Making connections between ultrafast protein folding kinetics and molecular dynamics simulations

Abstract

Determining the rate of forming the truly folded conformation of ultrafast folding proteins is an important issue for both experiments and simulations. The double-norleucine mutant of the 35-residue villin subdomain is the focus of recent computer simulations with atomistic molecular dynamics because it is currently the fastest folding protein. The folding kinetics of this protein have been measured in laser temperature-jump experiments using tryptophan fluorescence as a probe of overall folding. The conclusion from the simulations, however, is that the rate determined by fluorescence is significantly larger than the rate of overall folding. We have therefore employed an independent experimental method to determine the folding rate. The decay of the tryptophan triplet-state in photoselection experiments was used to monitor the change in the unfolded population for a sequence of the villin subdomain with one amino acid difference from that of the laser temperature-jump experiments, but with almost identical equilibrium properties. Folding times obtained in a two-state analysis of the results from the two methods at denaturant concentrations varying from 1.5-6.0 M guanidinium chloride are in excellent agreement, with an average difference of only 20%. Polynomial extrapolation of all the data to zero denaturant yields a folding time of 220 (+100,-70) ns at 283 K, suggesting that under these conditions the barrier between folded and unfolded states has effectively disappeared--the so-called "downhill scenario."

Fig. 1.

X-ray structure of villin headpiece subdomain, HP35(His27), (Protein Data Bank ID code 1YRF) showing key residues (sequence: LSDED FKAVF GMTRS AFANL PLWKQ QNLKK EKGLF) (23). Trp23 is the fluorescence probe; His27 replaces Asn27 of the wild-type sequence, and when protonated reduces the fluorescence of Trp23 upon folding; Lys24 and Lys29 make repulsive electrostatic interactions with protonated His27 and Arg14, respectively. The ϵ-amino nitrogen of Lys24 is 6.1 Å from the nearest protonated nitrogen of the imidazole ring of His27 and the ϵ-amino nitrogen of Lys29 is 5.3 Å from the nearest charged amino atom of Arg14. Removal of the ϵ-amino nitrogen groups of Lys24 and Lys29 to form norleucines in the mutant called HP35(Nle24,His27,Nle29) eliminates the repulsive interaction, thereby stabilizing the protein and increasing the folding rate (24, 25).

Fig. 2.

Schematic of tryptophan triplet-lifetime experiment. (Upper) A UV laser pulse excites tryptophan to its lowest excited singlet state that undergoes intersystem crossing in a few nanoseconds to the triplet state, which then lives for up to 100 µs. Diffusion of the unfolded polypeptide chain to form a close contact between the N-terminal cysteine and the tryptophan depopulates the triplet state, presumably via electron transfer from the tryptophan to the cysteine. The solid arrows are processes that contribute to the observed kinetics for the decay of the triplet-state population. (Lower) In the case of a two-state protein where (i) the spontaneous decay of the triplet state (k_s) is so slow that the triplet state only returns to the ground state via cysteine quenching in the unfolded state and (ii) the quenching rate is much faster than the unfolding and refolding rates (), the decay of the triplet-state population monitored by triplet–triplet optical absorption is biphasic, with the fast phase corresponding to the triplet-quenching rate in the unfolded state (k_q), the slow phase to the unfolding rate (), and the two amplitudes for the fast and slow phases given by the equilibrium fractions of the unfolded and folded states: and , respectively (, –36, 38). In the more realistic situation that we encounter with the double-norleucine mutant, Cys-HP35(Nle24,Nle29), where the timescales are not so clearly separable, the relaxation rates and amplitudes become complex functions of the four rate coefficients, which can be obtained by fitting the data with the solution of a simple differential equation model (see Eqs. 1–5).

Fig. 3.

Comparison of relaxation times for HP35(His27) measured in temperature-jump experiments using IR absorption (39) (red circles) or fluorescence (25) (blue circles) detection.

Fig. 4.

