NMR 15N Relaxation Experiments for the Investigation of Picosecond to Nanoseconds Structural Dynamics of Proteins

Summary

Nuclear magnetic resonance (NMR) spectroscopy can characterize structural protein dynamics in a residue-specific manner. We provide a hands-on protocol for recording NMR ¹⁵N R₁ and R₂ relaxation and {¹H}-¹⁵N heteronuclear Overhauser effect (hetNOE) experiments, sensitive to the picoseconds to nanoseconds timescale.

Abstract

Nuclear magnetic resonance (NMR) spectroscopy allows studying proteins in solution and under physiological temperatures. Frequently, either the amide groups of the protein backbone or the methyl groups in side chains are used as reporters of structural dynamics in proteins. A structural dynamics study of the protein backbone of globular proteins on ¹⁵N labeled and fully protonated samples usually works well for proteins with a molecular weight of up to 50 kDa. When side chain deuteration in combination with transverse relaxation optimized spectroscopy (TROSY) is applied, this limit can be extended up to 200 kDa for globular proteins and up to 1 MDa when the focus is on the side chains. When intrinsically disordered proteins (IDPs) or proteins with intrinsically disordered regions (IDRs) are investigated, these weight limitations do not apply but can go well beyond. The reason is that IDPs or IDRs, characterized by high internal flexibility, are frequently dynamically decoupled. Various NMR methods offer atomic-resolution insights into structural protein dynamics across a wide range of time scales, from picoseconds up to hours. Standard ¹⁵N relaxation measurements overview a protein's internal flexibility and characterize the protein backbone dynamics experienced on the fast pico- to nanosecond timescale. This article presents a hands-on protocol for setting up and recording NMR ¹⁵N R₁, R₂, and heteronuclear Overhauser effect (hetNOE) experiments. We show exemplary data and explain how to interpret them simply qualitatively before any more sophisticated analysis.

Introduction

The function of a protein is determined not only by its three-dimensional structure but also by its structural dynamics, encompassing its internal flexibility and structural transitions between different conformations the protein will adopt. Nuclear magnetic resonance (NMR) spectroscopy can investigate the structural dynamics of proteins in solution^1,2,3. Recent developments in proton-detected solid-state NMR also allow for the characterization of protein dynamics in a less soluble state, such as, e.g., a lipid bilayer membrane^4,5,6. In solution NMR, the structural dynamics of the protein backbone and protein side chains can be studied. For a globular protein, a structural dynamics study of the protein backbone can be achieved up to 50 kDa once the protein is ¹⁵N isotopically labeled. When side chain deuteration and transverse relaxation optimized spectroscopy (TROSY) are employed, this limit can be extended up to 200 kDa^7,8. When the focus lies on side-chain dynamics, the range of accessible proteins and complexes can be extended up to 1 MDa^2,9.

The named weight limitations do not apply to intrinsically disordered proteins (IDPs), which frequently show high intrinsic dynamics. Over 30% of the eukaryotic proteome comprises IDPs or intrinsically disordered regions (IDRs)^10,11,12,13. They play central roles in many cellular processes, such as signal transduction and transcription¹, and are frequently involved in intracellular phase separation^14,15,16,17. IDPs lack a well-defined three-dimensional (3D) native structure under physiological conditions and have a weakly funneled or rugged energy landscape^17,18. Due to a low hydrophobicity and strong electrostatic repulsion distributed over the backbone of IDPs or IDRs, a driving force for folding to a rigid structure is missing¹⁹. IDPs frequently adopt a folded conformation when complex with other binding partners^10,20,21. Also, post-translational modifications (PTMs) expand the folding possibilities of IDPs or IDRs^22,23. Misfolding of IDPs has been identified as a cause of various diseases, including neurodegenerative diseases^15,24,25,26.

IDPs and IDRs show high internal flexibility^21,27,28. Conformational ensembles displaying the variation of atomic positions and dihedral angles were derived from molecular dynamics simulations and restraints obtained from experimental data^29,30,31,32. Due to dynamics and resulting disorder in the frozen state, the diffuse electron density makes it difficult to structurally characterize them using state-of-the-art methods in structural biology, such as cryo-EM or X-ray crystallography. Also, crystallization conditions or sample preparation techniques for experiments at cryogenic temperatures may impact the conformational space experienced by IDPs. However, the solution NMR works well for highly dynamic proteins and is therefore well-suited for investigating IDPs^{16,20,22,28,29,30,31,32,33,34,35,36,37,38}.

As introduced above, solution NMR offers various techniques to study internal protein dynamics across a wide range of time scales (Figure 1), primarily based on spin relaxation^{31,33,38,39,40,41,42}.

Spin relaxation of the ¹⁵N nuclei in the amide groups of the protein backbone is induced by ¹H-¹⁵N bond angle orientation changes due to internal protein dynamics and collective motions (including, when relevant, rotational diffusion)^{27,43,44,45,46,47,48,49,50,51}. At timescales shorter than the rotational correlation time τ_R (the time the molecule needs to rotate one radiant, also dubbed overall tumbling correlation time), the chemical shift anisotropy (CSA) and the dipolar coupling (D) are active and not averaged by the rotational diffusion of the protein. Internal dynamics of the protein backbone, comprising variations in bond angles, reorientations of bonds, and rotational tumbling, induce stochastic fluctuations of the CSA and dipolar coupling tensor, resulting in a variation of the local magnetic field, ultimately leading to NMR spin relaxation^47,48,52,53. These fluctuations can be described by an overall correlation function. The Fourier transform of the overall correlation function is called the spectral density function. In the semi-classical Redfield relaxation theory, the NMR relaxation rate constants can be described by linear combinations of these spectral density functions⁵⁴.

Backbone ¹⁵N NMR relaxation experiments developed in the early 1990s comprise ¹⁵N R₁, R_1ρ, and {¹H}-¹⁵N nuclear Overhauser effect experiments, sensitive to the fast picosecond (ps) nanosecond (ns) timescale, faster than the rotational correlation time τ_R of the protein^45,55,56,57. To characterize backbone dynamics slower than the rotational correlation time τ_R, so-called relaxation dispersion experiments, R_1ρ, and Carr-Purcell-Meiboom-Gill (CPMG) experiments sensitive to microsecond (µs) - millisecond (ms) dynamics^{44,46,58,59,60,61} are used. Dynamics slower than microseconds can be captured by ¹⁵N chemical exchange saturation transfer (CEST) NMR⁶², exchange spectroscopy (EXSY, milliseconds to seconds), or Real-time (RT) NMR (seconds to hours)^63,64. The PRE (paramagnetic relaxation enhancement) effect of paramagnetic probes, as well as residual dipolar couplings (RDCs), can be used to assess the entire range of ps to ms dynamics^65,66,67,68.

Figure 1: Time scales of protein backbone dynamics and sensitive time window of different NMR dynamics experiments. NMR offers a variety of methods to characterize protein backbone dynamics across a wide range of timescales. Different motions experienced by the protein backbone are indicated at their respective timescales. The protein's rotational correlation time, τ_R, is the time the protein needs for an overall rotation (by one radiant). Motions faster than the protein's rotational correlation time, τ_R, can be associated with the protein's internal flexibility. Various NMR experiments and their sensitivity to the respective timescales are indicated below the arrow. Please click here to view a larger version of this figure.

The protocol below describes the setup of NMR relaxation experiments by Lakomek et al.⁶⁹ and Stief et al.⁷⁰, using a sensitivity-enhanced heteronuclear single quantum coherence (HSQC) detection scheme. Before proceeding to the experimental implementation, a very brief overview of NMR spin relaxation and NMR relaxation experiments is given. Due to size restraints and to keep this protocol comprehensible, this overview must remain simplistic (and therefore incomplete).

The longitudinal or spin-lattice relaxation, characterized by the T₁ time or the R₁ = 1/ T₁ rate constant, describes the return of magnetization to Boltzmann equilibrium. In equilibrium, the magnetization is aligned along the axis of the outer magnetic field, which defines the z-axis of the laboratory frame. Spectral densities at high (¹H) and small (¹⁵N) Larmor frequencies (the NMR resonance frequencies, e.g., 600 MHz for ¹H for a 14.1 Tesla magnet) and linear combinations of these Larmor frequencies contribute to the ¹⁵N R₁ relaxation, which is characterized by the ¹⁵N R₁ rate constants measured in rad·s^-1. Motions on timescales are inverse to these Larmor frequencies; thus, motions on the picosecond to nanosecond timescale contribute to the relaxation rate constant R₁. For molecules that show overall tumbling and where a rotational correlation time can be defined, the R₁ (T₁) curve shows a maximum (minimum) for ωτ_R = 1, with the rotational correlation τ_R and the Larmor frequency ω of the spin under consideration. If multiple Larmor frequencies contribute, the one with the lowest frequency is the dominant one, e.g., ω_N in the case of ¹⁵N R₁. The fast motion regime (ωτ_R much smaller than 1) applies to small molecules that tumble very fast and for low magnetic fields and low viscosity. The slow motion regime (ωτ_R much larger than 1) is valid for larger molecules that tumble slower and for high magnetic fields and high viscosity.

