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The anatomy of unfolding of Yfh1 is revealed by site-specific fold stability analysis measured by 2D NMR spectroscopy

Most techniques allow detection of protein unfolding either by following the behaviour of single reporters or as an averaged all-or-none process. We recently added 2D NMR spectroscopy to the well-established techniques able to obtain information on the process of unfolding using resonances of residues in the hydrophobic core of a protein. Here, we questioned whether an analysis of the individual stability curves from each resonance could provide additional site-specific information. We used the Yfh1 protein that has the unique feature to undergo both cold and heat denaturation at temperatures above water freezing at low ionic strength. We show that stability curves inconsistent with the average NMR curve from hydrophobic core residues mainly comprise exposed outliers that do nevertheless provide precious information. By monitoring both cold and heat denaturation of individual residues we gain knowledge on the process of cold denaturation and convincingly demonstrate that the two unfolding processes are intrinsically different.

the peak-intensities observed in unenhanced 2D 15 N-1 H HSQC spectra. Since the folded state of Yhf1 is in a chemical equilibrium with the unfolded state, the folding reaction needs to be in the slow-exchange regime (McConnell, 1958) on the NMR time scale for intensities to strictly be proportional with populations.
During the two INEPT periods of the unenhanced 15 N-1 H HSQC experiment, chemical exchange of transverse single-quantum 1 H coherences, Hx,y and 2Hx,yNz, between the folded and unfolded species leads to line-broadening and therefore to a loss of intensity. The effect of this line-broadening on the derived populations, ff(T), and thus on the derived stability curves, was estimated by simulating a two-site exchanging system with the Liouvillian evolution matrix (Allard et al., 1998): and R2,f and R2,u are the single-quantum proton transverse relaxation rates in the folded and unfolded species, respectively; Δωfu is the proton chemical shift difference between the folded and unfolded state (rad/sec); kfu and kuf are the rate constants for the unfolding and folding reactions, respectively; and Mf and Mu represent the (complex) transverse magnetisations in the folded and unfolded states. The one-bond 1 H-15 N scalar-coupling evolution was neglected.
The chemical shift differences, Δωfu, were calculated under the assumption that the chemical shifts of the unfolded state are those of a random-coil. Therefore, from the chemical shift assignment of the folded state and based on predicted random-coil chemical shifts (Wishart et al., 1995) for the unfolded state, Δωfu values were calculated for all residues for which a chemical shift assignment was available. The rate constants for the folding and unfolding reactions, kfu and kuf, were derived from Figure 4 of Bonetti et al. (2014), where 30 points for kfu and kuf were extracted in the temperature range from 271 K to 340 K.
Subsequently, a quadratic spline interpolation (scipy.interpolate.interp1d) was used to calculate the rate constants at any given temperature between 271 K and 340 K.
The intrinsic transverse relaxation rates were estimated by first calculating the rotational correlation time, τR, for the folded protein over the temperature range 278-313 K.
Based on previous 15 N relaxation studies on another frataxin ortholog (Rasheed et al., 2019) and on the size of Yhf1 (Maciejewski et al., 2000), it was assumed that the rotational correlation time is 6 ns at 298 K. Using known relationships between the viscosity, η, and temperature for H2O and D2O (Nagashima et al., 1977), the rotational correlation time was extrapolated from 298 K to the desired temperature using the relationship τR ∝ η(T)/T. This led to τR in the range from 11 ns to 4.2 ns for temperatures in the range from 278-313 K.
Subsequently, R2,f and R2,u were calculated using a numerical integration of the interaction Hamiltonians following standard Bloembergen-Purcell-Pound theory (Bloembergen et al., 1948;Abragam, 1961 (Lipari and Szabo, 1982), where: In all cases a fast internal librational motion with a time-constant of τe = 80 ps was assumed.
Order parameters, S 2 , of 0.8 and 0.15 were assumed for the folded and unfolded states respectively. This calculation led to a R2f between 30 s -1 and 12 s -1 and an intrinsic R2 for the unfolded state, R2,u,in, between 6.5 and 3.1 s -1 over the temperature range 278-313 K.
Hydrogen exchange was incorporated by assuming high protection factors in the folded state. Thus, the hydrogen-exchange rate, kHDX, is much smaller than the intrinsic transverse relaxation rate, kHDX << R2,f, and the hydrogen exchange within the folded state can be neglected. For the unfolded state, which was assumed to be a random-coil, hydrogen exchange rates were calculated using the SPHERE web-application (    In red is the fit from NMR intensities and in blue is the fit obtained by taking into account the three contributions. Bottom row: Correlation between the thermodynamic parameters (Hm, Tm, Tc, Ts) obtained from the fit of experimental NMR intensities (x-axis) and those obtained after added the three contributions and fitting the data again (y-axis). As such, the x-axis corresponds to the parameters from red curves shown in the top row and the y-axis corresponds to the blue curves. For this protein, Ts, but not the other parameters, is well determined simply using the NMR intensities.  Black solid line represents the best least-squares fit of the equation for the stability curve to the obtained ΔG; Grey lines are the confidence interval, represented by 250 randomly sampled curves from the covariance matrix (multi-variate normal distribution).

Figure S8
. Stability curves of some of the best residues of the β-strands (see Figure 5). Red circles are per-residue ΔG values derived from the populations; vertical red lines are estimated error in ΔG. Black solid line represents the best least-squares fit of the equation for the stability curve to the obtained ΔG; Grey lines are the confidence interval, represented by 250 randomly sampled curves from the covariance matrix (multi-variate normal distribution).