensemble with respect to denaturant concentration, and 3) a low-denaturant equilibrium intermediate with a midpoint near 1.5 M GdnHCl. A combined global analysis of the SAXS and trFRET data is best described using a 4-state equilibrium unfolding model with the following thermodynamic parameters: (the state numbering scheme follows the folding model in Figure 6, state “3” is not observed in equilibrium experiments): ΔG₅₄=1.6±0.2, ΔG₄₂=7.1±0.2, ΔG₂₁=2.1±0.8 kcal·mol⁻¹, with corresponding m-values of m₅₄=1.0±0.21, m₄₂=2.5±0.07, m₂₁=0.56±0.15 kcal·mol⁻¹M⁻¹. The total ΔG of unfolding from this analysis is ΔG_total=10.8±0.9 kcal·mol⁻¹ with an m-value of m_total=4.12±0.26 kcal·mol⁻¹M⁻¹. Fractional species populations and Kratky curves obtained from the global fit are shown in Figures 7 and 8, respectively.

Figure 5.

Equilibrium unfolding monitored by Trp fluorescence lifetime. The first three basis vectors obtained from an SVD analysis of the full data set are shown. The first (panels A and B), second (panels C and D) and third (panels E and F) basis vectors were significant, with the remaining ones consisting of random noise. The data along the [GdnHCl] axis (v₁, v₂ and v₃) were not adequately described by a 2-state equilibrium unfolding thermodynamic model. A fit using a 4-state equilibrium model without a Z-approximation³⁹ (solid line in panels B, D, and F) of the combined trFRET and SAXS data gave a statistically significant fit, with F=(χ_υ² 3-state)/(χ_υ² 4-state)=1.147, v₁=4667 and v₂=4548 and a probability P(F,v₁,v₂)=1.7×10⁻⁴. The v-vectors have been multiplied by their singular values. Normalized singular values are shown in the right panels (w₁, w₂ and w₃). It is important to note that the vectors are orthonormal mathematical descriptions of the data and do not necessarily correspond to species spectra or denaturant dependences. Extraction of the populations of each species requires a thermodynamic model and is shown in Figure 7.

Figure 6.

Kinetic model for cytochrome c folding. The semi-quantitative reaction coordinate shows the approximate free-energy and barrier heights for the various states in the folding of horse heart cytochrome c at neutral pH in the presence of 0.2 M imidazole. The scheme summarizes some of the key points of the model proposed in this work and in previous studies.^{22, 23, 50} Distinct thermodynamic ensembles (“2” and “3”) with marginal stability separated by a barrier are present before the rate limiting step to the native state (indicated by a blue diamond). A compact state, “3”, with high FRET efficiency and low fluorescence quantum yield forms with an approximately 30 µs time constant. Because of the marginal stability of “3”, refolding probed by fluorescence is sensitive primarily to the conversion of the unfolded-like low-FRET highly fluorescent species “2” (and possibly “1”) to the native state. Two reaction coordinates, those of R_g and average FRET efficiency, are also shown to illustrate the global and pairwise distance changes, respectively. A Kramers pre-factor of κ=(0.1 µs)⁻¹ was used to calculate the activation barriers.

Figure 7.

Species populations predicted from fits of equilibrium unfolding experiments. The mole fraction of native, unfolded and intermediate species predicted from the global 4-state fit of the Trp fluorescence lifetime data SVD vectors and SAXS data are shown. The corresponding states in the folding model shown in Figure 6 are also indicated. The low-denaturant intermediate, “4” is native-like and the high-denaturant intermediate, “2”, is unfolded-like in their fluorescence and SAXS properties.

Figure 8.

Kratky spectra of kinetic and equilibrium species. The spectra of the species populated under equilibrium conditions (states “1”, “2”, “4” and “5”) were obtained from a combined weighted 4-state global analysis of equilibrium unfolding data corresponding to the SAXS data at 110 scattering angles (Figure S6) and trFRET data at 134 decay points (data from Figure 5). Thermodynamic parameters are provided in the main text. State “3” is insufficiently populated in equilibrium experiments and, therefore, the spectrum of state “3” was estimated by deconvoluting it from the kinetic data at 300 µs using the full kinetic 5-state model shown in Figure 6 and the Kratky curves shown in Figure 8 extrapolated to 0.45 M GdnHCl. It is important to note that the Kratky spectrum of state “3” is, therefore, technically at 0.45 M GdnHCl whereas the other states are extrapolated to 0 M GdnHCl. In kinetic experiments at 0.45 M GdnHCl, states “2” and “3” are predicted to have very similar stability and be nearly equal in population.

