Accelerating 15 N and 13 C R 1 and R 1 q relaxation measurements by multiple pathway solid-state NMR experiments

Magic angle spinning (MAS) Solid-state NMR is a powerful technique to probe dynamics of biological sys- tems at atomic resolution. R 1 and R 1 q relaxation measurements can provide detailed insight on ampli-tudes and time scales of motions, especially when information from several different site-speciﬁc types of probes is combined. However, such experiments are time-consuming to perform. Shortening the time necessary to record relaxation data for different nuclei will greatly enhance practicality of such approaches. Here, we present staggered acquisition experiments to acquire multiple relaxation experiments from a single excitation to reduce the overall experimental time. Our strategy enables one to col- lect 15 N and 13 C relaxation data in a single experiment in a fraction of the time necessary for two separate experiments, with the same signal to noise ratio. (cid:1) 2021 The Authors. Published by Elsevier Inc. ThisisanopenaccessarticleundertheCCBYlicense(http:// creativecommons.org/licenses/by/4.0/).


Introduction
Quantifying biomolecular motions plays a fundamental role towards the understanding of biophysical processes as modulated by protein dynamics. In solid-state NMR the range of time scales that can be detected by relaxation experiments is not limited by overall tumbling as in solution-state NMR. Molecular processes that are characteristic of protein functions like enzymatic catalysis, protein folding, and ligand binding are on the order of ls-ms which is the same as the timescale amenable for study by solid state NMR using relaxation techniques. NMR relaxation [1][2][3][4] experiments, however, are time-consuming considering the very long delays necessary to adequately sample relaxation times and the large number of scans often required to achieve appropriate signal to noise ratios for challenging systems [5][6][7]. In particular, 15 N R 1 can be < 0.02 s À1 requiring relaxation delays up to~50 s (on top of the recycling delay). In addition, the description of protein motions spanning a wide range of time scales, often requires access to multiple independent probes in order to obtain a detailed view of dynamics, e.g. joint use of 15 N and 13 C' relaxation leads to an improved view of backbone dynamics [2]. Finally, some experiments require multiple measurements on the same probes under different conditions, e.g. relaxation dispersion where R 1q is measured as a function of the applied field strength of the spin-locking pulses [6,8] or variable temperature measurements [9,10]. Overall, this means that quantification of protein dynamics may involve recording many time-consuming experiments, which limits the wide adoption of this powerful methodology. In order to make such studies more widespread, it will be thus useful to develop approaches which reduce the overall experimental time required.
Paramagnetic doping is a widely applicable approach to reduce the recycling times in solid-state NMR experiments [11][12][13][14]. However, the addition of paramagnetic dopants will also change the measured 15 N and 13 C relaxation rates [6], with the contribution related to the distance of the monitored site to the paramagnetic centre often dominating the contributions from the local dynamics [15]. Similarly to paramagnetic doping, for a number of reasons, selective excitation methods popular in solution NMR [16,17] are not yet appropriate for accelerating quantitative relaxation measurements in solids.
Solid-state NMR experiments could be devised to use the available initial polarization more efficiently than standard approaches, e.g. time-shared experiments and sequential acquisition experiments that exploit orphaned polarization. Time-shared experiments [18,19] pass the signal through multiple polarization pathways and collect all experiments at once. In the Dual Acquisition Magic Angle Spinning (DUMAS) [20] acquisition scheme, the acquisition of the nitrogen and carbon-based experiments are separated in time (with polarization from one source being stored) to eliminate signal overlap from the separate experiments. This multiple acquisition scheme has been also used for 1 H detection [21], for detection of orphaned polarization [22], for use with multiple receivers [21], and for mixed dimensionality multi-receiver experiments [23]. Sequential acquisition results in a small timepenalty for the second acquisition but the time loss is usually very short compared to the recovery time.
In this study, we present experiments to measure 15 N/ 13 C R 1q [1,2,8,24,25] and R 1 [26,27], with staggered acquisition 1 Hdetected experiments. We demonstrate that relaxation measurements on a model protein obtained with staggered and standard acquisition are the same within the experimental error. We quantify sensitivity of the multiple acquisition experiments and the overall experimental time gains with respect to the standard experiments.