Globular folded proteins show overall tumbling in solution, and a rotational correlation time can be assigned. However, the concept of overall tumbling is no longer valid for intrinsically disordered proteins and frequently differs from assigning a single rotational correlation time. Here, the residue-specific internal correlation time becomes more critical.

The described pulse sequence measuring ¹⁵N R₁ relaxation rates (Figure 2) is based on a sensitivity-enhanced HSQC read-out experiment with an Echo/ Anti-Echo detection for quadrature detection^69,70,71. Short gradients with variable strength and length are used for coherence selection and improved water suppression⁷⁰. During that time, ¹⁵N longitudinal polarization will relax. Longer decay times lead to reduced intensities in the associated 2D planes of this pseudo-3D spectrum (delay data points are recorded in the third dimension). A loop element, described below, is executed an increasing number of times for longer relaxation times. As cross-correlated relaxation between the ¹⁵N chemical shift anisotropy (CSA) and the ¹H and ¹⁵N dipolar coupling (D) is also active during the relaxation delay, a central I-BURP-2 180° pulse⁷², selective on the amide protons, is necessary to refocus the contribution by cross-correlated relaxation (which if not refocused would lead to skewed and erroneous ¹⁵N R₁ rate constants).

Figure 2: NMR pulse sequence schemes for determining the NMR relaxation rate constants. (A) ¹⁵N R_1ρ, (B) ¹⁵N R₁, and (C) hetNOE experiment, using a sensitivity-enhanced HSQC read-out scheme^69,70. 90°(x) pulses are visualized by narrow rectangles and 180°(x) pulses by wide rectangles, unless indicated otherwise. The following phase cycle is applied: φ₆ = y, y, -y, -y; φ₇ = y, -y, φ_rec = y, -y, -y, y. Quadrature detection is achieved by inverting the polarity of gradient G5 and the phase cycle of φ7 (Echo/ Anti-Echo detection). (A) ¹⁵N R_1ρ experiment: The black rectangular represents the spin-lock, for which the duration varies to acquire different relaxation delays. The triangles before and after the spin-lock indicate the adiabatic shape pulses that align the magnetization along the effective magnetic field axis B_eff. G₁₀ is an optional gradient to prevent radiation damping of the water magnetization during the evolution phase. (B) ¹⁵N R₁ experiment: The bracketed part shows the sequence's loop element, repeated an n number of times to match the desired relaxation delay. (C) The hetNOE pulse scheme is similar to the second half of R₁ and R_1ρ pulse schemes, namely the t₁ evolution time and HSQC-detection element. However, ¹⁵N magnetization is excited directly without any INEPT. Saturation of the proton magnetization (to achieve cross-relaxation between ¹H and ¹⁵N) is achieved by a train of 180(¹H) pulses applied for at least 5 s. An idle delay of the same lengths (here, 5 s) without any pulse train is applied for the reference experiment. G₅ is an optional gradient to prevent radiation damping, and the inversion in polarity of gradient G4, in combination with phase φ7 = y, -y, -y, y, achieves quadrature detection. The magnetization transfer steps, represented by product operators, are marked in red. Please click here to view a larger version of this figure.

The relaxation rate constant R₂ describes the relaxation of transverse polarization (in the xy-plane orthogonal to the external magnetic field) due to loss of phase coherence between the spin, leading to decay of detectable magnetization^53,54. The spectral density function at high and small frequencies contributes to R₂, similar to R₁. However, the biggest contribution to R₂ originates from the spectral density at zero frequency. For this reason, R₂ is very sensitive to the rotational tumbling, described by the rotational correlation time τ_R, which is in the order of a few ns for a small globular protein at room temperature. Thus, slower backbone motions in the hundreds of ps to low ns regime contribute the most. Exchange dynamics of the backbone that cause a modulation of the isotropic part of the chemical shift tensor of the ¹⁵N nuclei, in principle, add an exchange contribution R_2ex to the R₂ rate constants^{43,44,49,60,61}. In the described experiments, the R_2ex contribution is suppressed by a spin-lock that refocuses dynamics slower than the inverse circular frequency of the spin-lock. The spin-lock is a long continuous wave radiofrequency pulse that keeps the magnetization aligned along the effective magnetic field axis B_eff (the vector sum of the spin-lock ω₁ field and the chemical shift offset from the ¹⁵N carrier frequency (see below)). The relaxation of the magnetization aligned along the B_1,eff axis is called R_1ρ relaxation, which has a R₁ component and a R₂ component. Using formula (1), R₂ can be calculated from R_1ρ and R₁^44,73:

(1).

The angle between the axis of the effective magnetic field B_eff and the external magnetic field B₀ is . ω₁ is the RF amplitude of the spin-lock and Ω the chemical shift offset between the ¹⁵N chemical shift of the corresponding residue and the ¹⁵N carrier frequency ^44,73.

The R_1ρ pulse scheme (Figure 2A, ⁷⁰) is very similar to the ¹⁵N R₁ scheme except for the relaxation delay. To measure the ¹⁵N R_1ρ relaxation rates, the spin-lock must be active after the magnetization has been aligned along the effective field axis B_eff by an adiabatic pulse with the same radio-frequency (RF) amplitude as the spin-lock. The length of the spin-lock will be varied to obtain the different relaxation delays.

The steady-state {¹H}-¹⁵N nuclear Overhauser effect (¹H-¹⁵N NOE), dubbed hetNOE in the following, is the ratio of the cross-relaxation rate and the ¹⁵N longitudinal relaxation rate. It leads to a reduction of the steady-state polarization on ¹⁵N due to cross-relaxation with the proton upon saturation of the proton polarization^{45,53,54,74,75}. The cross-relaxation depends on spectral density functions of the sum and difference of the ¹H and ¹⁵N Larmor frequencies. Therefore, the hetNOE is sensitive both to fast picosecond dynamics (< 100 ps) and also to ps-ns dynamics (due to its R₁ dependence). The sequence⁶⁹ (Figure 2C) is based on a sensitivity-enhanced HSQC read-out with Echo/ Anti-Echo gradients for quadrature detection. For saturation of the proton magnetization and the resulting hetNOE, the equilibrium proton magnetization is inverted and subsequently saturated by rapidly pulsing 180° pulses for about 5 times the ¹⁵ N T₁. For the reference experiment, the recovery delay is equal to the saturation delay but without the ¹H 180°pulse train. An extra delay of D1 = 2 s is added for the reference experiment and the one with ¹H saturation. Both experiments are recorded back-to-back and differ only in applying ¹H 180°pulses (saturation) or not (reference). The ratio of spectral intensities recorded in the experiment with ¹H saturation divided by the intensities of the reference experiment (without the 180° proton pulse train) gives the {¹H}-¹⁵N NOE (hetNOE) value.

The following protocol describes the setup of NMR relaxation experiments by Lakomek et al.⁶⁹ and Stief et al.⁷⁰. We focus on NMR pulse sequences using a sensitivity-enhanced HSQC detection scheme. The ¹⁵N R₁ and R_1ρ experiments are implemented as described in detail by Stief et al.⁷⁰, and the hetNOE experiment is described by Lakomek et al.⁶⁹.

Protocol

1. NMR sample preparation

NOTE: Isotope labeling of the proteins is performed for higher-dimensional NMR and advanced NMR experiments. When protein expression in E. coli and protein purification had been established using rich media (e.g., Luria-Bertani [LB] or 2x yeast extract tryptone medium [2YT]) with a yield of several milligrams per liter, preparing an isotopically labeled NMR sample is usually relatively straightforward.

1. For isotope labeling, use M9 minimal media for gene expression, where ¹⁵N ammonium chloride is the only nitrogen source and ¹³C-enriched glucose is the only carbon source.
2. For protein purification, follow the standard protocol established in the laboratory for the respective protein.
   ​NOTE: The results section shows representative results for an IDP, the monomeric SNARE protein Synaptobrevin-2 (1-96). NMR isotope labeling of Synaptobrevin-2 has been performed as described in⁷⁰. For very high-precision measurements, using low D₂O concentrations, less than 5%, is recommended. This is because of the deuterium isotope effect, which can be observed in Hahn-Echo ¹⁵N T₂ and at low-frequency ¹⁵N CPMG relaxation dispersion experiments (not discussed here) but has only a minimal impact in ¹⁵N R_1ρ experiments (where it is primarily refocused)⁷⁶.

