Local conformational dynamics in α-helices measured by fast triplet transfer

Abstract

Coupling fast triplet–triplet energy transfer (TTET) between xanthone and naphthylalanine to the helix–coil equilibrium in alanine-based peptides allowed the observation of local equilibrium fluctuations in α-helices on the nanoseconds to microseconds time scale. The experiments revealed faster helix unfolding in the terminal regions compared with the central parts of the helix with time constants varying from 250 ns to 1.4 μs at 5 °C. Local helix formation occurs with a time constant of ≈400 ns, independent of the position in the helix. Comparing the experimental data with simulations using a kinetic Ising model showed that the experimentally observed dynamics can be explained by a 1-dimensional boundary diffusion with position-independent elementary time constants of ≈50 ns for the addition and of ≈65 ns for the removal of an α-helical segment. The elementary time constant for helix growth agrees well with previously measured time constants for formation of short loops in unfolded polypeptide chains, suggesting that helix elongation is mainly limited by a conformational search.

Conformational dynamics is of fundamental importance for folding and function of biomolecules (1). Structural fluctuations in proteins occur on different time scales and involve various degrees of motions from side-chain rotations to complete folding/unfolding reactions. Only a few methods exist that allow the study of conformational transitions between different states in equilibrium. NMR spectroscopy, single-molecule fluorescence and hydrogen/deuterium (H/D) exchange experiments allow the characterization of different kinds of equilibrium dynamics, but they are insensitive for transitions on the nanoseconds to microseconds time scale (2, 3). On this time scale, large-scale backbone movements (4, 5) and structural transitions in α-helices (6–8) and β-hairpins (9) occur that play a key role in conformational transitions during protein folding, misfolding, and regulation. We therefore sought a method to study site-specific equilibrium transitions on the nanoseconds to microseconds time scale that allows us to gain insight into the dynamics of the α-helix-to-coil transition.

Isolated α-helices are multistate systems with higher helix content in the center compared with the helix ends (10–13). Numerous theoretical models for the helix–coil transition have been proposed (10, 11, 13–18). Theoretical models typically assume a nucleation–growth mechanism with the establishment of a first helical turn representing an entropically unfavorable, slow nucleation reaction. In the subsequent growth reactions, helical segments are added, which is supposed to be a fast process. Experimental studies on helix dynamics have been limited to perturbation methods starting from an ensemble of helical states (6–8, 19–23). Dielectric relaxation measurements (6) and ultrasonic absorption techniques (7) on long homopolymeric helices revealed relaxation times for helix unfolding on the hundreds of nanoseconds to microseconds time scale, depending on the nature of the solvent and on the amino acid sequence. From these experiments, time constants in the range of 0.1–10 ns were estimated for the growth reaction (7). Nanosecond temperature-jump (T-jump) methods on short alanine-based peptides also showed relaxation times for helix unfolding on the hundreds of nanoseconds to microseconds time scale (8, 19–22, 24) and also yielded similar time constants for helix growth (8). T-jump relaxation dynamics using an N-terminal fluorescence probe revealed faster helix unfolding in the N-terminal region compared with the decrease in average helix content (8). Site-specific IR studies on ¹³C-labeled peptides, in contrast, suggested only little position dependence of the relaxation times after a T-jump (22, 25–27). These studies gave insight into the kinetics of perturbation-induced helix unfolding, but they did not yield information on the dynamic properties of α-helices under equilibrium conditions. Equilibrium dynamics may substantially differ from perturbation-induced kinetics because of the non-2-state nature of the helix–coil transition. This complexity may lead to different dynamics depending on the initial conditions as observed for different-size T-jumps to identical final conditions (22).

