A 3D Time-Shared NOESY Experiment Designed to Provide Optimal Resolution for Accurate Assignment of NMR Distance Restraints in Large Proteins

Abstract

Structure determination of proteins by solution NMR has become an established method, but challenges increase steeply with the size of proteins. Notably spectral crowding and signal overlap impair the analysis of cross-peaks in NOESY spectra that provide distance restraints for structural models. An optimal spectral resolution can alleviate overlap but requires prohibitively long experimental time with existing methods. Here we present a time-shared 3D experiment optimized for large proteins that provides ¹⁵N and ¹³C dispersed NOESY spectra in a single measurement. NOESY correlations appear in the detected dimension and hence benefit from the highest resolution achievable of all dimensions without increase in experimental time. By design, this experiment is inherently optimal for non-uniform sampling acquisition when compared to current alternatives. Thus, ¹⁵N and ¹³C dispersed NOESY spectra with ultra-high resolution in all dimensions were acquired in parallel within about 4 days instead of 80 days for a 52 kDa monomeric protein at a concentration of 350 μM.

Introduction

Over the years, nuclear magnetic resonance has become a mainstay of protein structural studies as it allows structure determination both in the presence of molecular motions and at near physiological conditions. Structure determinations by solution NMR predominantly rely on 3D NOESY spectra to provide inter-proton distance restraints. These restraints are obtained from the intensity of cross-peak signals in NOESY spectra that report on nuclei that are spatially close. Thus, the accuracy of NMR structures depends on the completeness and accuracy of NOESY cross-peak assignments. In large proteins, both rapid transverse relaxation and spectral crowding impede proper assignment. Rapid transverse relaxation leads to weak and broad NMR signals; it is minimized to a large extent by the combination of transverse relaxation optimized spectroscopy (TROSY) (Pervushin et al. 1997) and deuteration (Gardner and Kay 1998). However, uniform incorporation of deuterons removes probes necessary for NMR structure determination. Hence, to combat relaxation while maintaining structural probes, samples are selectively protonated and ¹³C enriched for a subset of methyl moieties (e.g. for Ile (δ₁), Leu, Val, Ala) in an otherwise uniform ¹⁵N-²H-¹²C background (Gardner and Kay 1998; Goto et al. 1999; Goto and Kay 2000; Isaacson et al. 2007; Ayala et al. 2009). Thus, only methyl and amide protons (reintroduced by exchange with H₂O solvent) are detected. In principle, such a labeling scheme (e.g. ILV or ILVA labeling) alleviates spectral crowding and provides narrower signals. However, in practice, resolving such narrow signals is limited by the digital resolution of the spectra, which for indirect dimensions in NMR spectra is limited by experimental time. That is, the ability to identify correlations is no longer limited by relaxation and line-broadening but instead by the time necessary to achieve a resolution sufficient to resolve signals. Current 3D NOESY experiments designed for large proteins are ill-equipped to overcome this obstacle.

Here, we combine three strategies to provide ultra-high resolution 3D NOESY spectra within a conventional acquisition time. First, a novel time-shared strategy provides HC-HSQC-NOESY and HN-TROSY-NOESY spectra simultaneously with minimal losses in sensitivity. The savings in experimental time can then be reinvested in improving spectral resolution. Second, NOESY cross-peaks are featured along the detected dimension, as opposed to the indirect dimension in current time-shared 3D NOESY experiments. Therefore, the signals benefit from the detected dimension's intrinsically high resolution at no cost in experimental time. Finally, we show that the experiment is inherently optimal for accelerated data acquisition using non-uniform sampling in the indirect dimensions. In the end, a single acquisition provides two 3D spectra of unparalleled resolution in all dimensions within ∼4 days. The advantages of this experiment are demonstrated with a 350 μM, ILV labeled sample of a nonribosomal peptide synthetase heterocyclization domain, a 52 kDa monomeric protein.

Materials and Methods

Cloning, expression and purification of Cy1

All experimental data were recorded on a 52 kDa cyclization domain (Cy1) from the HMWP2 subunit of the Yersinia pestis yersiniabactin synthetase (Keating et al. 2000). The ∼1.4 kb fragment encompassing the Cy1 domain (residues 101 - 544) was amplified from pHMWP2.CH8 (Keating et al. 2000) (a gift from Christopher Walsh's lab, Harvard Medical School) ligated into the pET30a expression vector (Novagen, San Diego, CA) and transformed into E. coli BL21(DE3) cells (Novagen). This construct expresses the Cy1 protein with LEHHHHHH appended to the C-terminus (construct named Cy1H6).

