Fast protein folding kinetics

Abstract

Fast-folding proteins have been a major focus of computational and experimental study because they are accessible to both techniques: they are small and fast enough to be reasonably simulated with current computational power, but have dynamics slow enough to be observed with specially developed experimental techniques. This coupled study of fast-folding proteins has provided insight into the mechanisms, which allow some proteins to find their native conformation well <1 ms and has uncovered examples of theoretically predicted phenomena such as downhill folding. The study of fast folders also informs our understanding of even 'slow' folding processes: fast folders are small; relatively simple protein domains and the principles that govern their folding also govern the folding of more complex systems. This review summarizes the major theoretical and experimental techniques used to study fast-folding proteins and provides an overview of the major findings of fast-folding research. Finally, we examine the themes that have emerged from studying fast folders and briefly summarize their application to protein folding in general, as well as some work that is left to do.

Fig. 1. Macro- and microstates

(a) Kinetics coarse grained to the level of secondary and tertiary structure formation, the level of resolution probed by many fast folding experiments. Shown is a folded macrostate (green), an unfolded macrostate (blue) and a compact helix-rich trap (red). k_a = k_m exp(-G_a/RT) is analogous to the Arrhenius equation in the main text. The prefactor k_m^-1 = τ_m, the inverse of the molecular time, is the rate for crossing from one macrostate to another in absence of a barrier (G_a≈0) (b) A very fine grained picture, including backbone torsional angles and side chain conformations, reveals each macrostate as an ensemble of many structurally related microstates. Microstates typically interconvert in a nanosecond or faster, with barriers G^† ≈ 10 kJ/mole and prefactors ≈ 1 ps (for torsional angles). The vast majority of these micro-conversions leave the protein in the same macrostate; the protein is “waiting,” not “folding.” Eventually, through thermal fluctuations, the protein finds “bottleneck” microstates (purple and turqoise). Not all motion within this transition state ensemble (TSE) is productive because there are so many coordinates the protein can stray in. Thus when motion through the TSE is projected onto a few macroscopic coordinates, the crossing takes τ_m ~ 1 μs instead of nanoseconds or less. This delay is often modeled as friction (of the protein with itself or solvent), although some of the microscopic processes involved may have barriers G^†. In analogy to the example from classical kinetics in the text, the splitting of the observed rate k_a into prefactor (e.g. friction) and Boltzman factor (G_a) depends on the choice of macro coordinates.

Fig. 2. Multiple pathways for folding

A more fine-grained analysis does not have to go all the way to torsions of the backbone and sidechains. The left shows a simplified network of ‘mesostates’ from the hidden Markov analysis in (Noé et al., 2009). The denatured ensemble moves through a network of states, some of which directly convert to the native state, others reaching the native state through alternative routes, including a trap accessible from both denatured and native states. Upon strong coarse graining and elimination of minority paths, a two-state interconversion from a denatured ensemble to the native state accounts for most of the experimentally observed dynamics. An experiment that probes only a low-resolution reaction coordinate (e.g. tryptophan fluorescence upon T-jump), may be satisfactorily explained by the scheme on the right, but data with more resolution (e.g. e,g. 2-D IR) may require a more mesosocopic level of description.

Fig. 3. Characterization of equilibrium ensembles

(a) Schematic denaturation curves characteristic of two-state to downhill folding mechanisms. The inset shows the free energy landscape as a function of reaction coordinate ‘R.C.’ Under low stress (green), the folded state ‘F’ is more stable, under high stress (red), the unfolded state is more stable. Low stress = physiological condition, or absence of denaturant. Consider the case where the probe signal depends upon R.C., but not on the stress. (Top Left) An ideal two-state folder should not have a folded or unfolded baseline because the location of the folded and unfolded basins does not move significantly upon stress. (Top Center) Significant folded and unfolded baselines indicate the presence of shifting F and U free energy minima upon stress; the barrier is much lower, but one could still approximately call this a two-state folder. (Top Right) As the baselines get steeper, it becomes difficult to distinguish the transition from folded to unfolded. In the most extreme cases (as shown in the inset), this corresponds to a single-well landscape. The protein population unfolds not over a barrier, but by diffusion as the well moves along R.C. (b) Schematic single-molecule distributions at the denaturation midpoint for the scenarios in (a). As the protein deviates from two-state folding, the unfolded and folded peaks broaden and begin to overlap. On the right, it makes no sense to label the overlapping peaks as separate populations. The peak at low FRET efficiency arises from singly-labeled molecules and does not report on the protein’s conformational distribution.

