Backbone Torsion Angle Determination Using Proton Detected Magic-Angle Spinning Nuclear Magnetic Resonance

Protein torsion angles define the backbone secondary structure of proteins. Magic-angle spinning (MAS) NMR methods using carbon detection have been developed to measure torsion angles by determining the relative orientation between two anisotropic interactions—dipolar coupling or chemical shift anisotropy. Here we report a new proton-detection based method to determine the backbone torsion angle by recoupling NH and CH dipolar couplings within the HCANH pulse sequence, for protonated or partly deuterated samples. We demonstrate the efficiency and precision of the method with microcrystalline chicken α spectrin SH3 protein and the influenza A matrix 2 (M2) membrane protein, using 55 or 90 kHz MAS. For M2, pseudo-4D data detect a turn between transmembrane and amphipathic helices.

where, is the number of the experimental points; error -is the uncertainty in the peak amplitude, estimated from the RMSD of a noise region of the spectrum (the same region for all spectra in one series). Peak intensities were analyzed using software PINT (Ref. 2

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The MODERN signal is influenced by experimental imperfections, for example, rf-field inhomogeneity. Obtaining reasonable fits required modeling a distribution of flip angles, GH   The sensitivity to the flip angle deviation is increased with decreasing dipolar coupling constant. For example, Figure S1B shows the MODER5 curves with 90 0 flip angle ( Figure S1C demonstrates the ratio between these two values, DIS,output/ DIS,intput. In the ideal case this ratio is 1 (cyan). Above DIS,intput of 11 kHz, the output dipolar coupling is larger, while below the fit deviates towards smaller values. The deviations are symmetric with respect to the optimal value of αrf as was observed for the dependence of the MODER5 amplitude   For each sample, the first step in the experimental protocol was a careful optimization of the MODER5 power level by maximizing the signal dephasing at short times. For example, at ~0.07 ms a series of 1D spectra can be recorded as function of the rf-field power. The optimal rffield power is determinate when the MODERN signal has the lowest value. Figure S2A demonstrates the experimental HC MODER5 curve at 72 μs (expected first MODERN minimum for a 23 kHz dipolar coupling) as a function of the proton rf-field power in Watts. The applied optimal rf-field powers on HC and NH dipolar interactions were optimized separately. In our case, the applied proton rf-field powers to recouple HC and dipolar interactions had the same values of In addition to the influence of the rf-field inhomogeneity, we also found that the values of the proton to carbon CP times affected the performance of MODERN. Figure  After optimization of CP and rf-field powers, these same settings are used for dipolar coupling and torsion angle determination using MODERN.
For obtaining the dipolar coupling and torsion angle values, the experimental signals are compared with simulation in MATLAB (details in 'The MATLAB Code' section). Since the signal evolution is sensitive to the precise B1 rf-field, the influence of the rf-field inhomogeneity in the probes should be simulated. The profile of rf-field inhomogeneity in MAS probes was investigated before [5][6][7] . In these works, it was found that balanced probes result in symmetric profiles that are describe well by a Gaussian function. Since MODERN pulses have a symmetry around the optimal value (Fig S1), we used a half Gaussian function in simulations.
