Efficient ¹⁵N-¹³C Polarization Transfer by Third-Spin Assisted Pulsed Cross Polarization Magic-Angle-Spinning NMR for Protein Structure Determination

Abstract

We introduce a pulsed third-spin assisted recoupling experiment that produces high-intensity long-range ¹⁵N-¹³C cross peaks using low radiofrequency (rf) energy. This Proton-Enhanced Rotor-echo Short Pulse IRradiATION Cross Polarization (^PERSPIRATIONCP) pulse sequence operates with the same principle as the Proton-Assisted Insensitive-Nuclei Cross Polarization (^PAINCP) experiment, but uses only a fraction of the rf energy by replacing continuous-wave ¹³C and ¹⁵N irradiation with rotor-echo 90° pulses. Using formyl-MLF and β1 immunoglobulin binding domain of protein G (GB1) as model proteins, we demonstrate experimentally how ^PERSPIRATIONCP polarization transfer depends on the CP contact time, rf power, pulse flip angle, and ¹³C carrier frequency, and compare the ^PERSPIRATIONCP performance with the performances of ^PAINCP, ^RESPIRATIONCP, and ^SPECIFICCP for measuring ¹⁵N-¹³C cross peaks. ^PERSPIRATIONCP achieves long-range ¹⁵N-¹³C transfer and yields higher cross peak intensities than the other techniques. Numerical simulations reproduce the experimental trends and moreover indicate that ^PERSPIRATIONCP relies on ¹⁵N-¹H and ¹³C-¹H dipolar couplings rather than ¹⁵N-¹³C dipolar coupling for polarization transfer. Therefore, ^PERSPIRATIONCP is an rf-efficient and higher-sensitivity alternative to ^PAINCP for measuring long-range ¹⁵N-¹³C correlations, which are essential for protein resonance assignment and structure determination. Using cross peaks from two ^PERSPIRATIONCP ¹⁵N-¹³C correlation spectra as the sole distance restraints, supplemented with (φ, ψ) torsion angles obtained from chemical shifts, we calculated the GB1 structure and obtained a backbone RMSD of 2.0 Å from the high-resolution structure of the protein. Therefore, this rf-efficient ^PERSPIRATIONCP method is useful for obtaining many long-range distance restraints for protein structure determination.

Graphical Abstract

Introduction

Magic-angle-spinning (MAS) solid-state nuclear magnetic resonance (SSNMR) spectroscopy has become instrumental for determining the molecular structures and characterizing the functions of many biological macromolecules, including membrane proteins ^1-9, amyloid fibrils ^10-15, and cell walls of plants, bacteria and fungi ^16-23. To resolve the signals of ¹³C and ¹⁵N-enriched proteins and carbohydrates, multidimensional correlation experiments are crucial. The majority of these correlation techniques achieve polarization transfer using distance-dependent homonuclear and heteronuclear dipolar couplings ²⁴, so that cross peak intensities reflect inter-atomic distances in a semi-quantitative fashion. Since MAS averages dipolar couplings, a plethora of pulse sequences has been developed to recouple dipolar couplings to measure these correlation spectra and extract inter-atomic distances.

For protein resonance assignment, it is essential to correlate the amide ¹⁵N signal with ¹³C chemical shifts from the same residue as well as from the preceding residue. Both one-bond N-Cα and N-CO cross peaks and multi-bond N-CX correlations to sidechain carbons are required for assigning the chemical shifts. Once resonance assignment is obtained, ¹⁵N-¹³C correlations between residues that are well separated in the primary sequence are important for constraining the three-dimensional structure of the protein. Because of the low gyromagnetic ratios of ¹⁵N and ¹³C and the resulting weak dipolar couplings, multi-bond and long-range ¹⁵N-¹³C cross peaks are difficult to detect with high sensitivity. Cross polarization (CP) ²⁵ has been the most common approach for measuring ¹⁵N-¹³C cross peaks, although pulsed methods based on Rotational-Echo DOuble-Resonance (REDOR) have also been used ^26-27. The double-CP (DCP) ²⁸ and ^SPECIFICCP ²⁹ experiments correlate ¹⁵N and ¹³C chemical shifts in a broadband and band-selective fashion, respectively, by simultaneous continuous-wave (CW) irradiation on the ¹³C and ¹⁵N channels while decoupling protons with high rf power. The ¹³C and ¹⁵N transverse rf field strengths satisfy the centerband Hartman-Hahn condition in DCP, while an effective-field sideband-matching condition is used in the ^SPECIFICCP technique to achieve selective transfer from ¹⁵N to CΑ or ¹⁵N to CO. Since both DCP and ^SPECIFICCP require multi-channel high-power rf irradiation for several milliseconds, these techniques put a significant demand on the NMR probe. Moreover, since both methods rely on direct ¹⁵N-¹³C dipolar couplings for polarization transfer, ¹⁵N cross peaks with sidechain carbons often require an additional ¹³C-¹³C mixing period to detect. Although various homonuclear recoupling methods have been used for ¹³C mixing ^30-31, ¹³C spin diffusion remains to be the most common approach, and with increasing MAS frequencies, spin diffusion becomes inefficient, thus lowering the cross peak intensities.

Two alternative approaches have been developed in the last decade to measure ¹⁵N-¹³C cross peaks with higher sensitivity and to longer distances. The proton-assisted insensitive nuclei cross polarization (^PAINCP) approach ^32-33 relies on cross-terms between ¹H-¹³C and ¹H-¹⁵N dipolar couplings in the second-order average Hamiltonian to mediate polarization transfer between ¹⁵N and ¹³C. Because this technique relies on an intervening third spin, a proton, which has a much higher gyromagnetic ratio and hence stronger dipolar couplings, the ¹⁵N-(¹H)-¹³C polarization transfer is more efficient than DCP and ^SPECIFICCP, which allows long-range cross peaks to be measured with higher sensitivity. During ^PAINCP irradiation, proton-assisted ¹³C-¹³C recoupling (PAR) also occurs ^34-36, which further increases the intensities of carbons that are far from the ¹⁵N spin through relayed transfer. However, similar to DCP and ^SPECIFICCP, ^PAINCP requires CW irradiation of all three nuclei. Although there are multiple matching conditions for ^PAINCP, the most commonly used and reliable condition involves rf field strengths of ~50 kHz for all three channels. These ¹³C and ¹⁵N rf powers are significantly stronger than typically used in the DCP and ^SPECIFICCP experiments, which make ^PAINCP even more rf intensive than the two predecessors.

