Continuous-flow capillary mixing apparatus in fluorescence mode. a Schematic of the solution delivery system, mixer, observation cell and optical arrangement. b Expanded view of the mixer. c Diagram illustrating continuous-flow measurement.

Schematic log(rate) vs. [denaturant] plots (chevrons) for a two-state (a) and a three-state (b) folding/unfolding mechanism. The lower panels show the predicted amplitude for the main folding phases (a₁), the burst phase predicted for a three-state process (a₀ in panel d) and the equilibrium unfolding transition (a_eq).

Continuous-flow measurements of the quenching of NATA fluorescence by NBS used to determine the experimental dead-time. a Plot of NATA fluorescence (>324 nm) vs. time at several NBS concentrations. b NATA-NBS reaction rates from exponential fitting of the data in panel a vs. NBS concentration. Linear regression (line) yields a second-order rate constant of 7.9 10⁵ M⁻¹ s⁻¹.

Schematic of a microfluidic mixer designed by Bilsel et al.91. The 127-μm-thick mixer is sandwiched between quartz windows and is sealed in a stainless-steel holder using Teflon gaskets (1.6 mm thick). Solutions are delivered to and from the mixing region through holes in the upper layers (arrows). Reprinted with permission from ref 91. Copyright 2005 American Institute of Physics.

Initial stages of refolding of acid-denatured oxidized cyt c at pH 5 monitored by continuous-flow absorbance measurements at different wavelengths spanning the Soret heme absorbance band. The lines represent a global fit of a four-state folding mechanism to the family of kinetic traces. Reprinted with permission from ref 138. Copyright 2004 Elsevier Inc.

Sequential four-state mechanism involving two partially structured ensembles, I₁ and I₂, in addition to the acid-unfolded (U) and native (N) states. Cartoons of various states apomyoglobin consistent with the fraction of helical residues (f_H) and radius of gyration (R_g) reported in ref 89. Cylinders indicate the approximate position of α-helices in the native state and possible arrangement of core helices in the intermediates consistent with amide protection data.171,174

a Ribbon diagram of horse cytochrome c, based on the crystal structure266. b Refolding kinetics of acid-unfolded cyt c at pH 4.5, 22 °C measured by continuous-flow mixing, indicating heme-induced quenching of Trp59 fluorescence associated with chain collapse.76 Inset: Arrhenius plot for the rates of the major (circles) and the minor (squares) submillisecond phases. Adapted from ref 76 (Figure 2).

GuHCl-dependence of the rate constants (a) and kinetic amplitudes (b) of the fast (squares) and slow (circles) kinetic phases observed during folding of GB1. c Free energy diagrams for folding of GB1 under conditions where the intermediate, I is well populated (0 M) and unstable (2.5 M GuHCl). α represents the change in solvent-accessible surface area relative to the unfolded state U. Reprinted with permission from ref 78. Copyright 1999 Nature Publishing Group.

Kinetic mechanism of Im7 folding. a Ribbon diagram of Im7. b Representative kinetic trace measured by continuous-flow (●) and stopped-flow (○) fluorescence. The kinetics at this and all other urea concentrations measured is accurately predicted by on on-pathway mechanism (solid line) while schemes with off-pathway intermediates fail to reproduce the data (dashed line). c Observed (symbols) and predicted (solid lines) rates of folding and unfolding, based on mechanisms with on-pathway (left) and off-pathway (right) intermediates. Dashed lines indicate the corresponding elementary rate constants. Adapted from ref 81 (Figures 2 and 3).

Expanded region of the rate profile (log rate vs. [GuHCl[) for the two main phases (circles and squares) and a minor slower phase (dtriangles) observed during folding of F45W ubiquitin (pH 5, 25 °C). The solid lines show the rates predicted by a three-state model, and the dashed lines indicate the elementary rate constants used. The X-symbols show the apparent rates obtained by triple-exponential fitting (Figure 10b). Reprinted with permission from ref 14. Copyright 2005 Wiley-VCH.