Linking an irreversible process to a conformational transition is a powerful kinetic approach to study stability and dynamics of chemical equilibria. A well-known example is the use of H/D exchange to gain information on individual hydrogen bonds in proteins (2, 28, 29). H/D exchange occurs on the milliseconds to hours time scale, depending on pH, and is thus not suited to measure dynamics on the nanoseconds to microseconds time scale. We have previously applied diffusion-controlled triplet–triplet energy transfer (TTET) between a xanthone donor and a naphthylalanine acceptor group to observe intrachain loop formation in unfolded polypeptide chains (4, 5, 30). TTET through loop formation is an irreversible process that is based on Van der Waals contact between donor and acceptor. It should thus enable us to monitor dynamics in folded and partially folded structures when linked to a folding/unfolding equilibrium. Because loop formation occurs on the 10–100 ns time scale, depending on loop length, amino acid sequence, and on the position of the loop within the chain (5, 30), this approach allows us to monitor dynamics that are 4–5 orders of magnitude faster than those accessible to H/D exchange. A prerequisite for the application of TTET is that contact between the TTET labels can only occur by loop formation in the coiled state and is prevented in the folded structure. Experiments by Lapidus et al. (31) had indicated that contact formation between the ends of an α-helix does not occur. To investigate local helix folding and unfolding dynamics, we introduced xanthone and naphthylalanine with i,i+6 spacing at different positions along an α-helical peptide. This places the labels at opposite sides of the helix, which prevents TTET in the helical state and requires at least partial unfolding before triplet transfer can occur (Scheme 1; see also Scheme S1 in the supporting information). This approach allowed us to determine the local unfolding and refolding rate constants for the helix–coil transition at equilibrium for different positions in the α-helix. The results were compared with simulations of the helix–coil dynamics using a linear Ising model, which gave insight into the basic dynamics of the helix–coil transition.

Scheme. 1.

Results and Discussion

Design and Global Stability of the Helices.

We used an alanine-based model peptide with the sequence Ac-(A)₅-(AAARA)₃-A-NH₂ to measure local α-helix dynamics and stability. Similar peptides were shown to exhibit ≈70% helical content at low temperature (8, 32), and their unfolding kinetics have been probed in relaxation studies (8, 19–22). TTET labels were introduced at different positions along the peptide by using a xanthone moiety (Xan; X) as triplet donor and the nonnatural amino acid 1-naphthlylalanine (Nal; Z) as triplet acceptor (see Table 1). The labels were placed with i, i + 6 spacing to prevent contact between the labels in the helical state (Fig. 1A). Introducing the labels in the N-terminal region (X1–Z7), in the interior (X5–Z11, X7–Z13, X11–Z17) or in the C-terminal region (X15–Z21) allowed us to monitor local dynamics and stability in different regions of the helix. To compare the local dynamics with global helix unfolding and refolding, the TTET labels were positioned at the ends of the helix in the X0–Z21 peptide.

Table 1.

Sequences of helical peptides used in TTET experiments

Peptide	Sequence
X0–Z21	X-AAAAA AAARA AAARA AAARA ZGG-NH2
X1–Z7	Ac-XAAAA AZARA AAARA AAARA A-NH2
X5–Z11	Ac-AAAAX AAARA ZAARA AAARA A-NH2
X7–Z13	Ac-AAAAA AXARA AAZRA AAARA A-NH2
X11–Z17	Ac-AAAAA AAARA XAARA AZARA A-NH2
X15–Z21	Ac-AAAAA AAARA AAARX AAARA Z-NH2

X, xanthonic acid (Xan) attached to the N-terminus (X0–Z21) or to α,β-Dpr (all other peptides); Z, 1-naphthylalanine (Nal).

Fig. 1.

Structure and dynamics of the helical peptides labeled with donor and acceptor groups for TTET. (A) Schematic position of the labels in the helix. For sequences, see Table 1. (B) Far-UV CD spectra. (C) TTET kinetics measured by the decrease in xanthone absorbance at 590 nm. The colors of the lines correspond to the colors of the helical segments probed by TTET as shown in A. The black lines represent the results from double-exponential fits. As an example, the residuals for single- and double-exponential fits are displayed for the TTET kinetics in the X5-Z11 helix. Results for the X5-Z11 helix in the presence of 40% TFE are additionally shown in gray. Experiments were performed at 5 °C.