2. Preparations for running the NMR relaxation experiments on the spectrometer

NOTE: The described NMR relaxation experiments are specific for Bruker spectrometers. They have been tested on cryogenic and room temperature ¹H, ¹⁵N, and ¹³C triple resonance probes and Avance III and Avance Neo consoles operated by the Bruker software Topsin 3.6 or higher.

1. Follow the precautions.
   1. Do a safety briefing before working at the NMR spectrometer.
   2. Check the probe's power specifications of the used spectrometer and choose an appropriate pulse length and pulse power for every pulse, e.g., by comparing consistency with the Topspin "prosol" table entries.
2. Import the pulse sequences.
   1. Download the NMR pulse programs either from the website indicated below or from the extended Biological Magnetic Resonance Bank (BMRB) repository (bmrbig102) to the directory /opt/topspin4.1.4/exp/stan/nmr/lists/pp/user of the computer operating the NMR spectrometer. Please adjust the topspin version (here: topspin4.1.4 to the respective version installed on the spectrometer).
   2. Download the NMR-shaped pulses either from the website indicated below or from the extended Biological Magnetic Resonance Bank (BMRB) repository (bmrbig102) to the directory /opt/topspin4.1.4/exp/stan/nmr/lists/pp/user of the computer operating the NMR spectrometer. Please adjust the topspin version (here: topspin 4.1.4 to the respective version installed on the spectrometer).
3. Calibrate the spectrometer and sample.
   1. Set the temperature of interest. For temperature calibration, apply the facility's protocols. For example, use a Methanol-d4 sample and interpret the observed chemical shift difference using the web application NMR thermometer (https://chem.ch.huji.ac.il/nmr/software/thermometer.html); see also⁷⁷.
   2. Insert the sample (plus an additional 5% D₂O for the lock) and wait approximately 10 min to allow the sample to equilibrate its temperature. Lock the deuterium (²H) signal (command: lock, select H₂O+D₂O).
   3. Match and tune the ¹H, ¹⁵N, and ¹³C channels, e.g., using the atma or atmm routine. If no automatic matching and tuning unit is installed, manually match and tune the probe using the wobb command.
   4. Perform shimming for a homogenous B₀ field, e.g., using the topshim routine tg.
4. Calibrate the 90° (¹H) pulse length.
   1. Use the zg experiment. Use getprosol to import the probe parameters. Choose a short duration of 5 µs for P1. Check and correct the specified power level of the probe for PLW1 if needed.
   2. Start the experiment with zg. Process the data with efp. Adjust the phase with .ph so that the baseline is even and the NMR signal of the water resonance is in phase.
   3. Estimate a 360° (¹H) pulse by taking a common or approximate 90° (¹H) pulse (e.g., from the listed spectrometer specifications) and multiplying it by a factor of four. Run the experiment and process it.
      NOTE: The chosen duration is too long if the signal is positive and too short if negative. The 360° (¹H) pulse will be the zero crossing.
   4. Adjust the pulse length accordingly. Do this iteratively to find the zero crossing. Divide the obtained value by four. That will be the 90° (¹H) pulse.
      NOTE: An alternative to the described 360° method is the pulscal routine, which can be started from the command line and allows an automated ¹H pulse calibration.
5. Calibrate the carrier frequency O1 to the water resonance.
   1. Copy the zg experiment by typing edc in the command line to a new experiment number. Type rpar to open the parameter sets (Supplementary Figure 1A).
   2. Search for the parameter set ZGPR. Click on the parameter set ZGPR (Supplementary Figure 1A), click on Read, choose Execute "getprosol" and click OK (Supplementary Figure 1B).
   3. Change P1 to the calibrated 90° (¹H) pulse length. Choose a saturation length of D1 = 2 s and a pulse power of PLW9 of 50 dB. Set the receiver gain (rg) to 16. Alternatively, execute the receiver gain adjustment by typing rga and setting the receiver gain to the specified value (But avoid "receiver gain overflow").
   4. Type gs in the command line to start for a repeated, continuous acquisition. Go to the acquisition window and change the O1 to reduce the FID area dominated by the water signal (Supplementary Figure 2).
   5. Click below the marker to decrease the O1, and click above the marker to increase it. Use the sensitivity button to change the step size. Save the current O1; Close stops the repeated acquisition (Supplementary Figure 2).
6. Calibrate the 90° (¹⁵N) pulse length.
   1. Copy the zg experiment to a new experiment number (type edc). Type rpar to read the parameter set HSQCFPF3GPPHWG to change the pulse program to a ¹H-¹⁵N HSQC experiment. Use the option Keep parameters P1, O1, and PLW1 (Supplementary Figure 1).
   2. Type getprosol 1H <calibrated 90° (¹H) pulse length in µs> <90° (¹H) pulse strength in db> in the command line to import the probe parameters. Set the number of scans (NS) to 8 and the dummy scans (DS) to 2.
      NOTE: < > specifies here the values to be set. For example: getprosol 1H 8.5 -11.79.
   3. Run the first increment of the experiment by typing zg in the command line. Copy the first increment to a new experiment number with rser 1 <new experiment number>. Process the data with efp and phase the spectrum with .ph. Use the first increment (1D experiment) of the experiment for the following steps.
      NOTE: The < > specify the chosen number for the new experiment, e.g., rser 1 101.
   4. Type ased in the command line to open the pulse sequence parameters of the 1D experiment. Click on the E in the PULPROG line (see Supplementary Figure 3A) to open the pulse program editor.
   5. Use the following workflow to save the pulse sequence under a new name: Click File (left upper corner), Save as, enter the new name, and click OK. Then click Set PULPROG to the dataset (see Supplementary Figure 3B) and click OK.
   6. Modify the original ¹H-¹⁵N HSQC sequence (saved under a new name, see 2.6.4.) by multiplying the 90° (¹⁵N) after the t₁ evolution period (before the back transfer) by a factor of 2 (the 90° (¹⁵N) pulse is now 180° (¹⁵N)). Press Ctrl S to save the pulse sequence. Set the pulse length to 90° (¹⁵N) (P21) so that the NMR signal of the first increment will vanish (at the zero crossing) (Supplementary Figure 3B).
   7. Open the ¹H-¹⁵N HSQC experiment (2D experiment) and enter the calibrated 90° (¹⁵N) pulse length (P21). Type getprosol 1H <calibrated 90° (¹H) pulse length in µs> <90° (¹H) pulse strength in db> 15N <calibrated 90° (¹⁵N) pulse length in µs> <90° (¹⁵N) pulse strength in db> in the command line.
7. Determine the spectral widths and appropriation of acquisition times.
   1. In the acquisition parameter window for the ¹H-¹⁵N HSQC experiment (type eda in the command line), adjust the spectral width (acquisition parameter SW) and the number of dimension increments in direct and indirect dimensions (acquisition parameter TD).
      1. Choose for SW, 16 ppm in the direct (¹H) and 30 ppm in the indirect (¹⁵N) dimension. Choose for TD, 2048 in the direct (¹H) and 512 in the indirect (¹⁵N) dimension.
   2. Acquire the ¹H-¹⁵N HSQC experiment.
      1. Check that all signals of interest are detected and that no aliasing artifacts are present in the spectrum. Change the O3P if the center of the spectrum does not fit with the center of the protein signal distribution along the ¹⁵N axis.
      2. Increase the SW if the spectral window is too small. Increase the TD to gain a higher FID resolution (Check the probe specifications for the maximum duration of decoupling).
         NOTE: This is the general setup and the starting point for the setup of NMR relaxation experiments. It is recommended to record the ¹H-¹⁵N HSQC experiment at the beginning and end of the entire set of experiments and, for more extended experimental times, also in between to monitor sample integrity.

3. Implementing the NMR relaxation experiments

NOTE: The NMR relaxation pulse sequences (Figure 2) are available at https://www.ipb.hhu.de/en/teams/team-lakomek/pulsesequences  or at the extended Biological Magnetic Resonance Bank (BMRB) repository (bmrbig102).