Equilibrium unfolding curves. (A) Comparison of denaturant unfolding curves for Cys-HP35(Nle24,Nle29) and Cys-HP35(Nle24,His27,Nle29). Equilibrium CD data collected at 10 °C (20 mM sodium acetate, 1 mm Tris(2-carboxyethyl)phosphine (TCEP), 75 μm protein, pH = 4.9) as a function of GdmCl concentration. The experimentally measured ellipticities are the dark-blue points [Cys-HP35(Nle24,Nle29)] and the red points [Cys-HP35(Nle24,His27,Nle29)]. The blue and red solid lines are the two-state fits to the data. The dashed lines are the native baselines and the dotted lines are the unfolded baselines. The denaturation midpoint concentrations, [D]_mid, are 5.1( ± 0.2)M for Cys-HP35(Nle24,His27,Nle29) and 5.3( ± 0.1)M for Cys-HP35(Nle24,Nle29), whereas the m-values are 640 (+149,-112) cal mol^-1 M^-1 for Cys-HP35(Nle24,His27,Nle29) and 714(+88, -62) cal mol^-1 M^-1 for Cys-HP35(Nle24,Nle29). The error bars represent standard deviations from the average of at least three measurements on separately prepared solutions.

Fig. 5.

Tryptophan quantum yield (ϕ) as a function of time at 10 °C after a 5 K laser-induced T-jump for 300 μM solutions of Cys-HP35(Nle24,His27,Nle29) containing 20 mM sodium acetate, 1 mM TCEP, and either (A) 2.25 M GdmCl (blue), (B) 4 M GdmCl (green), or (C) 6 M GdmCl (red). The circles are the experimental data and the lines are fits with a single exponential function.

Fig. 6.

Triplet-lifetime results. Normalized tryptophan triplet–triplet absorbance at 440 nm as a function of time on a log scale at 10 °C for 100 μM solutions of Cys-HP35(Nle24,Nle29) containing 20 mM sodium acetate, 1 mM TCEP, and either (A) 2.25 M GdmCl (blue), (B) 4.5 M GdmCl (green), or (C) 6 M GdmCl (red). The absorbance is proportional to the sum of the populations of the triplet state in the folded and unfolded states. The circles are the experimental data and the lines are the fits with the kinetic model.

Fig. 7.

Comparison of folding times measured by temperature jump and tryptophan triplet lifetime at 283 K. (A) Folding times (points) as a function of GdmCl concentration and a quadratic fit to all the data (dashed line). The triangles (red points) correspond to folding times measured by temperature jump from experiments on Cys-HP35(Nle24,His27,Nle29), whereas the inverted triangles (blue points) are folding rates from the triplet-quenching experiment performed on Cys-HP35(Nle24,Nle29). It was not possible to obtain measurable amplitudes in temperature-jump measurements at 1.5 M GdmCl at 283 K; this data point was obtained by extrapolation from higher temperatures of observed rates by using an Arrhenius temperature dependence (Fig. S3 and Fig. S4). The parameters of the quadratic fitting function, log(τ_f) = α + βx + γx², are α = 2.34 ± 0.17, β = 0.89 ± 0.10, and γ = -0.066 ± 0.013. In this polynomial fit using the program MLAB the relative weights of the T-jump points were determined by the standard deviation from the average of three measurements at each denaturant concentration, whereas for the triplet-lifetime data, the relative weight was determined by the rms residuals between the data and the two-state model fit. The relative weights at the denaturant concentrations 1.5, 2.25, 3,3.5, 4, 4.5, 5.5, and 6 M for the triplet lifetime data are 0.218, 0.311, 0.608, 0.370, 0.337, 0.430, 1.0, 0.430, and 0.508 and for the T-jump data are 1.0, 0.414, 0.817, 0.146, 0.297, 0.673, 0.236, 0.259, and 0.178 . Because of the very small amplitude for the faster relaxation at 1.5 M GdmCl in the triplet-lifetime experiment (Table S2), this point was not included in the extrapolation to zero denaturant.