The second approach that has been proposed for measuring ¹⁵N-¹³C cross peaks is the Rotor-Echo Short Pulse IRradiATION Cross Polarization (^RESPIRATIONCP) ³⁷ experiment, which consists of short, rotor-synchronized pulses on the ¹³C and ¹⁵N channels that are interleaved with phase-alternating ¹³C recoupling pulses. The first-order average Hamiltonian of ^RESPIRATIONCP includes both first- and second-order Fourier components of the dipolar couplings, thus it achieves more efficient ¹⁵N-¹³C polarization transfer than DCP and ^SPECIFICCP ^38-39. However, because ^RESPIRATIONCP is a first-order recoupling sequence, long-distance ¹⁵N-¹³C polarization transfer remains difficult, and most intensities are restricted to one-bond N-Cα and N-CO correlations. Moreover, although no ¹⁵N CW irradiation is used in ^RESPIRATIONCP, strong ¹H decoupling is required during the contact time, and the rf field strength of the phase-alternating ¹³C recoupling pulses increases with MAS. Therefore, the rf power requirement of ^RESPIRATIONCP remains high at fast MAS.

Drawing on the individual strengths of ^PAINCP and ^RESPIRATIONCP, here we report a pulsed variant of the ^PAINCP technique, which we call Proton-Enhanced Rotor-echo Short Pulse IRradiATION Cross Polarization (^PERSPIRATIONCP). ^PERSPIRATIONCP consists of the same moderate CW irradiation on the ¹H channel as in ^PAINCP, together with rotor-echo 90° pulses on the ¹³C and ¹⁵N channels as in ^RESPIRATIONCP, but no CW irradiation is applied on the ¹³C or ¹⁵N channel. Thus ^PERSPIRATIONCP has a much lower rf duty cycle than ^RESPIRATIONCP and ^PAINCP. We show by experiments and simulations that ^PERSPIRATIONCP relies on cross-terms between ¹H-¹³C and ¹H-¹⁵N dipolar couplings and between ¹H-¹³C₁ and ¹H-¹³C₂ to achieve long-range ¹⁵N-¹³C polarization transfer, as in ^PAINCP and PAR. We compare the experimental ¹⁵N-¹³C transfer characteristics of ^SPECIFICCP, ^RESPIRATIONCP, ^PAINCP, and ^PERSPIRATIONCP using the model tripeptide formyl-MLF (f-MLF) and the microcrystalline β1 immunoglobulin binding domain of protein G (GB1). We also investigate the dependence of ^PERSPIRATIONCP on the ¹³C carrier frequency and pulse flip angle. Finally, we demonstrate the use of ^PERSPIRATIONCP for measuring 2D ¹⁵N-¹³C correlation spectra, and show that with ¹⁵N-¹³C cross peaks from two 2D spectra as the only distance restraints, we can already obtain a three-dimensional structure of GB1 with excellent agreement with the known high-resolution structure of this protein.

Materials and Methods

Sample Preparation

Uniformly ¹³C, ¹⁵N-labeled f-MLF was purchased from Cambridge Isotope Laboratories (Andover, MA) and center-packed into a 3.2 mm rotor without further purification. ¹³C, ¹⁵N-labeled GB1 was expressed in M9 minimal media containing uniformly ¹³C-labeled glucose and ¹⁵NH₄Cl according to previously published protocols ⁴⁰. The purified protein was dialyzed against pH 5.5 phosphate buffer to remove NaCl and reach the optimal pH for crystallization. The protein was then back-exchanged with D₂O and crystallized in a solution containing a 2:1 ratio of 2-methyl-2,4-pentanediol (MPD) to isopropanol (IPA) ⁴¹. Based on ¹H-¹⁵N CP spectra, we estimate that ~80% of labile protons are exchanged with ²H.

Solid-State NMR Experiments

All experiments were conducted on a 600 MHz (14.1 T) Bruker Avance III HD spectrometer using a ¹H/¹³C/¹⁵N 3.2 mm MAS probe. ¹³C chemical shifts were referenced to the 38.48 ppm CH₂ peak of adamantane on the TMS scale ⁴² while ¹⁵N chemical shifts were referenced to the 118.57 ppm peak of Leu in f-MLF on the liquid ammonia scale. Experiments on f-MLF and GB1 were conducted at set temperatures of 293 K and 278 K, respectively. The MAS frequency was 20 kHz for all experiments. At this MAS frequency, the actual sample temperature was estimated to be 10-20 K higher than the set point due to frictional heating ⁴³.

¹³C and ¹⁵N rf field strengths ranged from 10 to 50 kHz for the ¹⁵N-¹³C CP period (Table 1), while the ¹H irradiation field strengths were 38-63 kHz for the ^PAINCP and ^PERSPIRATIONCP experiments but 90-100 kHz for the ^SPECIFICCP and ^RESPIRATIONCP experiments. The ¹H CW irradiation field strengths were swept from 25 to 83 kHz when optimizing ^PAINCP and ^PERSPIRATIONCP; the field strengths that gave rise to the most uniform transfer to all ¹³C nuclei while maintaining high spectral sensitivity were chosen for the final experiments. During ¹³C detection, ¹H TPPM decoupling was applied with an rf field of 83 kHz ⁴⁴. 2D ¹⁵N-¹³C correlation spectra of f-MLF were measured using a 12 ms ¹³C acquisition time and a maximum ¹⁵N evolution time of 7 ms, while the GB1 spectrum was measured with a maximum ¹⁵N evolution time of 10 ms.

Table 1.

Contact times, rf field strengths and rf powers used for four ¹⁵N-¹³C CP experiments.

