Direct Measurements of Protein Backbone ¹⁵N Spin Relaxation Rates from Peak Line-Width using a Fully-Relaxed Accordion 3D HNCO Experiment

Abstract

Protein backbone ¹⁵N spin relaxation rates measured by solution NMR provide useful dynamic information with a site-specific resolution. The conventional method is to record a series of 2D ¹H-¹⁵N HSQC spectra with varied relaxation delays, and derive relaxation rate from the following curve fitting on the resonance intensities. Proteins with poorly resolved spectra often require several 3D HNCO spectra to be collected on a ¹⁵N/¹³C double labeled protein sample. In order to reduce the relaxation dimension Carr et al. (J. Magn. Reson. (1998) 132, 25–33) employed an Accordion type HNCO pulse sequence to obtain ¹⁵N or ¹³C T₁ relaxation rates by numerical fitting of the relaxation interfered free induction decay (FID) data. To avoid intensive analysis of the time domain data, we propose a modified protocol to measure ¹⁵N T₁ and T₂ relaxation rates from easily obtained line-widths in an Accordion-HNCO spectrum. Both T₁ and T₂ relaxation could be simultaneously convoluted into the constant-time evolution periods of ¹³C′ and ¹⁵N, respectively. The relaxation delay was allowed to reach at least 3×T₁ or 3×T₂ so that the signal was substantially decayed by the end of the FID, and the resulting peak Full-Width at Half Height (FWHH) could be directly used to calculate relaxation rate. When applied to the 76-residue Ubiquitin and the 226-residue Glutamine-Binding Protein (GlnBP), this method yielded T₁ and T₂ values deviating on average by 4–6% and 5–7%, respectively, from the measurements based on the conventional 2D method. In comparison, the conventional methods possessed intrinsic error ranges of 2–4% for T₁ and 3–6% for T₂. In addition to comparable accuracy, the fully-relaxed Accordion HNCO method presented here allowed measurements of relaxation rates for resonances unresolved in 2D spectra, thus providing a more complete dynamic picture of the protein.

Introduction

In solution NMR spectroscopy spin relaxation rates are linear summation of appropriate spectral densities derived from the rotational correlation function. [1] Knowledge of longitudinal (T₁) and transverse (T₂) relaxation rates provides rich dynamic information on the time scales ranging from sub-ns up to ms where conformational exchange contributes.[2; 3; 4] Generally for proteins, the dynamics studied with NMR can probe individual bond vectors connecting spin active nuclei. The most frequently measured spin nucleus is the ¹⁵N backbone amide nitrogen, which reports on the dynamics of the N-H bond vector.[5; 6] The conventional way to measure ¹⁵N spin relaxation rates (T₁ or T₂) is to record a series of 2D ¹H-¹⁵N HSQC spectra with various relaxation delays. The corresponding peak intensities are fit with an exponential decay function to obtain the relaxation rates. For proteins with poorly resolved ¹H-¹⁵N spectra, several 3D HNCO spectra with varied relaxation delays, which correlate the ¹H_i-¹⁵N_i moiety to spin of carbonyl ¹³C′_i-1 in the third dimension, can be collected instead.[7; 8] This solves the peak-overlap problem at the cost of experimental time.

One approach to shorten experimental time is to reduce dimensionality. Since both the spin relaxation scheme and the heteronuclear (¹⁵N or ¹³C) evolution period in triple-resonance pulse sequences are time dependent functions, it is possible to convolute the two. The idea of mixed-evolution was originally applied in measuring chemical exchange rates, and the type of pulse sequence was referred to as Accordion experiment because the time coordinate of the exchange was stretched or squeezed because of mixing, by Bodenhausen and Ernst.[9; 10] Later Kay and Prestegard estimated proton T₁ from the null position along the indirect t₁ evolution profile using an Accordion type COSY pulse.[11] Mandel & Palmer and Carr et. al. first employed the Accordion method to project T₁ relaxation of ¹⁵N or ¹³C′ onto the t₁ evolution period of the like nucleus in a constant time version of 3D HNCO experiment.[12; 13] In their method the full t₁ evolution profile, or free induction decay (FID), is obtained in two parts, termed as a “negative time” manner, to minimize any transverse relaxation leakage during t₁. The subsequent minimization of t₁ interferogram yields spin relaxation rates and Larmor frequencies, using the Hankel Singular Value Decomposition (HSVD) algorithm [14] and Levenberg-Marquardt nonlinear least-square fitting routine.

