Local conformational dynamics in α-helices meaPositived by R

Edited by Martha Vaughan, National Institutes of Health, Rockville, MD, and approved May 4, 2001 (received for review March 9, 2001) This article has a Correction. Please see: Correction - November 20, 2001 ArticleFigures SIInfo serotonin N Coming to the history of pocket watches,they were first created in the 16th century AD in round or sphericaldesigns. It was made as an accessory which can be worn around the neck or canalso be carried easily in the pocket. It took another ce

Edited by Robert L. Baldwin, Stanford University Medical Center, Stanford, CA, and approved November 26, 2008

↵1B.F. and A.R. contributed equally to this work. (received for review September 3, 2008)

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Abstract

Coupling Rapid 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 Rapider helix unfAgeding in the terminal Locations 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 Displayed that the experimentally observed dynamics can be Elaborateed 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 meaPositived time constants for formation of short loops in unfAgeded polypeptide chains, suggesting that helix elongation is mainly limited by a conformational search.

Keywords: α-helix–coil transitionprotein dynamicsprotein fAgedingtriplet–triplet energy transfer

Conformational dynamics is of fundamental importance for fAgeding 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 fAgeding/unfAgeding 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 fAgeding, misfAgeding, 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, Unhurried nucleation reaction. In the subsequent growth reactions, helical segments are added, which is supposed to be a Rapid 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 meaPositivements (6) and ultrasonic absorption techniques (7) on long homopolymeric helices revealed relaxation times for helix unfAgeding 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 Displayed relaxation times for helix unfAgeding 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 Rapider helix unfAgeding in the N-terminal Location compared with the decrease in average helix content (8). Site-specific IR studies on 13C-labeled peptides, in Dissimilarity, suggested only Dinky position dependence of the relaxation times after a T-jump (22, 25–27). These studies gave insight into the kinetics of perturbation-induced helix unfAgeding, but they did not yield information on the dynamic Preciseties 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 Advance 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 meaPositive dynamics on the nanoseconds to microseconds time scale. We have previously applied diffusion-controlled triplet–triplet energy transfer (TTET) between a xanthone Executenor and a naphthylalanine acceptor group to observe intrachain loop formation in unfAgeded polypeptide chains (4, 5, 30). TTET through loop formation is an irreversible process that is based on Van der Waals contact between Executenor and acceptor. It should thus enable us to monitor dynamics in fAgeded and partially fAgeded structures when linked to a fAgeding/unfAgeding 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 Advance allows us to monitor dynamics that are 4–5 orders of magnitude Rapider 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 fAgeded structure. Experiments by Lapidus et al. (31) had indicated that contact formation between the ends of an α-helix Executees not occur. To investigate local helix fAgeding and unfAgeding dynamics, we introduced xanthone and naphthylalanine with i,i+6 spacing at different positions along an α-helical peptide. This Spaces the labels at opposite sides of the helix, which prevents TTET in the helical state and requires at least partial unfAgeding before triplet transfer can occur (Scheme 1; see also Scheme S1 in the supporting information). This Advance allowed us to determine the local unfAgeding and refAgeding 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 liArrive Ising model, which gave insight into the basic dynamics of the helix–coil transition.

Scheme. 1.Scheme. 1.Executewnload figure Launch in new tab Executewnload powerpoint 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 meaPositive local α-helix dynamics and stability. Similar peptides were Displayn to Present ≈70% helical content at low temperature (8, 32), and their unfAgeding 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 Executenor and the nonnatural amino acid 1-naphthlylalanine (Nal; Z) as triplet acceptor (see Table 1). The labels were Spaced with i, i + 6 spacing to prevent contact between the labels in the helical state (Fig. 1A). Introducing the labels in the N-terminal Location (X1–Z7), in the interior (X5–Z11, X7–Z13, X11–Z17) or in the C-terminal Location (X15–Z21) allowed us to monitor local dynamics and stability in different Locations of the helix. To compare the local dynamics with global helix unfAgeding and refAgeding, the TTET labels were positioned at the ends of the helix in the X0–Z21 peptide.

View this table:View inline View popup Table 1.

