RESULTS AND DISCUSSION 50

Figure 3.14: Temperature dependent backbone E-CPMG relaxation dispersion profiles of residues in the β-hairpin region. (A) ¹⁵N Relaxation dispersion data of residues V23, D29, Q27 and T38 with global fits (black line) (B)¹H Relaxation dispersion data of residues V26, V33, F35 and L43 with global fits (black line). The RD data is only plotted up toνCPMG= 20 kHz for a better demonstration. (A,B) The data was acquired at 263 K (blue), 270 K (purple), 275 K (red), 280 K (orange) and 285 K (green). Only residues in theβ-hairpin region that showed a distinctR_ex contribution over the whole temperature range were considered for the analysis. All RD profiles are in very good agreement with the global two-state exchange model.

51 3.2. RESULTS AND DISCUSSION could be considered.

In theα-helices, the slow process was only visible under super-cooled conditions still show-ing only a small exchange contribution (R_ex <10 s). At the same temperature and with a similar exchange rate,β-strand residues showed an exchange contribution of up to 50 s⁻¹. While the data implies a correlation between the two processes, the limited temperature window in which the slow process could be detected in theα-helices did not allow a feasible temperature dependent analysis.

Due to the inaccuracy of the fit parameters obtained for the fast exchange process a tem-perature dependent analysis was also not feasible. Nevertheless the RD profiles of residues in theα-helices showed a decreasing trend of the exchange contribution to R2,eff with in-creasing temperature (Figure 3.15). This is expected in case of chemical exchange as it was explained above and can be used as a qualitative indication for the fast exchange process.

At 275 K the slow exchange process is barely detectable in α-helical residues, while the dominantR_ex contribution of the fast process is detectable up to 295 K.

Figure 3.15: Temperature dependent ¹H E-CPMG relaxation dispersion pro-files of selected residues in the α-helices. The RD profiles of residues R11 (α₁) and T54 (α₂) at 263 K (blue), 268 K (purple), 275 K (red), 285 K (orange) and 295 K (green) with best individual fit are shown. The three-state exchange is only detectable below 275 K and the initial decay inR_2,eff increases with decreasing temperature. The assumed fast exchange contribution also changes with temperature, supporting the hypothesis of two distinct exchange process involving theα-helices. The RD profiles for residues in the α-helices appear to be flat at 295 K, because the exchange rate is too fast compared to the chemical shift variance.

Assuming a two-state exchange for residues in theβ-hairpin region the obtained relaxation dispersion profiles were fitted with a global exchange rate using residues that showed a

3.2. RESULTS AND DISCUSSION 52 distinct conformational amplitude of>2 s⁻¹in all measured temperatures. Under this as-sumption the globally fitted exchange rates (Table 3.1) were analyzed using the Arrhenius model:

ln(kex) =ln(A)−−E_A R

1

T, (3.8)

in which, E_A is the activation energy of the exchange process,R is the gas constant and A is a pre-exponential factor, that describes the collision frequency according to collision theory.

Figure 3.16: Arrhenius analysis of globally fitted exchange rates from gpW backbone E-CPMG data. (A) Arrhenius (Equation (3.8)) fitting of global ex-change rates obtained from ¹⁵N E-CPMG experiments. The fitted Arrhenius parame-ters are A = (2.11 ± 2.05) 10¹¹Hz and E_A = 39.76 ± 2.25 kJ mol⁻¹. An extrapola-tion to the melting temperature of gpW (T_m= 340 K) resulted in an exchange lifetime of 4.70 ± 3.77µs. (B) Arrhenius (Equation (3.8)) fitting of global exchange rates obtained from ¹H E-CPMG. The fitted Arrhenius parameters are A = (7.45 ± 4.03) 10¹²Hz and E_A = 36.35 ± 1.26 kJ mol⁻¹. An extrapolation to T_m resulted in an exchange lifetime of 5.16 ± 3.62µs. Both extrapolated values are in good agreement with previously results from laser induced T-jump experiments (8.8µs) (Fung et al., 2008).