Xanthone and napthylalanine are expected to have a small helix-destabilizing effect compared with alanine. Fig. 1B shows that all peptides form similar amounts of helical structure as judged by the positive CD bands at 190 nm and the negative bands at ∼208 and 222 nm. Contributions of Nal to the CD signal at ≈220 nm prevent a quantitative determination of the helix content, but the relative differences between the peptides can be assessed. In the X0–Z21 reference peptide, the effect of the labels on helix stability should be negligible because of the low helix content at the termini (12). Introduction of the labels with i, i + 6 spacing has only little effect on global helix stability relative to the X0-Z21 peptide. A slight destabilization is observed when the labels are placed near the helix center, as expected from helix–coil theory (11–13). Based on the differences in CD signal at 222 nm, the helix content of the different peptides varies by <15%. This similarity in helical content was confirmed by thermal melting transitions, which showed similar changes in the CD signal upon unfolding for all peptides (Fig. S1).

Kinetics of TTET Coupled to a Helix–Coil Transition.

We performed TTET experiments at 5 °C to measure dynamics in the different peptides. TTET was monitored by the change in xanthone triplet absorbance at 590 nm (5). All peptides exhibit double-exponential TTET kinetics (Fig. 1C), which was confirmed by an analysis of the distribution of time scales for the observed kinetics (Fig. S2). The slowest kinetics were found for the X0–Z21 peptide with a main kinetic phase of λ₁ = 2.3·10⁵ s⁻¹ (90% amplitude) and a faster phase of λ₂ = 2.6·10⁶ s⁻¹ (10% amplitude). In the peptides with local i, i + 6 spacing, faster TTET kinetics with a larger amplitude of the fast phase are observed when the labels are attached near the termini compared with the central positions (Table 2). In all peptides, the 2 observable reactions are faster than spontaneous donor triplet decay, which occurs with λ_T = 2.5·10⁴ s⁻¹, measured in donor-only reference helices. This demonstrates that the observed triplet decay in the helical peptides is due to intrinsic dynamics in the helix–coil system and is not reflecting the triplet lifetime. The observed double-exponential kinetics suggest an equilibrium between 2 distinct populations of molecules. To test for the origin of the 2 kinetic phases, we stabilized the helical state by addition of 40% TFE (33), which results in slow single-exponential TTET kinetics with a rate constant of λ = 1.2·10⁵ s⁻¹ for the X5–Z11 peptide (Fig. 1) indicating the absence of the fast process. In contrast, addition of urea, which destabilizes helical structure (34), leads to an increase in amplitude of the fast phase in all peptides (see below). These results suggest that the slow process originates from molecules that contain a critical amount of helical structure between the labels. In these molecules, TTET can only occur via helix unfolding. The fast phase is related to TTET in conformations that are at least partially unfolded between the labels. This model is supported by the magnitude of the observed time constants. The slow phase has time constants on the microseconds time scale in the X0–Z21 peptide, which is similar to the observed relaxation times for helix unfolding after temperature jump (8, 19–22). The fast phase is on the 100-ns time scale, which is in agreement with the time constant for loop formation in unfolded polypeptide chains (5, 30).

Table 2.

Kinetic and thermodynamic parameters

Peptide	λ1(106 s−1)	λ2(106 s−1)	A1, %	A2, %	kf(106 s−1)	ku(106 s−1)	kc(106 s−1)	mf(J/mol)/M	mu(J/mol)/M	mc(J/mol)/M	Keq
X1-Z7	2.4 ± 0.3	12 ± 4.0	71 ± 5	29 ± 5	3.0 ± 0.6	3.3 ± 0.3	11.1 ± 1.5	696 ± 224	199 ± 89	136 ± 102	0.9 ± 0.3
X5-Z11	0.78 ± 0.08	8.2 ± 3.2	88 ± 3	12 ± 3	4.0 ± 0.7	1.0 ± 0.1	7.4 ± 1.1	908 ± 131	−66 ± 71	149 ± 97	3.9 ± 0.9
X7-Z13	0.55 ± 0.04	5.6 ± 3.5	81 ± 2	19 ± 2	1.9 ± 0.4	0.7 ± 0.1	8.0 ± 0.7	831 ± 116	−222 ± 73	230 ± 52	2.5 ± 0.6
X11-Z17	2.0 ± 0.3	8.0 ± 2.4	67 ± 10	33 ± 10	2.5 ± 0.6	3.0 ± 0.4	8.1 ± 1.1	687 ± 254	83 ± 140	200 ± 83	0.8 ± 0.3
X15-Z21	2.7 ± 0.5	11 ± 4.0	58 ± 10	42 ± 10	1.8 ± 0.5	3.7 ± 0.4	9.0 ± 1.2	772 ± 330	321 ± 149	154 ± 99	0.5 ± 0.2
X0-Z21	0.23 ± 0.03	2.6 ± 0.9	90 ± 2	10 ± 2	0.9 ± 0.2	0.3 ± 0.1	1.6 ± 0.3	537 ± 166	−116 ± 63	90 ± 80	—