Fig. 4. Kinetics from single-molecule and ensemble traces

(a) A free energy landscape of WW domain; blue shows the ‘wait’ (time scale of kinetics) and red shows the actual transition from unfolded to folded (molecular time scale). (b) Single-molecule folding trajectory simulated on this free energy landscape (adapted from (Liu et al., 2009b)); the ‘wait’ time (activated kinetics time scale, blue) and molecular time scales (actual reaction event, red) are again shown. (c) This ensemble folding trace was simulated by auto-correlating the single-molecule trajectory in (b). The molecular phase is again highlighted in red and the activated phase in blue. (d) Experimental ensemble T-jump relaxation trace obtained by temperature-jumping FiP35 WW domain from 65 to 71°C. The fast time scale (~1 μs, red) corresponds to the molecular timescale of contact formation, the slow timescale (~10 μs, blue) corresponds to the distribution of ‘wait’ times in activated kinetics (adapted from (Liu et al., 2009b)).

Fig. 5. Villin headpiece

Local and global unfolding can have individual spectroscopic signatures. Kinetic relaxation trace of the K24,29Nle stablilized mutant after T-jump from 343 to 348 K (black line is a bi-exponential fit). Arrhenius analysis of the slower phase yields a folding time of 730 ns at melting temperature (360 K). The fast phase is well fit to decay time of 70 ns at all jump temperatures (data modified from (Kubelka et al., 2006)). The fast and slow phases are attributed to local unfolding near the tryptophan probe and global protein unfolding, respectively. Inset shows the structure of the 35-residue domain (PDB 1YRF, (Chiu et al., 2005)). The highlighted residues show the 3 phenylalanine hydrophobic core of F6, F10, and F17.

Fig. 6. Trp-cage

Folding speed and protein stability are often correlated. (a) Trp-cage structure (PDB 2JOF (Barua et al., 2005)) with W6 highlighted in blue. P12 (gray) was targeted for the stablilizing P12W mutation. (b) Thermodynamic stability of Trp-cage (orange) and Trp-cage P12W (blue), measured by CD at 222 nm. The P12W mutation stabilizes Trp-cage by ~15 °C and also speeds up the folding rate by a factor >4 (data adapted from (Bunagan et al., 2006)).

Fig. 7. BBA

Comparison of BBA folding in simulation and in experiment. 20 ns folding trajectory of BBA5, terminating in a final structure with RMSD 2.2 Å. At the right is the folded structure of BBA5 (adapted from (Snow et al., 2002)). The simulated and experimental folding kinetics of two BBA mutants are comparable. This simulation was the first to be directly compared with experimental folding relaxation times and equilibrium constants.

Fig. 8. WW domain

Mutations can move proteins into the downhill folding regime. (a) The native Pin1 WW domain (gray, PDB 1PIN, (Ranganathan et al., 1997)) has a long loop, responsible for its binding function, connecting beta sheets 1 and 2. A stabilized mutant (FiP35) ((Jäger et al., 2006) magenta, PDB 2F21) exhibits faster folding kinetics, but reduced binding activity, both due to its shortened loop. (b) A plot of activated folding time (blue dots) vs. melting temperature for 35 WW domain mutants highlights the correlation between stability and folding speed, calculated from a single exponential fit at the temperature of fastest folding. The fastest-folding WW domains show a molecular phase (open red circles) when the kinetics are fit using a double exponential (the activated time is shown as an open blue circle), showing that these mutants approach the ‘speed limit’ of downhill folding (adapted from (Liu et al., 2008)).