The NMR sample used in our studies is uniformly labeled with ²H, ¹⁵N, and ¹²C, while the methyl groups of Ile (δ₁ position only), Leu and Val side-chains are labeled with ¹H and ¹³C. Phe and Tyr residues are protonated and enriched in ¹⁵N (Muchmore et al. 1989; Gross et al. 2003). BL21(DE3) cells with the pET30a-Cy1H6 plasmid were initially grown in an overnight 50 mL LB medium at 37 °C (250 rpm). 1 mL overnight culture was used to inoculate 1 L of M9 minimal medium (6 g/L Na₂HPO4, 3 g/L KH₂PO₄, 0.5 g/L NaCl, 2 mM MgCl₂, 0.1 mM CaCl₂) in 99.9 % D₂O (Sigma/Aldrich) containing 2 g/L ²H glucose (Cambridge Isotope Laboratories, CIL), 1g/L ¹⁵NH₄Cl (Sigma/Aldrich), 10 mL vitamin solution (0.5 g/L thiamine, 0.1 g/L D-biotin, 0.1 g/L choline chloride, 0.1 g/L folic acid, 0.1 g/L niacinamide, 0.1 g/L D-pantothenic acid, 0.1 g/L pyridoxal and 0.01 g/L riboflavin,in 99.9% D₂O), 2mL of trace element solution (in 99.9% D₂O)(Cai et al. 1998), and 50 mg/L kanamycin. At O.D.₆₀₀ ∼0.5, 75 mg of ¹³C-methyl-α-ketobutyrate (CIL), 125 mg of ¹³C₂-dimethyl-α-ketoisovalerate (CIL), 150 mg of ¹⁵N-Tyrosine (CIL), and 150 mg of ¹⁵N-Phenylalanine (CIL) were added. Once O.D.₆₀₀ reached about 0.6, cells were chilled to about 16°C (ice bath), and protein expression was induced with 0.5 mM IPTG for an additional 12 hours (16°C × 250 rpm) until an O.D.₆₀₀ of approximately 1.4 was reached. Cell pellets were harvested by centrifugation (4°C, 5000 × g, 20 minutes) and were kept at −80°C until further use. Cell pellets were thawed on ice and re-suspended in 50 mL of chilled lysis buffer (50 mM Tris, pH 8 at 4°C, 0.1 M NaCl, 5 mM Imidazole, 5 mM β-mercaptoethanol, 100 μg/mL Lysozyme, 50 μg/mL DNase I). All buffers used in the purification protocol were filtered with a 0.22 μm filter and degassed for 20 minutes before use. Cells were lysed with a microfluidizer (Microfluidics Inc. Waltham, MA) and cellular debris pelleted by centrifugation (4°C, 15000 × g, 30 minutes) followed by filtration using a 0.22•μm filter. The filtered lysate was loaded onto a 5 mL HisTrap HP column (GE Healthcare, Sweden) pre-equilibrated with His-Buffer A (50 mM Tris, pH 8 at 4°C, 0.5 M NaCl, 5 mM Imidazole, 5 mM β-mercaptoethanol). The HisTrap column was washed with 100 mL of His-Buffer A at 4mL/min after loading the lysate, and Cy1H6 was then eluted by a 0-100 % gradient of His-Buffer B (50 mM Tris, pH 8 at 4°C, 0.5 M NaCl, 0.5 M Imidazole, 5 mM β-mercaptoethanol) at a flow rate of 3 mL/min. Fractions containing Cy1 H6 (confirmed by SDS-PAGE) were pooled and dialyzed overnight at 4°C against the dialysis buffer (50 mM Tris, pH 8 at 4°C, 0.1 M NaCl, 20 mM β-mercaptoethanol, 1mM EDTA). The dialysate was filtered (0.22 um filter) and concentrated at 4000 × g and 4°C to ∼ 3 mL using an Amicon Ultra centrifugal filter (10,000 NMWL, Millipore, Ireland). The concentrated solution was injected in 1 mL batches onto a size exclusion chromatography (SEC) column (16/60 Superdex 75 column, GE Healthcare) equilibrated with SEC buffer (20 mM Sodium Phosphate buffer, 100 mM NaCl, 1 mM EDTA, 5 mM DTT, pH 7) at 0.7 ml/min. The single mono dispersed peak containing Cy1H6 (ε₂₈₀ = 88,265 M^-1 cm^-1) was then concentrated and buffer exchanged into the NMR buffer (20 mM Sodium Phosphate, 10 mM NaCl, 1 mM EDTA, 5 mM DTT, pH 7.0) using 10,000 NMWL Amicon Ultra centrifugal filters (4°C, 2000 × g). The final NMR sample contained 5 % D₂O and the final protein concentration was 350 μM.

Acquisition and Processing

All NMR experiments were conducted at 25 °C on a Bruker 600 MHz AVANCE III spectrometer equipped with a QCI cryoprobe^TM. Both 3D TS-HN-TROSY/HC-HSQC-NOESY (TS-TR/HS-NO) and TS-NOESY-HN-TROSY/HC-HSQC (TS-NO-TR/HS, see supplementary information S4) spectra (Figure 2) were acquired with 512 (¹H detected) × 150 (¹H indirect) × 30 (¹⁵N/¹³C indirect) complex points. The spectral widths in the detected ¹H and indirect ¹⁵N/¹³C dimensions were 16 ppm and 35 ppm / 24 ppm, respectively. The indirect ¹H dimension had a spectral width of 13 ppm for the TS-NO-TR/HS and 6.5 ppm for the TS-TR/HS-NO. The TS-NO-TR/HS was acquired with 16 scans per quadrature component (R(t₁)R(t₂), I(t₁)R(t₂), R(t₁)I(t₂), I(t₁)I(t₂)). For the TS-TR/HS-NO, 16 repetitions of the experiment were stored individually with each accumulating 4 scans. After processing (see below), both TS-NO-TR/HS and TS-TR/HS-NO have the equivalent of 16 scans per quadrature component. A recycle delay of 1 s was used for both experiments. The acquisition times were 4 days, 7 hrs, 2 minutes for TS-TR/HS-NO and 4 days, 7 hrs, 16 minutes for TS-NO-TR/HS.

Fig. 2.

Comparison of H/HnOe strips from TS-NO-TR/HS (a, b, c, d) and TS-TR/HS-NO (a', b', c', d') spectra. a, a') amide-amide and b, b') amide-methyl peaks in ¹⁵N dispersed spectra. c, c') methyl-methyl and d, d') methyl-amide peaks in ¹³C-dispersed spectra. X mark signal maxima. Black filled circles denote cross-peaks whose maxima are incorrectly identified in the TS-NO-TR/HS spectra. Open circles denote cross-peaks that are only resolved in the TS-TR/HS-NO spectra. Triangles mark diagonal peaks when applicable.

The TS-TR/HS-NO data is initially processed with a python script (available from the corresponding author upon request) which adds and subtracts interleaved acquisitions to separate the ¹⁵N and ¹³C pathways, recombines the transients according to tables 3 and 4 (Results and Discussion), and rearranges the data so that traditional NMRPipe (Delaglio et al. 1995) scripts can be used for processing (using the complex flag).

Table 3.