1. Set up the ¹⁵N R_1ρ experiment.
   1. Copy the HSQC experiment (type edc) to a new directory. Type ased and change the pulse program to the ¹⁵N R_1ρ experiment by clicking on the three dots of the parameter line PULPROG in the pulse sequence parameters (ased, see Supplementary Figure 3A). Double-click on the pulse program, click on Set PULPROG to dataset (see Supplementary Figure 3B), and click OK.
      NOTE: Some error messages may appear. Close these messages.
   2. Type gpnam in the command line to insert all missing gradient shapes (gpnam1- gpnam9) as described in the pulse sequence (Supplementary Figure 4).
   3. Type vplist in the command line. Click on the three dots (Supplementary Figure 5A), File (upper left corner), and New (Supplementary Figure 5B).
   4. Type a name for a new dummy vplist, and press OK. Create the dummy vplist (5m, 65m, 25m, 45m, 15m, 55m, 35m, 10m; a new row for each vplist entry). Press Ctrl S to save the list and close the window of the vplist (Supplementary Figure 5C).
   5. Double-click on the name of the newly created vplist (Supplementary Figure 5B).
      NOTE: This is necessary to avoid compilation errors in the pulse sequence. The appropriate entries of the vplist will be determined further below (point 3.1.29.).
   6. Type ased to open the pulse sequence parameters (Supplementary Figure 6). Enter all missing gradient strengths and gradient lengths as given in the pulse sequence (Supplementary Figure 6D).
   7. Enter for the loop counter L₃ (number of complex points in the indirect dimension) 1/2 of the ¹⁵N TD entry in the acquisition parameter window (eda). Enter for the loop counter L₆ the number of recorded relaxation data points used for fitting the relaxation curve.
      NOTE: This number L₆ corresponds to the number of vplist entries, here: 8 (Supplementary Figure 6A).
   8. Set the adiabatic TanhTan_half.nl pulse, downloaded from the website specified above, as the shape of the ¹⁵N SP8 pulse. Set the adiabatic TanhTan_2nd.nl pulse from the website as the shape of the ¹⁵N SP9 pulse (Supplementary Figure 6C).
   9. Set the P8 entry to the length of the adiabatic TanhTan pulse - sufficiently long to guarantee the adiabaticity of the pulse; here P8 = 3000 µs is chosen (Supplementary Figure 6C).
   10. Set the ¹⁵N decoupling (CPDPRG 3) to a garp decoupling scheme. Use for the length of decoupling PCPD3 200 µs (Supplementary Figure 6C).
   11. Set the interscan recovery delay to at least D1 = 2 s or longer.
       NOTE: For the choice of a proper recovery delay, see the Discussion section.
   12. Set the dummy scans (DS) to at least 64 for the final experiment (during the setup, DS = 4 is sufficient for time reasons). As a starting point, use a number of scans (NS) of 4; use multiples of 4 if the signal-to-noise (SNR) is too low (Supplementary Figure 6A).
   13. Set the O1 to the calibrated carrier frequency of step 2.5. Set the O2P to 176 ppm and copy the O3P from the ¹H-¹⁵N HSQC experiment (Supplementary Figure 6A-C).
   14. Set the pulse length P7 to the 90° (¹⁵N) pulse length calibrated in step 2.6. Also, copy the pulse power level of the 90° (¹⁵N) pulse from step 2.6 to PLW3 and PLW7 (Supplementary Figure 6C).
   15. Set the pulse length P1 and P19 to the 90° (¹H) pulse length calculated in step 2.4. (Supplementary Figure 6B).
   16. Set the number of increments in the indirect dimension TD = l₃ * 2 * l₆ (eda or type td in the command line).
       NOTE: All pulse sequence parameters described here are additionally annotated in the pulse sequence.
   17. Set the shape pulse SP5 to an I-BURP2 shape (Iburp2.1000). Set the pulse length P15 to 2000 µs. Open the shape tool display by clicking on the E next to the I-BURP2 shape pulse in the Topspin pulse sequence parameter window (ased) (Supplementary Figure 6B).
   18. Simulate the shape pulse with the correct length by clicking the Start NMR Simulation button. Check the shaped pulse length [µs] (= 2000 µs) and the rotation angle [°] (= 180°) in the simulation window. Click on Start NMR-SIM (Supplementary Figure 7A).
   19. Check the excitation range and choose the appropriate I-BURP2 pulse length to cover the protein's ¹H spectral dispersion but avoid excitation of the water at the same time. Set P15 to the Shaped pulse length of the simulation window with the best IBURP-2 pulse simulated (Supplementary Figure 7B).
       NOTE: The proper length is chosen if the I-BURP2 excites (> 95% effectiveness) the entire amide region. To simulate an I-BURP2 pulse with a different length, close the excitation profile window and edit the shaped pulse length in the simulation window. Click on Start NMR-SIM. Pulses with a shorter length have a broader excitation range in Hz.
   20. Set SPOFFS5 to change the carrier frequency of the I-BURP2 pulse and shift the excitation range to the left or right to avoid the I-BURP2 pulse touching and disturbing the water magnetization (Supplementary Figure 6B).
   21. To determine the appropriate power level of the shaped pulse, open the Bruker shape tool, click the Start NMR Simulation button, and set the I-BURP2 pulse length to Shaped pulse length [µs]. Remember the corresponding length of a soft rectangular 90° (¹H) pulse, visible in the simulation window at the corresponding 90° square pulse [µs] (Supplementary Figure 7A).
   22. Type calcpowlev. Use the hard 90° (¹H) pulse (P1) in microseconds as the reference length (Supplementary Figure 8B) and the 90° (¹H) soft rectangular pulse corresponding to the I-BURP2 pulse in microseconds as the new length (Supplementary Figure 8A). Remember the power difference Δ in dB between the hard 90° (¹H) pulse and the soft rectangular pulse (Supplementary Figure 8C). Copy the pulse strength of the hard 90° (¹H) pulse in dB to SPW5 and add the memorized difference Δ in dB (Supplementary Figure 6B).
   23. To determine the power level of the spin-lock, calculate the corresponding 90° (¹⁵N) pulse length of the spin-lock. Use the formula: 90° (¹⁵N) pulse length in s = 0.25 / (spin-lock power in Hz).
   24. Use calcpowlev to calculate the power difference Δ in dB between the power of the spin-lock and the 90° (¹⁵N) hard pulse (P7). New: 90° (¹⁵N) pulse length of the spin-lock in µs (Supplementary Figure 8A). Ref: hard 90° (¹⁵N) pulse length in µs (Supplementary Figure 8B). Copy the power level PLW7 of the 90° (¹⁵N) hard pulse in dB to the spin-lock power level PLW8 (Supplementary Figure 6C), and add the calculated power difference Δ in dB (Supplementary Figure 8C).
   25. Copy the power level of the spin-lock PLW8 to the power levels SPW8 and SPW9. (Supplementary Figure 6C).
   26. To determine the power level of the ¹⁵N decoupling, use calcpowlev to calculate the power difference Δ between the power of the 90° (¹⁵N) decoupling pulse (PCPD3) and the 90° (¹⁵N) hard pulse (P7). New: PCPD3 in µs (200) (Supplementary Figure 8A). Ref: hard 90° (¹⁵N) pulse length in µs (Supplementary Figure 8B). Copy the power level PLW7 of the 90° (¹⁵N) hard pulse in dB to the decoupling level PLW31 (Supplementary Figure 6C) and add Δ in dB (Supplementary Figure 8C).
   27. To use temperature compensation, include #define TEMP_COMPENSATION (by deleting the semicolon in the pulse sequence). Set P18 to the maximum duration of the spin-lock used in the ¹⁵N R_1ρ experiment.
       NOTE: Switching off the temperature compensation for the first trial of the experiment is recommended.
   28. In the case of ¹⁵N ¹³C labeled samples, include # to define LABEL_CN in the pulse program (by deleting the semicolon in the pulse sequence). Set P4 to the pulse length calculated with the formula in⁷⁸. For example, it corresponds to 23.70 µs at 600 MHz and 11.85 µs at 1200 MHz. Type calcpowlev to calculate the power difference in dB between P4 and the (¹³C) hard pulse. Copy the (¹³C) hard pulse power in dB to PLW4 and add the Δ in dB. Copy PLW4 to PLW2 (Supplementary Figure 6B).
   29. Determine the relaxation delays for appropriate sampling.
       1. Run the first eight FIDs (in case L₆ = 8) and process these (rser <number of FID> < new experiment number>). Choose the entries in the vplist that the peak intensity of the experiment with the longest delay decreases to at least 1/e (approx. 37%), but not less than 25% compared to the experiment with the shortest delay (which serves as the reference).
       2. Adjust the remaining entries of the vplist to achieve an even sampling of the intensity decreases between the FID with the longest delay and the FID with the shortest delay. Read the NOTE and the power specifications of the probe.
          NOTE: The slowly relaxing residues will dominate the first FID. Adjust the remaining entries of the vplist to achieve an even sampling of the intensity decreases between the first and second FID. Do not exceed the probe's maximum allowed spin-lock power and length (consult probe manual and probe specifications). In case of temperature compensation, check P18 (maximum spin-lock duration), as the overall spin-lock duration of P18 will be applied, split between the relaxation delay and temperature compensation. It holds time (relaxation delay) + time (temperature compensation) = const = P18. For a 2 kHz spin-lock, we prefer not to exceed a spin-lock duration of more than 65 ms, using a recovery delay (D1) of 2 s. In that case, a compromise between the maximum spin-lock duration and the longest relaxation delay must be taken in favor of the maximum allowed spin-lock duration. In case of longer D1 recovery delays, longer spin-lock powers may be applicable. What counts is the overall power deposition in the probe over time. If longer spin-lock durations are required, only increase the spin-lock lengths in small steps and watch the lock signal. As a rule of thumb, adjust the lock level in the upper third of your lock display. If the lock level reduces by more than two squares during the execution of the pulse sequence, the spin-lock power deposited in the probe is too much.
   30. Type rga in the command line to determine the receiver gain. For a good signal-to-noise ratio, aim for a receiver gain (rg) value between 128 and 256, which proves good water suppression.
       NOTE: A receiver gain between 128 and 256 cannot be reached indicates a too-strong water signal. In that case, the gradient power and durations are gently adjusted until the receiver gain is reached. See also the Discussion section.
   31. Start a test run of the ¹⁵N R_1ρ experiment by typing zg in the command line. Check that the water signal is well suppressed for all delays (1 to 8, in case of 8 delays in the vplist). Check also increment 9, which is the second increment of the quadrature detection scheme (Echo/ Anti-Echo).
2. Set up the ¹⁵N R₁ experiment.
   1. Copy the ¹⁵N R_1ρ experiment and change the pulse program to the ¹⁵N R₁ experiment.
   2. Type vclist, generate a vclist, and enter the dummy vclist described in⁷⁰: 0, 24, 6, 20, 4, 16, 8, 12; a new row for each vclist entry).
   3. Open ased. Check the gradient lengths and strengths. Change GPZ9 to 14%.
   4. Check pulse lengths, pulse shapes, and pulse strengths (the correct values should have been copied from the ¹⁵N R_1ρ experiment).
   5. In the case of ¹⁵N¹³C labeled samples, use #define LABEL_CN in the pulse program.
   6. For the use of temperature compensation, include #define TEMP_COMPENSATION.
   7. Run the first eight FIDs (in case L₆ = 8) and process these (rser <number of FID> < new experiment number>). Choose the entries in the vclist that the peak intensity of the experiment with the longest delay decreases to at least 1/e (approx. 37%) but not less than 25% compared to the experiment with the shortest delay. Adjust the remaining entries of the vplist to achieve an even sampling of the intensity decreases between the FID with the longest delay and the FID with the shortest delay.
      NOTE: Only even numbers are allowed for vclist entries.
3. Set up the {¹H}-¹⁵N NOE experiment.
   1. Copy the ¹⁵N R₁ relaxation experiment and change the pulse sequence to the {¹H}-¹⁵N NOE pulse scheme.
   2. Set the length of the saturation period with the loop counter L₈. The spacing between 180° (¹H) pulses is 22 ms⁷⁹ (2* 1 / J_NH). To achieve the most accurate results, use a saturation period of about 5 times the protein's ¹⁵N T₁(¹⁵N). Here: 5 s. That would correspond to L8 = 230.
      NOTE: The Discussion section provides additional advice on choosing the saturation period/recovery delay.
   3. Change the length and strength of the gradients as described in the pulse scheme. Use sine.20 gradient shapes.
   4. Set the number of increments in the indirect dimension equal to TD = l₃ * 2 * 2
   5. In the case of ¹⁵N¹³C labeled samples, use #define LABEL_CN and -DLABEL_CN as a ZGOPTNS.
   6. Run the pulse schemes by typing zg in the command line.