All experiments were performed on a Bruker Avance III spectrometer, using a Bruker HCND Probe operating in triple resonance at 700.13 1 H Larmor frequency and sample spinning rate of 100 kHz +/-3 Hz. The experiments were carried out at a nominal temperature of 281.2 K (based on external calibration, calculated by the difference between the water and sodium 3-(trimethylsi lyl)propane-1-sulfonate (DSS) peaks) using a gas flow of 400 L/h [30,31]. The nutation frequencies for the 90 pulses were calibrated so that 1 H is at 2 ls (m 1 = 125 kHz); 13 C, 2.5 ls (m 1 = 100 kHz); and 15 N, 4.15 ls (m 1 = 60.24 kHz). The 15 N carrier radiofrequency (RF) was centred at 120 ppm, while the 13 C was placed at 55 ppm and 175 ppm, for 13 C a and 13 C' respectively. The carbon frequency was moved by changing the carrier frequency in the Bruker pulse code using pre-determined constants. The 1 H carrier was placed near the water frequency (~4.7 ppm) for the standard 15 N R 1q relaxation experiment. Each 1 H free induction decay was acquired for 30 ms with a spectral width of 35 ppm with 16 coadded transients. Both the 15 N and 13 C' dimensions for the R 1q experiments were acquired with 82 rows with a dwell of 300 ms, with a spectral width of 47 ppm ( 15 N) and 19 ppm ( 13 C'), for a total of 12.6 ms in the indirect dimensions. In the hcaC'caHa + hNH N variant, both the 15 N and 13 C' dimensions were acquired with 72 rows with a dwell of 300 ms, maintaining the same spectral widths. The number of rows sampled in the indirect dimension of the two parts of the simultaneous experiment must be the same, but the spectral width is not restricted in this way. For the R 1 measurements 15 N and 13 -C'dimensions were acquired with 64 rows with a dwell of 300 ms, with a spectral width of 47 ppm ( 15 N) and 19 ppm ( 13 C'), for a total of 9.6 ms in the indirect dimensions. The recovery delay was 2.5 s for all the R 1q experiments and 1.5 s for the R 1 measurements. The States-TPPI method was employed for quadrature detection in the indirect dimensions [32]. Heteronuclear 1 H decoupling (~10 kHz WALTZ-64 [33]) was applied during t 1 evolution on 13 C, 15 N, and during the COSY-based transfers. Heteronuclear decoupling on the 13 C channel (~10 kHz WALTZ-64) was applied during both direct acquisitions, while 15 N heteronuclear decoupling (~10 kHz WALTZ-64) was only used for the HN acquisition. The MISSISSIPPI [34] solvent suppression scheme was applied with a spinlock field of~50 kHz for four 20 ms intervals for the R 1q and R 1 singleton experiments, and the R 1 staggered experiments. For the R 1q staggered experiments the four MISSISSIPPI intervals were 20 ms for the first 13 C' pathway acquisition, and 7.5 ms for the subsequent 15 N pathway. All spinlock fields for the R 1q experiments were cal-ibrated to be v 1 = 5 kHz by nutation; eleven points from 2 ms to 210 ms were collected. The spacing between points in the delay schedules for the R 1 measurements is based on the spacing of the Fibonacci sequence where appropriate beginning and ending times were chosen based on previous experience. The complete set of time-points used for both R 1q and R 1 can be found in the supporting information.
Simultaneous cross-polarization (SIM-CP) [35] was used for the initial excitation of 13 C and 15 N, where the average 1 H field was~130 kHz with a linear 15% ramp (85%-100%, from~121.5 to 139.5 kHz) using a zero-quantum (ZQ) match condition transfer for both 13 C and 15 N, where both channels are irradiated at~30 kHz, and the carrier is on resonance with the indicated resonance. The contact times for 13 C a , 13 C' and 15 N were optimized on both the single and staggered pathway correlation experiments.
The contact time was 2.1 ms for 1 H-13 C' CP and 150 ls for the 1 H-13 C a CP. For the 1 H-15 N CP, the contact times were 2 ms and 1.7 ms for individual and staggered R 1q measurements respectively. The 1 H pulse duration is set to the longest contact time of the two nuclei for SIM-CP. Polarization is always stored on the low-gamma nuclei after CP, no matter which CP time is longer, to provide the most flexibility in CP times. Our pulse sequence naming convention indicates all transfer steps in the sequence by nucleus name. An upper-case nucleus indicates that the chemical shift is evolved. A lower-case name indicates that polarization is transferred through, but there is no chemical shift evolution (this is sometimes designated with parentheses). A pulse sequence name with square braces where nucleus names are separated by commas indicates separate polarization pathways in the same experiment. In the text, we refer to these experiments with a ''+" between the independent experiments.