The Xan triplet decays of all peptides can be fitted by double exponential functions yielding the apparent rate constants λ ₁ and λ ₂ and the relative amplitudes A, which are given only for the decays in the absence of urea. The microscopic rate constants k_f, k_u, and k_c were obtained by a global analysis of all decays at different urea concentrations using the 3-state model (Scheme 1) and are given for 0 M urea. Their sensitivity toward urea is described by the m_i values. K_eq gives the local equilibrium constant between closed and open conformations between the labels.

Rate Constants for Local Helix Formation and Unfolding.

The observation of 2 observable rate constants, λ₁ and λ₂, for TTET in the helical peptides allows the determination of the microscopic rate constants k_u and k_f reporting on unfolding and formation of helical structure and of k_c, the rate constant for loop formation in the unfolded state in a single experiment (see Scheme 1). We use the analytical solutions for the mechanism shown in Scheme 1 (see SI Text) to analyze the kinetics without any simplifying assumptions. It should be noted that this approach is different from the classical EX1 and EX2 limits commonly used to analyze H/D exchange kinetics, which allow the determination of either the equilibrium constant between a folded and an unfolded state (EX2) or the microscopic rate constant for the unfolding process (EX1) and is only applicable if the unfolded state is populated to very low amounts. It further uses simplified equations that are only valid under certain conditions (29). Determination of all microscopic rate constants from these experiments thus requires a change in the experimental conditions from the EX2 limit to the EX1 limit.

Because of the low amplitude of the fast phase in the central parts of the helix, the experiments were performed in the presence of different urea concentrations between 0 and 7 M. This allows a more reliable determination of all microscopic rate constants and gives additional mechanistic insight into the dynamics (35). We assumed that urea has a linear effect on ln(k_f) and ln(k_u) (34, 36) as well as on ln(k_c) (5, 37) according to

where k_i denotes a given microscopic rate constant, k_i(H₂O) is the rate constant in the absence of urea, and m_i denotes the sensitivity of the respective reaction to urea (m value).

Double-exponential TTET kinetics are observed for all peptides and at all urea concentrations. The urea dependences of λ₁ and λ₂ and of the respective amplitudes A₁ and A₂ were fitted globally to the analytical solution of the 3-state model shown in Scheme 1 (38) to yield the microscopic rate constants k_i(H₂O) and their urea dependences (m_i) (see SI Text). Fig. 2 shows the results from the global fit for all helices, which reveal that λ₁, λ₂, A₁, and A₂ contain contributions from all microscopic rate constants. This allows a reliable determination of k_f, k_u, and k_c in all helical peptides. The k_f and k_u values obtained for the different peptides reflect the local dynamics for helix folding and unfolding at different positions in the helix (Fig. 3 and Table 2). Comparison of the results for the different helices shows that local helix formation does not systematically depend on the position along the helix and has a time constant (1/k_f) ≈400 ns in all peptides (Fig. 3A). Local helix opening, in contrast, is ≈6-fold faster at the termini (1/k_u = 250 ns) compared with the helix center (1/k_u = 1.4 μs; Fig. 3B). This difference does not arise from the effect of the labels on helix stability, because the destabilization is largest at the helix center (Fig. 1) (12) where the slowest rate constants for unfolding are observed. Attaching the labels at the ends of the helix in the X0–Z21 reference peptide yields slower dynamics compared with all local folding/unfolding reactions with time constants of 1.1 μs for helix formation and 3.3 μs for helix unfolding (Fig. 1 and Table 2). This observation suggests that end-to-end contact formation monitors more global structural transitions.