FRET-detection of an early folding intermediate in a helix-bundle protein, ACBP. a Ribbon diagram of ACBP, based on an NMR structure. The two tryptophan residues and the mutated C-terminal isoleucine are shown in ball and stick. The two lower panels show refolding kinetics of unmodified ACBP (b) and AEDANS-labeled ACBP,I86C (c) in pH 5.3 buffer containing 0.34 M GuHCl at 26 °C. In both panels data from continuous-flow (○) and stopped-flow (▽) experiments were matched and combined. Reprinted with permission from ref 83. Copyright 2002 National Academy of Sciences of the USA.

Comparison of quadruple (a) and triple (b) exponential fitting of the kinetics of refolding of F45W ubiquitin at final GuHCl concentrations of 0.5 and 1.0 M (pH 5, 25 °C). Fluorescence traces measured in continuous- and stopped-flow experiments were normalized with respect to the unfolded protein in 6 M GuHCl. The residuals (top two traces in each panel) indicate that four exponentials are required to obtain a satisfactory fit of the data over the time window shown. Reprinted with permission from ref 14. Copyright 2005 Wiley-VCH.

Stopped-flow fluorescence evidence for an unresolved rapid process (burst phase) during folding of cyt c (pH 5, 10 °C). a Tryptophan fluorescence changes during refolding of acid-unfolded cytochrome c (pH 2, ~15 mM HCl) at a final GuHCl concentration of 0.7 M. The initial signal S(0) at t=0 (determined on the basis of a separate dead-time measurement) falls short of the signal for the unfolded state under refolding conditions, S_pred(U), obtained by linear extrapolation of the unfolded-state baseline (see dashed line in b). b Effect of the denaturant concentration on the initial (squares) and final (circles) fluorescence signal, S(0) and S(∞), measured in a series of stopped-flow refolding experiments at different final GuHCl concentration. Reprinted with permission from ref 138. Copyright 2004 Elsevier Inc.

Folding mechanism of SNase probed by tryptophan fluorescence. a Fluorescence emission spectra of the Trp76 variant of SNase under native and denaturing conditions (solid) and a folding intermediate populated at equilibrium (dashed). The spectrum of the intermediate was determined by global analysis of the fluorescence spectra as a function of urea concentration (pH 5.2, 15 °C). b Time-course of folding (triggered by a pH jump from 2 to 5.2) for wild-type SNase (Trp140) and a single-tryptophan variant (Trp76) measured by continuous-flow (< 10⁻³ s) and stopped-flow (> 10³ s) fluorescence. c ANS fluorescence changes during ANS binding/folding of Trp76 SNase measured by continuous-flow experiments at 15°C in the presence of 160 μM ANS. U → A: Salt concentration jump from 0 M to 1 M KCl at pH2.0; U → N: refolding induced by a pH-jump from 2.0 to 5.2; A+ANS → A•ANS: ANS binding kinetics in the presence of 1 M KCl at pH 2.0; native control: ANS binding kinetics under the native condition (pH 5.2). Adapted from ref 87 (Figures 3 and 5).

Characterization of an intermediate populated during folding of cytochrome c (pH 6, 10 °C).173 a Fractional degree of labeling vs. pulse pH for a representative set of NH groups measured by 2D NMR analysis of refolding cytochrome c samples that were exposed to a 50 ms labeling pulse of increasing pH at a folding time of 100 ms. Solid lines represent a fit of the data yielding the rates of formation and unfolding of the intermediate state (see text). Dashed lines indicate the labeling profiles expected in the absence of structure. b Equilibrium constant for formation of the intermediate, K_UI = k_UI/k_IU, based on the fits of the labeling results in a. Values of K_UI ≥ 1 indicative of persistent hydrogen bonded structure are mainly found for residues in the N- and C-terminal helices. Cys 14, Ala15 and His 18 (gray bars) are protected even in the unfolded state. Adapted from ref 173 (Figures 3 and 4), with permission by the authors.