Gaussian Q3 cascade pulses were calibrated for selective 13 C inversion where a 320 ls pulse gives a bandwidth of 10.5 kHz (~60 ppm) and 760 ls produces a bandwidth of 5.3 kHz (~30 ppm) for 13 C' and 13 C a respectively. For the selective 13 C a -13 C' coherence transfer, the J-coupling delay (s) was 3.5 ms in the R 1q measurements and 3 ms in the R 1 measurements for the period were the 13 C a magnetization is transverse and 4.25 ms for the period where 13 C' is transverse. The pulse sequences, datasets, lists, compound pulse lists, and pulse shapes can be found online in the Mendeley Data: http://dx.https://doi. org/10.17632/x7kk4rkpj3.1. All relaxation rates are reported at the 95% confidence level from 2000 steps of Monte Carlo error analysis [36].

Results and discussion
Quantification of protein dynamics based on relaxation rates relies on suppression of coherent effects that can obscure the information on the molecular motions encoded in the measured rates [4]. For example, in uniformly [ 1 H, 13 C, 15 N] labelled samples, spin diffusion [27,37,38] will lead to the averaging of the rates for nearby sites, compromising their site-specific nature. In addition, coherent effects can lead to additional decay of magnetisation compromising R 2 and R 1q measurements [3,24]. However, the leftover anisotropic interactions, especially strong 1 H-1 H proton dipolar couplings, can be reduced by fast spinning and combined with deuteration and/or alternating labelling to effectively average out the interactions [27,38,39]. The exact conditions to attenuate the spin diffusion sufficiently so that it has a negligible effect on the site-specificity of the rates depends on the exact type of relaxation probes. For example, for 15 N nuclei spinning frequencies > 20 kHz are sufficient to obtain site-specific 15 N R 1 rates [38,40] and spinning rates > 60 kHz are sufficient to obtain site-specific 15 N R 1q rates without the need for deuteration or any special labelling pat-tern [24]. For 13 C' nuclei spinning frequencies > 60 kHz are adequate for recording site-specific R 1 /R 1q rates [2,27] but for the aliphatic carbons more demanding conditions need to be met: for 13 C a either (1) a combination of alternate 13 C labelling, and extensive deuteration and 50-60 kHz spinning need to be employed for site specific R 1 measurements [39] or (2) a combination of alternate 13 C labelling and > 80 kHz spinning [29] or (3) > 100 kHz spinning for uniformly 13 C-labelled samples [29]. Alternate 13 C labelling is still required in fully protonated samples in order to collect site specific aliphatic 13 C R 1q rates since many sidechain sites still show spin diffusion even at 100 kHz spinning in uniformly labelled samples [29].
Based on the above discussion recording 15 N and 13 C' R 1 and R 1q relaxation rates in uniformly 15 N and 13 C labelled samples at 100 kHz spinning should result in measurements with negligible influence of coherent effects. In addition, under these conditions 1 H-detected spectroscopy in fully protonated samples is the most practical detection mode. Consequently, below we will explore a range of solutions for simultaneous measurements of 15 N and 13 C' relaxation rates using 1 H-detected experiments.

Constructing Multiple Acquisition Psuedo-3D experiments from 2D correlation experiments
To construct multiple pathway experiments, we will adapt 2D 1 H-detected correlation experiments into pseudo-3D experiments by adding relaxation periods at the appropriate places in the pulse sequence ( Fig. 1a,b and Fig. 3a,b). For the 13 C' measurements, we found that a direct adaptation of the standard CP-based 1 H-detected 13 C-1 H correlation experiment was not sufficient. The final 13 C'-1 H transfer spreads the polarization to several nearby protons, causing reduction of the sensitivity and increasing the spectral overlap. The polarization can be transferred either to the 13 C a or to the 15 N to have a single ''read-out" proton. We have chosen to transfer through the 13 C a to the 1 H a (Fig. 1a, 3a) to avoid disturbing any stored 15 N polarization, and because we have sufficient resolution in this sample at this spinning rate. This results in an hC'caHa experiment, where the 2D correlation spectrum encodes the i th residue 13 C' and 1 H a frequency. The transfer efficiency of the COSY [41] scheme used for 13 C-13 C polarization transfer is similar to, or better than, a 13 C-15 N transfer and is much easier to set up experimentally. While we chose COSY mixing for ease of use, any number of other homonuclear mixing schemes could be used.