The resulting activation energies from the two-state exchange model fit were 39.8 ± 2.2 kJ mol⁻¹ and 36.4 ± 1.3 kJ mol⁻¹ for ¹⁵N and ¹H, respectively (Figure 3.16). The

1H E-CPMG data results in a slightly lower energy barrier than the obtained E_A from the ¹⁵N data set. A possible explanation could be an additional contribution of solvent exchange to the observed relaxation dispersion. Such an exchange would increase the observed exchange rates and thus lead to a lower energy barrier in the temperature de-pendent analysis.

The fitted values of the collision number A were (2.11 ± 2.05) 10¹¹s⁻¹ and (7.45 ± 4.03) 10¹⁰s⁻¹ for ¹⁵N and ¹H E-CPMG, respectively. Both results showed large uncer-tainties, that could be rationalized as following. In a chemical reactionAaccounts for the

53 3.2. RESULTS AND DISCUSSION frequency of collisions in the correct orientation that lead to a reaction. In the application to folding kinetics it would correspond to an upper limit of the exchange process at an infinite temperature. During the fit this value has to be extrapolated from the limited temperature range that is accessible. Small changes in the activation energy that describes the slope of the model curve, will have a large effect on the estimated value ofA. While the fitted activation energies of the two data sets show similar results, the estimated A value differs by a factor of roughly three. Thus, the narrow range of temperatures that is feasible for biomolecules does not allow an accurate estimation of this parameter.

Using the results of the Arrhenius analysis the kinetics at the melting temperature of gpW (Tm= 340 K) could be extrapolated. This led to an exchange lifetime (1/kex) of 4.70 ± 3.77µs and 5.16 ± 3.62µs for ¹⁵N and ¹H data, respectively. Both results are in very good agreement with the 8.8µs reported by laser-induced T-jump experiments in the literature (Fung et al., 2008). These results indicate that the partial unfolding of gpW in solution can be described by a two-state exchange model with an energy barrier higher than≈ RT as it would be assumed for an ultra-fast folding protein.

In summary the application of the E-CPMG experiment to the amide backbone nuclei of gpW added two new residues V23 and D29 to the analysis, which were formerly broad-ened beyond detection under conventional CPMG conditions. Furthermore a slow decay of R_2,eff that was primarily seen in residues located in the α-helical region was detected (Figure 3.17). This indicates that gpW in solution is involved in an additional exchange process, which majorly involves theα-helices (Figure 3.17). A full characterization of this second exchange process was not possible due to insufficient quenching of the exchange contribution. Nevertheless, the¹H E-CPMG experiment suggested that the corresponding exchange rate is similar to or faster than 200000 s⁻¹.

The combined use of super-cooled sample conditions and the E-CPMG approach revealed relaxation dispersion profiles that showed a discrepancy to the two-state exchange model.

The use of a three-site exchange model showed a better accordance to the data. A com-parison of the two model fits by the corrected Akaike information criterion supported the assumption that these residues are involved in a three-site exchange process. In this model the fitted k_ex^S indicated that the α-helices are also affected by an exchange process that takes place on the same time scale as the one observed in theβ-hairpin region.

These findings support the hypothesis of the hydrophobic collapse, where the preformed α-helices form the hydrophobic core followed by the folding of the β-hairpin region as the last step of the folding process. In this scenario the large exchange contributions seen in the RD profiles of residues in the β-strands can be explained by the transition from a disordered to an ordered structure. In this conformation new intermolecular contacts and less solvent exposure cause the chemical environment of the involved nuclei to change largely. In the same folding process, the α-helices are already formed and close contacts of the backbone amide nuclei do not change. The Φ values of these residues are expected to be smaller than for residues in the β-hairpin. Thus, a smaller exchange contribution to the transverse rate is expected and the folding process becomes visible only when the

3.2. RESULTS AND DISCUSSION 54