Pulse sequence	Sample	Mixing time (ms)	Time-averaged rf fields (kHz)			Total rf energy (mJ)	Relative rf energy
			13C	15N	1H
PERSPIRATIONCP	f-MLF	5	5	5	57	248	1.0
PAINCP		2	50	50	63	717	2.9
SPECIFICCP + CORD		1.5, 60	10	30	100, 13.3	260	1.0
RESPIRATIONCP		5	45	5	100	655	2.6
PERSPIRATIONCP	f-MLF	5	5	5	38	76	1.0
PAINCP		2	25	25	48	204	2.7
RESPIRATIONCP		5	45	5	100	525	7.0
PERSPIRATIONCP	GB1	5	5	5	54	315	1.0
PAINCP		5	35	35	54	1245	4.0
SPECIFICCP + CORD		1.5, 100	12.5	32.5	90, 13.3	593	1.9
RESPIRATIONCP		5	45	5	90	874	2.8

Spectral Processing, Numerical Simulations and Structure Calculations

NMR spectra were processed in the TopSpin software (Bruker Biospin) using Gaussian window functions with parameters of LB = −15 Hz and GB = 0.05. Numerical simulations were conducted using the SpinEvolution software package ⁴⁵. Atomic coordinates and ¹³C isotropic chemical shifts for a fragment containing the Met Cα, Cβ, C’, N, H^N, Hα, Hβ1, and Hβ2 from the SSNMR structure of f-MLF ⁴⁶ were used to create an eight-spin system. Explicit coordinates and chemical shift anisotropy (CSA) parameters used in the simulations are listed in Table S1 ^{32, 47}. Simulated data was processed and analyzed in MATLAB (MathWorks, Natick, MA). GB1 structure calculations were performed using the CYANA software ⁴⁸. A total of 100 conformers were created, each with 35,000 (φ, ψ) torsion angle steps. The ten conformers with the lowest target function were included in the final ensemble.

Results and Discussion

Fig. 1 shows the ¹⁵N-¹³C CP schemes incorporated into 2D correlation pulse sequences. The most commonly used ¹³C, ¹⁵N and ¹H rf field strengths for the ¹⁵N-¹³C CP period are indicated. The ^SPECIFICCP sequence requires CW irradiation on all three channels, including strong ¹H decoupling, to achieve efficient ¹⁵N-¹³C transfer. The ^PAINCP pulse sequence uses moderate ¹H rf fields but requires stronger rf fields for ¹⁵N and ¹³C compared to ^SPECIFICCP. The ^RESPIRATIONCP sequence requires strong ¹H decoupling, but only employs ¹⁵N pulses at the rotor echoes while the ¹³C channel employs both rotor-echo pulses and CW irradiation at a field strength of twice the MAS frequency. In comparison, the ^PERSPIRATIONCP sequence uses the lowest rf energy: the ¹H irradiation is slightly milder than ^PAINCP and only rotor-echo pulses are applied on the ¹³C and ¹⁵N channels.

Figure 1.

¹⁵N-¹³C polarization transfer pulse sequences compared in this study. (a) ¹⁵N-¹³C ^SPECIFICCP followed by ¹³C-¹³C spin diffusion by CORD. (b) ^PAINCP. (c) ^RESPIRATIONCP, where simultaneous short ¹³C and ¹⁵N pulses at rotor echoes are interspersed with phase-alternating ¹³C recoupling pulses during the rotor period with ω₁ = 2ω_r. (d) ^PERSPIRATIONCP sequence, where simultaneous ¹³C and ¹⁵N pulses are applied on the rotor echoes. Typical rf field strengths for the ¹⁵N-¹³C CP block that lead to high-efficiency polarization transfer are indicated.

Since ^PERSPIRATIONCP scheme is an amalgam of the ^PAINCP and ^RESPIRATIONCP schemes, we first summarize the mechanisms of polarization transfer by these two techniques. The ^RESPIRATIONCP first-order average Hamiltonian under the condition of ¹³C and ¹⁵N 90˚ rotor-echo pulses and ¹³C recoupling field strength of ω₁ = 2ω_r is ${\overline{\tilde{H}}}_D^{(1)}=\left(4b_{IS}∕3\sqrt{2}\right)\sin 2\mathrm{\beta }\cos \gamma \left({\mathit{I}}_y{\mathit{S}}_z-{\mathit{I}}_z{\mathit{S}}_y\right)+\left(b_{IS}∕2\sqrt{2}\right){\sin }^2\mathrm{\beta }\cos 2\gamma \left({\mathit{I}}_y{\mathit{S}}_y+{\mathit{I}}_z{\mathit{S}}_z\right)$, where b_IS is the dipolar coupling constant and (β, γ) specify the polar and azimuthal angles of the ¹⁵N-¹³C dipolar vector in the rotor-fixed frame ³⁷. The coefficients in front of the two spin-operator terms correspond to the first- and second-order Fourier components of the dipolar couplings, thus ^RESPIRATIONCP provides more complete orientational averaging of the dipolar coupling than γ-encoded recoupling sequences and hence is more efficient ⁴⁹. In comparison, zero-quantum ^PAINCP relies on trilinear terms of the form N C^±H_z for ¹⁵N-¹³C polarization transfer ^32-33, while the PAR mechanism that is also active during the CP contact time involves a similar trilinear term $C_1{C}_2^{\pm }{H}_z$ for ¹³C-¹³C coherence transfer ³⁴. By using second-order cross terms between the ¹³C-¹H and ¹⁵N-¹H dipolar couplings instead of direct ¹⁵N-¹³C and ¹³C-¹³C dipolar couplings, ^PAINCP allows polarization transfer over longer distances, and significantly avoids the dipolar truncation problem, which is present in first-order homonuclear recoupling sequences due to non-commuting terms in the effective Hamiltonians ⁵⁰. Dipolar truncation can also be present in heteronuclear recoupling sequences with longitudinal average Hamiltonians such as REDOR, where non-commuting terms arise when the recoupling pulses take up significant fractions of the rotor period.