To adapt the individual experiments into simultaneous experiments the initial excitation period is turned into a SIM-CP period so that both pathways are excited. We then must identify the longestlived state and store this state after the SIM-CP excitation. The experiment is acquired on the short-lived state(s) first. Then, the stored polarization is re-excited, and an experiment is acquired on the long-lived state with a second, separate acquisition. This approach should mitigate losses from relaxation and simplifies the timings and polarization transfers that would be needed for a single acquisition of multiple pathways.
( Fig. 1c). A schematic representation of the magnetization pathways is found in Fig. 2a. The individual pseudo-3D alters the 2D correlation experiment by adding a relaxation delay after the chemical shift encoding and immediately before the water suppression (we choose simultaneous rather than sequential relaxation periods to avoid large increases in experimental times due to required long relaxation delays). It is not strictly necessary to encode the chemical shift before the relaxation period. Indeed, the resolution could be better for 13 C a rather than 13 C', however 13 C' was labelled to prove the desired polarization pathway was achieved. Alternative schemes for the 13 C homonuclear transfer and chemical shift labelling may be more efficient than this implementation [42]. To combine the two experiments, the initial CP is converted to simultaneous cross-polarization (SIM-CP), and then the 15 N and 13 C' chemical shift is encoded simultaneously (time-shared). Once the longest of the chemical shift delays is finished, the clock for both T 1 delays starts. The delays required to sample the relaxation times of each nucleus are on the same order of magnitude, but the 13 C' relaxation time is approximately half of the 15 N relaxation time. The 13 C' experiment is thus finished relaxing well before the 15 N. Therefore, the 13 C' pathway is acquired while the 15 N is still relaxing. This has the consequence that the 15 N delay has to be sufficiently long to allow the 13 C' pathway experiment to finish, which includes the 13 C' relaxation delay time, homonuclear transfer, and the acquisition on 1 H a .
To ensure appropriate alignment of the two polarisation transfer pathways, the remainder of the 15 N delay (D T1 ) is calculated as shown by equation (1.1).
The duration of the solvent suppression (MS), COSY transfer, 13 -C a -1 H a CP and acquisition is on the scale of 100 ms, so the first point of the 15 N relaxation time must be longer than this time. A long initial time delay is only relevant when fast relaxing 15 Ns are present in the sample but is not much of a concern in general. For example, if the initial time point is 100 ms the signal would be lost for an 15 N with a T 1 < 30 ms, but typical backbone 15 N T 1 s are on the order of dozens of seconds. 1 H-15 N/ 13 C' cross-correlation effects are thought to be negligible due to self-decoupling effects [43,44]. To ensure that cross-correlated relaxation effects are completely supressed a series of p-pulses on the 1 H channel could be applied [45] (and easily incorporated into our sequences) but in our hands such procedure made no difference for fully protonated GB1 at 100 kHz spinning [29]. Consequently, since there is no requirement for any complex irradiation schemes during the relaxation delay, there is no need for separate relaxation delays for the two types of nuclei. The 13 C' experiment is effectively collected during the 15 N experiment, which means that the overall pulse sequence duration is equal to the standard 15 N R 1 experiment. Thus, with the same overall experimental time of a 15 N R 1 experiment we also obtain a 13 C' R 1 measurement. The same concept can be applied for aliphatic carbons ( 13 C ali ) on the peptide side chain in an alternately 13 C-labelled sample (i.e. samples expressed using (1,3) or (2) 13 C glycerol, (1) or (2) 13 C glucose, or other such labelling schemes). Fig. 3a and 3b show the 2D 1 H a -13 C' and 1 H-15 N 2D GB1 correlation spectra from the first slice of the staggered hC'caHa + hNH N experiment. Fig. 3b is a typical 2D 1 H-15 N fingerprint GB1 spectrum, while Fig. 3a is the 2D hC'caHa correlation with 60 observable peaks, considering two 1 H a for each glycine. The latter spectrum is detected on 1 H a , which is possible due to the good spectral resolution at 100 kHz spinning frequency [46,47] and the efficient water suppression from the MISSISSIPPI scheme [34]. The sensitivity of the hC'caHa spectrum is~80% the hNH N spectrum principally due to signal lost during the C' to C a COSY transfer. The signal derived from the 13 C' of glycine residues is transferred to both of the 1 H a protons, resulting in a lower relative signal intensity. The individual relaxation rates extracted from one consistent 1 H a -13 C' glycine peak is fitted and reported.