Combination of transients for sensitivity enhanced quadrature detection and line selection in HN-TROSY-NOESY spectra. S_N is the amplitude of the detected amide proton signal and ω_H is the frequency of the NOESY cross-peak encoded in the detected proton dimension (t₃). R & I refer to real and imaginary data for the respective evolution periods. The subscript N added to all transients emphasize that methyl signals have been eliminated (using the pulse phase ω₂, see above). The negative sign of the ¹⁵N gyromagnetic ratio and J_NH < 0 was accounted for in all calculations.

Quadrature Components	Transient Combinations	Signal
R (t1) R (t2)	A1xN + A2xN - A3xN + A4xN	SN ${\mathrm{e}}_{\mathrm{H}3}^{\left(-\mathrm{i}\mathrm{\omega }\mathrm{t}\right)}$ c-N c+HN
I (t1) R (t2)	-(A1yN + A2yN + A3yN - A4yN)	SN ${\mathrm{e}}_{\mathrm{H}3}^{\left(-\mathrm{i}\mathrm{\omega }\mathrm{t}\right)}$ s-N c+HN
R (t1) I (t2)	A1yN + A2yN - A3yN + A4yN	SN ${\mathrm{e}}_{\mathrm{H}3}^{\left(-\mathrm{i}\mathrm{\omega }\mathrm{t}\right)}$ c-N s+HN
I (t1) I (t2)	A1xN + A2xN + A3xN - A4xN	SN ${\mathrm{e}}_{\mathrm{H}3}^{\left(-\mathrm{i}\mathrm{\omega }\mathrm{t}\right)}$ s-N s+HN

Table 4.

Combination of transients for quadrature detection in HC-HSQC-NOESY spectra. S_C is the amplitude of the detected methyl proton signal and ω_H is the frequency of the NOESY cross-peak encoded in the detected dimension (t₃). R & I refer to real and imaginary data for the respective evolution periods. The subscript C added to all transients emphasize that amide signals have been eliminated (using the pulse phase ω₂, see above).

Quadrature Components	Transient Combinations	Signal
R(t1) R (t2)	A1xC - A3xC	Sc ${\mathrm{e}}_{\mathrm{H}3}^{\left(-\mathrm{i}\mathrm{\omega }\mathrm{t}\right)}$ cos (ωct1) cos (ωHc t2)
I (t1) R (t2)	-(A2yC - A4yC)	Sc ${\mathrm{e}}_{\mathrm{H}3}^{\left(-\mathrm{i}\mathrm{\omega }\mathrm{t}\right)}$ sin(ωct1) cos (ωHct2)
R (t1) I (t2)	A1yC - A3yC	Sc ${\mathrm{e}}_{\mathrm{H}3}^{\left(-\mathrm{i}\mathrm{\omega }\mathrm{t}\right)}$ cos (ωct1) sin (ωHc t2)
I (t1) I (t2)	A2xC - A4xC	Sc ${\mathrm{e}}_{\mathrm{H}3}^{\left(-\mathrm{i}\mathrm{\omega }\mathrm{t}\right)}$ sin (ωct1) sin (ωHc t2)

Both TS datasets, TS-TR/HS-NO and TS-NO-TR/HS, were processed with the same cosine-squared bell apodization functions for the respective dimensions. Linear prediction was used to double the number of points in the indirect dimensions, which were subsequently zero-filled to 256 and 512 points in the¹⁵N/¹³C and ¹H dimensions, respectively. The detected dimensions were zero-filled to 1024 points before being Fourier transformed. NMRPipe (Delaglio et al. 1995) scripts were used to perform all the spectral processing mentioned above. All strips and overlays displayed in Figures 2 and 3 were created in CARA (Keller 2003). Peak Picking in each spectrum was performed using the program NMRDraw.

Fig. 3.

TS-TR/HS-NO spectra from uniform (US, red) and non-uniform sampling (NUS, blue). a and b are overlays of US and NUS 2D projections of the indirect dimensions of 3D ¹⁵N and ¹³C dispersed spectra respectively. c, d, e, f) H/HnOe strips centered on the signals labeled in the projections. nOe's can only be assigned appropriately in d and f. Triangles mark diagonal peaks. The asterisk marks a cross-peak that belongs to methyl peak 3.

The non-uniformly sampled TS-TR/HS-NO spectra in Figure 3 were collected in the same time frame (4 days, 4 hrs, 48 min) and had the same spectral widths and acquisition parameters as its uniformly sampled counterpart. A sampling schedule spanning 45000 complex points (150 ¹⁵N/¹³C × 300 ¹H complex points) with a sampling factor of 10% was generated with the software PoissonGap (Hyberts et al. 2012). The seed used to generate the schedule was 12321. The TR-NO and HS-NO datasets were separated using the python script mentioned earlier and the indirect dimensions were reconstructed using the iterative soft thresholding software hmsIST (Hyberts et al. 2012) using 500 iterations per plane. Linear prediction was not used for the indirect dimensions. Apodization and zero-filling in the direct and indirect dimensions were performed as in the uniformly acquired dataset.