^PERSPIRATIONCP results in efficient long-range ¹⁵N-¹³C transfer using mild rf fields

We compared the performance of these four ¹⁵N-¹³C CP techniques using uniformly ¹³C, ¹⁵N-labeled tripeptide formyl-Met-Leu-Phe (f-MLF) ²⁷ and GB1 ⁴⁰ (Fig. 2). We monitor two quantitative features of the spectra: the overall sensitivity of a ¹³C spectrum and the relative intensities of the Cα, CO, and aliphatic sidechain regions. We measure the overall sensitivity as the integrated intensities of the whole ¹⁵N-transferred ¹³C spectrum relative to the integrated intensity of a ¹H-¹³C CP spectrum. On the anhydrous f-MLF, the four ¹⁵N-¹³C CP sequences gave sensitivities of 2-7% relative to ¹H-¹³C CP (Fig. 2a-e). This percentage range is expected based on the typical ¹H, ¹³C and ¹⁵N spin densities in proteins. f-MLF contains 32 protons, 3 nitrogens, and 20 carbons. Thus, the ¹⁵N-transferred ¹³C magnetization, which results exclusively from the three ¹⁵N spins, carry 3·32/(32 + 3)= 2.7 units of ¹H magnetization. Assuming equal distribution of the magnetization between ¹⁵N and ¹³C, the total ¹³C magnetization after ¹⁵N-¹³C CP should then be 1.35 units of ¹H magnetization. In comparison, the ¹³C magnetization after ¹H-¹³C CP results from all 32 protons, which amounts to 20·32/(32 + 20)= 12.3 units of ¹H magnetization. Therefore, the maximum theoretical efficiency of ¹⁵N-¹³C CP is expected to be ~11% that of ¹H-¹³C CP when normalized by the full ¹³C spectral intensity. This differs from the commonly used normalization by Cα intensities, which gives higher numerical values of efficiencies in the literature.

Figure 2.

¹³C spectra of f-MLF (a-e) and GB1 (f-j) measured using difference CP schemes. All spectra were measured under 20 kHz MAS. Indicated for each spectrum are the ¹³C/¹⁵N/¹H rf field strengths for the CP period, the ¹⁵N-¹³C CP contact time, ¹³C carrier frequencies (arrows), and relative total spectral intensities. (a) ^PERSPIRATIONCP spectra of f-MLF, measured with ¹³C/¹⁵N/¹H rf fields of 50/50/57 kHz and 25/25/38 kHz. (b) ^PAINCP spectra of f-MLF, measured with two strong and weak rf field strengths at two different ¹³C carrier frequencies. (c) ^RESPIRATIONCP spectra of f-MLF. (d) N-Cα ^SPECIFICCP spectra of f-MLF, measured with rf fields of 10/30/100 kHz with and without ¹³C-¹³C mixing. (e) ¹H-¹³C CP spectrum measured using 70-100% ramp on ¹³C for 0.75 ms. (f) ¹⁵N-¹³C ^PERSPIRATIONCP spectrum of GB1. (g) ¹⁵N-¹³C ^PAINCP spectrum of GB1. (h) ¹⁵N-¹³C ^RESPIRATIONCP spectrum of GB1. (i) N-Cα ^SPECIFICCP spectra of GB1 with and without ¹³C-¹³C mixing. (j) ¹H-¹³C CP spectrum of GB1 using 70-100% ramp on ¹³C for 0.75 ms.

^SPECIFICCP combined with 60 ms ¹³C spin diffusion by CORD ⁵¹ gave rise to the highest overall sensitivity among the four CP sequences for f-MLF. This high sensitivity can be attributed to the strong ¹H decoupling field of 100 kHz, which was more than 3-times larger than the ¹³C and ¹⁵N rf field strengths. In addition, the relatively short ¹⁵N-¹³C CP contact time of 1.5 ms minimized ¹³C and ¹⁵N T_1ρ relaxation while still being sufficient for one-bond transfer in N-Cα and N-CO pairs. The other three CP schemes gave lower total sensitivities, which were 2.1-3.8% for ^PAINCP and 3.9-6.0% for ^PERSPIRATIONCP and ^RESPIRATIONCP.

While ^SPECIFICCP has high total sensitivity, polarization transfer to sidechains carbons does not occur without ¹³C mixing. When a CORD mixing time of 60 ms was added, the spectrum shows decreasing intensities toward the methyl region (Fig. 2d), consistent with the known attenuation of ¹³C spin diffusion with increasing chemical shift difference. ^RESPIRATIONCP gave the lowest polarization transfer to sidechains among the four CP methods (Fig. 2c). ^PAINCP gave higher magnetization transfer to sidechains, but the performance is significantly worsened at lower ¹³C, ¹⁵N and ¹H rf field strengths of 25, 25, and 48 kHz, respectively (Fig. 2b). In comparison, ^PERSPIRATIONCP exhibits efficient magnetization transfer to sidechain carbons at both strong and weak rf powers as well as higher overall sensitivity compared to ^PAINCP.

These ¹⁵N-¹³C polarization transfer trends are qualitatively reproduced in hydrated GB1 (Fig. 2f-j), whose ¹³C and ¹⁵N T_1ρ relaxation times are shorter than those of anhydrous f-MLF ^{27, 46}. We used the same ¹⁵N and ¹³C rf field strengths of 35 kHz, a contact time of 5 ms, and a ¹³C carrier frequency of 42 ppm for all but the ^SPECIFICCP experiment. ^PERSPIRATIONCP gave higher-sensitivity spectra and more efficient polarization transfer to sidechain carbons than ^RESPIRATIONCP and ^SPECIFICCP followed by ¹³C mixing. ^PAINCP at similar rf field strengths gave the highest polarization transfer to the sidechains, but had low overall sensitivity. ^PERSPIRATIONCP only underperformed in one aspect, which is the transfer to Thr Cβ and Cγ and to Ala Cβ, suggesting that the sequence has a stronger dependence on resonance offset than ^PAINCP. The carrier dependence of these CP experiments is further investigated below by simulations.