The final point of concern is whether the application of pulses on the 13 C and 1 H channels during the 15 N R 1 relaxation delay interferes with the measurement itself. However, since the 13 C' and 15 N R 1 rates found using the single and combined experiments are the same within error (Fig. 3c,d) we conclude that any interference effects are here negligible.

Simultaneous measurement of 15 N and 13 C' R 1q
The individual 13 C' and 15 N R 1q experiments are adapted for 1 Hdetection by adding a spinlock into correlation experiments that were used in the previous section, as shown in Fig. 4a,b. Since 15 N is expected to have the greater T 1q , and there is only an inversion during the 13 C experiment, we perform the 13 C-based transient of the experiments first, and then do the 15 N-based transient (Fig. 4c). To be more specific, in the first multiple pathway variant (Fig. 2b) the magnetization is transferred from 1 H to 13 C' and 15 N, generating two polarization paths from the ''bulk" 1 H polarization. SIM-CP for 13 C' and 15 N may draw from the same pool of polarization so the 13 C' might leech polarization from the 15 N, or vice versa. To prevent dilution of the initial polarization pool, a pathway (Fig. 2c) was devised where the polarization is transferred from the 1 H a to the 13 C a , and from 1 H N to 15 N using short duration, one-bond transfers, so specific 1 H polarization pools are utilized. An experiment was then constructed to chauffeur the polarization from 1 H a to 13 C a to 13 C', and then back (Fig. 4d). The source of the polarization should, thus, be different for 13 C' and 15 N, which could improve the initial CP efficiency enough to compensate for the extra transfers. In both experiments, after the SIM-CP, the 15 N polarization is stored while the spingymnastics are happening on the 13 C channel. The experiments are the same after the COSY transfer to 13 C'. The R 1q spinlock is applied on the 13 C', followed by 13 C' chemical shift evolution. The 13 C' coherence is then transferred to 13 C a through COSY transfer and the signal acquired on 1 H a after 13 C a -1 H a CP. A waiting period is inserted after the first detection period so the 15 N measurement starts at a constant time after excitation to avoid any T 1 ( 15 N) contribution to the observed rate. The 15 N and 13 C' spinlocking fields are implemented sequentially rather than simultaneously to avoid any potential interference or recoupling effects between 15 N and 13 C pulses. The 15 N magnetization is then re-excited to encode the 15 N R 1q and 15 N chemical shift, and the signal is acquired on 1 H N after 15 N-1 H CP. 15 N decoupling is turned off during the 1 H a acquisition to preserve the stored polarization; its application has a negligible effect on the 1 H a linewidth. 13 C decoupling is applied during all acquisition periods, even though there is little effect on the H N resonance, because the 13 C polarization was detected previously, and thus it is not important to preserve. A soft-hard p-pulse pair is used during chemical shift evolution to ensure that the proper 13 C pathway is selected; the removal of the homonuclear scalar coupling is a secondary bonus of this approach.
