*4.2. Measurements of "Local" Kinetic Parameters of the Folding*/*Unfolding Reaction with 2D High-Pressure NMR*

As for the steady-state parameters ∆*V* <sup>0</sup> and ∆*G* <sup>0</sup> discussed above, 2D real-time high-pressure NMR can allow a residue specific analysis for the kinetic parameters of the folding/unfolding reaction: the values of the unfolding and folding rate constants *k*u0 and *k*f0, as well as the value of the activation volume of unfolding ∆*V* ‡ *u*0 (or folding, ∆*V* ‡ *f* 0 ). This can be readily done by following the exponential decrease in intensity (or volume) after a *P*-Jump of cross-peaks corresponding to the native protein in a series of 2D [1H,15N] HSQC spectra recorded with time. These experiments can allow a residue-specific description of the TSE, with the location of internal voids already formed at this step of the folding reaction. In other words, they provide a structural description of the TSE, with the location of the "dry" folded regions (∆*V* ‡ *f* 0 /∆V 0 close to 1) and of the hydrated unfolded ones (∆*V* ‡ *f* 0 /∆V 0 close to 0) (Figure 6).

τ ∆ ‡ ∆ **Figure 6.** Residue-specific analysis of the unfolding reaction kinetics of Titin I27 domain. (**A**) Examples of residue-specific chevron plots measured for Titin I27 domain. The residue-specific relaxation times τ have been extracted from the decay with time of the intensity of cross-peaks belonging to the native protein species in a series of sixty 2D [1H-15N]- SOFAST-HMQC experiments (2 min measuring time each) recorded during 2 h after P-jumps of 200 bar. (**B**) Residue-specific values for the ratio ∆*V* ‡ *f* 0 /∆V 0 deduced from the fit of residue-specific chevron plots with Equation (6) and plotted versus the sequence of Titin I27.

∆ Nevertheless, the time resolution of NMR spectroscopy is limited: the recording time of a 2D [1H,15N] HSQC ranges from 10 to 40 min, depending on the sample concentration and the digital resolution needed. In addition, such experiments can be used only for proteins with very slow relaxation times, in the range of one to several hours. For instance, this method was successfully applied to wild-type ∆+PHS SNase and a series of variants having extremely slow relaxation time (up to 12 h) [65]. This drawback has been at least partially circumvented by methodological developments during the last decade: advances have been realized in the field of "real-times" measurement of NMR multidimensional

∆

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experiments [66–69], extending the application of real-time 2D NMR. Now, 2D correlation experiments can be acquired in tens of seconds, and sometimes even in less than one second, instead of tens of minutes. For example, 2D [1H-15N]- SOFAST-HMQC experiments [67,69] recorded in two minutes have been used to monitor the kinetics of unfolding of Titin I27 domain (Figure 6), exhibiting relaxation times of about 30 min (see Figure 3B). Similar experiments, but recorded in only 25 s, have been used for the L125A variant of ∆+PHS SNase, with relaxation times shorter than 10 min [65]. The use of "ultra-fast" 2D NMR spectroscopy [66], allowing to record a 2D spectrum in only one scan, can in principle extend the use of real-time 2D spectroscopy to proteins with shorter relaxation times, in the minute range. In addition, fast or ultra-fast experiments can be used in combination with Non Uniform Sampling (NUS) methods [70–72], which can speed up data collection. These methods allow for a decrease in the total number of points (the number of FIDs) used for sampling the indirect dimension ( <sup>15</sup>N dimension in the [1H,15N] HSQC experiments), maintaining the digital resolution at the expense of possible artifacts in the processed spectrum. Currently, a 4-fold gain in measuring time can be obtained, compared with the conventional method.

Obviously, the main limitation of this method remains the sensitivity, combined to a correct spectral resolution, of these experiments. In addition, playing with (increasing) the *P*-Jump amplitude in order to increase the sensitivity of the measurement, due to the subsequent increase in the intensity change for the cross-peaks, reaches also some limits. Indeed, the *P*-jump amplitude should remain moderate to avoid any imbalance between the folding and the unfolding reactions. Thus, an excessive positive *P*-jump will favor the unfolding reaction at the expense of the folding reaction, yielding erroneous values for the kinetic parameters. For instance, in the case of Titin I27, we have used pressure jumps of 200 bar, corresponding to about 10 percent of the pressure range needed to fully unfold the protein (2000 bar) [44].

Real-time 2D NMR spectroscopy remains inappropriate to study sub-second folding kinetics, which is the case for a lot of globular proteins. In the case of proteins with fast relaxation times (<1s), other NMR approaches are available, mainly based on 2D exchange spectroscopy techniques. The use of high-pressure ZZ-exchange experiments was introduced by Zhang et al. to obtain residue-specific folding rates for the two autonomous N-terminal and C-terminal domains of the ribosomal protein L9 [73]. This method is applicable to any proteins under experimental conditions where the folded/unfolded species exchange in a few tens to a few hundreds of milliseconds.

More recently, Charlier et al. significantly improved the pressure jump apparatus originally designed by Kremer et al. for introducing pulsed pressure perturbation in 1D and 2D NMR experiments [51], allowing for the switching of pressure on a millisecond time scale [74]. Combined with adequate 2D heteronuclear NMR experiments, this system allows measuring the rate of exchange and chemical shifts of the folded, intermediate, and unfolded states.