The f-MLF data also show how these ¹⁵N-¹³C CP sequences depend on the rf field strengths. ^RESPIRATIONCP showed higher sensitivity under low-power (25 kHz) rotor-echo pulses than high-power (50 kHz) pulses, indicating that CP leakage from ¹³C to ¹H under high-power irradiation is detrimental to ¹⁵N-¹³C polarization transfer. For ^PAINCP, low-power irradiation resulted in more band-selective polarization transfer as well as lower overall sensitivity (55%) than high-power irradiation. We attribute this finding to faster ¹³C and ¹⁵N T_1ρ relaxation under weaker spin lock fields as well as narrower matching conditions. ^PERSPIRATIONCP showed efficient polarization transfer to sidechains under both low-power and high-power irradiation, but the high-power condition gave 40% higher intensity.

Fig. 3 plots the measured ¹⁵N-¹³C polarization transfer intensities for the Met signals of f-MLF as a function of contact time for ^PERSPIRATIONCP, ^PAINCP, and ^RESPIRATIONCP. The three sequences show distinct dependences on internuclear distances, rf field strengths, and contact times for maximum polarization transfer. ^RESPIRATIONCP shows the strongest distance dependence: for example, one-bond N-Cα and N-CO transfer reached maximum intensity at ~4 ms, while two-bond N-Cβ transfer reached maximum at 6-7 ms. ^PAINCP exhibits a more moderate distance dependence. Under the strong rf condition, maximum one-bond transfer is achieved at ~1.5 ms while two-bond N-Cβ transfer reached a plateau at ~3 ms. Weak rf fields significantly suppressed the extent of polarization transfer for ^PAINCP. ^PERSPIRATIONCP shows the weakest distance dependence: all carbons reached similar magnitudes of maximum transfer and at similar contact times of about 6-8 ms.

Figure 3.

Experimental ¹⁵N-¹³C polarization transfer curves of f-MLF as a function of CP contact time. (a) ^PERSPIRATIONCP. (b) ^PAINCP. (c) ^RESPIRATIONCP. Left column shows data measured using low rf field strengths while the right column shows data measured using strong rf fields. The ¹³C carrier frequency was 37.5 ppm for the ^PERSPIRATIONCP data and the low-power ^PAINCP data, and 100 ppm for the other data. The ¹³C, ¹⁵N and ¹H rf field strengths during ¹⁵N-¹³C CP are given in the individual panels.

To further understand the spin dynamics of ^PERSPIRATIONCP, we simulated the CP buildup curves using an eight-spin system that corresponds to the Met residue in f-MLF (Fig. 4). These simulations reproduce the experimentally measured polarization transfer profiles, and moreover give insight into the mechanism of transfer. ^PERSPIRATIONCP has relatively uniform transfer rates for all carbons. For both ^PERSPIRATIONCP and ^PAINCP, the polarization transfer is unchanged when ¹⁵N-¹³C dipolar couplings are turned off, but no transfer occurs when ¹³C-¹H and ¹⁵N-¹H dipolar couplings are turned off (Fig. 4c, d). Therefore, ^PERSPIRATIONCP, like ^PAINCP ^{32, 34}, operates through a ¹H-assisted mechanism. The main difference between these two sequences is that when ¹³C-¹³C and ¹H-¹H dipolar couplings are turned off, N-Cβ transfer became much more efficient in the ^PERSPIRATIONCP experiment while unchanged in the ^PAINCP experiment. In contrast, ^RESPIRATIONCP transfer shows strong distance dependence, and the transfer is suppressed when ¹⁵N-¹³C dipolar couplings are turned off but speeded up when ¹H-¹⁵N and ¹H-¹³C dipolar couplings are turned off. These results confirm the first-order nature of the ^RESPIRATIONCP sequence.

Figure 4.

Simulated ¹⁵N-¹³C polarization transfer efficiencies as a function of contact time for ^PERSPIRATIONCP, ^PAINCP, and ^RESPIRATIONCP sequences. (a) An eight-spin system containing Cα, Cβ, C’, N, H_N, H_Cα, H_Cβ1, and H_Cβ2 used in the simulations and comparison of N-Cα and N-Cβ CP transfer curves for the three CP sequences. (b-d) Dependence of the N-Cα and N-Cβ polarization transfer efficiency on C-N, N-H, C-H dipolar couplings and C-C and H-H dipolar couplings for the (b) ^PERSPIRATIONCP, (c) ^PAINCP, and (d) ^RESPIRATIONCP experiments. ^PERSPIRATIONCP and ^PAINCP do not require ¹⁵N-¹³C dipolar couplings but require ¹³C-¹H and ¹⁵N-¹H dipolar couplings.

^PERSPIRATIONCP is optimal with 90˚ pulses and with the ¹³C carrier in the aliphatic region

^RESPIRATIONCP is relatively insensitive to the pulse flip angles and allows 5-175˚ pulses to be used on the rotor echoes. To investigate how ^PERSPIRATIONCP depends on the pulse flip angles, we varied the ¹³C and ¹⁵N pulse lengths from 60˚ to 360˚ using 50 kHz rf fields on f-MLF. We also tested longer pulses up to a full rotor period under 20 kHz MAS, which corresponds to a 900˚ flip angle. Similar tests were conducted for GB1, but using an rf field of 35 kHz for both ¹³C and ¹⁵N and varying the pulse flip angles from 60˚ up to a rotor period. Fig. 5 shows that the highest polarization transfer is achieved for 90˚ pulses. Slightly larger flip angles (120˚) enhance the signals of aliphatic sidechain peaks such as Leu Cδ2 (19.6 ppm) in f-MLF and Thr Cγ (16-21 ppm) in GB1 while slightly smaller flip angles (60°) enhance the signal of carbonyl peaks. 360˚ pulses quenched polarization transfer, while 180˚ pulses performed poorly for GB1 but still gave some intensities for f-MLF. Numerical simulations (Fig. 6a, Fig. S1) confirm these observations, showing maximum polarization transfer at 90˚ and vanishing transfer at integer multiples of 180°. Simulated pulses slightly shorter than 90° favor transfer to the carbonyl peak at 172 ppm, while pulses slightly longer than 90° favor aliphatic sidechain peaks. Because a significant range of flip angles can yield good overall transfer (75-120°), ^PERSPIRATIONCP is insensitive to B₁ inhomogeneity. Finally, the width of the null is wider at 360˚ than at 180˚ and 540˚, consistent with the experimental data. Further simulations indicate that it is the flip angle of the rotor-echo pulses rather than rf field matching that dictates polarization transfer (Fig. S2). Therefore, there is considerable freedom in setting up experiments when the ¹⁵N rf field strengths are more limited than ¹³C, as is often the case in triple-resonance MAS probes.