Fig. 2.

Effect of urea on the TTET kinetics in different helical peptides at 5 °C. The observable rate constants λ₁ (●) and λ₂ (○) (Upper) and their corresponding amplitudes, A₁ (●) and A₂ (●) (Lower) obtained from double-exponential fits to the Xan triplet decays (see Fig. 1C) are shown. The results from the global fit to the 3-state model (Scheme 1) are displayed for the observable rate constants and their amplitudes (black lines) as well as for the microscopic rate constants k_u (red lines), k_f (blue lines), and k_c (green lines).

Fig. 3.

Position dependence of local helix dynamics and stability. The horizontal bars indicate the regions of the helix probed in the different peptides. The microscopic rate constants for helix formation, k_f (A), and helix unfolding, k_u (B), obtained from the global fit of the TTET kinetics (see Table 1) are shown in addition to the equilibrium constant, K_eq (C). For comparison, the results from the simulations using the kinetic Ising model (○) with s = 1.31, σ = 0.003 and γ_h = γ_c = 2 are displayed. The rate constants used in the simulations were scaled with k₁ = 2.1·10⁷ s⁻¹ (see Eqs. 2–6).

The urea dependence of k_f shows an almost position-independent m_f value of ≈800 (J/mol)/M (Table 2). The m_u values are much smaller and show complex behavior, with positive values at the helix termini and negative values for the central positions. In terms of a classical interpretation of protein folding m values, this indicates that the transition state for helix formation has native-like solvent-accessible surface area (35).

The microscopic rate constants for contact formation k_c in the coil state are ≈100 ns in all peptides (Table 2). These values are slightly lower than the rate constants observed for formation of i, i + 6 interactions in polyserine model chains at 5 °C (39), which is expected, taking into account that loop formation in the helical peptides involves interior parts of the chain, which are less flexible than the ends (30). The m_c values are approximately 200 (J/mol)/M and virtually position independent. This value is identical to the m_c values found for loop formation in unfolded model polypeptide chains (5, 37). These results indicate that in the alanine-based helical peptides the ensemble of conformations that can form contact between the labels has similar properties as an ensemble of unfolded polypeptide chains.

Position Dependence of Local α-Helix Stability.

The results from the TTET experiments reveal higher helix content in the central part of the helix compared with the termini, which is in agreement with helix–coil theory (11, 10) and has previously been observed experimentally by amide hydrogen exchange (32, 40), by NMR spectroscopy (41, 42), and by electron spin resonance (43). The k_f and k_u values determined for the different peptides allow the determination of local helix stability. The equilibrium constant, K_eq = k_f/k_u obtained from the TTET experiments is ≈3.9 in the central part of the helix and ≈0.5 near the ends (Fig. 3C). These equilibrium constants for local helix stability are slightly lower in all regions of the helix compared with equilibrium constants for individual hydrogen bonds measured in H/D exchange experiments under the same conditions (32). This difference can be explained by the helix-destabilizing effect of the TTET labels. The local equilibrium constants from the TTET experiments are in good agreement with predicted helix contents based on the AGADIR algorithm (44) when the TTET labels are modeled with Trp residues. AGADIR predicts equilibrium constants ≈5 in the helix center and ≈1.5 near the termini. In further agreement with our experimental results, AGADIR predicts higher helix content in the N-terminal regions than in the C-terminal region.

Simulation of Local Helix–Coil Dynamics with a Linear Ising Model.