Folding kinetics of GB1 at pH 5.0, 20 °C, in the presence of 0.4 M sodium sulfate. Panel a shows a representative kinetic trace at 1.12 M GHCl monitored by continuous-flow (circles) and stopped-flow (diamonds) fluorescence along with controls for fully unfolded (U) and folded (N) solutions. Single- and double-exponential fits and residuals are shown with solid and dashed lines, respectively. Reprinted with permission from ref 78. Copyright 1999 Nature Publishing Group. Panel b shows a family of refolding traces at the final GuHCl concentrations indicated. Solid lines show the time course predicted on the basis of a three-state model (Scheme 3), using the following parameters: k_UI° = 2300 s⁻¹, m_UI^‡ = −0.6 kcal mol⁻¹M⁻¹, k_IU° = 70 s⁻¹, m_IU^‡ = 1.15 kcal mol⁻¹M⁻¹, k_IN° = 600 s⁻¹, m_IN^‡ = 0, k_NI° = 0.14, m_NI^‡ = 0.3 kcal mol⁻¹M⁻¹ (see Figure 11a, ref 78). The relative signals for the N-, I- and U-states were s_N = 0.29 ± 0.01, s_I = s_U = 0.98 ± 0.02. Dashed lines indicate a best “fit” of a two-state mechanism, using rate constants falling on a linear extrapolation of the chevron plot between 1.5 and 3 M GuHCl to lower denaturant concentrations (cf. ref 213).

As a first application of absorbance-detected continuous-flow mixing, we measured the changes in heme absorbance in the Soret region (~360–430 nm) associated with the folding of oxidized horse cyt c.138 The reaction was initiated by a rapid jump from pH 2, where the protein is fully unfolded, to pH 4.7, where folding occurs rapidly with minimal complications due to non-native histidine-heme ligands. A series of kinetic traces covering the time window from 40 μs to ~1.5 ms were measured at different wavelengths spanning the Soret region (Figure 6). A parallel series of stopped-flow experiments (data not shown) was performed under matching conditions to extend the data to longer times (2 ms to 10 s). Global fitting of the family of kinetic traces to sums of exponential terms yielded three major kinetic phases with time constants of 65 μs, 500 μs and 2 ms, respectively, consistent with accumulation of two intermediate species, I and M (Scheme 1), with absorbance properties distinct from both the initial (U) and final (N) states. In previous continuous-flow fluorescence measurements on horse cyt c,76,77 we also observed three kinetic phases with very similar time constants, indicating that a basic four-state mechanism is sufficient to describe the folding process of cyt c in the absence of complications due to non-native heme ligation and other slow events, such as cis-trans isomerization of peptide bonds.

While these findings clearly indicate that many small proteins can fold rapidly without going through intermediates, there is little support for the notion that early intermediates slow down the search for the native conformation,164,255,256 except in cases where they contain features inconsistent with the native fold, such as nonnative proline isomers, metal ligands163,164,257 or intermolecular interactions.258 In fact, solution conditions that favor accumulation of intermediates, such as low denaturant concentrations or stabilizing salts, generally accelerate the overall rate of folding.10 Conversely, mutations that destabilize or abolish early intermediates often result in much slower rates of folding,195,259,260 which is a strong indication that they are productive states. Although continuous-flow results are fully consistent with a sequential mechanism involving obligatory intermediates,76,78,83,138 it has been difficult to rigorously demonstrate that early intermediates are obligatory states on a direct path to the native state (Scheme 3). Alternative mechanisms involving formation of nonproductive states (Scheme 4) or mechanisms with parallel pathways and non-obligatory intermediates (Scheme 5) can be ruled out only if (i) the two transitions are kinetically coupled (i.e., they have similar rates), (ii) both phases are directly observable and kinetically resolved, and (iii) the experimental probe used to monitor folding can discriminate native from intermediate and unfolded populations. Under these circumstances, the transient accumulation of an obligatory intermediate leads to a detectable lag in the appearance of the native population whereas an off-path intermediate gives rise to a rapid increase in the population of N during the initial phase. Clear evidence for such a lag phase was obtained in a stopped-flow fluorescence study on a proline-free variant of staphylococcal nuclease.206 On the other hand, a thorough kinetic analysis, using a double-jump protocol, indicated that a late intermediate during folding of lysozyme is non-obligatory.115 Other efforts to detect a lag phase during folding of interlukin-1β261,262 and apoMb230 were inconclusive because of the disparate time scales of early and rate-limiting folding events. In order to determine the kinetic role of early folding intermediates, it is necessary to directly measure the population of native molecules on the submillisecond time scale, either by double-jump experiments or via a specific spectroscopic probe for the native state.