Figure 5.

Dependence of ^PERSPIRATIONCP polarization transfer on the ¹³C and ¹⁵N pulse flip angles. (a) f-MLF data. (b) GB1 data. Both the flip angle and the pulse fraction of the rotor period are indicated. The ¹³C/¹⁵N/¹H rf field strengths for ¹⁵N-¹³C CP were 50/50/57 kHz for MLF and 35/35/54 kHz for GB1. The ¹³C carrier frequency was 37.5 ppm for f-MLF and 42 ppm for GB1.

Figure 6.

Simulated dependences of ¹⁵N-¹³C polarization transfer efficiencies on pulse flip angle and ¹³C carrier frequency. (a) ^PERSPIRATIONCP efficiency as a function of the pulse flip angle. The fraction of the rotor period occupied by the pulses is shown on the top x-axis. (b) ^PERSPIRATIONCP efficiency as a function of ¹³C carrier frequency. (c) ^PAINCP efficiency as a function of ¹³C carrier frequency. All simulations used a 5 ms CP contact time.

The isotropic chemical shift evolution during the delays in the ^PERSPIRATIONCP sequence is expected to cause a stronger offset dependence than the spin-lock based ^PAINCP experiment. Indeed, Fig. 7a shows that ^PERSPIRATIONCP gives optimal polarization transfer when the ¹³C carrier frequency is centered in the aliphatic region (near the Met Cγ peak for f-MLF) but almost no transfer when the carrier is placed at 100 ppm. Numerical simulations confirm these experimental results (Fig. 6b). In comparison, ^PAINCP gives optimal polarization transfer with the ¹³C carrier at 100 ppm (Fig. 7b, 6c). However, the carrier dependence of ^PAINCP is sensitive to the rf field strengths. With ¹³C/¹⁵N/¹H rf field strengths of 48.9/50/63 kHz, the ¹³C carrier dependence differ significantly from the carrier dependence when the ¹³C rf field is slightly changed to 50 kHz or 49.5 kHz (Fig. S3). For example, with 50 kHz ¹³C pulses, a carrier frequency of 100 ppm results in weak transfer to Cα and almost no transfer to Cβ or CO.

Figure 7.

Dependence of ^PERSPIRATIONCP and ^PAINCP on the ¹³C carrier frequency, which is denoted by an arrow below each spectrum. (a) ^PERSPIRATIONCP. (b) ^PAINCP. The ¹⁵N carrier frequency was fixed at 118.5 ppm.

To better understand the carrier dependence of ^PERSPIRATIONCP, we consider the first-order average Hamiltonian of the experiment. Approximating the ¹³C and ¹⁵N rotor-echo 90° pulses as δ-function pulses, the various nuclear spin Hamiltonians in the interaction frame of the ¹³C and ¹⁵N pulses are:

$$\begin{array}{cc}\hfill H_{t_0\to t_1}& ={\omega }_{NC}2N_z{C}_z+{\omega }_{CH}2C_z{H}_z+{\omega }_{NH}2N_z{H}_z+{\omega }_C{C}_z+{\omega }_N{N}_z+{\omega }_H{H}_z+{\omega }_{1,H}{H}_x\hfill \\ \hfill H_{t_1\to t_2}& ={\omega }_{NC}2N_y{C}_y+{\omega }_{CH}2C_y{H}_z+{\omega }_{NH}2N_y{H}_z+{\omega }_C{C}_y+{\omega }_N{N}_y+{\omega }_H{H}_z+{\omega }_{1,H}{H}_x\hfill \\ \hfill H_{t_2\to t_3}& ={\omega }_{NC}2N_z{C}_z-{\omega }_{CH}2C_z{H}_z-{\omega }_{NH}2N_z{H}_z-{\omega }_C{C}_z-{\omega }_N{N}_z+{\omega }_H{H}_z+{\omega }_{1,H}{H}_x\hfill \\ \hfill H_{t_3\to t_4}& ={\omega }_{NC}2N_y{C}_y-{\omega }_{CH}2C_y{H}_z-{\omega }_{NH}2N_y{H}_z-{\omega }_C{C}_y-{\omega }_N{N}_y+{\omega }_H{H}_z+{\omega }_{1,H}{H}_x\hfill \end{array}$$ (1)

The spin interactions in the above Hamiltonians correspond to, from left to right, ¹⁵N-¹³C dipolar coupling, ¹³C-¹H dipolar coupling, ¹⁵N-¹H dipolar coupling, ¹³C chemical shift, ¹⁵N chemical shift, ¹H chemical shift, and the ¹H rf Hamiltonian. The pulse sequence is cyclic for the least common multiple of 4τ_r and 2π/ω_{1, H}. When ¹³C and ¹⁵N spins are on resonance, the first-order average Hamiltonians for all interactions, calculated in the interaction frame of the ¹H rf pulse, can be shown to be zero ⁵²:

$${\overline{\tilde{H}}}_{D,NC}^{(0)}={\overline{\tilde{H}}}_{D,CH}^{(0)}={\overline{\tilde{H}}}_{D,NH}^{(0)}={\overline{\tilde{H}}}_{CS,C}^{(0)}={\overline{\tilde{H}}}_{CS,N}^{(0)}={\overline{\tilde{H}}}_{CS,H}^{(0)}=0$$ (2)