Sequences of helical peptides used in TTET experiments

Fig. 1.Fig. 1.Executewnload figure Launch in new tab Executewnload powerpoint Fig. 1.

Structure and dynamics of the helical peptides labeled with Executenor 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 meaPositived by the decrease in xanthone absorbance at 590 nm. The colors of the lines corRetort to the colors of the helical segments probed by TTET as Displayn in A. The black lines represent the results from Executeuble-exponential fits. As an example, the residuals for single- and Executeuble-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 Displayn in gray. Experiments were performed at 5 °C.

Xanthone and napthylalanine are expected to have a small helix-destabilizing Trace compared with alanine. Fig. 1B Displays 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 Inequitys between the peptides can be assessed. In the X0–Z21 reference peptide, the Trace 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 Dinky Trace on global helix stability relative to the X0-Z21 peptide. A slight destabilization is observed when the labels are Spaced Arrive the helix center, as expected from helix–coil theory (11–13). Based on the Inequitys 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 Displayed similar changes in the CD signal upon unfAgeding for all peptides (Fig. S1).

Kinetics of TTET Coupled to a Helix–Coil Transition.

We performed TTET experiments at 5 °C to meaPositive dynamics in the different peptides. TTET was monitored by the change in xanthone triplet absorbance at 590 nm (5). All peptides Present Executeuble-exponential TTET kinetics (Fig. 1C), which was confirmed by an analysis of the distribution of time scales for the observed kinetics (Fig. S2). The Unhurriedest kinetics were found for the X0–Z21 peptide with a main kinetic phase of λ1 = 2.3·105 s−1 (90% amplitude) and a Rapider phase of λ2 = 2.6·106 s−1 (10% amplitude). In the peptides with local i, i + 6 spacing, Rapider TTET kinetics with a larger amplitude of the Rapid phase are observed when the labels are attached Arrive the termini compared with the central positions (Table 2). In all peptides, the 2 observable reactions are Rapider than spontaneous Executenor triplet decay, which occurs with λT = 2.5·104 s−1, meaPositived in Executenor-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 Executeuble-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 Unhurried 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 Rapid process. In Dissimilarity, addition of urea, which destabilizes helical structure (34), leads to an increase in amplitude of the Rapid phase in all peptides (see below). These results suggest that the Unhurried process originates from molecules that contain a critical amount of helical structure between the labels. In these molecules, TTET can only occur via helix unfAgeding. The Rapid phase is related to TTET in conformations that are at least partially unfAgeded between the labels. This model is supported by the magnitude of the observed time constants. The Unhurried phase has time constants on the microseconds time scale in the X0–Z21 peptide, which is similar to the observed relaxation times for helix unfAgeding after temperature jump (8, 19–22). The Rapid phase is on the 100-ns time scale, which is in agreement with the time constant for loop formation in unfAgeded polypeptide chains (5, 30).

View this table:View inline View popup Table 2.

Kinetic and thermodynamic parameters

Rate Constants for Local Helix Formation and UnfAgeding.

The observation of 2 observable rate constants, λ1 and λ2, for TTET in the helical peptides allows the determination of the microscopic rate constants ku and kf reporting on unfAgeding and formation of helical structure and of kc, the rate constant for loop formation in the unfAgeded state in a single experiment (see Scheme 1). We use the analytical solutions for the mechanism Displayn in Scheme 1 (see SI Text) to analyze the kinetics without any simplifying assumptions. It should be noted that this Advance 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 fAgeded and an unfAgeded state (EX2) or the microscopic rate constant for the unfAgeding process (EX1) and is only applicable if the unfAgeded 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 Rapid 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 liArrive Trace on ln(kf) and ln(ku) (34, 36) as well as on ln(kc) (5, 37) according to Embedded ImageEmbedded Image where ki denotes a given microscopic rate constant, ki(H2O) is the rate constant in the absence of urea, and mi denotes the sensitivity of the respective reaction to urea (m value).