The 15 N read-out portion is delayed by: where T 1qMAX is the longest spinlocking pulse that will be used in the experiment, T 1q(n) is the current spinlocking pulse time, and 10 ms is arbitrarily added to avoid negative times. If detuning or heating from the 13 C spinlocking pulse are a concern, the spinlock field could be turned on during this waiting period. In the context of presented here experiments, removing D altogether would reduce the experiment time by~1 h compared to 10 h total time but might introduce variation from 15 N longitudinal relaxation. Fig. 5a-d shows the comparison of the measured site-specific 13 C' and 15 N R 1q rates for the individual/singleton and the staggered hC'caHa + hNH N and hcaC'caHa + hNH N implementations of the experiment. The sensitivity of the hC'caHa spectrum is~60% of the HN spectrum principally due to signal lost during the 13 C' to 13 C a COSY transfer. The sensitivity of the hcaC'caHa spectrum is~40% of the HN spectrum, which indicates that selecting the polarization pool did not compensate for the polarization lost during the transfer; the direct 1 H-13 C' CP version is more efficient. The measured rates for all comparable experiments are the same within the experimental error. This demonstrates that the measured 13     To reduce the experiment time further, the chemical shift and spinlock periods can be optimized with time-sharing. The chemical shift is allowed to evolve on the two nuclei, 13 C' (t 1 ) and 15 N (t' 1 ) at the same time (Fig. 6a). The evolution time is implemented so that the polarization for both nuclei is stored for the longest of the two nested evolutions t 1 and t' 1 . To avoid unintended magnetization transfers or any other interference during the spinlock, (e.g. CP), the spinlocks are never applied at the same time. The spinlock pulses are combined by SimultaneousLy Increasing and DEcreasing (SLIDE) the times, where the 13 C time increments but the 15 N decrements to fit the experiments in a constant time period (Fig. 6b). This SLIDE period is constructed by inserting the delay D SLIDE between the two spinlock periods to limit the contribution from T 1 and to separate the spinlock pulses on the two nuclei. The delay D SLIDE , is described by: These modifications reduce the experiment time by 1 h from the staggered experiment, for a total of 9 h acquisition, a total savings of 40% with respect to the two individual experiments (15 h in total). If sample heating during the spinlock periods is a concern, compensatory pulses can be added either before the initial excitation or after the final acquisition. , -y, -y, y, -y, y, y, -y, -y, y, y, -y, y, -y, -y, y, -y, y, y, -y, y, -y, -y, y, y, -y, -y, y, -y, y, y, -y, -y, y, y, -y, y, -y, -y, y, y, -y, -y, y, -y, y, y, -y, y, -y, -y, y, -y, y, y, -y, -y, y, y, -y, y, -y, -y, y}for the hC'caHa portion. u 12 = {x*2, -x*2}, u 14 = {y, -y}, u 16 = {x*4, -x*4} and acquisition u 31 = {-y, y, y, -y, y, -y, -y, y, y, -y, -y, y,y, y, y, -y} for the hNH N portion. States-TPPI is employed on u 4 (a, c, d) and u 14 (b, c, d).
A concern with the SLIDE experiment is the introduction of changes in the peak intensity due to T 1 relaxation into the T 1q data. For crystalline GB1 this is not a large concern since the T 1q of 15 N and 13 C' are an order of magnitude shorter than T 1 , and thus the differences in the intensity due to T 1 relaxation are smaller than the overall experimental error. If T 1 s were shorter, the use of constant time periods throughout the experiment will negate any T 1 effects.
Since the 15 N pulse does not always start at the same time, the T 1 relaxation could have an effect on the measured R 1q rates. However, in our case this is negligible because the longest time wait on 15 N, 210 ms (D + T 1 ( 13 C'), for the last time-point delay) should result in the intensity changes < 2%. This is demonstrated in the comparison of the resulting R 1q rates between SLIDE and the indi-vidual hC'caHa and hNH N experiments, which are the same within error (Fig. 6c,d), and in the sensitivity of SIM-CP (see below).
As a comparison between SLIDE and the other staggered R 1q variants, the delay D in the hC'caHa + hNH N and hcaC'caHa + h NH N experiments, an additional time waiting with respect to SLIDE, is not required and could be eliminated, since T 1 effects do not introduce a large error in the R 1q rates measurements. This would save one hour in our reference experiment, calculated with the sum of D for each FID, making hC'caHa + hNH N last as long as SLIDE. This statement is valid for GB1, which has long relaxation times, but for other bio-macromolecules, typically with shorter T 1 s, D becomes fundamental to assure that the longitudinal relaxation does not compromise the 15 N R 1q data, where the 15 N experiment always has the same starting point relative to the initial excitation.

Sensitivity and Time Savings
To get a better idea of time savings achievable with staggered experiments, we compare the staggered experiments time with the singleton experiments run sequentially. If there were no losses in sensitivity between standard and SIM-CP and there were no differences in relaxation delay schedules, staggered experiments could produce a maximum factor of 2 in time saving. However, SIM-CP is typically slightly less sensitive than standard CP (i.e. individual 1 H-15 N and 1 H-13 C) meaning that more transients need to be acquired to obtain the same signal-to-noise ratio (SNR) in the staggered experiments compared to equivalent singleton experiments. In the first instance, we have used SIM-CP settings obtained from optimisation of individual CPs. In this case, we observed that we lose 12% and 8% efficiency when employing SIM-CP in R 1 measurements rather than individual 1 H-13 C' and 1 H-15 N CP steps, respectively (see Fig. 7). For the R 1q measurements with the favourable hC'caHa + hNH N pathway the observed decreases in efficiency are 15 and 10% for the staggered 13 C' and 15 N relaxation measurements (see Fig. 8). This means that by accounting for the additional transients that need to be acquired to get the same SNR as in individual experiments the staggered experiments time saving factors would be reduced from the theoretical maximum of 2 to~1.6 for R 1 and~1.5 for R 1q.