Results and Discussion

Time-Shared NOESY Pulse Sequence

Time-shared (TS) experiments allow simultaneous acquisition of spectra involving different nuclei that would otherwise require individual measurements (Farmer II 1991; Boelens et al. 1994; Sattler et al. 1995). TS acquisition is only beneficial when sensitivity losses in the resulting spectra do not exceed 40% compared to those obtained sequentially. Thus, time-shared coherence transfers must be efficient for both nuclei and the experiment must minimize additional spin manipulations when compared to individual experiments. Würtz et al. (2007) have shown that the optimal TS back-transfer for methyl and amide groups combines a simple HSQC (Bodenhausen and Ruben 1980) with the so-called planar mixing HN-TROSY implementation (Yang and Kay 1999; Nietlispach 2005). The planar mixing HN-TROSY implementation offers higher sensitivity (Yang and Kay 1999) than the ST2-PT scheme (Pervushin et al. 1998) for amide moieties, and in TS implementation, it allows methyl proton magnetization to be stored longitudinally for a substantial period, thereby minimizing losses stemming from relaxation (Würst et al. 2007). However, in the TS experiment of Würst et al, amide proton detection is performed by gradient selection in contrast to methyl protons. Therefore, simultaneous detection of amide and methyl signals requires long selective pulses and a number of compensation periods. Similar constraints also occur when pairing an HN-TROSY with an HC-HMQC. In general, spin manipulations that are selective to a single pathway lead to sensitivity reduction for both amide and methyl signals due to transverse relaxation, a common problem in TS experiments (Frueh et al. 2006; Guo and Tugarinov 2009). Hence, in order to maximize sensitivity, we designed a novel TS block pairing an HC-HSQC with a novel planar mixing HN-TROSY scheme employing phase cycling rather than gradient selection. Our phase-cycled scheme enables simultaneous detection of amide and methyl proton signals in TS experiments without additional spin manipulations. Addition of a NOESY block following our TS scheme yields the 3D TS-HN-TROSY/HC-HSQC-NOESY (TS-TR/HS-NO) experiment (Figure 1) featuring nOe correlations in the direct dimension. In the end, our 3D TS-TR/HS-NO experiment provides a 3D-HN-TROSY-NOESY (TR-NO) with no detected loss in sensitivity and a 3D-HC-HSQC-NOESY (HS-NO) with only 21% loss in sensitivity when each spectrum is compared to that of an individual experiment (supplementary information S2).

Fig. 1.

Pulse sequence of the 3D TS − HN-TROSY / HC-HSQC-NOESY experiment. Narrow and wide bars represent 90° and 180° hard pulses, respectively. All pulses are applied along the x axis unless mentioned otherwise. The empty ellipsoids represent water-selective 90° rectangular pulses. The block labeled 3-9-19 is a WATERGATE water suppression scheme (Piotto et al. 1992). The delays are Δ=1/(4J_NH), Δ'=1/(4J_CH) and, t_m = 150 ms (mixing time). The delays d1 = pw_N, d₂ = 3* pw_C + pw_N, and d₃ = 2*pw_C are used to prevent first order phase corrections in indirect dimensions; pw_C and pw_N are the 90° pulse widths for ¹³C and ¹⁵N nuclei, respectively. The time-shared evolution of ¹⁵N and ¹³C coherences has been implemented as published previously (Würtz et al. 2007). κ = SW(C)/SW(N) − ½ with SW(C) and SW(N) the spectral widths of ¹³C (24 ppm) and ¹⁵N (35 ppm), respectively. The filled ellipsoids (line labeled G_z) are 1 ms smoothed-square shaped-pulse gradients: g₁= −36 G/cm, g₂ = 7.5 G/cm, g₃ = 25.5 G/cm, g₄ = 2.5 G/cm, g₅ = −40 G/cm and g₆ = 4 G/cm; each gradient pulse is followed by a 200 μs recovery delay. ¹³C and ¹⁵N decoupling during detection are both achieved using WALTZ-16 sequences (Shaka et al. 1983), with field strengths of 0.71 kHz. Simultaneous ¹³C and ¹⁵N decoupling necessitates the use of lower field strengths and synchronous pulsing to prevent artifacts (Van Ingen et al. 2002). The pulse phases detailed henceforth are spin-dynamic phases and should be modified appropriately depending on the NMR spectrometer used (Roehrl et al. 2005). Spin state selection (¹⁵N) and quadrature detection in both indirect dimensions (t₁ & t₂) is achieved by post-acquisition combinations of transients that are recorded and stored separately. These transients have the following phase settings: A1: ϕ_• = y, ϕ₂ =x, ϕ₃ = -x, ψ₁ = y -y, ψ ₂ = -y, ψ ₃ = x, ω₁ = x -x, ω ₂ = x, ω ₃ = x x -x -x; A2: ϕ₁ = x, ϕ₂ = y, ϕ₃ = -y, ψ₁= y -y, ψ ₂ = -x, ψ ₃ = y, ω₁ = y -y, ω ₂ = x, ω ₃ = x x -x -x; A3: ϕ₁ = y, ϕ₂ = x, ϕ₃ = x, ψ₁ = y -y, ψ ₂ = -y, ψ ₃ = x, ω₁ = x -x, ω ₂ = x, ω ₃ = x x -x -x; A4: ϕ1 = x, ϕ₂ = y, ϕ₃ = y, ψ₁ = y -y, ψ₂ = -x, ψ ₃ = y ω₁ = y -y ω₂ = x, ω₃ = x x -x -x. ω _rec = x -x x -x, for all transients. It should be noted that the 4-step phase cycle in each transient is used to remove artifacts and not for quadrature detection and line-selection. A1 to A4 are recorded either with ϕ₄ = -y and ϕ₅ = x (A1_x to A4_x) or with ϕ₄ = x and ϕ₅ = y (A1_y to A4_y), where the subscript denotes the phase of ϕ₅. To delineate ¹⁵N and ¹³C edited spectra, these 8 transients are recorded a second time with the phase of ω₂ inverted. TPPI (Marion and Wuthrich 1983) is implemented during t₁ evolution using the phases ψ₁, ω₁ and ϕ_rec. The 90° ¹³C pulse applied at point d is used to cancel weak dispersive artifacts which result from incomplete conversion of strong methyl proton antiphase coherences into in-phase coherences in the period b to c. All experiments were conducted at 25 °C on a 600 MHz Bruker Avance III spectrometer equipped with a CP-QCI ¹H/³¹P/¹³C/¹⁵N-²H cryoprobe™ with a single axis gradient coil. Both Bruker and Agilent pulse programs can be obtained by contacting the corresponding author.