This averaging of the first-order average Hamiltonians is expected for a second-order recoupling technique. However, ¹³C chemical shift offset interferes with this averaging. For example, for a 5-kHz off-resonance ¹³C spin, at 20 kHz MAS, after one rotor period, the ¹³C spin will have precessed by 90°, thus making the three spin interactions that are linear with the ¹³C spin operator non-vanishing. On the other hand, ¹³C spins that are 20 kHz off resonance will have precessed for 360˚ after one rotor period and thus will behave as if they were on resonance. Therefore, the ^PERSPIRATIONCP sequence should exhibit an offset dependence that is related to the MAS frequency. This is seen in both experiments and simulations. In the f-MLF and GB1 ^PERSPIRATIONCP spectra in Fig. 2a, f, which were measured with the ¹³C carrier at ~40 ppm, near-resonance aliphatic ¹³C signals as well as ¹³CO signals that are ~130 ppm or ~20 kHz off resonance both show high intensities, while the aromatic ¹³C signals, which are ~90 ppm (or 13.5 kHz) off resonance, are suppressed. For the same reason, Thr Cβ and Cγ2 and Ala Cβ signals, which lie at the edges of the aliphatic region, ~3.8 kHz off resonance, show lower transfer efficiencies than near-resonance aliphatic ¹³C signals. Fig. 6b shows simulated ¹⁵N-¹³C transfer efficiencies as a function of the ¹³C carrier frequency. With the carrier in the aliphatic region, efficient transfer to ¹³C signals within ±3 kHz of the carrier and to the CO signals is observed. An identical band of carrier frequencies that exhibit high transfer efficiencies is found in the carbonyl region, which is ~20 kHz away from the Cα and Cβ chemical shifts on a 600 MHz spectrometer.

Inter-residue cross peaks are readily observed in 2D ¹⁵N-¹³C ^PERSPIRATIONCP correlation spectra

We compared the 2D ¹⁵N-¹³C correlation spectra of f-MLF (Fig. 8) measured using the four CP experiments. ^SPECIFICCP followed by 60 ms ¹³C CORD spin diffusion ⁵¹ gave rise to the expected intra-residue and inter-residue cross peaks in the 2D NCACX and NCOCX spectra, but with this mixing time, the cross peak intensities of Cγ and other carbons down the sidechains drop off significantly (Fig. 8a). ^RESPIRATIONCP gave strong one-bond N-Cα and N-CO cross peaks but weaker cross peaks to sidechain carbons than ^SPECIFICCP, consistent with the exclusive dependence of ^RESPIRATIONCP on ¹⁵N-¹³C dipolar couplings. The 2 ms ^PAINCP spectrum showed stronger long-range intra- and inter-residue cross peak intensities than both ^SPECIFICCP and ^RESPIRATIONCP, consistent with its proton-assisted recoupling mechanism. In particular, cross peaks between the isolated Met Cε and the Met and Phe ¹⁵N are observed (Fig. 8c). The 5 ms ^PERSPIRATIONCP 2D spectrum showed higher cross peak intensities for Cβ and Cγ carbons than the 2 ms ^PAINCP spectrum, even though the total rf energy in 5 ms ^PERSPIRATIONCP is only a third of the rf energy in 2 ms ^PAINCP (Table 1). The only cross peaks that are weaker in the ^PERSPIRATIONCP spectrum are the Met Cε cross peaks, which can be attributed to the offset dependence of ^PERSPIRATIONCP. With a contact time of 9 ms, the ^PERSPIRATIONCP spectral intensities are nearly fully equilibrated and are much higher than the ^PAINCP intensities.

Figure 8.

2D ¹⁵N-¹³C correlation spectra of f-MLF measured using the four CP schemes. (a) ^SPECIFICCP NCACX and NCOCX spectra, measured with a 1.5 ms contact time, ¹³C/¹⁵N/¹H rf field strengths of 10/30/100 kHz and 60 ms ¹³C-¹³C mixing. (b) ^RESPIRATIONCP spectrum, measured with a 5 ms contact time and ¹³C/¹⁵N/¹H field strengths of 50/50/100 kHz. (c) ^PAINCP spectrum, measured with a 2 ms contact time and ¹³C/¹⁵N/¹H field strengths of 50/50/63 kHz. (d) ^PERSPIRATIONCP spectra, measured with contact times of 5 ms and 9 ms and ¹³C/¹⁵N/¹H rf field strengths of 50/50/57 kHz.

The 2D spectra of GB1 (Fig. 9, 10a) reproduce the trends observed for f-MLF. The 5 ms ^PERSPIRATIONCP spectrum gives more long-range ¹⁵N-¹³C cross peaks than the sum of the NCACX and NCOCX 2D spectra measured with 100 ms ¹³C spin diffusion mixing. For example, A48N-K50Cδ and F30N-V29Cβ cross peaks, which correspond to 5 Å distances, are observed in the ^PERSPIRATIONCP spectrum but are absent in the sum of the 2D NCACX and NCOCX spectrum (Fig. 9d). The 5.0 ms 2D ^PERSPIRATIONCP spectrum used rotor-echo pulses of 112.5° rather than 90° to broaden the bandwidth of polarization transfer in the aliphatic region and to enhance the Thr Cβ (72-62 ppm), Thr Cγ₂ and Ala Cβ (21-16 ppm) intensities. Increasing the ^PERSPIRATIONCP transfer time to 10 ms gave rise to additional cross peaks (Fig. 10a), many of which correspond to longer distances than in the 5 ms spectrum. For example, cross peaks assigned to L12N-N8Cα, T16N-I6Cβ, V54N-L5Cα, and E56N-K10Cε correspond to distances of 6.5 – 7.0 Å.

Figure 9.

2D ¹⁵N-¹³C correlation spectra of GB1 measured using (a) 2D NCΑCX (blue) and NCOCX (red) experiments and (b) 2D NCCX ^PERSPIRATIONCP experiment with a 5 ms contact time. (c) Representative ¹⁵N cross sections from the three spectra. The sum of the 2D NCACX and NCOCX spectra (green) has lower intensities than the ^PERSPIRATIONCP spectrum after taking into account the 2-fold difference in the number of scans. (d) Selected region of the 2D ^PERSPIRATIONCP spectra and the sum of the ^SPECIFICCP spectra. The ^PERSPIRATIONCP spectrum shows several intra- and inter-residue cross peaks for ~5 Å distances, which are not observed in the sum of the two ^SPECIFICCP spectra.