The high denaturant and low denaturant equilibrium intermediates have been observed previously although not in the same data set. The high denaturant intermediate (state “2” in Figure 6) is similar in mid-point, stability and scattering curve to that observed by Segel et al.³³ Kratky spectra for this intermediate extrapolated from the global fit are shown in Figure 8. Although there are clear changes in the scattering curves over the 3 to 7 M GdnHCl range corresponding to the transition from the high denaturant intermediate, state “2”, to the unfolded ensemble, state “1”, (Figure S6A) the R_g is unchanged (Figure S6C). Consistent with the SAXS data, the Trp excited state lifetimes for this intermediate are very similar to those of the unfolded ensemble (state “1” in Figure 6). Both the Trp excited state lifetimes and the R_g are constant over the 3.5 to 7 M GdnHCl concentration range, arguing that the size of cytochrome c does not change as a function of denaturant concentration. Control experiments on a 12-residue peptide spanning Trp59 also showed minimal differences in lifetime over a broad range of denaturant concentrations (0 to 6 M GdnHCl, data not shown). The primary differences between the high denaturant intermediate and the unfolded state are a change in the relative amplitudes of the Trp excited state lifetimes (presumably, rotamer populations) and a change in the Kratky spectrum at q>0.05 Å (see below). Refolding kinetics initiated at varying initial populations of the intermediate (estimated to be ~20% at 4.5 M GdnHCl and ~5% at 6.0 M GdnHCl, Figure 7) were indistinguishable, suggesting that the equilibration of this high denaturant intermediate (state “2”) with the unfolded ensemble (state “1”) is significantly faster than the ~27 µs time resolution of the CF-trFRET experiment.

The unfolding titrations and thermodynamics do not depend on protein concentration or on the presence of imidazole, consistent with the absence of intermolecular associations facilitated by His misligation. The high denaturant intermediate, state “2”, with a maximal population near 3.5 M GdnHCl, (Figure S6) has not been observed in studies using steady-state fluorescence³⁷ or absorbance detection³⁸ and highlights the increased sensitivity afforded by fluorescence lifetime detection and liquid-handling robotics.

The high denaturant random-coil like intermediate, state “2” in Figure 6, with a CD spectrum nearly indistinguishable from the unfolded state³⁷ yet having a non-negligible m-value is not without precedent.^{39, 40} The I2 intermediate of the α-subunit of tryptophan synthase, whose existence has been established by NMR and mutagenesis,^{40, 41} has an m-value, ~0.8 kcal·mol⁻¹Murea⁻¹, approximately double that of the high-denaturant intermediate of cytochrome c (using the approximate conversion values of Meyers et al.)⁴² yet exhibits a CD spectrum very similar to the unfolded state. The formation of hydrophobic clusters without significant accumulation of secondary structure was proposed as one possible explanation for the phenomenon. Long and medium-range non-native hydrophobic clusters at high denaturant concentrations have also been observed for lysozyme⁴³ and NTL9.⁴⁴ An increasing number of observations suggest that branched aliphatic side-chains, Ile, Leu and Val, may play a dominant role in stabilizing non-local interactions and bias the search process, particularly in the early stages of folding.⁴⁵

Discussion

Consistent picture of barrier-limited collapse by SAXS and lifetime-resolved FRET

trFRET and SAXS analyses of cytochrome c, at equilibrium under highly denaturing conditions and during refolding to native conditions, provide compelling evidence for a barrier-limited collapse reaction.^{23, 24} This is supported by: 1) the concomitant decrease in an unfolded-like population with an increase in a collapsed population, as illustrated by the CF-trFRET data (Figures 2A and 3), 2) nearly identical Trp excited state lifetimes under refolding and unfolding conditions (Figure 2B and 2C), 3) comparable extrapolated R_g values of the unfolded state under native conditions from kinetics and equilibrium (Figure 4) and 5) insensitivity of the R_g in the unfolding baseline observed in equilibrium SAXS (Figure S6C). Independent corroboration using two complementary techniques with very different weighting of distances (1/r⁶ vs. r²) reinforces these findings. Although SAXS and FRET have, in several prominent instances, been in disagreement on the properties of the denatured state ensemble as a function of denaturant^{4, 13} the trFRET and SAXS results in this work lead to a consistent picture.