To compare the experimental results with predictions from kinetic models for the underlying microscopic dynamics, we performed Monte Carlo simulations of helix–coil dynamics using a linear Ising model. The helix is represented by a finite sequence of 21 identical residues, which can be either in the helical state h or the coil state c. We use the statistical weights of Zimm and Bragg to assign the equilibrium constants for the following types of reactions (10):

• helix elongation:

  
• helix nucleation:

  
• coil nucleation:

  

This formalism considers only nearest-neighbor interaction as in the widely used 2 × 2 matrix approximation of Zimm and Bragg (10). Additional factors for helix nucleation, γ_h, and coil nucleation, γ_c, were introduced by Schwarz (16) to allow for additional kinetic effects on the nucleation reactions relative to elongation:

Schwarz suggested that it is reasonable to assume that 1 ≤ γ = 1/$\sqrt{\sigma }$ (16). In the simulations, we used a σ value of 0.003 and a position-independent s value of 1.31, which is the average s value experimentally determined for a similar peptide at 5 °C (45). Varying γ_h and γ_c between 1 and 9 has only little effect on the results. Values of γ_h = γ_c = 2 were used for all simulations. The simulations were performed based on a reduced time, t′, by using k₁ as reference (t′ = t·k₁). All other rate constants were scaled to k₁ according to Eqs. 2–6. The simulations were started with an equilibrium ensemble of helices. The time evolution of the system was simulated with discrete time steps of Δt′ = 0.05. These simulations are similar to the method applied by Poland (46) to simulate nonequilibrium dynamics of helix formation. A detailed description of the simulations is given in the SI Text.

Fig. 4 shows a typical result from the equilibrium simulations that yield an average helix content of 58.2%. This value agrees well with the experimentally determined helical content and with equilibrium Zimm and Bragg theory, which predicts 58.3% average helical content. A closer inspection of the results from the simulations reveals that the equilibrium dynamics are largely dominated by shrinking and growth of an existing helix, whereas helix and coil nucleation events are rare. This explains the insensitivity of the simulations to variations in γ_h and γ_c and suggests that the equilibrium TTET experiments do not yield information on the dynamics of helix nucleation events. The simulations further reveal that the commonly used single-sequence approximation (10, 13) holds most of the time, but 2 separate helical regions are sometimes observed (Fig. 4).

Fig. 4.

Snapshot of a typical simulation showing 5,000 discrete steps (Δt′ = 0.05, i.e., t′ = 250) of a 21-residue helix. Helical segments h are represented as white boxes and coil segments c as black boxes. The parameters used in the simulations were s = 1.31, σ = 0.003 and γ_h = γ_c = 2.

Comparison of Experiment with Simulation.

For comparison with the experimental time constants, we extracted first-passage times (FPTs) for local folding and unfolding kinetics from the simulations. Histograms of the FPTs for folding and unfolding were used to calculate rate constants k_u/k₁ and k_f/k₁ for the local unfolding and refolding reactions (Fig. S3). Because TTET experiments probe a region of 5 residues between the labels, we calculated kinetics for segments of 5 residues, which are counted as helical if at least 4 of these residues are helical at a given time. However, the results do not critically depend on the segment length used in data analysis. Monitoring the dynamics of single segments gives nearly identical results (see Fig. S4). Fig. 3 shows that the simulations yield the same position dependence of the rate constants for local helix folding and unfolding as the TTET experiments. The resulting rate constants for helix formation are virtually position independent. Helix unfolding, in contrast, occurs faster at the ends compared with the helix center despite the assumption of position-independent microscopic rate constants in Eqs. 2–6. The rate constants obtained from the simulations match the experimental values when the reduced time is scaled with a constant factor of 2.1·10⁷s⁻¹ = 1/(48 ns), which represents the elementary rate constant k₁ for helix elongation. In combination with the s value of 1.31, this yields an elementary time constant for helix unfolding, 1/k₂, of ≈63 ns (Eq. 2). The assumption of a single helical segment between the labels being sufficient to prevent loop formation yields values of 1/k₁ = 37 ns and 1/k₂ = 49 ns. The local differences between the experimental data and the results from the simulations (Fig. 3) are most likely due to the use of a uniform sequence with an average s value in the simulations. The experimentally investigated model helices, in contrast, contain arginine residues to increase solubility and are asymmetric molecules with a macrodipole.