While these findings clearly indicate that many small proteins can fold rapidly without going through intermediates, there is little support for the notion that early intermediates slow down the search for the native conformation,164,255,256 except in cases where they contain features inconsistent with the native fold, such as nonnative proline isomers, metal ligands163,164,257 or intermolecular interactions.258 In fact, solution conditions that favor accumulation of intermediates, such as low denaturant concentrations or stabilizing salts, generally accelerate the overall rate of folding.10 Conversely, mutations that destabilize or abolish early intermediates often result in much slower rates of folding,195,259,260 which is a strong indication that they are productive states. Although continuous-flow results are fully consistent with a sequential mechanism involving obligatory intermediates,76,78,83,138 it has been difficult to rigorously demonstrate that early intermediates are obligatory states on a direct path to the native state (Scheme 3). Alternative mechanisms involving formation of nonproductive states (Scheme 4) or mechanisms with parallel pathways and non-obligatory intermediates (Scheme 5) can be ruled out only if (i) the two transitions are kinetically coupled (i.e., they have similar rates), (ii) both phases are directly observable and kinetically resolved, and (iii) the experimental probe used to monitor folding can discriminate native from intermediate and unfolded populations. Under these circumstances, the transient accumulation of an obligatory intermediate leads to a detectable lag in the appearance of the native population whereas an off-path intermediate gives rise to a rapid increase in the population of N during the initial phase. Clear evidence for such a lag phase was obtained in a stopped-flow fluorescence study on a proline-free variant of staphylococcal nuclease.206 On the other hand, a thorough kinetic analysis, using a double-jump protocol, indicated that a late intermediate during folding of lysozyme is non-obligatory.115 Other efforts to detect a lag phase during folding of interlukin-1β261,262 and apoMb230 were inconclusive because of the disparate time scales of early and rate-limiting folding events. In order to determine the kinetic role of early folding intermediates, it is necessary to directly measure the population of native molecules on the submillisecond time scale, either by double-jump experiments or via a specific spectroscopic probe for the native state.

A second line of evidence supporting accumulation of early folding intermediates has been based on the dependence of folding rates on denaturant concentration (usually guanidine HCl or urea), as illustrated schematically in Figure 9. In the absence of populated intermediates, a logarithmic plot of the measured rate constant of folding, k_f, vs. denaturant concentration (panel a) often describes a V-shape with a decreasing linear dependence at denaturant concentrations below the midpoint of the unfolding transition (C_m), a minimum at C_m, and a linearly increase for the rate of unfolding at denaturant concentrations above C_m (hence the name “chevron plot”).95,197,198 As illustrated by Figure 9b, accumulation of intermediate states prior to the rate-limiting folding step can give rise to a non-linear folding branch of the chevron plot, usually a downward curvature with decreasing denaturant concentration. The discovery of this so-called rollover effect is often attributed to Matouschek et al.,96 who found that the chevron plot for barnase showed a pronounced curvature at low denaturant concentrations. However, Matthews and colleagues described similar complexities in the folding kinetics of the α-subunit of tryptophan synthase as early as 1981.199 A quantitative connection between folding intermediates and the rollover effect was established be several groups in the mid-1990’s who used quantitative kinetic models to explain the curvature in the log(k_f) vs. [denaturant] dependence in terms of accumulation of an early (obligatory) folding intermediate.195,200,201 Khorasanizadeh et al.195 further showed that both the rollover and burst-phase effects can be modeled quantitatively by a three-state folding mechanism (Scheme 3) involving rapid formation of an intermediate prior to the rate-limiting formation of the native state. In this scenario, a partially folded state is sufficiently stable to become populated at low denaturant concentrations and limits the overall rate of folding, which gives rise to both deviation from linearity in the chevron plot (Figure 9b) and a drop in the observable kinetic amplitude of the main (rate-limiting) folding phase (Figure 9d). In many cases, the observed folding times at low denaturant concentrations approach values in the millisecond range, which rules out the possibility that the rate-limiting process represents cis/trans isomerization of a proline peptide bond.37,202,203 Moreover, the amplitude behavior shown in Figure 9d where the fast kinetic phase is dominant at low denaturant concentrations (a_o approaching 1) and decreases in amplitude at the expense of the slow phase (a₁) is characteristic of a sequential folding process with an on-pathway intermediate. In contrast, slow isomerization steps, such as proline isomerization, that precedes the formation of the native state generally gain amplitude under destabilizing conditions approaching the midpoint of the unfolding transition.203