4. Processing and analysis of the recorded NMR experiments

NOTE: Spectra have been recorded using a Bruker system. Processing is performed using a Unix or Linux operating system. Spectra processing and data analysis were performed using NMRPipe⁸⁰ and python3. The NMRPipe software can be downloaded at https://www.ibbr.umd.edu/nmrpipe/index.html. NMRPipe-based processing scripts are downloaded from the website: https://www.ipb.hhu.de/en/teams/team-lakomek/pulsesequences or from the extended Biological Magnetic Resonance Bank (BMRB) repository (bmrbig102). It is recommended to use NMRPipe. If NMRPipe is not available or desired, alternatives such as CCPN⁸¹ or SPARKY (SPARKY 3, or its successors NMRFAM-SPARKY⁸² or POKY⁸³ ) can be used.

1. Process and analyze ¹⁵N R₁ experiment.
   NOTE: The following commands are executed in a Unix Terminal.
   1. Copy the files in the downloaded directory R1_processing to the directory containing the experimental R1 data (working directory).
   2. Make the files executable by the terminal command: > chmod u+x *.com
   3. Execute > bruker to open the NMRPipe Conversion Utility and generate the fid.com file. Click Read Parameters. Change the Dimension Count to two if three dimensions are counted, and click Read Parameters again. Then click Clear Script, Update Script, and Save Script (Supplementary Figure 9).
      NOTE: If the carrier frequency is not correct, change the Center Position PPM after clicking Read Parameters the second time.
   4. Execute > ./fid.com
   5. Convert the vclist in a vplist with ms entries: delay in ms = 40 ms * entry of vclist. Use > cp vclist vplist and edit the vplist.
   6. Use > ./split.com to split the pseudo 3D data into eight 2D files.
   7. Edit the tauValues (vplist values in order of the vplist) and the idxExpmt values (order of tauValues regarding the time) in nmrproc.com (Supplementary Figure 10).
   8. Use > ./nmrproc.com to process the raw data of all eight 2D spectra.
   9. Use > nmrDraw to draw the spectra.
      1. Use the reference spectrum (first entry in vplist) for these steps. Switch to that spectrum by changing the z dimension to one (upper left corner). Adjust the contour level using the + and - next to the Factor button. Redraw the spectrum with the button Draw.
      2. Use a contour level where all signals of interest can be recognized with only a few signals coming from the noise (the contour level is at the edge of the noise level) (Supplementary Figure 11).
   10. Correct the spectrum phase, type v for vertical 1D-signal projection and h for horizontal 1D-signal projection. Adjust the phase with P0 and P1 (Supplementary Figure 11), remember the phase difference, and correct the phase in the nmrproc.com file (Supplementary Figure 10).
       NOTE: If the spectrum is flipped in the ¹⁵N dimension, remove the -neg in the line: | nmrPipe -fn FT -neg \ (Supplementary Figure 10).
   11. Close nmrDraw and process again with > nmrproc.com. For Peak picking (after the spectrum is phased correctly and the reference spectrum is displayed with a contour level where all peaks are present), type K (shift + k), press Detect, and click on Save. (Supplementary Figure 11).
   12. Copy a peak list to the working directory and change -assName in ass.com to the name of the peak list (Supplementary Figure 12).
       NOTE: An example of a peaklist in the correct format is available at https://www.ipb.hhu.de/en/teams/team-lakomek/pulsesequences
       and at the extended Biological Magnetic Resonance Bank (BMRB) repository (bmrbig102).
   13. Execute > ./ass.com to assign the spectra. Verify the assignment that the script suggests for the various peaks. Use the left mouse button to assign and the right mouse button to deassign peaks. Use the Next button to go to the following amino acid and Prev to go to the previous amino acid (Supplementary Figure 13).
       NOTE: The contour level can be changed with + and - at the top right corner. Use the button Draw to redraw the spectrum with the new contour level (Supplementary Figure 13).
   14. After completing the assignment, click Save and then Save again. Afterward, click on Quit, Cancel, and Exit (Supplementary Figure 13).
   15. Execute > python3 NoneDeleter.py to create relax.tab, which contains only information on assigned peaks.
   16. Execute > ./relax.com to generate the autofit.com script.
   17. Execute > ./autoFit.com to perform a Fourier Interpolation and generate pseudo ratios of the different delay times for each amino acid (axt.tab and nlin.tab are generated).
   18. Execute > ./model.com to generate the modelExp.com script based on the data in nlin.tab.
   19. Execute > ./modelExp.com to fit the evolution curve of each residue with a non-linear Least-Squares Optimization model.
   20. Execute > bash summary.tcl -in relax.tab > t1.tab. Ignore a potential error message: GDB Notice: 21 missing values in the table file can occur.
   21. Copy t1.tab into a newly created directory R1R2.
2. Process and analyze the ¹⁵N R_1ρ experiment.
   1. Copy the files in the downloaded directory R1rho_processing to the directory containing the experimental R_1ρ data (working directory).
   2. Execute > chmod u+x *.com
   3. Execute > bruker to open the NMRPipe Conversion Utility and generate the fid.com file. See also the processing of the ¹⁵N R₁ spectra.
   4. Execute > ./fid.com
   5. Execute > ./split.com to split the pseudo 3D data into eight 2D files.
   6. Execute > ./nmrproc.com (Edit the tauValues [vplist values] and the idxExpmt beforehand) to process the raw data of all eight 2D spectra (Supplementary Figure 10).
   7. Execute > nmrDraw to draw the spectra and pick the peaks. Use the reference spectrum (first entry in vplist) for these steps. Follow the same procedure as for the ¹⁵N R₁ experiment.
   8. Copy a peak list to the working directory and change -assName in ass.com to the name of the peak list (Supplementary Figure 12).
   9. Execute > ./ass.com and follow the same procedure as for the ¹⁵N R₁ experiment.
   10. Execute > python3 NoneDeleter.py to create relax.tab, which contains only information on assigned peaks.
   11. Execute > ./relax.com
   12. Execute > ./autoFit.com
   13. Execute > ./model.com
   14. Execute > ./modelExp.com
   15. Execute > bash summary.tcl -in relax.tab > t1rho. tab. Ignore potential error message: GDB Notice: 21 missing values in the table file may occur.
   16. Copy the following header in the t1rho.tab file (the values can be obtained from the fid.com file) (Supplementary Figure 14):
       REMARK 600MHz for T1rho
       REMARK -yOBS = 60.818 (put here the value found in fid.com)