We are proposing a fully-relaxed type of Accordion HNCO experiment to measure ¹⁵N relaxation rates, aiming to ease both acquisition and computational work. Both T₁ and T₂ relaxation processes were synchronized with heteronuclear evolution periods. The relaxation delay period covered at least 3×T₁ or 3×T₂ so that the full-relaxation should be ensured for nearly every nucleus. The spin relaxations time constants were directly estimated from peak Full-Width at Half Height (FWHH) on the corresponding indirect dimensions. Our protocol yielded comparable accuracy of relaxation rates as the conventional method for the model proteins 76-residue Ubiquitin and 226-residue Glutamine-Binding Protein (GlnBP). In addition, for the medium sized protein GlnBP, which consists of similar contents of α-helix and β-sheet,[15] the proposed method allowed measurements for 97% of assigned spin nuclei, in contrast to the 79% from the typical 2D method. The improvement is expected to be even more dramatic for α-helix rich proteins and unfolded proteins with less-dispersive resonances.

Materials and Methods

Pulse Sequence and Acquisition Parameters

The published gradient-enhanced sensitivity HNCO pulse sequence [16] was adopted with the addition of backbone ¹⁵N relaxation blocks and the adjustment for constant-time evolutions (Figure 1A). The magnetization transfer will not be repeated here, but specifically the in-phase N_x magnetization was prepared right before the T₂ relaxation loop, subject to the later transverse and longitudinal spin relaxation. Since the relaxation delay increment was synchronized with heteronuclear evolution, the envelope of the FID in the indirect dimension should code solely for the relaxation incorporated exponential decay function with the use of constant-time acquisition. The pulse sequence was tested using 1 mM ¹⁵N/¹³C doubly labeled Ubiquitin and GlnBP samples on a 600 MHz Bruker DMX spectrometer equipped with a triple-resonance TXI probe containing an xyz-gradient coil. Most pulse sequence related acquisition parameters were described in the caption of Figure 1.

Figure 1.