Figure 10.

(a) Selected region from the 10 ms ^PERSPIRATIONCP ¹⁵N-¹³C correlation spectra of GB1. Numerous medium and long-range cross peaks are observed. (b) GB1 structure calculated using ¹⁵N-¹³C distance constraints from the ^PERSPIRATIONCP spectra. (c) High-resolution SSNMR structure of GB1 (PDB: 2LGI). Dashed lines indicate the residue pairs for which medium and long-range cross peaks were observed in the ^PERSPIRATIONCP spectra.

^PERSPIRATIONCP yields many distance constraints for protein structure determination

To investigate the utility of ^PERSPIRATIONCP for protein structure determination, we calculated the structure of GB1 using only distance restraints from the 5 ms and 10 ms ^PERSPIRATIONCP 2D ¹⁵N-¹³C correlation spectra. A total of 32 medium- and long-range distance constraints were assigned from these two spectra, along with 81 sequential cross peaks and 109 intra-residue cross peaks (Table 2). These distance constraints supplement the (φ, ψ) torsion angles predicted from assigned chemical shifts ⁵³. We set the upper distance limits to 5 Å for all cross peaks detected in the 5 ms ^PERSPIRATIONCP spectrum and 7 Å for additional cross peaks observed in the 10 ms spectrum. These upper limits are estimated based on comparison with the ^PAINCP data in the literature ^32-33 and by calibrating with intra-residue ¹⁵N cross peaks with sidechain carbons with approximately known distances. The ensemble of ten lowest-energy structures calculated using CYANA shows a backbone RMSD of 1.4±0.3 Å and a heavy-atom RMSD of 2.1±0.3 Å. The structure correctly recapitulates the known three-dimensional fold of GB1 and the relative positions and orientations of the α-helix, β-strands, and loops (Fig. 10b). Compared to the high-resolution SSNMR structure of GB1 (PDB: 2LGI) ⁵⁴ (Fig. 10c), the ^PERSPIRATIONCP structure has a backbone RMSD of 2.0 Å and a heavy-atom RMSD of 3.0 Å. This agreement is remarkably good considering that we only used the ¹⁵N-¹³C distance restraints from two ^PERSPIRATIONCP spectra. The main deviation of the ^PERSPIRATIONCP structure from the high-resolution structure is the separation between β-strands 1 and 2, which is a direct consequence of the relative sparseness of ¹⁵N-¹³C constraints between these two strands. Thus, the resolution and accuracy of the calculated structure can be easily improved by measuring longer mixing-time ¹⁵N-¹³C ^PERSPIRATIONCP spectra, and by adding ¹³C-¹³C distance restraints, which are readily measurable from 2D ¹³C-¹³C correlation experiments. In arriving at this GB1 structure, we also tested alternative distance upper limits for the two mixing times, such as 6 Å and 8 Å, or 4 Å and 6 Å. These combinations gave structures with either larger RMSDs for the ensemble or larger deviations from the high-resolution structure. The structure calculated with the 5 Å and 7 Å upper limits has the lowest RMSDs for the ensemble, the best agreement with the high-resolution structure, and the lowest constraint violation. These comparisons thus calibrate the maximum ¹⁵N-¹³C distances observable with 5 ms and 10 ms ^PERSPIRATIONCP to be 5 Å and 7 Å.

Table 2.

¹⁵N-¹³C distance constraints obtained from ^PERSPIRATIONCP spectra used for GB1 structure calculation.

PERSPIRATIONCP time (ms)	Intra-residue constraints	Sequential constraints ( ∣i-j∣ = 1 )	Medium-Range constraints (2 ≤ ∣i-j∣ ≤ 4)	Long-Range Constraints (∣i-j∣ ≥ 5)
5	101	69	9	8
10	8	12	2	13

Conclusions

The above experiments and simulations show that ^PERSPIRATIONCP is an rf-efficient pulsed variant of ^PAINCP that operates by a third-spin proton-assisted recoupling mechanism. Both techniques combine ¹⁵N-¹³C polarization transfer with ¹³C-¹³C mixing, and have an attenuated dependence on ¹⁵N-¹³C distances compared to first-order recoupling sequences such as ^SPECIFICCP and ^RESPIRATIONCP. While this weaker dependence decreases the accuracy of individual distances, it massively increases the number of observable cross peaks, thus ultimately improving the ability for structure determination. Because ^PERSPIRATIONCP requires only rotor-echo 90˚ pulses on ¹⁵N and ¹³C and moderate CW irradiation on ¹H, it uses 3-7 times less rf energy compared to ^PAINCP and ^RESPIRATIONCP, and up to 2-fold less rf energy than ^SPECIFICCP (Table 1). Even a 9 ms ^PERSPIRATIONCP experiment uses only 60% of the rf energy compared to 2 ms ^PAINCP for similar ¹³C/¹⁵N/¹H rf field strengths of ~50/50/60 kHz. In addition to rf efficiency, ^PERSPIRATIONCP shows higher ¹⁵N-¹³C polarization transfer efficiency than ^PAINCP, especially at low rf field strengths. The rotor-echo pulse flip angles in ^PERSPIRATIONCP can deviate from 90˚ by a moderate amount to compensate for the increased offset dependence of the technique due to the windowed delays.

2D ¹⁵N-¹³C ^PERSPIRATIONCP spectra of GB1 show higher intensities than the sum of the NCACX and NCOCX spectra measured with ^SPECIFICCP. The distance constraints measured from only two ^PERSPIRATIONCP spectra were sufficient to yield a GB1 structure with only a 2.0 Å backbone RMSD from the high-resolution structure. Therefore, ^PERSPIRATIONCP is a robust and rf-efficient alternative to the existing CP pulse sequences for resonance assignment and structure determination of proteins, and should be useful for measuring long-range intramolecular ¹⁵N-¹³C distance restraints in uniformly labeled proteins and long-range intermolecular distance restraints in mixed labeled proteins.