Fig. 9. NTL9

NTL9 shows two-state folding behavior in experiments, but simulations show multiple folding pathways. (a) Structure of NTL9 (PDB 2HBA). Highlighted in black is the mutated residue 12 (from lysine to methionine). The K12M mutant shows increased stability and folding speed. (b) Folding rate as a function of GuHCl denaturant concentration; native NTL9 (blue) and the K12M mutant (orange) relaxation kinetics were measured by stopped flow (adapted from (Horng et al., 2003)). The K12M mutant is more stable, determined by the position of intersection of the two arms of the chevron plot. The folding rate at 0 M GuHCl is determined by the intercept with the y-axis. The native protein folding time is 1.3 ms, while K12M folds in ~827 μs. Similar results are obtained with Urea induced folding. The straight arms at extreme GuHCl concentrations are consistent with 2 state folding. (c) The observation of two distinct folding energy landscapes in folding simulations of NTL9 (blue and orange) is inconsistent with the two-state behavior found in experiments. (d) Corresponding folding paths on the two energy landscapes for NTL9 observed in long all-atom simulations (c and d adapted from (Lindorff-Larsen et al., 2011)). The discrepancy between experimental and computational results may be due to force field errors, or to the existence of dynamics invisible to the experimental probe used (tryptophan fluorescence).

Fig. 10. Cold shock proteins

One member of the Csp family exhibits a downhill folding phase. (a) Structure of CspB from Bacillus subtilis (PDB 1CSP (Schindelin, Marahiel & Heinemann, 1993)). (b) Two phase unfolding of CspA from E. coli detected by IR absorbance in the amide I band after a temperature jump from 60 to 80 °C. The double exponential fit (red and blue) matches the data better than the single exponential fit (black). The fast relaxation (27 μs, red) is attributed to a minority downhill folding process (data adapted from (Leeson et al., 2000)).

Fig. 11. Protein A

The structure of Protein A is conserved even when the folding mechanism is altered. (a) Structure of Protein A (PDB 1BDC (Gouda et al., 1992)). The residues targeted by mutation are highlighted in black (F13W and G29A). (b) Folding rate constants for the F13W/G29A mutant calculated from NMR lineshape analysis upon denaturation using a mixture of Urea and Thiourea (3.3:1). The folding rate extrapolated to 0 M denaturant is 450,000 s^-1 (τ_fold ≈ 2 μs) (data adapted from (Arora et al., 2004)). (c) Unfolding of F13W/G29A in 2.2 M GuHCl. Traces monitored by CD (orange) and Tryptophan fluorescence (blue) are super-imposable, indicating that mutated protein exhibits 2-state folding (data adapted from (Dimitriadis et al., 2004)). The data in (b) and (c) show that, unlike the wild type, the mutated protein folds in a single, extremely fast, phase despite maintaining a similar folded structure.

Fig. 12. Homeodomain

Mutations can stabilize transiently formed intermediates. (a) Structure of wild-type homeodomain (top, PDB 2JWT (Religa, 2008)) and the isolable intermediate L16A (bottom, PDB 1ZTR (Religa et al., 2005)). Highlighted in black in each is the mutated residue 16. (b) Slow (circles) and fast (squares) rates of folding measured by of L16A as a function of temperature for different salt concentrations. Under low salt conditions, the L16A mutant forms a folding intermediate of the native protein, while under high salt its folding is similar to that of the native sequence. 100 mM NaCl (orange circles) has only a fast phase, corresponding to formation of the intermediate-like structure. 500 mM NaCl (blue circles and squares) shows both a fast and a slow phase, which matches well with the slow folding phase of the wild type protein (black line) (data adapted from (Religa et al., 2005)).

Fig. 13. Trpzips

Temperature influences the shape and roughness of the energy landscape. (a) Computational studies of trpzip folding reveal that the shape and the location of the free energy minimum changes with temperature. Shown here are representative structures obtained in the low- and high- temperature basins (adapted from (Yang et al., 2004)). At low temperatures, multiple minima exist within ≈ 4 RT of the native basin. (b) The computational predictions are supported by kinetic measurements that detect temperature- and probe-dependent temperature jump unfolding traces. The observable χ₁ is a measure of how the tryptophan lifetime changes during the reaction. Population of multiple basins is detected via temperature jumps monitoring fluorescence from more (orange) or less (blue) solvent exposed tryptophan. Both probes exhibit 2 distinct phases, but the microsecond phase is faster for the more exposed probe (data adapted from (Yang & Gruebele, 2004a)). This difference increases at higher temperatures.