The 3D fully-relaxed type of Accordion HNCO pulse sequence for measuring ¹⁵N spin relaxation rates (A) with enlarged details for T₁ and T₂ blocks (B). Narrow and wide rectangular pulses correspond to flip angle of 90º and 180º, respectively. Open and filled shaped pulses on carbonyl ¹³C′ channel are sinc-shaped 90º and 180º, respectively. The ¹H and ¹⁵N Waltz decoupling pulse strength was 4.2 kHz and 1.3 kHz, respectively. The RF used for carbonyl ¹³C′ pulse was 1.3 kHz. The ¹³C′ pulse width was 53 μs and 23.7 μs for flip angle of 90º and 180º, respectively. The default pulse phase is along x. Phase cycles are listed as follows, φ₁ = y, −y; φ₂ = (x)₄, (−x)₄; φ₃ = (x)₂, (−x)₂; φ₄ = −x; φ_rec = x, (x)₂, x, −x, (x)₂, −x. Delay durations τ₁, τ₂, and τ₃, are 2.6 ms, 12.5 ms, and 0.25 ms, respectively. The duration, strengths and direction for gradient pulses were as follows, G₁ = 1.1 ms, 12.5 G/cm, y; G₂ = 1.0 ms, 10 G/cm, x; G₃ = 0.7 ms, 12.5 G/cm, y/z; G₄ = 1.3 ms, 17 G/cm, y; G₅ = 2.694 ms, -17 G/cm, z; G₆ = 2.694 ms, 17 G/cm, z; G₇ = 1.0 ms, 17 G/cm, x; G₈ = 1.0 ms, 17 G/cm, y; G₉ = 0.2 ms, 17 G/cm, z; G₁₀ = 0.0756 ms, -30 G/cm, z. Gradient pulses G₅, G₆, G₉, and G₁₀ were rectangular shaped while the rest were sine-shaped. Quadrature detection on the ¹⁵N dimension was achieved via Echo-Antiecho method. [23; 24; 25] P- and N-type coherences were collected for each increment of t₂ with the gradient pulse switch between G₅ and G₆. Concomitantly ¹⁵N pulse phase φ₄ had to be interchanged between −x and +x for P- and N-coherence selection. Quadrature detection on ¹³C′ dimension was achieved via States-TPPI method [26] by incrementing ¹³C′ pulse phase φ₃ and receiver phase φ_rec. The constant time period for ¹⁵N evolution (T_N) needs to be the larger value of 5.5 ms and (Npts+1)×(Δt_N/4), where Npts is the total real points on ¹⁵N dimension and Δt_N equals the inverse of ¹⁵N spectral width. Similarly the constant time period for ¹³C′ evolution (T_C) equals (Cpts+1)×(Δt_C/4), where Cpts is the total real points on ¹³C′ dimension and Δt_C is the inverse of ¹³C′ spectral width. The 180º pulse repetition delays τ_T1 and τ_T2 in T₁ and T₂ blocks was set as 8 ms and 1 ms, respectively, but they could be customized. The loop counters L_T1 and L_T2, initialized as 0, had to be co-incremented with either ¹⁵N or ¹³C′ evolution. L_T1 and L_T2 ranged from 0 to Cpts-1 and Npts-1, respectively, during acquisition. The beginning blocks for heat compensation should be identical to T₁ and T₂ blocks except that τ_T1 might be shortened to 0.2 ms. The loop counters h₁ and h₂ were decremented from the initial values of Cpts and Npts, respectively, to 1, in concert with the incrementing of L_T1 and L_T2 so that the total number of ¹H and ¹⁵N pulses stayed the same from scan to scan.

For Ubiquitin the temperature was set at 293°K. The carrier frequencies were set at 4.80 ppm for ¹H, 115.4 ppm for ¹⁵N, 178.1 ppm for ¹³C′, and 56.1 ppm for ¹³C′. The spectral widths were set as 7184 Hz for ¹H, 1786 Hz for ¹⁵N, and 1563 Hz for ¹³C′. The number of real data points collected on ¹H, ¹⁵N and ¹³C′ dimensions were 512, 41 (Npts) and 51 (Cpts), respectively. During acquisition the loop counters for T₂ and T₁ relaxation (Figure 1B) were incremented from 0 to Npts-1 and Cpts-1, respectively. It is essential to let the last relaxation delay reach a period longer than 3×T₁ or 3×T₂, to avoid truncation effects during FT. T₂ and T₁ relaxation unitary blocks were 12 ms and 32 ms in length, respectively (Figure 1B), thus the intensities of the last collected points on ¹⁵N and ¹³C′ FIDs code for relaxation delays of 480 ms (40×12 ms) and 1600 ms (50×32 ms), respectively. The total experimental time for T₁ and T₂ incorporated fully-relaxed type of Accordion HNCO experiment was 79 hours with 1.1 second recycle delay, 16 scans per FID, and 512 dummy scans.

For GlnBP the temperature was set at 312°K. The carrier frequencies were set at 4.61 ppm for ¹H, 117.9 ppm for ¹⁵N, 176.0 ppm for ¹³C′, and 56.1 ppm for ¹³C′. The spectral widths used were 7184 Hz for ¹H, 2174 Hz for ¹⁵N, and 1667 Hz for ¹³C′. T₂ and T₁ relaxations were collected separately using two HNCO experiments because of low sensitivity associated with dual-collection within one experiment. Both relaxation schemes were convoluted with ¹⁵N evolution. For the T₁ encoded HNCO experiment the number of real data points collected on ¹H, ¹⁵N and ¹³C′ dimensions were 512, 41 (Npts) and 39 (Cpts), respectively. For the T₂ encoded HNCO experiment the number of real data points collected on ¹H, ¹⁵N and ¹³C′ dimensions were 512, 43 (Npts) and 48 (Cpts), respectively. Different from the set-up for Ubiquitin, the numbers of 180º pulses in Figure 1B were adjusted so that T₂ and T₁ relaxation unitary blocks were 6 ms and 64 ms in length, respectively. The total experimental time for T₁ and T₂ separately incorporated fully-relaxed type of Accordion HNCO experiment were 79 and 63 hours, respectively, with 1.1 second recycle delay, 16 scans per FID, and 512 dummy scans.

