*4.1. Measurement of "Local" Thermodynamic Parameters for Folding*/*Unfolding Reaction: Tracking Folding Intermediates in the Protein Energy Landscape with 2D High-Pressure NMR*

Figure 4 displays the evolution of the correlation peaks on [1H,15N] HSQC experiments recorded with increasing pressures. According to the slow exchange regime between the folded and unfolded species, already visible and discussed for 1D NMR spectra, one observes the disappearance of correlation peaks belonging to the native form with the concomitant appearance of new peaks (centered at 8.5 ppm on the proton chemical-shift axis), which correspond to the spectrum of the unfolded species. As discussed above, the weak spectral dispersion of the cross-peaks corresponding to the unfolded protein is due to the loss of the through-space effects in the "random coil-like" structure of the unfolded states.

It is then possible to measure the evolution with pressure of either the intensity (peak height) or the volume of each cross-peak in the HSQC 2D spectrum: for instance, the loss of intensity of the native state resonances directly reflects the decrease in population of the folded state as detected locally by each residue. Note that, although global unfolding of a protein can obey complex models, locally the loss of the native state cross-peak intensity represents a two-state transition, that can be safely fitted with Equation (6). Thus, the fit of the local pressure unfolding curves yields residue-specific values for the apparent volume change (∆*V* 0 ) and apparent free energy (∆*G* 0 ) difference between the folded and unfolded states (Figure 4C,D).

∆ ∆

∆ ∆ **Figure 4.** Monitoring unfolding of Titin I27 domain with high pressure 2D NMR. (**A**) Examples of [ <sup>1</sup>H-15N] HSQC-NMR spectra recorded on a <sup>15</sup>N-labeled sample of Titin I27 at different pressures as indicated (same other experimental conditions as in Figure 1); (**B**) Overlay of 3 different residue-specific pressure denaturation curves obtained from the fit with Equation (6) of the cross-peak intensities measured at equilibrium from the corresponding residues. For clarity, the cross-peak intensities have been normalized. (**C**) Residue-specific ∆*G* <sup>0</sup> and (**D**) ∆*V* <sup>0</sup> measured from residue-specific pressure unfolding curves of Titin I27 domain.

Note that one usually prefers to fit the sigmoidal decay of the native resonances rather than the sigmoidal growth of the unfolded resonances, even though similar results should be obtained, as mentioned above for the indole resonance of the tryptophan residue (see Figure 2). This is because of the considerably better spectral resolution observed in the HSQC spectrum of the folded protein, which is also usually assigned, contrary to the spectrum of the unfolded states.

**2020**, , x; doi: Large variations in the ∆*V* <sup>0</sup> and ∆*G* <sup>0</sup> values within the protein sequence sign deviation from a simple two-state unfolding transition and suggest the potential presence of folding intermediates. For instance, in the case of Titin I27, whereas a ∆*V* 0 for unfolding of ≈ −70 mL/mol was measured for most of the residues, ∆*V* 0 fell to a value < 55 mL/mol for some residues, meaning that some regions of the protein unfold earlier than others and suggesting the presence of partially folded intermediates in the protein energy landscape with some degree of stability (Figure 4). In this particular case, 2D HP-NMR clearly revealed the existence of a folding intermediate where the N-terminal β-strand is detached from the Ig-like β-sandwich. This intermediate was generally not detected in chemical denaturation studies [55] and only suspected in force spectroscopy studies [56,57] of Titin I27 multi-modules constructs. This is a clear demonstration of the potency of HP-NMR that can bring unprecedented details in the analysis of protein folding pathways.

Structural information on the folding intermediates can also be obtained from residue-specific denaturation curves [12,58,59]. To this aim, the residue specific curves must be first normalized (Figure 5). Then, at a given pressure, the value of 1 measured for a given cross-peak (*I* = *I<sup>F</sup>* = 1) can be associated with a probability of 1 (100%) to find the corresponding residue "i" in the native state, whereas, at the

same pressure, a residue "j" for which the corresponding cross-peak has disappeared (*I* = *I<sup>U</sup>* = 0) from the HSQC spectrum has a probability equal to zero to be in a native state.

∆ ≈ −

β

*Δ Δ*

∆

β

≤ **Figure 5.** Pressure denaturation of Titin I27 domain. (**A**) Overlay of the normalized residue-specific denaturation curves obtained for Titin I27 domain. The vertical dashed red line at 600 bar represents the pressure used for analysis of the data presented here. (**B**) Contact map built from the best solution structure obtained for Titin I27 Ig-like domain [44]. All native contacts are displayed below the diagonal, whereas only native contacts for which a probability can be calculated from corresponding residue-specific denaturation curves are presented above the diagonal. In addition, the contacts above the diagonal have been colored in red when contact probabilities *p*(ij) lower than 0.5 are observed at 600 bar. (**C**) Ribbon representations of the solution structure of I27 where the red sticks represent contacts that are weakened (*p*(ij) ≤ 0.5) at 600 bar. Residues involved in these contacts are also colored in red on the ribbon.

(, ) = ඥ() × () α Considering now a pressure where these two residues i and j are in an intermediate situation where the probability to be in a folded state are *p*(i) and *p*(j) (0 < *p*(i) and *p*(j) < 1), if these two residues are in contact in the native state (at atmospheric pressure) their probability *p*(i,j) to be in contact at this pressure is given by the geometric mean of the two individual probabilities: *p*(*i*, *j*) = p *p*(*i*) × *p*(*j*) [60]. These contact probabilities can be displayed with a color code on contact maps constructed from the 3D crystal or NMR native structure of the protein, by measuring all contacts (usually only those concerning Cα atoms of the different residues, for simplicity) between different atoms (Figure 5). When combined with molecular dynamic simulations, this approach can give a pictorial representation of the conformational ensemble. To this aim, native contact lists generated from contact maps and weighted by the probabilities of contact *p*(ij) at a given pressure are used in Go-model simulations in order to generate multiple conformers and to possibly solve the structure of folding intermediates [12].

**2020**, , x; doi: Beside this now well-established method, the use of the pressure dependence of amide exchange rates was proposed to characterize intermediate states. Again, a residue-specific measurement of amide exchange rate constants can be obtained from the decrease in intensity of their corresponding cross-peak in the [1H-15N]-HSQC after dissolving a lyophilized protein sample in D2O buffer. The use of H/D exchange measurements [54] has been proposed to identify local stabilities in globular proteins [61,62] through the values of individual amide protection factors (PF) calculated from the experimental exchange rate constants [63]. Note that the values of PF strongly depend on the physical and chemical parameters of the system: pH, temperature, and also pressure [63,64].

H/D exchange experiments combined with pressure perturbation have been used for the first time to examine the energetics of apocytochrome b562 [64]. With increasing pressure, a systematic decrease in the protection factors was observed, and changes on apparent volume for exchange (∆*V*ex) were estimated from the linear dependence of the free energy of exchange with pressure (∆*G*ex(p) = ∆*G*ex <sup>0</sup> + p∆*V*ex). Three regions with distinct stabilities and pressure sensitivities can be identified [64]. We have used this method for ∆+PHS SNase and several of its cavity mutants and found results in good agreement with our previous equilibrium unfolding data [65]. Nevertheless, one limitation of this method is that it applies only to solvent protected amide protons, under conditions where H/D exchange rates are still measurable (relatively low pH and low temperature).