The pulse sequence uses a time-shared INEPT element (Farmer II 1991; Boelens et al. 1994) to convert amide and methyl proton polarizations into ¹⁵N and ¹³C single-quantum coherences (SQCs), respectively (Figure 1, a). Using the scheme designed by Würtz et al., ¹⁵N SQCs evolve during t₁ with attenuated transverse relaxation while evolution under ¹J(CH) scalar couplings is refocused for ¹³C SQCs. Next, ¹⁵N and ¹³C coherences are simultaneously converted back to ¹H coherences using our HN-TROSY scheme (Figure 1, d to h, Table 1) paired with a reverse HC-INEPT scheme (Figure 1, d to e). As in the experiment by Würtz et al., methyl magnetization is stored longitudinally during the second half of the HN-TROSY scheme (Figure 1, f to g, Table 1) to minimize signal losses. Table 1 displays the density operator elements present throughout the time-shared transfer (Figure 1, c to h). Methyl and amide proton chemical shifts are encoded during t₂ (Figure 1, h) followed by a mixing period (t_m) and finally, at point i, a 3-9-19 water-suppression scheme is applied before detection. The amide and methyl proton coherences encoded with t₁ and t₂ evolutions are listed in the supplementary information (S3). Amide and methyl signals are separated during processing by addition and subtraction of interleaved acquisitions recorded with opposite phases of ω2, which only inverts the phase of the methyl signals (Frueh et al. 2006).

Table 1.

Amide (HN-TROSY) and methyl (HC-HSQC) coherences at points c through h for the TS-TR/HS-NO pulse sequence in Figure 1. J_NH is the coupling constant between amide protons and nitrogens. The negative sign of the ¹⁵N gyromagnetic ratio and J_NH < 0 was accounted for in all calculations. c⁺_N = cos [(ω_N + πJ_NH)t₁], c^-_N = cos [(ω_N - πJ_NH)t₁], s⁺_N = sin [(ω_N + πJ_NH)t₁], and s^-_N = sin [ (ω_N - πJ_NH)t₁]. ¹/₂ (c⁺_N + c^-_N) = cos (ω_N t₁) cos (πJ_NH t₁), etc. ω_N and ω_c are the amide nitrogen and methyl carbon frequencies respectively encoded during t₁ evolution. ^NH and ^CH refer to amide and methyl proton coherences respectively. Only operators that contribute to observable signals are shown.

HN-TROSY
	c	d	e	f	g	h
A1	-2 NHzNx -Ny -2 NHzNy Nx	2 NHxNz -Ny -2 NHxNy -Nz	NHy 2 NHzNx 2 NHxNy Nz	NH2 2 NHyNz 2 NHxNy Nx	- NH2 NHx -2 NHxNy -2 NHzNy	- NHy NHx 2 NHxNz 2 NHyNz	1/2 (c+N + c-N) 1/2(s+N - s-N) 1/2 (s+N + s-N) 1/2(cN - c+N)
A2	-2 NHzNx -Ny -2 NHzNy Nx	2 NHyNx -Nz 2 NHyNz Nx	-2 NHyNx Nz NHx -2 NHzNy	-2 NHyNx -Ny - NHz -2 NHxNz	2 NHyNx 2 NHzNx NHz - NHy	2 NHyNz -2 NHxNz - NHx - NHy	1/2 (c+N + c-N) 1/2(s+N - s-N) 1/2 (s+N + s-N) 1/2(c-N - c+N)
A3	-2 NHzNx -Ny -2 NHzNy Nx	2 NHxNz -Ny -2 NHxNy -Nz	NHy 2 NHzNx 2 NHxNy Nz	NHz 2 NHyNz 2 NHxNy Nx	-NHz NHx -2 NHxNy -2 NHzNy	NHy NHx 2 NHxNz -2 NHyNz	1/2 (c+N + c-N) 1/2(s+N - s-N) 1/2 (s+N + s-N) 1/2(cN - c+N)
A4	-2 NHzNx -Nv -2 NHzNy Nx	2 NHyNx -Nz 2 NHyNz Nx	-2 NHyNx Nz NHx -2 NHzNy	-2 NHyNx -Ny - NHz -2 NHxNz	2 NHyNx 2 NHzNx NHz -NHy	2 NHyNz 2 NHxNz NHx -NHy	1/2 (c+N + c-N) 1/2(s+N - s-N) 1/2 (S+N + S-N) 1/2(c-N - c+N)
HC-HSQC
A1	2 CHzCz	2 CHxCz	-cHy	- CHz	CHz	cHy	cos (ωct1)
A2	- 2 CHzCz	2 CHyCz	- CHx	CHz	- CHz	CHx	sin (ωct1)
A3	2 CHzCz	2 CHxCz	-cHy	- CHz	CHz	-cHy	cos (ωct1)
A4	- 2 CHzCz	2 CHyCz	- CHx	CHz	- CHz	- CHx	sin (ωct1)

Sensitivity enhancement and spin-state selection for amide groups and quadrature detection for all indirect dimensions are all achieved simultaneously with an unconventional data acquisition scheme. Eight transients with different phase settings (A1_x to A4_x and A1_y to A4_y, Table 2) are stored separately and later recombined during processing. That is, we do not use receiver phase cycling to perform the HN-TROSY line selection, nor do we store real and imaginary components of a dimension sequentially. This strategy was not only key in designing an HN-TROSY experiment with sensitivity-enhancement, but it also enabled implementing an efficient time-shared scheme, as described below. Tables 3 and 4 display the combinations of transients necessary to obtain the phase-sensitive HN-TROSY-NOESY and HC-HSQC-NOESY spectra, respectively.

Table 2.