Data Processing and Extraction of T₁ and T₂

Generally, every FID from direct dimension (¹H) was apodized with a cosine function and zero-filled to double the number of data points. FIDs in the ¹⁵N and ¹³C′ dimensions were either apodized with a cosine function or left untouched if relaxation parameters were going to be extracted from this dimension. Nevertheless, FIDs on all indirect dimensions were zero-filled to 512 points before FT and no phase correction was applied. The first data point on each FID, both direct and indirect, was scaled by half before FT. The final 3D spectra were generally stored in a matrix size of 400(¹H)× 512(¹⁵N)×512(¹³C′).

Relaxation parameters T₁ and T₂ were always extracted separately from differently processed spectra even if both could be collected within the same HNCO experiment. For instance, for Ubiquitin when T₁ was going to be extracted according to natural line-width in the ¹³C′ dimension, apodization was applied to the ¹⁵N dimension which encoded the T₂ relaxation to give a better resolution, and vice versa.

In theory Fourier transform of a sinusoid curve convoluted with a single exponential decay function should yield a Lorentzian-shaped peak with its FWHH corresponding to the inverse of decay time constant (T) (Eq. [1]). However, in the Accordion experiment the time axis labeling for chemical shift evolution is different from that for relaxation delay. The time scaling factorκ, in the same definition as Carr et al., [12] is needed to account for the difference. In Eq. [2] T_B was the time period of one unitary block for the T₁ or T₂ loop (Figure 1B) and Δt, the inverse of spectral width, was the time evolution between two successive real points in indirect dimension; the difference of the two defined the Accordion type stretching or squeezing of the time axis. The measured FWHH, could then be converted to a real relaxation time constant T using Eq. [3].

$$\mathit{FWHH}=1/(\pi T)$$ [1]

$$\kappa =T_B/\mathrm{\Delta }t$$ [2]

$$T=\kappa /(\pi \times \mathit{FWHH})$$ [3]

Correction to T₁ and T₂

Relaxation time constants for most amide ¹⁵N nuclei were measured with the protocol described above. However because of truncation effects during FT, extremely long relaxation time constants could be underestimated. Application of an exponential decay or line-broadening function before FT was adopted to obtain long T₁ and T₂. A simple slope check procedure was performed to identify spins requiring forced-damping on the FID. Basically, data processing was repeated three times with the only difference being the line-broadening (lb) function applied to the target domain with the size of 0, 0.5 c, and c Hz for lb, which yielded three relaxation time constants T for each spin nucleus using Eq. [4]. The slope of T vs. lb for each nucleus was obtained using linear regression. The average slope <s> and its standard deviation SD were calculated. Slopes above <s> + 1.5 SD were considered to indicate underestimation of T₁ or T₂.

$$T=\kappa /[\pi (\mathit{FWHH}-lb)]$$ [4]

$$L{W}_N=4/[\pi (\mathit{Npts}-1)\mathrm{\Delta }{t}_N]$$ [5]