We found that reliable fits required consideration of rf inhomogeneity, which was modeled as a Gaussian flip angle distribution between 1 and a minimal value (maximum deviation, Δ GH,-Q& : To confirm the Gaussian profile of the rf-field inhomogeneity in the probe we recorded a series of 1D HCαNH experiments as a function of the length of the first proton pulse from 1.8 to 184.2 μs with a 1.6 μs step. Figure S2C shows the FFT of such signal (black stars), the Gaussian function (red line) and half of the flip angle distribution function, which is used in simulations (cyan dashed line). All experimental and simulated FFT spectra coincide very well and symmetry around maximal value is observed.  curves for each sample. Table S1 summarizes the obtained parameters. For α-PET SH3 samples (short and long CP) 6,%HH has a smaller influence than for fully protonated SH3. The α-PET SH3 (short CP) dataset had the smallest apparent value of Δ GH,-Q& , suggesting that the CP time may influence the special distribution of the detected signal e.g. the edges versus the middle of the coil.   Using the obtained Δ GH,-Q& and 6,%HH from Table S1, we obtained HC and NH dipolar coupling values for α-PET SH3 (short CP and long CP) and SH3 (long CP). Figures S4-S5 show the experimental and simulated MODER5 curves for α-PET SH3 (short CP) and SH3 (long CP).  Table S1). Eqn. S3 represents the simulated signal. The fitting errors were obtained by generating 100 Monte Carlo curves, assuming a Gaussian noise distribution (~1.5σ).  Table S1). Eqn. S3 represents the simulated signal. The fitting errors were obtained by generating 100 Monte Carlo curves, assuming a Gaussian noise distribution (~1.5σ).
For processing the α-PET SH3 (long CP) MODERN data, we had to add an additional parameter, p, which defined the population of protonated Cα signal ( Figure S6A). The particular α-PET sample used had incomplete incorporation of alpha protons (due to incomplete production of keto acids in the enzymatic digestion step) The deuterated alpha carbons, DαCα, are increasingly polarized at longer CP times, e.g. from nearby protons such as the backbone amide proton. The signal from this part of the sample is then transferred on through CP to nitrogen and then detected at the amide proton. However, there can be no CH MODERN oscillation for this part of the sample. The dipolar interaction between Cα and remote protons is ~8 times weaker in comparison to directly bonded protons. At short CP mixing times, only directly bonded HC groups are excited. However, at long mixing times, the total CP signal is the sum of the strong (directly bonded protons) and weak (remote protons) CH groups. Note that p is not a labelling population, but also depends on the local geometry of nearby protons, which explains the different p values fit to different residues of the same type ( Figure S8).     (Table S1).
Eqn. S4 represents the simulated signal. The fitting errors were obtained by generating 100 Monte Carlo curves, assuming the Gaussian noise distribution (~1.5σ). Figure S8 shows the population of the protonated backbone Cα carbons for different residues. For some residues, Cα are fully protonated (Q16 and L31), whereas for others an apparent 35% of the signal comes from deuterated alpha carbon (T24).

Torsion Angle Determination
The sequential application of MODERN pulses to recouple both HC and NH dipolar interactions allows measurement of the projection angle between these interactions, 'GL{ . The projection angle can be visualized by translation of the HC bond to the NH bond such that C and N atoms coincide.  Figure   S10A with the curves in Figure S10B, it is clear that HC/NH curves are more sensitive to ϕproj than H2C/NH curves, in particular below 0.05 ms. It shows the advantage of measuring the torsion angles with the deuterated α-PET SH3 sample, in which Cα of GLY residues (G28 and G51) contain only one proton and the second is replaced with deuterium.  However, the desired angle is a torsion angle, ϕH, which is produced by two planes defined by atoms Cα-N-H N and Hα-C-N. The next Eqn. links the torsion and projection angles: where €•‚R is the H N -N-Cα angle; ′ •‚R€R = 180 L − •‚R€R , where •‚R€R is the NCαHα angle. Figure    To obtain € values we used the set of the HC, NH dipolar coupling values, Δ GH,-Q& , and 6,%HH as the input parameters. For torsion angle determination, € value was the only fit variable. Figures S12-S14 show the comparison of the experimental and simulated MODER5-MODER5 curves for all three samples. Figure 12 also shows a plot of Eqn. S5. Figure S13. The first and third columns: Experimental SH3 (long CP) and simulated MODER5-MODER5 curves (solid lines). The second and fourth columns: 5 6 (Eqn. S1) as a function of torsion angle, ϕH. The simulated MODER5-MODER5 curves were obtained with Δ GH,. and 6,%HH of Table S1 and measured dipolar coupling values. The fitting errors were obtained by generating 300 Monte Carlo curves (grey curves, the black curve is the average), assuming a Gaussian noise distribution (~1.5σ) and considering the errors in the measured dipolar coupling values. The Figure in the black frame shows the projection angle as a function of the torsion angle for ′ •‚R€R = 71 L and €•‚R = 120 L . Figure S14. The first and third columns: Experimental α-PET SH3 (long CP) and simulated MODER5-MODER5 curves (solid lines). The second and fourth columns: 5 6 (Eqn. S1) as a function of torsion angle, ϕH. The simulated MODER5-MODER5 curves were obtained with Δ GH,. and 6,%HH values in Table S1 and measured dipolar coupling values. The fitting errors were obtained by generating 300 Monte Carlo curves (grey curves, the black curve is the average), assuming a Gaussian noise distribution (~1.5σ) and considering the errors in the measured dipolar coupling values.