The two probes used in this study, trFRET and SAXS, share the common property of being sensitive to distance distributions.⁴⁶ Additionally, because trFRET takes place faster (< several ns) than known folding events and x-ray scattering occurs faster than molecular vibrations, dynamic conformational averaging is minimized. This renders both techniques suitable for revealing sub-populations that may be difficult to resolve by steady-state methods. The cytochrome c CF-trFRET data illustrate the insights obtainable from these distributions, identifying extended structures reminiscent of the unfolded state and/or high-denaturant intermediate state that persist after the collapse reaction is complete for a sub-population (Figures 2 and 3). The presence of two sub-populations, compact and unfolded-like, suggests that the kinetic intermediate populated in ~30 µs must have marginal stability under strongly refolding conditions, i.e., ΔG ≤ 2 kcal·mol⁻¹ in the absence of denaturant, and even less under typical experimental conditions, because of the non-negligible population of extended unfolded-like conformations. It is worth noting that a rapid (<<27 µs) inter-conversion among extended conformations precedes the collapse because the fluorescence kinetics are independent of the initial denaturant concentration. Estimates of the chain reconfiguration time from FCS data on yeast cytochrome c indicate that chain dynamics under strongly denaturing conditions occur faster than 4 µs.⁴⁷ A chain reconfiguration time on the order of a microsecond would place a lower limit of ~2 kcal·mol⁻¹ on the free-energy barrier, in keeping with the absence of a distribution of structures during the collapse reaction.

Comparison between smFRET and ensemble continuous-flow measurements

The ensemble based kinetic measurements presented here give a different view of the unfolded ensemble for cytochrome c under native conditions than what one would expect based on single-molecule FRET studies of other proteins, most notably the studies on protein L and CspB.^11–15 One significant difference between the aforementioned smFRET studies and the current study is that cytochrome c contains a heme cofactor, indicating that generalizing the results of this study should be approached with caution. Additionally, the smFRET studies were performed on smaller two-state folding proteins whereas cytochrome c has been known to populate a rich set of partially folded structures.⁴⁸ However, keeping these caveats in mind, it is also worth noting that the smFRET studies are typically conducted with binning times on the order of 1 ms, suggesting that the effective time resolution in the experiments are different by well over an order of magnitude (~1 ms vs. 27 µs for CF-trFRET). Although deviation from two-state behavior has not been observed in smFRET studies showing collapse of the unfolded ensemble, one origin of the difference may be that the ms averaging may lead to inadvertent inclusion/averaging of marginally stable (i.e., ΔG<1 kcal·mol⁻¹) or unstable (i.e., ΔG≤0 kcal·mol⁻¹) partially folded and/or compact species as part of the unfolded ensemble. Although lifetime and/or distance distribution analysis is possible on sub-populations obtained from smFRET studies, this has been pursued only for CspB.⁴⁹ The denaturant dependence of the unfolded ensemble in several smFRET studies¹² resembles the stopped-flow burst phase of cytochrome c acquired with steady-state fluorescence detection.¹⁷ The averaging timescales, typically ~1 ms, are comparable and cytochrome c kinetics appear two-state under these conditions.¹⁷ For cytochrome c, however, as this averaging time is shortened in continuous-flow experiments to ~27 µs an additional kinetic step, corresponding to a barrier-limited collapse, emerges. This also raises the possibility that scenarios intermediate between a barrier-limited and continuous shifting transition state may occur, mediated by a similar underlying phenomenon, i.e. the population of partially folded intermediates with marginal stability and non-local contacts.