The size of c was chosen based on the criterion that the average peak FWHH, for instance, in the ¹⁵N dimension, from the spectrum processed with a line-broadening of c Hz would be close to the target line-width LW_N specified in Eq. [5], where Δt_N was the inverse of spectral width on the ¹⁵N dimension. The value of LW_N was expected to be the lower limit for the obtainable line-width free of truncation effects, which required a smooth decay of ¹⁵N FID signal to noise level or null. Following the above reasoning, the denominator (Npts−1)Δt_N in Eq. [5], the full evolution time for ¹⁵N spin nuclei, should cover the length of several (> 3) apparent exponential time decay constants of the FID curve. For simplicity a value of 4, the numerator in Eq. [5], was used, and the magnitude of the last point on the apodized FID was expected to be about 1.8% (e⁻⁴) of the initial intensity. Ideally the numerator in Eq. [5] should equal ln(S/N) for individual spin, however, a global value is chosen here as a good compromise for the purpose of checking for the slope. The target line-width LW_C for ¹³C′ dimension could be calculated similarly using Eq. [5].

Not all spins identified with significantly high slope (T vs. lb) were subject to the correction. The second filter was their S/N ratio. Spins with their S/N larger than the sum of mean and standard deviation, calculated from the first spectrum (lb = 0 Hz) of the above three, were chosen for correction. The correction was performed for each spin nucleus that required it. That is, one line-broadening processing was performed specifically for one spin. The corrected relaxation time constant was calculated using Eq. [4]. The size of lb was chosen so that the resulted FWHH for that spin reached the mean value of line-width from the first spectrum that carried 0 Hz line-broadening during processing.

Conventional Method for T₁ and T₂

The reference T₁ and T₂ values were measured using conventional 2D method. [17] Identical relaxation blocks (Figure 1B) were kept in the corresponding HSQC pulses. Six spectra were collected for each measurement with varied relaxation delay covering the range of 0 to 1.5 T₁ or 1.5 T₂. The standard deviation from the curve fitting was used as the intrinsic error range of the measurement. For accuracy comparison with the fully-relaxed Accordion method, the pair-wise difference, |T_accord.−T_conv.|/T_conv., was calculated for each spin resolvable in the 2D spectra and the average of differences was presented.

The program NMRPipe was employed for all NMR data processing.[18] The measurement of FWHH and exponential curve fitting were carried out using the routines in Sparky 3.1. (T. D. Goddard and D. G. Kneller, UCSF) The linear regression was performed in Grace 5.1. (Grace Development Team)

Results

Generally when tested on Ubiquitin and GlnBP, the proposed NMR data processing protocol yielded satisfactory sensitivity and resolution of the HNCO spectrum. Most of the relaxation time constants were measured from FWHH on the spectrum that had no line-broadening function applied (lb = 0 Hz). A couple of spins with sufficient S/N ratio were subject to specific correction. Some important acquisition and processing parameters were presented in Table 1. Complete results on the two proteins were as follows.

Table 1.

Essential acquisition, processing parameters, and results of fully-relaxed Accordion HNCO experiment

Protein		Dimension a	Npts/Cpts	ΔtN/ΔtC (μs)	TB (ms)	c (Hz)	Average FWHH (Hz)	LWN/LWC (Hz)	Pair-wise difference b	Intrinsic error range c
Ubi	T1	13C′	51	640	32	8	32.8	39.8	3.6%	1.5%
	T2	15N	41	560	12	10	48.5	56.8	4.7%	2.9%
Gln BP	T1	15N	41	460	64	18	55.0	69.2	5.6%	3.8%
	T2	15N	43	460	6	7	59.8	65.9	7.4%	6.4%

^aThe evolution period of nucleus where relaxation was incorporated.

^bFor Ubiquitin all available measurements, spins from 70 residues, from both methods were compared. For GlnBP only 176 measurements from the conventional 2D methods were available for comparison.

^cThe average standard deviations out of curve fitting in the conventional method were treated as the error range.

Ubiquitin

The backbone chemical shift assignments of Ubiquitin were taken from Wang et al. [19] A total of 70 peaks out of 76 residues were observed on the current Accordion type HNCO spectrum with the absence of M1, P19, P37, P38, E24, and G53, the last two of which experience significant conformational exchange.[20] ¹⁵N T₂ and T₁ relaxations were synchronized with ¹⁵N and ¹³C′ evolutions, respectively. Typical relaxation incorporated FIDs on ¹³C′ and ¹⁵N dimensions were shown in Figure 2A and 2B, respectively, for residue I13. FT of indirect FIDs without any apodization should yield T₁ and T₂ from FWHH (Figure 2C) with proper conversion using Eq. [3]. Although it was possible to measure T₁ and T₂ simultaneously from one spectrum as shown in Figure 2C, we realized better sensitivity and resolution could be obtained if T₁ and T₂ were extracted separately from individually processed spectra.