The Figure in the black frame shows the projection angle as a function of the torsion angle for ′ •‚R€R = 71 L and €•‚R = 120 L . Figure S15A summarizes the obtained torsion angles as a function of the x-ray crystallography-derived angles from the pdb file 2NUZ. Figure S15B compares the absolute differences between the obtained torsion angles from α-PET SH3 using short CP and the x-ray crystallography-derived angles from pdb 2NUZ (red stars) and pdb 1SHG file (blue diamonds).
These two structures have comparable unit cell parameters, but were reported independently from two different research groups. About a 5° rms deviation is observed between the two crystal structures. This can be compared with the 17.82 o and 17.31 o rms deviation from the NMR data.    among these CP conditions. The same dependence was found for M2 wild type. Table S2 summarizes the optimized parameters: Δ GH,-Q& and 6,%HH .  (Table S2).
Eqn. S4 represents the simulated signal. The fitting errors were obtained by generating 100 Monte Carlo curves, assuming a Gaussian noise distribution. Error bars are displayed at 1.5σ. The dataset was recorded as pseudo 3D.   Figure S20 summarizes the obtained HC (A) and NH (B) dipolar coupling values. Figure   C shows the population of CαH pairs with a strongest dipolar coupling. Since this sample did not contain deuteration, the physical interpretation behind this population could be e.g. a small amount of overlapping signal from carbonyl resonances. At faster spinning, CP conditions can be broad enough for some carbonyl signal to survive the CP transfers, despite relatively selective CP conditions. In the pseudo-3D data, the carbon frequency is not sampled, such that carbonyl signal would overlap.     As an example, Table S3 shows an example input file for dipole coupling determination with optimization of flip angle distribution and 6,%HH .  Table S4 shows the example of the output file with the optimal values.  Additionally to the previous files, one more file should be created -'Names.dat' (line 27). For example, 'Names_aPET_long_CP.dat' contains the names of V9:CH and V9:NH.
To obtain dipolar coupling plots with GH,-Q& and 6,%HH optimization: 'Optimization_rf_T2=1' (Flag at line 21) Dipolar_Torsion = 0' (Flag at line 9) The same file with the names of the residues should be prepared.
For example, 'Names_Phi.dat' contains the names of V9 and G28.
To obtain dipolar coupling plots with GH,-Q& and 6,%HH optimization: 'Optimization_rf_T2=1' (Flag at line 21) 'Dipolar_Torsion = 1' (Flag at line 9) The same file with the names of the residues should be prepared.   Additionally to the mentioned input files (as examples), we provide a set of the input files, which can be used for running the codes (the experimental data of α-PET SH3 (short CP)): 'T2_RF_OPT_EXP.dat' (contains the experimental NH data of V9, Y13, A56 and L61 residues); 'Exp_D.dat' (contains the experimental CH data of V9, Y13, A56 residues and then the experimental NH data of V9, Y13, A56 residues); 'Exp_Phi.dat' (contains the experimental CH-NH data of V9, Y13, A56 residues);