Folding mechanism of cytochrome c

The evidence that a compact intermediate with marginal stability is formed in the sub-100 µs time scale provides the basis for a reexamination of the folding mechanism of cytochrome c. These results build on studies by the Roder, Winkler and Sosnick groups^{17, 23, 50} and prompt a reexamination of the interpretation of the stopped-flow fluorescence burst phase¹⁷ and kinetic folding mechanism of cytochrome c.²² A kinetic model consistent with the available data is proposed in Figure 6. A pre-equilibrium between collapsed and extended species prior to the rate-limiting barrier reconciles previously proposed models.

State “1” corresponds to the unfolded state ensemble that is described, on average, by a statistical random coil model. The Kratky curve and R_g are consistent with this assignment, although this does not rule out low-probability short, medium or long range contacts in the unfolded ensemble.⁴⁴ State “2” is the high denaturant equilibrium intermediate with an R_g similar to state “1” but a Kratky curve that deviates from that of a random coil, suggesting the presence of more persistent intra-molecular contacts in an otherwise random-coil-like ensemble. Although these contacts may be non-local in sequence, the similarity of the Trp excited lifetime to those in state “1” and an R_g consistent with that of a random-coil suggest that conformations in which the N and C-termini are in contact must be small in population. States “1” and “2” equilibrate within the time resolution of our folding experiment (i.e., faster than ~30 µs) whereas state “2” proceeds in a barrier-limited manner to form state “3” with an ~30 µs time constant. The transition from state “2” to state “3” and concomitant compaction, however, is not the rate limiting step in folding under strongly folding conditions; instead, the dominant barrier to the native state occurs from a transition between state “3” and the collapsed species on the native side of the barrier, which occurs with a 650 µs time constant at 0.45 M GdnHCl. Although this view is generally consistent with the view advocated by Roder and colleagues²³ it can also be reconciled with data previously used to support compaction as the rate limiting event in cytochrome c folding.¹⁷ A key point that reconciles these models is that because state “3” is marginally stable a Boltzmann-weighted mixture of states “1”, “2” and “3” is present after the ~30 µs kinetic step. States “1” and “2”, however, are the only species with significant fluorescence quantum yield because the excited state lifetime of state “3” is ~45 ps (Figures 2B and 3C). Experiments using steady state fluorescence detection with a time resolution along the folding time axis slower than 150 µs observe the Boltzmann and quantum yield weighted average of states “1”, “2” and “3”.

Correspondence between equilibrium and kinetics

Our estimate of the global stability of cytochrome c from equilibrium trFRET and SAXS, ~10.8±1.4 kcal·mol⁻¹, is consistent with estimates of the global stability (~10 kcal·mol⁻¹) obtained by CD in previous studies.^{29, 37} Estimates of the global stability from fluorescence studies, however, tend to be somewhat lower, typically between 7.5 and 8.5 kcal·mol⁻¹.⁵¹ The lower stability estimated from some fluorescence studies may be partly related to not taking into account the high denaturant intermediate observed here by trFRET and SAXS. The omission of this high denaturant intermediate leads to an underestimate of the stability in fluorescence measurements. For example, a (statistically poor) two-state fit of the data in Figure 5 yields a ΔG=7.6±0.36 kcal·mol⁻¹, which is significantly less than the 9.3±0.99 kcal·mol⁻¹ obtained from the 3-state global fit of the trFRET fluorescence data alone and the 10.8±0.9 kcal·mol⁻¹ obtained from the combined fluorescence/SAXS 4-state global analysis. Below, we suggest that the correspondence between kinetics and equilibrium in previous fluorescence studies⁵¹ is a consequence of incomplete measurement of the global stability in equilibrium and the omission of the burst-phase stability. The underestimate of global stability and the burst-phase stability are comparable in magnitude (~2–3 kcal·mol⁻¹) and their fortuitous cancellation has led to previous interpretations of two-state folding for cytochrome c.