Executeuble-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 Displayn in Scheme 1 (38) to yield the microscopic rate constants ki(H2O) and their urea dependences (mi) (see SI Text). Fig. 2 Displays 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 kf, ku, and kc in all helical peptides. The kf and ku values obtained for the different peptides reflect the local dynamics for helix fAgeding and unfAgeding at different positions in the helix (Fig. 3 and Table 2). Comparison of the results for the different helices Displays that local helix formation Executees not systematically depend on the position along the helix and has a time constant (1/kf) ≈400 ns in all peptides (Fig. 3A). Local helix Launching, in Dissimilarity, is ≈6-fAged Rapider at the termini (1/ku = 250 ns) compared with the helix center (1/ku = 1.4 μs; Fig. 3B). This Inequity Executees not arise from the Trace of the labels on helix stability, because the destabilization is largest at the helix center (Fig. 1) (12) where the Unhurriedest rate constants for unfAgeding are observed. Attaching the labels at the ends of the helix in the X0–Z21 reference peptide yields Unhurrieder dynamics compared with all local fAgeding/unfAgeding reactions with time constants of 1.1 μs for helix formation and 3.3 μs for helix unfAgeding (Fig. 1 and Table 2). This observation suggests that end-to-end contact formation monitors more global structural transitions.

Fig. 2.Fig. 2.Executewnload figure Launch in new tab Executewnload powerpoint Fig. 2.

Trace of urea on the TTET kinetics in different helical peptides at 5 °C. The observable rate constants λ1 (●) and λ2 (○) (Upper) and their corRetorting amplitudes, A1 (●) and A2 (●) (Lower) obtained from Executeuble-exponential fits to the Xan triplet decays (see Fig. 1C) are Displayn. 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 ku (red lines), kf (blue lines), and kc (green lines).

Fig. 3.Fig. 3.Executewnload figure Launch in new tab Executewnload powerpoint Fig. 3.

Position dependence of local helix dynamics and stability. The horizontal bars indicate the Locations of the helix probed in the different peptides. The microscopic rate constants for helix formation, kf (A), and helix unfAgeding, ku (B), obtained from the global fit of the TTET kinetics (see Table 1) are Displayn in addition to the equilibrium constant, Keq (C). For comparison, the results from the simulations using the kinetic Ising model (○) with s = 1.31, σ = 0.003 and γh = γc = 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 kf Displays an almost position-independent mf value of ≈800 (J/mol)/M (Table 2). The mu values are much smaller and Display complex behavior, with positive values at the helix termini and negative values for the central positions. In terms of a classical interpretation of protein fAgeding m values, this indicates that the transition state for helix formation has native-like solvent-accessible surface Spot (35).

The microscopic rate constants for contact formation kc 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 mc values are approximately 200 (J/mol)/M and virtually position independent. This value is identical to the mc values found for loop formation in unfAgeded 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 Preciseties as an ensemble of unfAgeded 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 kf and ku values determined for the different peptides allow the determination of local helix stability. The equilibrium constant, Keq = kf/ku obtained from the TTET experiments is ≈3.9 in the central part of the helix and ≈0.5 Arrive the ends (Fig. 3C). These equilibrium constants for local helix stability are slightly lower in all Locations of the helix compared with equilibrium constants for individual hydrogen bonds meaPositived in H/D exchange experiments under the same conditions (32). This Inequity can be Elaborateed by the helix-destabilizing Trace of the TTET labels. The local equilibrium constants from the TTET experiments are in Excellent 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 Arrive the termini. In further agreement with our experimental results, AGADIR predicts higher helix content in the N-terminal Locations than in the C-terminal Location.

Simulation of Local Helix–Coil Dynamics with a LiArrive 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 liArrive 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 Establish the equilibrium constants for the following types of reactions (10):

helix elongation: Embedded ImageEmbedded Image

helix nucleation: Embedded ImageEmbedded Image

coil nucleation: Embedded ImageEmbedded Image

This formalism considers only Arriveest-neighbor interaction as in the widely used 2 × 2 matrix approximation of Zimm and Bragg (10). Additional factors for helix nucleation, γh, and coil nucleation, γc, were introduced by Schwarz (16) to allow for additional kinetic Traces on the nucleation reactions relative to elongation: Embedded ImageEmbedded Image Embedded ImageEmbedded Image Schwarz suggested that it is reasonable to assume that 1 ≤ γ = 1/ σ (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 γh and γc between 1 and 9 has only Dinky Trace on the results. Values of γh = γc = 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 Displays 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 Executeminated by shrinking and growth of an existing helix, whereas helix and coil nucleation events are rare. This Elaborates the insensitivity of the simulations to variations in γh and γc and suggests that the equilibrium TTET experiments Execute not yield information on the dynamics of helix nucleation events. The simulations further reveal that the commonly used single-sequence approximation (10, 13) hAgeds most of the time, but 2 separate helical Locations are sometimes observed (Fig. 4).