Fig. 14. α₃D

α₃D folding cannot be modeled as a 1-dimensional process. (a) Structure of α₃D (PDB 2A3D (Walsh et al., 1999)). (b) 2D free energy surface as calculated by (Scott & Gruebele, 2010) using Langevin dynamics. (c) Kinetic rates measured by fluorescence (purple) and IR absorption (black) spectroscopy. Only the fluorescence data show a significant temperature dependence. 1D (dashed) and 2D (solid) models both fit the data, but the 1D fit diffusion coefficient is unrealistic, signaling that the model cannot fully capture the dynamics (adapted from (Scott & Gruebele, 2010)). (d) Time traces of Q (percent native contacts) and C_α-RMSD from (Lindorff-Larsen et al., 2011) are similar, but not identical for these two different coordinates. The low calculated barriers (< 3 RT) and probe-dependent dynamics (in both experiment and simulation) suggest that α₃D may be an incipient downhill folder. Here a future temperature-dependence simulation would be very useful.

Fig. 15. λ repressor fragment

λ_6-85 downhill folding increases with protein stability. (a) NMR lineshapes at 1.35 M (black) and 2 M (orange) Urea. The folded peak amplitude decreases with increasing urea concentration (data adapted from (Huang & Oas, 1995b)). (b) The relative amplitude of the molecular phase (A_m/A_a) decreases when lambda repressor fragment is stabilized and the activated rate approaches k_m (data adapted from (Yang & Gruebele, 2004b)): when the barrier decreases towards downhill folding upon protein stabilization, the activated population becomes sizeable and reacts promptly upon T-jump. (c) Free energy landscape of λ repressor, calculated from molecular dynamics simulations. Note the extremely low barrier between the folded and unfolded states (data adapted from (Lindorff-Larsen et al., 2011)), in agreement with the experimental measurement (Yang & Gruebele, 2004b). Inset shows the structure of λ_6-85 (PDB 3KZ3 (Liu et al., 2010)).

Fig. 16. BBL

BBL exhibits signatures of downhill folding in both experiments and simulations. (a) BBL folding monitored by MRE₂₂₂ as a function of pH. The CD signal changes approximately linearly with stress, indicative of a single basin free energy minimum (adapted from (Cerminara et al., 2012)). (b) The calculated free energy landscape of BBL from long, all-atom trajectories. (c) Snapshot of a single-molecule folding trajectory (b, c adapted from (Lindorff-Larsen et al., 2011)). The transitions from folded to unfolded are rather ‘fuzzy,’ as expected when distinct populations no longer exist.

Fig. 17. System size dependence of dynamical complexity

For small systems (e.g. organic chemical bond breaking), the dynamics are usually well captured by a single ‘reaction coordinate.’ For large and highly symmetrical systems that approach the thermodynamic limit (e.g. ice melting to water), system dynamics can be described by employing a single ‘order parameter.’ Intermediate-size systems, like proteins are not small enough for a single reaction coordinate, nor large and symmetrical enough for a single order parameter. They may require several coordinates for an adequate description.

Fig. 18. Folding in enthalpy and free energy

(Left) Protein enthalpy (H_c) as a function of configurational entropy (S_c) for two proteins. Enthalpy is reduced as both proteins fold because native contacts are made as the chain collapses. For one protein (red), the entropy decreases before the enthalpy decreases. For the other protein (blue), enthalpy and entropy decrease together. The enthalpy-entropy relationship is often plotted symmetrically (dotted red and blue) to convey the idea that many more coordinates are involved in this ‘funnel.’ Furthermore, the trace is usually roughened to convey the idea that non-native interactions may cause dips in the enthalpy. (Right) The ‘blue’ vs. ‘red’ difference is reflected in the free energy landscapes of the two proteins. While ΔG is similar for both proteins, only the ‘red’ protein encounters an activation barrier to folding (ΔG^†), caused by the initial drop in entropy without a compensating drop in enthalpy. The ‘blue’ protein folds downhill because enthalpy and entropy compensate along the way to the folded state. Solvent effects can be included in this description by modifying G(x). Non-native contacts can be included by adding small wells (‘roughness’), or by adding a coordinate-dependent diffusion coefficient, depending on how coordinates are chosen to describe the system. The ‘choice problem’ arises for the reasons illustrated by Fig. 17.