       ​REMARK -yCAR = 119.06 (put here the value found in fid.com)
   17. Execute > ./extract_PPM.com to generate a table called fusionOffset.tab that contains the offset of the peak ¹⁵N frequency relative to the carrier frequency (which will be needed to calculate the angle θ for the extraction of R₂ data from the R₁ and R_1ρ data).
3. Summarize the relaxation data.
   1. Copy the t1rho.tab and the fusionOffset.tab into the directory R1R2.
   2. Copy the script crtR1p.tcl in the directory R1R2, adjust the spectrometer frequency and spin-lock power, and execute bash crtR1p.tcl | sort -n > R1R2.tab. (Supplementary Figure 15). R1R2.tab will contain the fitted R_1ρ rate constants, theta angle, R₂ rate constants, and R₁ rate constants.
4. Process and analyze the hetNOE experiment.
   1. Copy the files in the downloaded directory NOE_processing to the experimental NOE data directory (working directory).
   2. Execute > chmod u+x *.com
   3. Execute > bruker to open the NMRPipe Conversion Utility and generate the fid.com file. Click Read Parameters. Change the Dimension Count to two if three dimensions were counted and press Read Parameters again. Then press Clear Script, Update Script, and Save Script.
   4. Execute > ./fid.com
   5. Execute > ./split.com (A vplist with two entries (0, 1) has to be created before)
   6. Execute > ./ft2.com
   7. Execute > nmrDraw to draw the spectrum and pick the peaks in the reference spectrum (z-dimension = 1). Extract and remember the noise (press T = shift + t). Phase correction and peak picking follow the same procedure as the ¹⁵N R₁ experiment.
   8. Copy a peak list to the working directory and change -assName in ass.com to the name of the peak list (Supplementary Figure 12)
   9. Execute > ./ass.com to assign the spectra. Follow the same procedure as detailed for the ¹⁵N R₁ experiment.
   10. Execute > python3 NoneDeleter.py to create relax.tab.
   11. Execute > ./script.com
   12. Execute > ./autoFit.com
   13. Change the noise in error_hetnoe.tcl.
   14. Execute > bash error_hetnoe.tcl |sort -n > hetNOE.tab

Results

The following shows some exemplary NMR relaxation data recorded on the vesicular SNARE protein Synaptobrevin-2 (1-96), frequently called VAMP2 (vesicle-associated protein 2). For recording the NMR data, we used a 171 µM ¹⁵N Synaptobrevin-2 (1-96) sample (dubbed Syb-2 in the following) in 50 mM MES (pH 6.0) buffer containing 150 mM NaCl, 0.1 mM TCEP, and 1 mM EDTA. All experimental data was recorded at 278.15 K using a 250 µL volume filled in a 3 mm NMR sample tube. Experiments were performed at a Bruker 600 MHz AVANCE III HD spectrometer equipped with a Bruker 5 mm QCI ¹H, ¹⁵N, ¹³C, ³¹P quadruple resonance cryoprobe.

Figure 3 displays the residue-specific ¹⁵N R₁ and R₂ relaxation rate constants fitted to the NMR relaxation curves obtained from the NMR relaxation experiments. On the y-axis, the respective relaxation rate constants are plotted for the individual residues along the protein sequence (on the x-axis). Also, ¹H-¹⁵N heteronuclear NOE values (hetNOE) extracted from the intensity ratios of the saturated and non-saturation (reference) experiments of the ¹H-¹⁵N heteronuclear NMR measurement are shown.

Heteronuclear NOE data and ¹⁵N R₂ rate constants are more easily interpreted than ¹⁵N R₁ data. Therefore, we will start with them.

Heteronuclear NOE:
Heteronuclear {¹H}-¹⁵N NOE are sensitive to internal dynamics on the fast picosecond timescale (<100 ps, because of its cross-relaxation dependence) but also to ps - ns dynamics (due to its R₁ dependence) and can take values usually between 0 and (a bit less than) 1 for folded proteins. At higher fields they will be systematically higher (but always lower than 1).

They describe the internal flexibility of the protein. When hetNOE values at the same field strengths are compared, it holds: The smaller the {¹H}-¹⁵N NOE, the more dynamic the respective residue is. For IDPs, typically small residue-specific {¹H}-¹⁵N NOE are observed, e.g., in the order of 0.5 and smaller at 600 MHz. However, negative {¹H}-¹⁵N NOE are also found for IDPs, even down to -2 at 500 MHz. For monomeric Syb-2, {¹H}-¹⁵N NOE measured at 600 MHz range between -0.5 for the N-terminus and 0.5 for the C-terminal linker domain. Values increase gradually from the N- to the C-terminus, indicating a gradually decreasing flexibility/increasing rigidity (Figure 3C).

¹⁵N R₂ rate constants
¹⁵N R₂ rate constants are sensitive to ps - ns dynamics that modulate the N-H bond vector orientation by the overall tumbling of the protein, the motion of the peptide planes, and the torsion of backbone dihedral angles. Different from the {¹H}-¹⁵N NOE values and R_1, the ¹⁵N R₂ rate constants are dominated by the J(0) spectral density associated with the overall (rotational) tumbling of the protein. Therefore, for globular folded proteins, the ¹⁵N R₂ rate constants are scaled in size according to the overall tumbling and size of the protein. For true IDPs, no global rotational correlation time can be assigned. Still, a chain-length dependent slow correlation time can be fitted⁸⁴, as expected for polymers, but residue-specific internal dynamics have a larger impact on the ¹⁵N R₂ rate constants. Within the same protein, ¹⁵N R₂ rate constants allow for the discrimination of structures vs non-structured regions with different internal residue-specific mobility. The smaller the observed ¹⁵N R₂ rate constant, the more mobile the respective residue is. High ¹⁵N R₂ rate constants are characteristic of secondary structure elements, such as α-helices or β-strands. Low R₂ relaxation rate constants are characteristic of loop and intrinsically disordered regions. For monomeric Syb-2 (1-96), we observe overall low ¹⁵N R₂ rate constants consistent with its intrinsically disordered character. The internal rigidity increases (mobility decreases) from the N-terminus up to the C-terminal linker domain before trailing off to the flexible C-terminus (Figure 3B).

¹⁵N R₁ rate constants
The R₁ relaxation rates are sensitive to picosecond (ps) and faster nanosecond (ns) dynamics. However, their direct interpretation of internal dynamics is more complex than previous ones. There is a field T₁ (R₁) minimum (maximum) when T₁ is plotted as a function of the rotational correlation τ_R: T_1min at τ_{R, min} = 1/ ω. For fast tumbling molecules with a τ_R < τ_{R, min}, e.g., small molecules or small globular proteins, lower R₁ rate constants indicate increased protein backbone dynamics (same as for R₂). In the case of larger proteins, with τ_R > τ_{R, min}, it is the opposite, and higher R₁ relaxation rate constants represent increased dynamics (opposite to R₂).