Transients recorded before separation of amide and methyl signals. A1 to A4 are recorded with ϕ₅ = x (A1_x to A4) and ϕ₅ = y (A1_y to A4_y), where the subscript denotes the phase of ϕ₅. S_N and S_c are the amplitudes of the detected amide and methyl proton signals respectively and ω_H is the frequency of the NOESY cross-peak encoded in the detected proton dimension (t₃). c⁺_N, c^-_N, s⁺_N, and s^-_N are described in Table 1. c⁺_HN = cos [ (ω_HN + πJ_NH)t₂], c^-_HN = cos [ (ω_HN - πJ_NH)t₂], s⁺_HN = sin [ (ω_HN + πJ_NH)t₂], s^-_HN = sin [ (ω_HN - πJ_NH)t₂]. ω_HN and ω_HC are the amide proton and methyl proton frequencies encoded during t₂ evolution. The negative sign of the ¹⁵N gyromagnetic ratio and J_NH < 0 was accounted for in all calculations.

Transients Recorded
A1x	SN ${\mathrm{e}}_{\mathrm{H}3}^{\left(-\mathrm{i}\mathrm{\omega }\mathrm{t}\right)}$ ( c+N c-HN - s+N s-HN + c-N c+HN + s-N s+HN) - Sc ${\mathrm{e}}_{\mathrm{H}3}^{\left(-\mathrm{i}\mathrm{\omega }\mathrm{t}\right)}$ cos (ωct1) cos (ωHC t2)
A2x	SN ${\mathrm{e}}_{\mathrm{H}3}^{\left(-\mathrm{i}\mathrm{\omega }\mathrm{t}\right)}$ (- c+N c-HN + s+N s-HN + c-N c+HN + s-N s+HN) - Sc ${\mathrm{e}}_{\mathrm{H}3}^{\left(-\mathrm{i}\mathrm{\omega }\mathrm{t}\right)}$ sin (ωct1) sin (ωHC t2)
A3x	SN ${\mathrm{e}}_{\mathrm{H}3}^{\left(-\mathrm{i}\mathrm{\omega }\mathrm{t}\right)}$ (- c+N c-HN - s+N s-HN - c-N c+HN + s-N s+HN) + Sc ${\mathrm{e}}_{\mathrm{H}3}^{\left(-\mathrm{i}\mathrm{\omega }\mathrm{t}\right)}$ cos (ωct1) cos (ωHC t2)
A4x	SN ${\mathrm{e}}_{\mathrm{H}3}^{\left(-\mathrm{i}\mathrm{\omega }\mathrm{t}\right)}$ (- c+N c-HN - s+N s-HN + c-N c+HN - s-N s+HN) + Sc ${\mathrm{e}}_{\mathrm{H}3}^{\left(-\mathrm{i}\mathrm{\omega }\mathrm{t}\right)}$ sin (ωct1) sin (ωHC t2)
A1y	SN ${\mathrm{e}}_{\mathrm{H}3}^{\left(-\mathrm{i}\mathrm{\omega }\mathrm{t}\right)}$ ( c+N s-HN + s+N c-HN + c-N s+HN - s-N c+HN) - Sc ${\mathrm{e}}_{\mathrm{H}3}^{\left(-\mathrm{i}\mathrm{\omega }\mathrm{t}\right)}$ cos (ωct1) sin (ωHC t2)
A2y	SN ${\mathrm{e}}_{\mathrm{H}3}^{\left(-\mathrm{i}\mathrm{\omega }\mathrm{t}\right)}$ (- c+N s-HN - s+N c-HN + c-N s+HN - s-N c+HN) + Sc ${\mathrm{e}}_{\mathrm{H}3}^{\left(-\mathrm{i}\mathrm{\omega }\mathrm{t}\right)}$ sin (ωct1) cos (ωHC t2)
A3y	SN ${\mathrm{e}}_{\mathrm{H}3}^{\left(-\mathrm{i}\mathrm{\omega }\mathrm{t}\right)}$ (- c+N s-HN + s+N c-HN - c-N s+HN - s-N c+HN) + Sc ${\mathrm{e}}_{\mathrm{H}3}^{\left(-\mathrm{i}\mathrm{\omega }\mathrm{t}\right)}$ cos (ωct1) sin (ωHC t2)
A4y	SN ${\mathrm{e}}_{\mathrm{H}3}^{\left(-\mathrm{i}\mathrm{\omega }\mathrm{t}\right)}$ (- c+N s-HN + s+N c-HN + c-N s+HN + s-N c+HN) - Sc ${\mathrm{e}}_{\mathrm{H}3}^{\left(-\mathrm{i}\mathrm{\omega }\mathrm{t}\right)}$ sin (ωct1) cos (ωHC t2)

Quadrature detection for the indirect dimensions of the ¹⁵N-edited NOESY is performed in a manner similar to Echo-AntiEcho sensitivity-enhanced schemes. Real and imaginary components of the interferogram are obtained simultaneously, as can be seen in Table 2. In what follows, ¹⁵N and ¹³C pathways have been separated and the subscript N is added to the transient labels (e.g. A1_xN) to emphasize that only amide signals are being discussed. During processing, combinations of the transients provide real and imaginary components while simultaneously selecting for the slowly relaxing component of the HN multiplet (Table 3). Sensitivity enhancement in the amide spectrum can only be achieved by storing transients separately. Indeed, as seen in Table 3, all eight transients are used twice when performing quadrature detection; A1_xN, A2_xN, A3_xN and A4_xN are used to provide both the components R(t1)R(t₂) and I(t₁)I(t2). Likewise, I(t₁)R(t₂) and R(t₁)I(t₂) are obtained with A1_yN through A4_yN. In a conventional NMR acquisition, phase cycling of the receiver is used to perform such combinations. However, the receiver would select either the combination providing R(t₁)R(t₂) or that providing I(t₁)I(t₂) (the same is true for R(t₁)I(t₂) and I(t1)Rt₂)). Quadrature detection and TROSY line selection can still be achieved but a total of 16 transients need to be acquired, although half of the data are redundant. This doubling in experimental time results in a √2 loss in sensitivity when compared to separate storage of transients. The same method has been used before to perform sensitivity-enhanced, Echo-AntiEcho quadrature detection with ST2-PT TROSY schemes (Brutscher et al. 1998; Zhu et al. 1999). As mentioned above, ST2-PT schemes lead to severe sensitivity losses in TS experiments (Würtz et al. 2007).