Figure 2.

Examples of relaxation incorporated FIDs on indirect dimensions (A and B) and their Fourier transformed spectrum (C). Traces of FIDs for residue I13 of Ubiquitin were shown along T₁ convoluted ¹³C′ dimension (A) and T₂ convoluted ¹⁵N dimension (B). The dashed line indicated the zero intensity (A and B). T₁ or T₂ could be estimated from line-width on the corresponding dimension (C).

We extracted the T₂ employing the described protocol. First the raw NMR data were processed with zero line-broadening applied (lb = 0 Hz) on the ¹⁵N time domain and a cosine apodization on the ¹³C′ dimension. The line-width, FWHH, was measured for all spins and T₂ was calculated using Eq. [3]. We had to decide if correction was needed for some long T₂ nuclei. The average FWHH of the resonances along the ¹⁵N dimension was 48.5 Hz (lb = 0 Hz), away from the target value LW_N of 56.8 Hz. When line-broadening of 10 Hz, the value of c, was applied during processing, the average FWHH became 56.5 Hz, matching the target value LW_N. A triple processing of the raw data with lb value of 0, 5 and 10 Hz was performed and T₂ out of each processing were calculated using Eq. [4]. The following linear regression on T₂ vs. lb curve could reveal spins that have extremely long T₂. Shown in Figure 3 were typical slope check results for the spin with regular T₂, ¹⁵N of residue I13 yielding flat slope, and the one with extremely long T₂, ¹⁵N of residue G76 yielding significantly positive slope. ¹⁵N spins of residues R74 through G76 were identified to have significant positive slope (> mean + 1.5 SD). Since the line-broadening correction would reduce S/N ratio and affect accuracy of extracted FWHH, only spins with sufficient S/N ratio to start with were chosen. All identified three residues R74-G76 had enough S/N ratio according to the criterion stated in Materials and Methods section. The correction value of lb was chosen for each spin to ensure the resulted ¹⁵N FWHH of that spin roughly equal, within 1 Hz difference, the mean FWHH value from the first processed spectrum with no line-broadening applied. The values of lb were 22, 29 and 32 Hz for residues R74, G75 and G76, which also indicated the increasing T₂ values towards the C-terminus of Ubiquitin. The final T₂ values for all 70 spins differ on average by 4.7% from those measured using conventional 2D methods. The pair-wise difference is comparable to the intrinsic uncertainty, 2.9%, associated with conventional 2D methods.

Figure 3.

Plot of typical T₂ vs. lb slopes, flat or steep. Residues I13 and G76 of Ubiquitin were shown in circles and tri-angles, respectively. T₂ of residue G76 was under-estimated and need line-broadening correction.

A similar treatment was used to extract T₁ values from the ¹³C′ dimension. Corrections were made on the spins of residues G75 and G76. The final T₁ values differ on average by 3.6% from those measured using conventional 2D methods, while the latter possesses an intrinsic uncertainty of 1.5%.

The comparison of T₁ and T₂ profiles between the fully-relaxed Accordion method and the conventional method are shown in Figure 4. Some essential acquisition and processing parameters are presented in Table 1.

Figure 4.

Comparisons of T₁ (A) and T₂ (B) profiles of Ubiquitin measured using the fully-relaxed Accordion 3D HNCO method (tri-angle) and the conventional 2D method (circles). Error bars for conventional method were standard deviations out of curve fitting.