We have investigated whether the SIM-CP losses can be minimised if the optimisation is performed directly on the SIM-CP experiment instead of transferring the settings from optimisations for individual CPs. Indeed, if SIM-CP is optimised directly on crystalline GB1 the losses compared to individual CPs can be reduced. Fig. 8 shows comparisons between first points for singleton and staggered R 1q experiments where SIM-CP was optimised directly rather than using settings from individual CPs. We can see that for the preferential hC'caHa + hNH N pathway the SIM-CP losses are reduced to 12 and 3% for 13 C' and 15 N relaxation measurements. This means that in theory we could get~1.7 times saving from employing staggered R 1q and, by extrapolation, up to~1.76 times from staggered R 1 experiments.
For a completely fair comparison of time savings between singleton and staggered experiments we also have to: 1. take into account that one may choose different relaxation delay schedules for these experiments and 2. account for differences in pulse sequence duration in the case of sequential experiments.
For backbone R 1 measurements, relaxation delays much longer than the recycle delay are often required and a few experiments with the longest relaxation delays dominate the overall experimental time. In the case of singleton experiments, the relaxation delays can be tailored to individual relaxation probes with longer final delays for the nuclei with longer T 1 s and shorter final delays for nuclei with shorter T 1 s. In the case of staggered experiments, the longest relaxation delays will be dictated by the slower

Residue number
Residue number d) 13 C' relaxing nucleus: typically, 15 N. In R 1q measurements where the relaxation times are typically shorter than the recycle delay, the choice of the longest delays has a less dramatic effect on the overall experimental time.
For the staggered acquisition R 1 measurements, the 13 C' sampling schedule is built into the 15 N schedule, so the staggered experiments have the same length as the 15 N individual experiments. In this context, the saved time from staggered implementation corresponds to the duration of the 13 C' experiments: 13 C' experiment takes place during the 15 N R 1 measurements and the relaxation delay is shared. However, if 13 C' T 1 s are significantly shorter than 15 N T 1 s the longest relaxation delays in singleton 13 C' experiments can be shorter than the relaxation delays dictated by 15 N T 1 s in a staggered experiment.
Comparisons can get very quickly complicated depending on precise choice of sampling and experimental conditions. Consequently, below we discuss one illustrative example in order to highlight general considerations for running staggered vs. singleton experiments rather than provide absolute numbers.
At 700 MHz spectrometer in crystalline GB1 at room temperature the average 15  h. This means that if there is no difference in sensitivity, the staggered experiment would take~1.55 times shorter rather than 2 times shorter. Considering the decreases in sensitivity due to lower efficiency of SIM-CP we discussed above, the real time saving factor for running staggered R 1 measurement would be~1.4 times.
It is important to point out that in the above comparison the main difference comes from the experiments with the longest relaxation delays. In the example discussed above the last 2D with relaxation delay of 25 s would take~14.3 h, which is more than all the other six points in this experiment or almost as long as all 7  13 C' and d) 15 N R 1q rates per residue between the standard hC'caHa and hNH N experiments (blue) and SLIDE (pink). Error bars represent two standard deviations within the correspondent rate. For the severely overlapping peaks, values were removed. Narrow and broad black lines represent 90 and 180 hard pulses, respectively. Rounded pulses represent 180°s elective shaped pulses. When not shown, the phase of the pulses is x. The phase cycling for both the experiments is as follow: u 1 = {x*8, -x*8}, u 2 = {x*2, -x*2}, u 3 = {y*4, x*4}, u 4 = {-y, y}, u 6 = {x*16, -x*16}, u 8 = {x*32, y*32} and acquisition u 30 = {y, -y, -y, y, -y, y, y, -y, -y, y, y, -y, y, -y, -y, y, -y, y, y, -y, y, -y, -y, y, y, -y, -y, y, -y, y, y, -y, -y, y, y, -y, y, -y, -y, y, y, -y, -y, y, -y, y, y, -y, y, -y, -y, y, -y, y, y, -y, -y, y, y, -y, y, -y, -y, y} for the hC'caHa portion. u 12 = {x*2, -x*2}, u 14 = {y, -y}, u 16 = {x*4, -x*4} and acquisition u 31 = {-y, y, y, -y, y, -y, -y, y, y, -y, -y, y, -y, y, y, -y} for the hNH N portion. States-TPPI is employed on u 4 and u 14 in a. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) points in the individual 13 C R 1 measurement (14.7 h). This highlights that the percentage time gain from using a staggered experiment will be better the closer to each other the maximum relaxation delays for 13 C and 15 N experiments are, and that for more dynamic samples with shorter relaxation times (i.e. more challenging samples) the percentage gains will improve as well.