Chevron analysis of cytochrome c

To demonstrate that the barrier-limited formation of a compact state reconciles data previously interpreted as compaction of the unfolded state we performed a chevron analysis of the data by Krantz et al.¹⁷ The chevron analysis was performed using a graphical eigenvalue/eigenvector analysis tool written in LabVIEW and available at www.osmanbilsel.net. The chevron analysis (Figure S8) includes a fast component with a time constant corresponding to the 30 µs kinetic phase, observed in Figures 2 and 3 and also by rapid mixing and temperature-jump studies.^23–25 The modeling of the chevron (Figure S8) yields a global stability of 10.5 kcal·mol⁻¹ and an m-value of 3.9 kcal·mol⁻¹M⁻¹, which compare favorably with values obtained from equilibrium (ΔG_{total, EQ}=10.8±0.9 kcal·mol⁻¹, m_{total, EQ}=4.12±0.26 kcal·mol⁻¹M⁻¹). The rates, amplitudes (FRET efficiencies) and m-values from the simulation in Figure S8 are schematically illustrated in the free-energy reaction coordinate diagram in Figure 6.

In contrast, a quasi-2-state model (Figure S7) corresponding to the scenario in Figure 1A gives a slightly poorer fit of the observed rates at low denaturant concentrations, where the marginally stable collapsed species are expected to be most significantly populated. More significantly, this model is unable to represent the burst-phase amplitudes without gradual contraction of the unfolded state ensemble, an assumption inconsistent with the CF-trFRET and SAXS data presented in this paper. The quasi-2-state model also yields a global stability from kinetics that is significantly lower than equilibrium measurements using CD, SAXS and trFRET.

Origins of the barrier for collapse

The physical origin of the barrier in cytochrome c may arise from the reduction in conformational entropy,^{52, 53} electrostatics,^{24, 54} bond rotations⁵⁵ and desolvation⁵⁶ in the transition state. Measurement of activation enthalpy and entropy provide valuable insights into the physics of the transition state.^55–60 Hagen and Eaton²⁴ have measured a solvent viscosity corrected activation enthalpy of 9 k_BT (~5 kcal·mol⁻¹ at room temperature) for cytochrome c in temperature-jump experiments in nearly identical conditions. A positive activation enthalpy change for a number of other systems^{55, 57–60} has been suggested^{56, 58} to arise from desolvation, stemming from the positive enthalpy and entropy of desolvating hydrocarbon groups.⁶¹ Simulations by Chan and colleagues⁵⁶ have shown that desolvation of hydrophobic residues can lead to cooperative folding behavior, as is observed for the ~30 µs collapse transition in cytochrome c. The product of the collapse reaction, state “3” in Figure 6, has an m-value of 1.55 kcal·mol⁻¹M⁻¹ out of a total 4.12 kcal·mol⁻¹M⁻¹, suggesting that over 1/3 of native solvent accessible surface area is buried in this state. Consistent with a significant role for desolvation of hydrocarbon groups, Roder and colleagues have observed protection in sub-ms hydrogen exchange experiments for all three of the main helical segments (N-terminal, 60’s helix and C-terminal helix), most notably the aliphatic residues that dock on the heme (e.g., L64, L68, I9 and L94).²³ Perfectly funneled topology based simulations also demonstrate significant contributions to the blue, green and yellow foldons (Figure S1) from these regions and the heme.⁶²

Conclusions

Kinetic folding studies coupled with SAXS and fluorescence lifetime detected FRET have allowed direct observation of the early compaction step in horse cytochrome c. The correspondence of Trp59 lifetimes early in folding with those in the GdnHCl denatured state and the consistent R_g in the unfolding baseline in SAXS measurements show that the unfolded ensemble exhibits very little contraction when transferred to native-like conditions. The correspondence between FRET and SAXS results demonstrate that there is no inherent inconsistency between the techniques because the same WT protein construct was used for both measurements in these studies.

The lack of contraction of the unfolded state as the solvent quality decreases has led to a reexamination of the folding mechanism of cytochrome c. The proposed model includes at least one barrier-limited folding event in the sub-100 µs timescale prior to the transition state leading to native formation. These results underscore the importance of using techniques sensitive to distributions of distances and presence of sub-populations. One must also consider the possibility of marginally stable states in rapid equilibrium with the unfolded ensemble when interpreting folding data.

Materials and Methods

Mixer construction

Details of the mixer used in fluorescence experiments have been presented in detail elsewhere.^{28, 63} Briefly, the mixer was made from laser-machined 127 µm thick PEEK (polyetheretherketone) film with 75 µm wide channels. Typical flow rates were 20 mL·min⁻¹, which gave rise to flow velocities of 27 µs·mm⁻¹.