Frequency discrimination for the methyl proton indirect dimension cannot be achieved by conventional sequential acquisition of real and imaginary signal components. In a conventional ¹³C-edited NOESY, hypercomplex data (R(t₁)R(t₂), I(t₁)R(t₂), R(t₁)I(t₂), I(t₁)I(t₂)) would be obtained by varying the phases ω₁ or ω ₂ for methyl carbons and ϕ₃ or ϕ₅ for methyl protons. However, the phases ϕ₃ and ϕ₅ have been set to provide sensitivity-enhanced quadrature detection and HN-TROSY line selection for the amide pathway, as discussed previously. To overcome this constraint, the real and imaginary components of the methyl proton dimension are acquired in a nested manner (Table 2) as dictated by the phases imposed by the amide protons. The appropriate pairing of the transients A1_xC to A4_xC and A1_yC to A4_yC (Table 4) resulting from such a nested acquisition provides hypercomplex data in the ¹³C-edited NOESY (subscript C added to the transients to emphasize that only methyl signals are being discussed). Additionally storing the transients separately was exploited to suppress artifacts in the ¹³C-edited NOESY in a manner akin to phase cycling. The nested acquisition imposes that each component of the methyl proton dimension (R & I) be recorded twice. Since A1_xC to A4_xC and A1_yC to A4_yC can all be accessed during processing, various combinations can be used to retrieve real and imaginary components. Thus, the combinations shown in Table 3 can produce the R(t₁)R(t₂), I(t₁)R(t₂), R(t₁)I(t₂), and I(t₁)I(t₂) components not only for amide groups but also for methyl groups. However such a combination results in artifacts in the ¹³C-edited NOESY spectrum. These artifacts are suppressed if instead the combinations of Table 4 are employed. We exploited this advantage by reducing the size of traditional phase cycling in our experiment.

In summary, 16 transients stored separately (A1_x to A4_x and A1_y to A4_y, each also recorded with opposite phases of co2) are efficiently used to i) separate ¹⁵N- and ¹³C-dispersed spectra, ii) achieve sensitivity-enhanced quadrature detection in amide proton and nitrogen indirect dimensions, iii) perform TROSY line selection, iv) obtain quadrature detection in methyl proton and carbon indirect dimensions, and v) suppress artifacts in ¹³C edited NOESY. A single python script (available from the corresponding author upon request) separates ¹⁵N and ¹³C dispersed spectra, combines the transients according to tables 3 and 4, and rearranges the data so that traditional NMRPipe (Delaglio et al. 1995) scripts can be used for processing (using the complex flag).

Demonstration on a 52 kDa monomeric protein

The critical impact of spectral resolution in NOESY experiments on the quality of NMR structures has been discussed thoroughly (Tikole et al. 2013). Here, we illustrate with selected examples the advantages of our newly developed 3D TS-HN-TROSY/HC-HSQC-NOESY (TS-TR/HS-NO) experiment over the existing TS NOESY experiment (Frueh et al. 2006) that features nOe correlations in the indirect dimension. For this comparison we used a TS-NOESY-HN-TROSY/HC-HSQC (TS-NO-TR/HS) (Frueh et al. 2006), updated with recent developments (supplementary information, S4), which provides a 3D NOESY-HN-TROSY (NO-TR) and a 3D NOESY-HC-HSQC (NO-HS) spectrum. Both TS experiments were acquired with the same number of points in all dimensions and within the same experimental time (∼4 days). In what follows, only resolution is being considered; with our experimental conditions the TS-TR/HS-NO benefits from an improvement in sensitivity (∼15% in HN and ∼20% in HC), over the TS-NO-TR/HS experiment (see supplementary information S5).

Figure 2 a-d and a'-d' compare H/H_nOe strips for a TS-NO-TR/HS and a TS-TR/HS-NO recorded at 600 MHz in the same time and for the same monomeric 52 kDa protein. The superior resolution of the nOe dimension in the TS-TR/HS-NO spectra (18.8 Hz/pt) reveals cross-peaks that are not resolved and hence undetected in the TS-NO-TR/HS (52 Hz/pt) spectra. Missing and erroneously assigned distance restraints drastically decrease the quality of structural models and may prevent determination of the proper fold (Nabuurs et al. 2006). Furthermore, in the TS-NO-TR/HS, the chemical shifts of signal maxima are shifted in the presence of overlap. As a result, these signals may be erroneously assigned. For example, the high resolution of the TR-NO in Figure 2a' reveals two cross-peaks below 7.5 ppm (open circles), each providing a distance restraint. Using the NO-TR spectrum (Figure 2a) and comparing the chemical shifts of all amide protons picked in the spectrum with that of the single signal observed (black circle), one finds that the correct assignments (open circles) rank 7^th and 10^th. In this case, the NO-TR spectrum misses two correct distance restraints and instead produces one erroneous restraint. Similar examples are shown for amide-methyl (Figure 2b, b'), methyl-methyl (Figure 2c, c') and methyl-amide (Figure 2d, d') cross-peaks. As a result, not only are the assignments provided by TS-NO-TR/HS spectra incomplete but also erroneous. Clearly, both the inability to resolve ambiguities and the risk of producing erroneous assignments is catastrophic in the context of manual and automated nOe assignment procedures and consequently the structure determination process (Jee and Güntert 2003; Nabuurs et al. 2006). Indeed, automated peak picking resulted in at least 118 (¹⁵N dispersed) and 127 (¹³C dispersed) additional peaks when TS-TR/HS-NO was used in place of TS-NO-TR/HS. Here the threshold for peak picking was adjusted to compensate for differences in signal intensity, so these numbers reflect only the ability to resolve peaks (supplementary information S6). As discussed above, the differences between these numbers not only reflect missing correlations but also correlations for which assignment may be erroneous. Thus, the TS-TR/HS-NO spectra critically alleviate the shortcomings of the TS-NO-TR/HS when used in the NMR structure determination of large proteins.