Notably for R 1q measurements where relaxation delays are typically shorter than recycle delay, the impact of the different sampling schedules in the individual vs. staggered experiments will be much smaller than for R 1 measurements. Overall, one could expect 1.3-1.6 times real saving in time by using staggered experiments for measuring 15 N and 13 C' R 1 and R 1q relaxation. Even though these savings might not appear very large as percentage gain, because relaxation measurements can be really time consuming, real time savings may be very respectable in absolute terms when applied to challenging samples. For example, measurement of 15 N R 1 on GB1:IgG complex requires about two-three weeks of experimental time and most likely comparable amount of time for 13 C' R 1 measurements. In this particular case, staggered experiments would result in real time savings of about two weeks compared to individual experiments.

Conclusion
In summary, we propose approaches for simultaneous acquisition of 15 N and 13 C R 1 and R 1q using 1 H-detected experiments at fast (100 kHz) spinning on fully protonated protein samples. We employ sequential 15 N and 13 C acquisition with concurrent relaxation delay periods for R 1 and sequential 15  Calculation of the real time gains takes into account SNR losses due to application of SIM-CP compared to conventional CP and additional delays, as well as pulse sequence duration increases due to sequential acquisition. These gains should improve further for dynamic proteins with shorter relaxation times and thus shorter required relaxation delays. The approaches demonstrated here improve the practicality of powerful but time-consuming relaxation measurements for quantifying protein dynamics in the solid-state.
This approach may be less effective with other typical sample preparation protocols, for example triply labelled and back exchanged samples. In triply labelled samples the amide protons are the only available source of polarization, so the efficiency of SIM-CP is expected to be reduced. Both experiments lose sensitivity due to sharing one polarization source, with additional loss for 13 C' due to the long 13 C'-1 H CP contact time that increases the number of correlations (where the 13 C'-13 C a transfer would be removed). While the application of these experiments to samples with one polarization source does not seem promising that does not preclude its application to all deuterated samples. Our approach might be worthwhile to improve the measurement rate of sidechain relaxation in samples with high degree of deuterium   15 N for the R 1q individual experiment (i, blue), staggered hC'caHa + hNH N (ii, orange), SLIDE (iii, pink) and hcaC'caHa + hNH N (iv, gold). The individual hcaC'caHa intensity is shown in (a, iv) in dotted line on gold solid line and the SIM-CP is 15% lower than the individual experiment. The 1 H 1D integrated spectrum intensity of each staggered acquisitions is indicated as a percentage scaled to the individual experiment (100%). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) labelling. In the case of the R 1 experiments only, these results indicate that it should be possible to run other experiments while waiting on the relaxation similar to embedded experiments on materials [48].
The resolution of the spectra is another factor in the applicability of these experiments, as it is for all pseudo-3D methods. While it is not routinely done, it should be possible to adapt these experiments into pseudo-4D experiments. The 3D experiments would be combined around a common pulse sequence elements such as a CN/NC transfer in the hNCH and hCNH, and the relaxation period is added at an appropriate place before the transfer back to proton. The experiment time to acquire a series of 3Ds is likely to be prohibitively long (which is one reason they are rarely acquired), so a reduced dimensionality style experiment or sparse sampling scheme would likely need to be applied. In that same vein, the resolution of the 13 C spectra could probably be improved by labelling the chemical shift of the 13 C a nucleus or combining the 13 C' and 13 C a chemical shift evolution.

Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.