A modification to the continuous-flow SAXS studies was that data were collected using a standard SAXS setup and a micro-SAXS setup. The mixer used for SAXS experiments was adapted from Akiyama et al.³⁴ and has been previously described.⁶³ The mixing “T” had ~35 µm channels that expanded after 100 µm to 200 µm or 250 µm in width. The channel depth was 400 µm and the observation region was 2 mm long. The window material was 8 µm thick Kapton. For SAXS studies using a micro-SAXS setup an arrow shaped mixing region with 35 µm channels was used. This region expanded to a maximum channel width of 100 µm and resulted in a dead-time of ~90 µs. The micro-SAXS also increased the duty cycle of the experiment to >90%.⁶⁴

Time-resolved fluorescence

Tryptophan excited-state decay kinetics were obtained using the time-correlated photon counting (TCSPC) method as described previously.²⁸ Lifetime decays at various distances along the direction of flow in the observation region of the microchannel mixer were obtained by translating the mixer relative to the excitation beam using a computer controlled stepping motor. Counting rates in each detector channel were limited to 2×10⁴ counts per second (cps) when using a microchannel plate and to 1×10⁵ cps when using a fast photomultiplier tube. Excitation power was typically several hundred µW at 292 nm, obtained from the tripled output of a Ti:sapphire laser.⁶³

A buffer blank, N-acetyl tryptophanamide (NATA) control and protein measurement were obtained in an alternating fashion as described previously.^{28, 63} The approximately 5–10% variation in excitation intensity along the channel was corrected by the integrated intensity of the NATA control at each point along the channel.

Equilibrium titrations were performed with a Hamilton Microlab 500 series dual syringe pump interfaced using custom software (available at www.osmanbilsel.net) to the TCSPC instrumentation. The cuvette was placed in one position of a 4-position turret (Quantum Northwest, Pullman, WA) with NATA and a blank in two of the other positions. The index of refraction was measured for all stock solutions using a refractometer and the volume in the cuvet was measured before and after each titration to confirm the accuracy of the titration.

Small-angle x-ray scattering

Small-angle x-ray scattering measurements were performed at the BioCAT beamline at the Advanced Photon Source, Argonne, IL.⁶⁵ A monochromatic 12 keV x-ray beam was focused ~63 m from the undulator source onto the mixer channel. Equilibrium SAXS measurements were performed by interfacing a home-built autosampler running custom software (schematic and software available at www.osmanbilsel.net) to the standard glass sample capillary (1.5 mm diameter, 10 µ thick walls) at the BioCAT beamline. Samples were flowed using a Hamilton Microlab 560 dual syringe pump at a flow rate calculated to expose the sample to the beam for a total of ≤2 ms to minimize radiation damage (typically corresponding to a flow rate of 40 µL·s⁻¹). The flow was unidirectional and sample exposed to the beam was discarded and not used for further data collection. Approximately 15×1 s exposures were collected for each well of a 96-well microplate with 6 seconds in between each exposure to allow sufficient time for heat dissipation. A buffer blank under identical conditions was collected immediately before each protein sample. The samples (i.e., matching protein and buffer wells) were collected in a random order to avoid a systematic bias in the data. The setup included 8-position valves on the syringe pump to enable a multi-cycle wash of the capillary after each measurement containing protein. The wash consisted of a water, bleach, water, isopropyl alcohol and water rinse in successive order. Approximately 10 samples (blank, protein pair) were measured per hour.

Kinetics monitored using the standard SAXS arrangement were performed as previously described.⁶⁶ The experimental details of sub-millisecond kinetics measured using the micro-SAXS setup have been previously described.⁶⁴ The final protein concentration in both setups was 2 mg•mL⁻¹.

Data analysis

CF-trFRET

The continuous-flow TCSPC data was analyzed as previously described^{63, 67} using custom software for performing summation, subtractions, corrections and SVD analysis (available at www.osmanbilsel.net).