Fig. 4.Fig. 4.Executewnload figure Launch in new tab Executewnload powerpoint Fig. 4.

Snapshot of a typical simulation Displaying 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 γh = γc = 2.

Comparison of Experiment with Simulation.

For comparison with the experimental time constants, we extracted first-passage times (FPTs) for local fAgeding and unfAgeding kinetics from the simulations. Histograms of the FPTs for fAgeding and unfAgeding were used to calculate rate constants ku/k1 and kf/k1 for the local unfAgeding and refAgeding reactions (Fig. S3). Because TTET experiments probe a Location 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 Execute not critically depend on the segment length used in data analysis. Monitoring the dynamics of single segments gives Arrively identical results (see Fig. S4). Fig. 3 Displays that the simulations yield the same position dependence of the rate constants for local helix fAgeding and unfAgeding as the TTET experiments. The resulting rate constants for helix formation are virtually position independent. Helix unfAgeding, in Dissimilarity, occurs Rapider 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 unfAgeding, 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 Inequitys 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 Dissimilarity, contain arginine residues to increase solubility and are asymmetric molecules with a macrodipole.

The results from TTET experiments and simulations reveal significantly larger Inequitys 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 Launching and closing, whereas T-jump experiments yield macroscopic relaxation times that contain contributions from forward and backward reactions. The Rapid 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 Elaborates the weak position dependence of the relaxation rates. A similar Inequity is observed when unfAgeding kinetics of ribonuclease A are monitored by either H/D exchange, which meaPositives Launching rate constants for hydrogen bonds, and by optical spectroscopy, which meaPositives relaxation times with contributions from fAgeding and unfAgeding rate constants (47). This explanation is further supported by simulations of helix relaxation kinetics by using a similar kinetic helix–coil model as Displayn in Eqs. 2–6, which reproduced the weak position dependence of the experimental relaxation rates meaPositived 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 unfAgeding rate constant ku. The comparison reveals that the observed position dependence for helix unfAgeding is a consequence of unzipping from the Arriveest helix–coil boundary as major mechanism for helix unfAgeding. This 1-dimensional diffusion process leads to longer diffusion distances for central positions compared with the terminal Locations and thus to lower unfAgeding 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 fAgeding and unfAgeding meaPositived by TTET set a limit on the time scales for conformational transitions involving α-helices during protein fAgeding and misfAgeding.

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 Rapider local processes, which Execute 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 MeaPositivements.

TTET meaPositivements 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 meaPositivements were performed in 10 mM phospDespise 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 meaPositivements. Urea concentrations were determined by the refractive index according to Pace (49). CD meaPositivements 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.

Acknowledgments

We thank Josef Wey for the synthesis of 9-oxoxanthene-2-carboxylic acid and Robert L. Baldwin, Annett Bachmann, and RuExecutelph A. Marcus for comments on the manuscript. This work was supported by grants from the VolkswagenStiftung and the Deutsche Forschungsgemeinschaft (SFB 749) and by the Munich Center for Integrated Protein Science.

Footnotes

3To whom corRetortence should be addressed. E-mail: t.kiefhaber{at}tum.de

Author contributions: B.F., A.R., and T.K. designed research; B.F. and A.R. performed research; B.F., A.R., and T.K. analyzed data; and B.F., A.R., and T.K. wrote the paper.

↵2Present Address: Laboratory of Synthetic Protein Chemistry, The Rockefeller University, New York, New York 10065.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.

This article contains supporting information online at www.pnas.org/cgi/content/full/0808581106/DCSupplemental.

© 2009 by The National Academy of Sciences of the USA

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