Figure 3: NMR relaxation data. Data were recorded and evaluated following the protocol and workflow described above. (A) Residue-specific ¹⁵N R₁ relaxation rate constants along the protein backbone of Syb2 (1-96). (B) ¹⁵N R₂ relaxation rate constants, calculated from R_1ρ and R₁ data using formula (1). (C) hetNOE transfer rates along the backbone of Syb2 (1-96). Please click here to view a larger version of this figure.

Supplementary Figure 1: Reading in of NMR parameters. The interface of macro rpar is displayed. (A) Overview of all parameter sets. The red box marks the search bar. The red numbers refer to the respective steps in the protocol. DoubleClick to choose a parameter set. (B) Overview of parameters that can be imported to the current experiment. Options to execute getprosol or to keep specific parameters of the current experiment are marked with red boxes. Please click here to download this File.

Supplementary Figure 2: Positioning the ¹H carrier frequency for optimal water suppression. The interface of macro gs is displayed. While the experiment is looped, it is possible to change different parameters of the experiment. The marker can be used here to change the chosen parameter during the acquisition. Clicking above the marker raises the parameter by the value specified under "sensitivity". The sensitivity switch can be used to adjust the step size of the marker. On the right side, the live FID is visible. For calibration of the O1, the aim is to minimize the FID area marked with a red box, as the FID is usually dominated by the water signal. The reduction of the FID area goes in hand with decreased water signal and improved water suppression. The red numbers refer to the respective steps in the protocol. Please click here to download this File.

Supplementary Figure 3: A closer look at the ¹H-¹⁵N HSQC pulse sequence and its acquisition parameters. (A) Pulse sequence parameters of the ¹H-¹⁵N HSQC experiment HSQCFPF3GPPHWG. Click on "E" to open the pulse program editor window in B. (B) Pulse program editor of the ¹H-¹⁵N HSQC experiment HSQCFPF3GPPHWG. The commented line (line 91) with a ¹⁵N 90° pulse shows the original line for a ¹H-¹⁵N HSQC experiment. In line 92, the ¹⁵N 90° pulse is changed to a ¹⁵N 180° pulse. This change makes the ¹H-¹⁵N HSQC experiment a calibration pulse program for the 90° ¹⁵N hard pulse calibration. To edit pulse sequences, save the sequence under a new name first. Use the following workflow: Click File, Save as, enter the new name, click OK, and click Set PULPROG to the dataset. The red numbers refer to the respective steps in the protocol. Please click here to download this File.

Supplementary Figure 4: Setting up the Gradients. The interface of the gpnam macro to change gradient shapes, lengths, and strengths is shown. To open the pulse sequence parameter interface used, all gradient shapes GPNAM must be entered. The red numbers refer to the respective steps in the protocol. Please click here to download this File.

Supplementary Figure 5: Setting up the relaxation delays. Interface of the vplist macro (identical to the vclist macro). (A) Interface to choose a vplist. By clicking on the three dots, interface B opens. (B) Interface to choose a vplist by DoubleClick, or create a new list by clicking on File, and New. (C) The interface opens by creating a new list or editing an existing list. The list can be saved by clicking File and Save. The red numbers refer to the respective steps in the protocol. Please click here to download this File.

Supplementary Figure 6: Pulse sequence parameters of the 15N R1ρ experiment. (A-D) All essential parameters that must be changed in the protocol are marked with red boxes and the associated steps. Please click here to download this File.

Supplementary Figure 7: Interface of the shapetool macro. An I-BURP2 (used in the experiments) is opened as a shape pulse. (A) Parameters of the selected shape pulse. By clicking the Start NMR Simulation button marked with a red box, the Simulation parameter windows open with the simulation parameters Shaped pulse length [µs] (= 2000 µs) and the Rotation angle [°] (= 180°). Clicking the Start NMR-SIM button opens the (B) simulation window, which shows the inversion bandwidth of the I-BURP2 pulse. The red numbers refer to the respective steps in the protocol. Please click here to download this File.

Supplementary Figure 8: Interface of the calcpowlev macro. (A) Input window for the pulse length of the pulse whose power is to be calculated. (B) Input window of the reference pulse (mostly the 90° hard pulse). (C) The result window shows the pulse strength difference in dB between a pulse with the new pulse length and a pulse with the reference pulse length. Attention: This difference is only valid if both pulse lengths correspond to the identical pulse regarding shape and rotation angle. The red numbers refer to the respective steps in the protocol. Please click here to download this File.

Supplementary Figure 9: NMR spectra processing: Interface of the NMRPipe conversion tool. Clicking on Read Parameters automatically reads the experiment's parameters. The conversion script is shown on the right. All parameters can be set individually. After changing parameters using Clear Script, Updating theScript is recommended. Click on Save Script to save the script under fid.com, as shown on the right. The red numbers refer to the respective steps in the protocol. Please click here to download this File.

Supplementary Figure 10: The nmrproc.com file for spectral processing. The code used in the nmrproc.com file to process the raw data in NMRPipe format is shown. The tauValues entry and idxExpmt entry have to be set before processing. The tauValues correspond to the vplist entries in ms for the ¹⁵N R_1ρ experiment (vclist entries recalculated in ms for the ¹⁵N R₁ experiment). Regarding their relaxation delay length, the idxExpmt entries correspond to the order of the vplist entries (vclist entries for the 15N R1 experiment). In the script, the positions to change the phase of the spectrum are marked with red boxes. The red numbers refer to the respective steps in the protocol. Please click here to download this File.

Supplementary Figure 11: NMR spectra display and peak picking. An overview of nmrDraw with an open spectrum is shown. Use the + and - to change the Factor, which goes in hand with a change in the contour level. Changing the Z dimension allows for the switch between the HSQC experiment with different relaxation delays. Use Draw to redraw the spectrum with the changed parameters. The P0 slider and P1 slider allow changes in the phase of the spectrum. These phase changes will not be saved in the processed data; the phase change has to be entered in the nmrproc.com file manually, and the nmrproc.com file has to be executed again. The Peak Detection macro allows picking the spectrum peaks at the contour level set. The red numbers refer to the respective steps in the protocol. Please click here to download this File.

Supplementary Figure 12: Semi-automated NMR peak assignment with NMRDraw. The code of the ass.com file is shown, and it must be executed to start the NMR signal assignment. Change -assName to the peak list of interest generated. This peak list has to be in the same format as the attached peak list ass.syb2.hn_1200.tab in the folder peaklist (In the zip folder downloaded at https://www.ipb.hhu.de/en/teams/team-lakomek/pulsesequences). The red number refers to the respective step in the protocol. Please click here to download this File.

Supplementary Figure 13: Visual NMR peak and assignment inspection. The Interface of the assignment macro is opened by executing ass.com. Use the left mouse button to assign peaks and the right mouse button to deassign peaks. Use Next to go to the following amino acid and Prev to go to the previous amino acid. With + and -, the contour level can be changed using Draw, which redraws the spectrum. Using the workflow: Quit, Save, and Exit saves the assignment and ends the program. The red numbers refer to the respective steps in the protocol. Please click here to download this File.

Supplementary Figure 14: Extracting the ¹⁵N R₂ rate constants from R_1ρ and R₁ data. Step 1. The content of the t1rho.tab file is shown. A code marked with a red box has to be added before calculating the R₂ rates from the R_1ρ rates. The red number refers to the respective step in the protocol. Please click here to download this File.

Supplementary Figure 15: Extracting the ¹⁵N R₂ rate constants from R_1ρ and R₁ data. Step 2. The content of the crtR1p.tcl file is shown. Before executing, the entries in the red box must be changed as described in the protocol. The red numbers refer to the respective steps in the protocol. Please click here to download this File.

Discussion

This protocol described the setup of NMR ¹⁵N relaxation experiments by Lakomek et al.⁶⁹ and Stief et al.⁷⁰. We focused on NMR pulse sequences using a sensitivity-enhanced HSQC detection scheme. The ¹⁵N R₁ and R_1ρ experiments are implemented as described in detail by Stief et al.⁷⁰, and the hetNOE experiment is described by Lakomek et al.⁶⁹.

When setting up the NMR relaxation experiments, the ¹⁵N R_1ρ is the most critical one, as choosing a too-long maximum relaxation period or a too-high RF amplitude of the spin-lock can damage the probe. For the relaxation period, sampling the full decay curve equally from 100% intensity to 25% intensity (compared to the reference experiment) is desirable. For slowly relaxing proteins, such as IDPs, with long ¹⁵N T₂ times, it will frequently not be affordable to sample the decay curve to the full extent because the power deposition into the probe needs to be limited.