Glutamine-Binding Protein

We also tested our method on the 226-residue Glutamine-Binding Protein. The backbone spin assignments of GlnBP, missing HNCO correlations for residues A1, D2, P15, P47, P55, P137, P159, P190, P225, G21, D22, D73, and N97-99, were taken from Yu et al. [21] We further excluded non-observed residues K131 and G171 and overlapping residues L146, K205, F81, and F189. A total of 205 peaks remained for analysis. For relatively large proteins like GlnBP short ¹³C′ T₂ will result in relatively low sensitivity and the longer ¹⁵N T₁ will increase experimental time in the T₁ and T₂ doubly coded Accordion-HNCO experiment. We chose to incorporate T₁ and T₂ relaxations separately into two HNCO experiments, and both were encoded on the ¹⁵N dimension thus leaving ¹³C′ dimension solely for peak-resolving purposes.

Similar data processing to Ubiquitin was applied. Essential acquisition and processing parameters are shown in Table 1. Almost all relaxation time constants were measured without applying any line-broadening. Corrections were made for T₂ of residue K226 and T₁ of residue K37. The final T₂ and T₁ values differ on average by 7.4% and 5.6%, respectively, from those measured using conventional 2D methods, while the latter possesses an intrinsic uncertainty of 6.4% and 3.8% for T₂ and T₁, respectively. It is worth noting relaxation times for only 167 residues were available from the 2D method and used for the pair-wise comparison, while those from 205 residues were measured using the fully-relaxed Accordion method (Figure 5).

Figure 5.

Comparisons of T₁ (A) and T₂ (B) profiles of GlnBP measured using the fully-relaxed Accordion 3D HNCO method (tri-angle) and the conventional 2D method (circles). Error bars for conventional method were standard deviations out of curve fitting.

Conclusions and Discussions

We demonstrated the applicability of using a fully-relaxed Accordion type 3D HNCO pulse sequence to measure T₁ and T₂ values from peak line-width. Both relaxations could be measured within one HNCO experiment, given sufficient sensitivity. The current method to extract T₁ and T₂ values are different from the original Accordion approach,[12] which includes numerical minimization on indirect FIDs. The sensitivity can be further improved by the availability of the cryogenic probe and sample perdeuteration. Though the gradient enhanced version of HNCO pulse sequence was adopted here, the TROSY-HNCO pulse scheme can be easily adapted to help the sensitivity issue associated with larger proteins.

The major consideration during acquisition was that the final relaxation delay should reach 3×T₁ or 3×T₂ so that the peak line-width is relatively insensitive to truncation effects during FT. The data processing is largely straightforward. The accuracy is comparable to conventional 2D methods. In addition, for the 226-residue protein GlnBP, which possesses appreciable amount of β-sheet structure, we obtained relaxation data for over 23% more spin nuclei than those from the 2D method. The improvement is expected to be more significant for α-helix rich proteins and that typically have worse resonance dispersion in 2D ¹H-¹⁵N HSQC spectra. One may also measure relaxation times using conventional method with several 3D HNCO spectra [7; 8] being collected at optimal relaxation delay intervals of 0–1.2×T.[22] The total Accordion-HNCO acquisition time is 63 hours for the T₂ measurement of GlnBP. The time period for an HNCO experiment with the same setup is about 36 hrs. Thus the conventional discrete sampling method using HNCO pulses and the same amount of spectrometer time will allow 2-point or alternatively 4-point collection can be achieved if the number of real points in ¹³C dimension is cut half. However, a Monte-Carlo simulation shows more accurate measurements with error range of about 4% can be obtained with Accordion method, while about 7% error will be in the 2-point or 4-point sampling (Supplementary Materials). This is primarily due to the Accordion method sampling more points, equal to the number of indirect FIDs, on the relaxation decay curve.

In addition to T₁ and T₂ the heteronuclear ¹H-¹⁵N NOE data are necessary to provide complementary dynamics on sub-ns time scale. This experiment only requires two measurement points and the HNCO version for NOE measurements are available elsewhere.[7; 8] The presented fully-relaxed Accordion experiment, maximally exploiting the advantage of resolution from heteronuclear NMR, should offer a more complete and site-specific picture of dynamics of potentially challenging proteins.