15N relaxation data (T1 and T2) were collected at 600 MHz on a Bruker AVANCE NEO II (Indiana University – Bloomington). Started pseudo3D interleaved pulse sequences were used with delay times of 0.1, 0.2, 0.3, 0.4, 0.5, and 0.6 s for T1 and 0.0157, 0.0314, 0.0470, 0.0627, 0.0786, and 0.0941 s for T2. Relaxation data were analyzed in SPARKY and relaxation parameters extracted were using the Sparky “rh” command.
To measure 1H PRE, gadodiamide powder was dissolved in NMR buffer at a stock concentration of 500 mM. T1 recovery time spectra with delay times of 0.10, 0.15, 0.20, 0.25, 0.30, 0.50, 1.0, and 3.0 s were recorded for 350 μM [U‐15N,U‐13C] pNTS1(H8–Ctail) in NMR buffer plus 12 mM (d26)‐DH7PC with addition of 0, 3, 6, 12, and 24 mM gadodiamide at 35°C. Spectra were recorded as a series of 15N HSQCs with an appended 180° 1H pulse at the start of the sequence, followed by the T1 recovery delays above. T1 relaxation times were estimated for peptide residues by measuring change in peak height relative to increasing delay times for each gadodiamide concentration. First, all peak height values were normalized to the final delay time (3 s) peak height. Normalized data was then fitted to the following model using Bayesian Parameter Estimation: It=1−2e−t/T1+N0σ, where I is the normalized peak heights, t is the delay time. In this model the values of It ranges from −1 at t=0 and 1 at t=∞, representing full inversion and full recovery. After 3 seconds of delay recovery (our longest delay) we appeared to have achieved very close to full recovery (Figure 6a). Extracted parameters are T1, the inversion recovery (T1) estimate and σ, the standard deviation of a normal distribution centered at zero, N0σ. In this model, σ is a measure of the error of our data to the fitted model. For 1H spins measured in the putative helix the magnitude of σ did not exceed 0.1% or 5% of the range from −1 to 1, indicating our data are well described by the fitted model. This can be seen by the posterior predictive data points in Figure 6a (black dots), which are predictions of data from the fitted model at the time delays recorded.
T1 values at the gadodiamide concentrations listed above were then fitted to a straight‐line model to extract the PRE as the gradient of the line. The following Bayesian Parameter Estimation model was used: T1Gd=P·Gd+Nbσ where T1Gd is the measured T1 value above at concentration of Gadodiamide Gd. Extracted parameters are P, the PRE, b, the offset T1 value at a Gd concentration of zero and σ is a measure of the error of our data to the fitted model. Values of σ were always lower than 5% of the highest T1Gd value, indicating the above linear model describes our data well out to 24 mM gadodiamide. This can be seen with the posterior predictive data points generated from our fitted model in Figure 6c.
The PRE values were used to estimate the orientation of the helix with respect to the micelle by using the following model derived by Respondek et al. (2007 (link)) for a helix buried away from a PRE agent, inside a micelle, modified with a noise factor: PRE=kπ6A+1.5·sinτ·x−1−cosτ·B·cos1.745·x−1+ρ3+N0σ, where x is the number of the amino acid in the sequence of the helix, starting at the N‐terminus, A is the immersion depth of the helical axis at the first residue, B is the radius of the helix for the atoms undergoing PRE (1.95 Å for 1HN). The parameters estimated from data are τ, the tilt angle, ρ, the azimuth or the rotation angle of the helix, k, a constant to account for a combination of proportionality constants in the system to do with the strength of the PRE effect from the gadodiamide and finally, σ, to account for noise in the data during Bayesian Parameter Estimation. The estimation of σ was 0.019 which is ~7% of the highest PRE value recorded in the helix at ~0.27 s−1 mM−1 for S386, showing our fitted model is in good agreement with the data (see Figure 6d).