Equilibrium data analysis

Analysis of the equilibrium data was carried out as previously described.³⁹ Singular value decomposition⁶⁸ was used to obtain initial parameter estimates prior to a direct full global analysis of the raw data using Savuka.⁶⁹ For both the fluorescence and SAXS data sets, the multi-state models (see below) did not use the Z-approximation to describe the optical properties of the intermediate state(s). This was necessary because of the uncertainty introduced by the steep baselines in the SVD vectors for extracting species spectra of the intermediate states.

SAXS

Data analysis was performed using Igor Pro macros written by the BioCAT staff at APS. Guinier and Kratky analysis was performed as previously described.^{34, 66, 69}

Equilibrium data analysis

Equilibrium data was analyzed by fitting the data globally using a 4-state equilibrium unfolding model as described below. Fits to 2- and 3-state models were also carried for comparison and to establish the statistical validity of the 4-state model:

$$1^{*}\leftrightarrow 2^{*}\leftrightarrow 3^{*}\leftrightarrow 4^{*}$$

where 1=native, 2=low-denaturant intermediate, 3=high-denaturant intermediate and 4=unfolded state. (Note that the asterisk is used to indicate that the numbering in the above scheme is general for any equilibrium denaturation and does not correspond to the numbering scheme in the mechanism in Figure 6 of the main text). The fractional population of each species is given by X_i:

$$X_i=\frac{e^{\raisebox{1ex}{$-\mathrm{\Delta }{G}_{1,i}$}\!\left/ \!\raisebox{-1ex}{$RT$}\right.}}{Q}$$

where i=1,2,3 or 4 is the state number, ΔG_i,j is the free energy of unfolding from state i to state j, R is the gas constant and T is temperature. Q is the partition function for an unfolding model with N states:

$$Q=1+\sum _{i=2}^N{e}^{\raisebox{1ex}{$-\mathrm{\Delta }{G}_{1,i}$}\!\left/ \!\raisebox{-1ex}{$RT$}\right.}$$

A linear dependence of the free-energy on denaturant concentration, [D], was assumed, with the denaturant dependence given by m_eq for each state:

$$\mathrm{\Delta }{G}_{1,i}=\sum _{i=1}^i\mathrm{\Delta }{G}_{1,i}^{°}+m_{i,j,\mathit{\text{eq}}}·[D]$$

The total SAXS scattering intensity, I_tot(q_j) at a given scattering angle, q_j, is given by the sum of the scattering from each species, j:

$$I_{\mathit{\text{tot}}}(q_j)=\sum _{i=1}^N{I}_i(q_j)X_i$$

The scattering, I_i(q) at a given denaturant concentration is calculated from the scattering intensity in the absence of denaturant according to:

$$I_i(q_j)=I_i^{°}(q_j)+{\mathit{\text{slope}}}_{q_j}·[D]$$

The time-resolved decay, I_tot(t_k) is, similarly, the sum of contributions of the decay of individual components:

$$I_{\mathit{\text{tot}}}(t_k)=\sum _{i=1}^N{I}_i(t_k)X_i$$

where, t_k, is the time of the k^th point of the decay trace. The denaturant dependence is handled analogous to the scattering data:

$$I_i(t_k)=I_i^{°}(t_k)+{\mathit{\text{slope}}}_{t_k}·[D]$$

The thermodynamic parameters, ΔG_i,j and m_i,jeq are treated as variable global parameters in the optimization and the spectroscopic parameters, I(q) and I(t) and their slopes are treated as local parameters. The final global fits were performed using the raw SAXS and TCSPC data instead of the SVD v-vectors.

Research Highlights.

• Chain collapse in cytochrome c is compared using lifetime-resolved FRET and SAXS.

• Trp59- heme FRET pair require no extrinsic modifications for FRET or SAXS.

• Collapse proceeds without population of distances between compact and random coil.

• Minimizing dynamic averaging gives consistent results between FRET and SAXS.

• Marginally stable states in dynamic equilibrium with U need to be considered.

Abbreviations

CD

circular dichroism

CF

continuous-flow

FRET

Förster resonant energy transfer

GdnHCl

Guanidinium hydrochloride

SAXS

small-angle x-ray scattering

SVD

singular value decomposition

TCSPC

Time-correlated single-photon counting