For the ¹⁵N radio frequency (RF) amplitude, theoretically, the higher the RF amplitude, ν_spin-lock, the better, as more exchange processes can be refocused. As a rule of thumb, exchange processes slower than 1 / (2π ν_spin-lock ) can be refocused. However, RF power limitations apply. For example, in our hand, we would not exceed a maximum spin-lock period of 65 ms when an RF amplitude of 2 kHz is applied to stay on the safe side. At the same time, the spin-lock RF amplitude at a 600 MHz spectrometer should be higher than 1 kHz, e.g., 1.4 kHz at 600 MHz, which has proven sufficient for the small globular protein gb3⁶⁹. To cover the spectral widths and avoid off-resonance effects at higher field strengths, the corresponding RF amplitude should scale with the magnetic field, e.g., 1.5 times higher at 900 MHz (ν_spin-lock  2 kHz). However, it must stay within the limitations of the probe. (Refer to the local list of spectrometer power limitations and contact your NMR facility manager for advice.)

For the choice of the spacing of relaxation delays between the reference experiment (shorted delay) and the longest delay period (determined by the factors discussed above), we prefer equal spacing of the relaxation delay data points and choose a number of 8 (if allocated measurement time and signal-to-noise allows). The first increment (and subsequent ones) will be dominated by the most intense (and frequently slowest relaxing) residues. Therefore, depending on the dynamic range of the protein, the NMR signals of several residues in the protein sequence may have already decayed after the chosen maximum relaxation period. By equally spacing delay points, we ensure that the relaxation curves of the fast relaxing residues will also be covered by a sufficient number of data points sampling the relaxation curve.

Also, a good choice of recovery delay is essential to get accurate relaxation data and avoid long-term damage to the probe. We choose a recovery delay of at least D1 = 2 s to prevent any damage to the probe. For accurate results, the protein ¹H and ¹⁵N longitudinal polarization must also be given sufficient time to return to equilibrium or at least a stable, steady state. The ¹H T₁ usually varies between 1 s and 4 s at 600 MHz for a small or medium-sized protein (up to 20 kDa); for larger proteins and higher fields, the ¹H T₁ will increase further. For the small globular protein gb3, we found D1 = 3.5 s sufficient for the ¹⁵N R₁ and R_1ρ experiments. For the small IDP Syb-2 presented in this protocol, we recently showed that D1 = 2 s was adequate⁷⁰.

The ¹⁵N hetNOE has the lowest sensitivity, as excitation starts on ¹⁵N, and no ¹H-¹⁵N INEPT at the beginning of the pulse sequence is applied. Further, the ¹H saturation period and ¹⁵N recovery delay should be 5 times ¹⁵N T₁ to obtain accurate data. While for the IDP Syb-2 presented here, a 5 s saturation/ recovery delay plus an extra 2 s D1 recovery delay (total 7 s) was sufficient, for larger proteins and/ or deuterated proteins, this time can be substantially longer, e.g., 10 s or longer. However, if qualitative data are good enough, a slight systematic offset can be accepted. In that case, reasonable results can be obtained already at 3 times ¹⁵N T₁, as 95% of the saturation will be achieved. In that case, resulting hetNOE values will show a systematic offset to higher values.

In this protocol, we worked with fully protonated ¹⁵N Syb-2, which is most cost-efficient. Side-chain deuteration is recommended to reduce the number of relaxation pathways and work with the most isolated ¹H-¹⁵N backbone amide spin pairs. However, comparing ¹⁵N²H Syb-2 and ¹⁵N syb-2, we notice only very few differences between deuterated and fully protonated samples⁷⁰. For practical purposes, NMR relaxation data are frequently recorded on the double or triple-labeled samples (¹⁵N¹³C or ²H¹⁵N¹³C). The discussed NMR pulse sequences are capable of refocusing J coupling evolution between ¹³C with ¹H or ¹⁵N nuclei. Obviously, also relaxation pathways will increase when ¹³C labeling is introduced. However, in our hands, for practical purposes, the introduced error, if at all, is less than 5% and might be acceptable when only qualitative data are needed.

When working with proteins of different sizes for detection, there is frequently the question of whether to choose sensitivity-enhanced HSQC-detected experiments⁷⁰ or TROSY-detected experiments⁶⁹. For small proteins, the sensitivity-enhanced HSQC-detected NMR experiments offer a two-fold gain in signal-to-noise (provided that good water suppression can be obtained). For larger proteins, the TROSY-detected experiments will win over. The break-even is roughly 20 kDa for folded proteins. For IDPs, for which low R₂ rate constants can be obtained that increase roughly linearly with increasing chain lengths, the break-even may be shifted to higher molecular weights. For practical purposes, we recommend implementing both the sensitivity-enhanced HSQC-detected or TROSY-detected experiments when in doubt. Then, choose the one that gives the best signal-to-noise in the first increment.

The discussion of whether to choose the sensitivity-enhanced HSQC-detected or TROSY-detected experiments only applies when signal-to-noise is the main criterion. When the smallest line widths and highest resolution are required, TROSY will always win. TROSY also always offers the best water suppression, as fewer proton pulses and no proton decoupling are required. We refer to the previously published article⁶⁹ for a more extended discussion.

One more remark on the issue of water suppression. While setting the receiver gain (rg) to 16 may be sufficient on Bruker Avance NEO consoles, a receiver gain in the range of 128-256 is usually desirable for (older) Bruker Avance consoles. The achievable rg (determined by the Bruker command rga) is frequently obtained from the intensity of the residual water signal to the noise level. A bad water suppression will always introduce additional noise in the spectra. Thus, even if an rg = 16 can be achieved on a Bruker Avance NEO console, the remaining water signal can substantially contribute to the noise level. Therefore, the signal-to-noise ratio would be reduced. Consequently, we recommend aiming at an rg level of 128-256. The presented pulse sequences⁷⁰ have been tested at 600 MHz and 1200 MHz. Both field strengths work with the same gradient setup, as written in the pulse sequence. We recommend them at least as a good starting point for further optimization.

As mentioned in the introduction, the discussed NMR relaxation experiments cover only the picosecond to nanosecond time range. For insights into the microsecond to millisecond dynamics, we refer to relaxation dispersion experiments, CPMG experiments, and an extension of the R_1ρ experiments with changing spin-lock amplitudes (or carrier frequencies) are used^{44,46,58,59,60,61,85,86} . Dynamics slower than microseconds can be captured ¹⁵N CEST (Chemical exchange saturation transfer) NMR⁶², exchange spectroscopy (EXSY, milliseconds to seconds), or RT (Real-time) NMR (seconds to hours)^63,64. The PRE (paramagnetic relaxation enhancement) effect of paramagnetic probes, as well as residual dipolar couplings (RDCs), can be used to assess the entire range of ps to ms dynamics^65,66,67,68.

All these experiments cover only backbone dynamics. To investigate side-chain dynamics, Kay and co-workers introduced another plethora of NMR experiments, providing information on side-chain dynamics for proteins up to 1 MDa^2,87.

To obtain more quantitative insights into protein backbone dynamics, a combined analysis of all three NMR parameters, ¹⁵N R₁, R₂, and hetNOE, is necessary - sometimes involving even further parameters, such as cross-correlated relaxation rate constants. Different sophisticated analysis methods have been developed. The so-called model-free approach has been widely applied in biomolecular NMR^{43,88,89,90,91}. Also, spectral density mapping can provide valuable insights^55,92,93. While these are powerful analysis methods for globular proteins with well-defined rotational correlation time, their applicability is limited for IDPs. A folded domain is necessary to define a rotational correlation time³⁹. This can be partially circumvented when correlation function C(t) can be modeled by the sum of exponentially decaying functions in case the different timescales involved can be well-separated^23,31,84. In the absence of a well-defined rotational correlation time, alternative approaches involving a distribution of correlation times, e.g., the IMPACT analysis⁹⁴ or the DETECTOR analysis^95,96, are an alternative. Furthermore, a combined analysis of NMR relaxation data and MD simulations is also promising for IDPs⁹⁷; currently, we are still facing sampling and force-field limitations for full-atom simulations of larger IDPs^31,98.

Materials

List of materials used in this article

Name	Company	Catalog Number	Comments
Bruker 600 MHz AVANCE III HD spectrometer	Bruker	https://www.bruker.com/en/products-and-solutions/mr/nmr/avance-nmr-spectrometer.html	NMR experiments conducted