The TS-TR/HS-NO experiment can be paired with non-uniform sampling (NUS) to provide spectra with high resolution in all dimensions. NUS accelerates data acquisition by recording only a subset of evolution times in indirect dimensions (quantified by a so called-sampling factor) instead of measuring all evolution times (Barna et al. 1987; Orekhov et al. 2003; Rovnyak et al. 2004; Marion 2006; Coggins et al. 2010; Kazimierczuk and Orekhov 2011; Holland et al. 2011; Maciejewski et al. 2012; Hyberts et al. 2012). For large proteins, this acceleration is exploited to maximize the resolution that can be obtained within a given spectrometer time and hence minimize signal overlap. The complete dataset is recovered using special reconstruction techniques (Barna et al. 1987; Orekhov et al. 2003; Rovnyak et al. 2004; Marion 2006; Coggins et al. 2010; Kazimierczuk and Orekhov 2011; Holland et al. 2011; Maciejewski et al. 2012; Hyberts et al. 2012). The quality of the reconstructed spectrum depends on the interplay between the sampling factor and the sparsity of signals present in indirect dimensions; spectra with fewer signals can tolerate lower sampling factors (Hyberts et al. 2014). Within this framework, the TS-TR/HS-NO has at least two advantages over the TS-NO-TR/HS. First and foremost, for the same resolution and acquisition time, the sampling factor is effectively doubled in the TS-TR/HS-NO. The spectral width of the indirect proton dimension in TS-NO-TR/HS must encompass both amide and methyl proton chemical shifts (here 13 ppm) and hence must be twice as big as that of TS-TR/HS-NO, which only needs to encompass the largest spectral width i.e. either methyl or amide protons (usually amides, here 6.5 ppm). Second, since NOESY cross-peaks appear in the detected dimension, fewer signals must be reconstructed in the indirect dimensions of TS-TR/HS-NO, so sparsity is increased. Although the improvements provided by using the TS-TR/HS-NO experiment will depend on the method used for the reconstruction, all methods are expected to perform better with a higher sampling density and fewer signals to reconstruct (Orekhov and Jaravine 2011; Hyberts et al. 2014)

The improvement provided by non-uniform sampling was verified with an NUS-TS-TR/HS-NO spectrum acquired in the same experimental time as that used for conventional uniform acquisition (∼4days). A schedule of 4500 complex points spanning 300 (¹H) × 150 (¹⁵N) = 45,000 complex points was generated with the software package Poisson gap (10% sampling factor) (Hyberts et al. 2012). Spectral reconstruction was performed with the iterative soft thresholding technique (Hyberts et al. 2012). Figure 3 highlights the advantages of increased resolution in the indirect dimensions within the context of NOESY cross-peaks assignment. In Figure 3a, two (H, N) correlations (labeled 1 and 2) are separated by 0.001 ppm in ¹H and 0.314 ppm in ¹⁵N. Without NUS the two corresponding H/H_nOe strips both feature the same five correlations (Figure 3c). The increased resolution in the NUS spectrum reveals that only two cross-peaks belong to the first (H, N) correlation while the other three belong to the second (Figure 3d). Likewise, with conventional acquisition, three NOESY cross-peaks can each be assigned to either of two (H, C) correlations (Figure 2b, e), which are separated by 0.001 ppm in ¹H and 0.223 ppm in ¹³C. Increased resolution in the NUS spectrum permits unambiguous assignment of these cross-peaks. Incidentally, the cross-peak marked with an asterisk belongs to a third correlation (Figure 3b, labeled 3) and could only be discerned in the NUS spectrum (Figure 3f). Automated peak picking of NOESY cross-peaks in NUS-TS-TR/HS-NO, provides at least 74 (¹⁵N dispersed) and 41 (¹³C dispersed) additional peaks when compared to the conventional acquisition (S6). The increased accuracy and completeness of automated peak picking that was facilitated in the NUS spectrum will translate into more reliable automated structure determination (Tikole et al. 2013).

Conclusion

We have developed an NMR experiment that enables more accurate and complete assignment of NOESY cross-peaks in large proteins. The experiment provides maximal digital resolution within a realistic acquisition time for amide-amide, amide-methyl, methyl-methyl and methyl-amide nOe correlations in a single experiment. The novel HN-TROSY scheme allowed implementing the TS strategy with superior sensitivity over sequential acquisition of both spectra. The reduced experimental time is particularly beneficial for data acquisition on short-lived, expensive protein samples. While this experiment was demonstrated on an ILV sample, it can also be used when methyl groups of other residues are labelled as ¹³C-¹H (e.g. Ala, Thr, Met) (Gelis et al. 2007; Isaacson et al. 2007; Ayala et al. 2009; Sinha et al. 2011), provided the carbon adjacent to the methyl groups are not enriched in ¹³C. At 600 MHz, our experiment provides at least a 2.8-fold increase in resolution along the nOe dimension over traditionally used NO-TR/HS experiments and improves both interactive and automated nOe assignment procedures. The experiment can be modified to suppress diagonal signals in the TR-NO spectrum as described by Meissner et al. (Meissner and Sørensen 2000), albeit with sensitivity losses in both TR-NO and HS-NO spectra. The full potential of our experiment was harnessed by implementing NUS along the indirect dimensions. The combined use of TS and NUS techniques provided in 4 days a pair of spectra that would otherwise require 80 days of spectrometer time. The resulting spectra possess optimal resolution in all dimensions and resolve ambiguities in assigning distance restraints. The TS-TROSY/HSQC-NOESY experiment will both facilitate the structure determination of large proteins and improve their accuracy, further increasing the molecular weight of monomeric proteins amenable for NMR structural studies.