The results from TTET experiments and simulations reveal significantly larger differences in helix dynamics between the ends and the central part of a helix compared with T-jump relaxation kinetics. This is due to the different types of processes monitored by the different techniques. As discussed above, irreversible TTET coupled to a helix–coil equilibrium allows the determination of microscopic rate constants for helix opening and closing, whereas T-jump experiments yield macroscopic relaxation times that contain contributions from forward and backward reactions. The fast and position-independent rate constant for helix closing observed in TTET experiments contributes strongly to the observed relaxation rate in T-jump experiments at all positions. This explains the weak position dependence of the relaxation rates. A similar difference is observed when unfolding kinetics of ribonuclease A are monitored by either H/D exchange, which measures opening rate constants for hydrogen bonds, and by optical spectroscopy, which measures relaxation times with contributions from folding and unfolding rate constants (47). This explanation is further supported by simulations of helix relaxation kinetics by using a similar kinetic helix–coil model as shown in Eqs. 2–6, which reproduced the weak position dependence of the experimental relaxation rates measured in T-jump experiments (48).

Mechanism of Equilibrium Helix–Coil Dynamics.

Comparison of the experimental results with the simulations gives a mechanistic explanation for the experimentally observed position dependence of the unfolding rate constant k_u. The comparison reveals that the observed position dependence for helix unfolding is a consequence of unzipping from the nearest helix–coil boundary as major mechanism for helix unfolding. This 1-dimensional diffusion process leads to longer diffusion distances for central positions compared with the terminal regions and thus to lower unfolding rate constants in the center of the helix. The elementary processes of adding and removing helical segments occur with position-independent time constants of ≈50 and ≈65 ns, respectively. These rate constants for local equilibrium helix folding and unfolding measured by TTET set a limit on the time scales for conformational transitions involving α-helices during protein folding and misfolding.

TTET coupled to helix dynamics is sensitive for processes between ≈1 ns and 50 μs. Therefore, the elongation time constant (1/k₁) of ≈50 ns reflects the time for formation of a helical segment that is at least stable for some nanoseconds. Much faster local processes, which do not lead to formation or decay of stable structure are not monitored, although they may occur during the experiments. The rate constant for helix elongation, k₁, obtained from the comparison of the simulations with the experimental data are virtually identical to the experimentally determined rate constant for formation of short protein loops at 5 °C (5), indicating that helix elongation is mainly limited by a conformational search.

Materials and Methods

Peptide Synthesis.

All peptides were synthesized by using standard Fmoc-chemistry on an Applied Biosystems 433A peptide synthesizer (5). The Xan derivative 9-oxoxanthene-2-carboxylic acid was synthesized and attached either to the N-terminus (in the X0–Z21 peptide) or to the β-amino group of a α,β-diaminopropionic-acid (Dpr) residue (in all peptides with i, i + 6 labeling) (5, 30). Naphthalene was incorporated as the nonnatural amino acid 1-naphthylalanine (Bachem). All peptides were purified to >95% purity by preparative HPLC on a RP-8 column. Purity was checked by analytical HPLC, and the mass was determined by MALDI mass spectrometry.

TTET and CD Measurements.

TTET measurements were performed on a Laser Flash Photolysis Reaction Analyzer (LKS.60) from Applied Photophysics with a Quantel Nd:YAG Brilliant laser (354.6 nm, ≈4 nm pulse width, ≈50 mJ). Transient absorption traces were recorded at 590 nm to monitor the xanthone triplet band. All measurements were performed in 10 mM phosphate buffer (pH 7.0) at 5 °C. Peptide concentrations were 50 μM as determined by the Xan absorbance at 343 nm (ε₃₄₃ = 3,900 M⁻¹cm⁻¹). All solutions were degassed before the measurements. Urea concentrations were determined by the refractive index according to Pace (49). CD measurements were performed on an Aviv DS62 spectropolarimeter. The experimental data were analyzed by using the ProFit software (QuantumSoft).

Simulations on the Helix–Coil Transition.

The model is based on Eqs. 2–6 and the underlying assumptions as discussed in the article. Details of the simulations are given in the SI Text.