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Multi-dimensional Fourier Transform (FT) NMR spectroscopy is broadly used in chemistry and spectral resolution is pivotal for its performance. Phase-sensitive, pure absorption mode signal detection[1a,2] is required for achieving high spectral resolution since an absorptive signal at frequency Ω0 rapidly decays proportional to 1/(Ω0-Ω)2 while a dispersive signal slowly decays proportional to 1/(Ω0-Ω). Hence, a variety of approaches were developed to accomplish pure absorption mode signal detection.[1a,2] Moreover, by use of techniques such as spin-lock purge pulses, phase cycling,[1a] pulsed magnetic field gradients, or z-filters, radio-frequency (r.f.) pulse sequences for phase-sensitive detection are designed to avoid ‘mixed’ phases, so that only phase errors remain which can then be removed by a zero- or first-order phase correction.
A limitation of the hitherto developed approaches[1a,2] arises whenever signals exhibit phase errors which cannot be removed by a zero- or first-order correction, or when aliasing limits[2a] first-order phase corrections to 0° or 180°. Due to experimental imperfections, such phase errors inevitably accumulate to some degree during the execution of radio-frequency (r.f.) pulse sequences[1a,2] which results in superposition of the desired absorptive signals with dispersive signals of varying relative intensity not linearly correlated with Ω0. This not only exacerbates peak identification, but also reduces the signal-to-noise (S/N) and shifts the peak maxima. In turn, this reduces the precision of chemical shift measurements and impedes spectral assignment based on matching of shifts.
Furthermore, phase-sensitive, pure absorption mode detection of signals encoding linear combinations of chemical shifts relies on joint sampling of chemical shifts as in Reduced-dimensionality (RD) NMR and its generalization, G-matrix Fourier transform (GFT) projection NMR. The latter is broadly employed, in particular also for projection-reconstruction (PR), high-resolution iterative frequency identification (HIFI), and automated projection (APSY) NMR. Importantly, the joint sampling of chemical shifts entangles phase errors from several shift evolution periods. Hence, zero- and first-order phase corrections cannot be applied in the GFT dimension,[7h] which further accentuates the need for approaches which are capable of eliminating (residual) dispersive components.
Here we describe novel, generally applicable acquisition schemes for phase-sensitive detection of clean absorption mode signals devoid of dispersive components. Those were established by generalizing mirrored time domain sampling (MS) to ‘phase shifted MS’ (PMS). MS was originally contemplated for absolute-value 2D resolved NMR spectroscopy and was later introduced for phase-sensitive measurement of spin-spin couplings in J-GFT NMR. [7h] In general, the evolution of chemical shift α can be sampled as c±n: = cos(±αt+ nπ/4+Φ), with ‘±’ indicating forward (‘+’) and backward (‘−’) sampling, n = 0,1,2 or 3 yielding a phase shift by nπ/4, and Φ representing the phase error giving rise to a dispersive component.
Forward sampling with n = 0 and 2 results in ‘States’ quadrature detection,[1a,2] which is denoted (c+0,c+2)-sampling here and yields a signal S(t) cosΦ eiαt + sinΦ eiπ/2 eiαt. Corresponding backward (c−0,c−2)-sampling yields S(t) cosΦ eiαt − sinΦ eiπ/2 eiαt, so that addition of the two spectra [corresponding to ‘Dual States’ (c+0,c+2,c−0,c−2)-sampling] cancels the dispersive components (Supporting Information I.1). Thus, a clean absorption mode signal S(t) cosΦ eiαt is detected(Figure 1).
Forward sampling and backward sampling with n = 1 results in (c+1,c−1)-PMS, which yields S(t) cosΦ eiαt − sinΦ e−iαt (Supporting Information I.2), i.e., two absorptive signals are detected: the desired signal at frequency α with relative intensity cosΦ, and a quadrature image (‘quad’) peak at frequency −α with intensity sinΦ. (c+1,c−1)-PMS thus eliminates a dispersive component by transformation into an absorptive quad peak. Without phase correction, this results in clean absorption mode signals (Figure 1). Corresponding (c+3,c−3)-PMS sampling yields S(t) cosΦ eiαt + sinΦe−iαt, so that the quad peak is of opposite sign when compared with (c+1,c−1)-PMS. Addition of the two spectra cancels the quad peak (Figure 1), and such combined (c+1,c−1,c+3,c−3)-sampling is named dual PMS (DPMS).
Forward sampling with n = 0 and backward sampling with n = 2 results in (c+0,c−2)-PMS yielding S(t) cosΦ eiαt − sinΦ eiπ/2 e−iαt (Supporting Information I.3), i.e., the quad peak is dispersive. This feature allows one to distinguish genuine and quad peaks if required. In (c−0,c+2)-PMS, the quad peak is of opposite sign when compared with (c+0,c−2)-PMS, (i.e., S(t) cosΦ eiαt + sinΦ eiπ/2e−iαt. Thus, (c+0,c−2,c−0,c+2)-DPMS likewise enables cancellation of the quad peak yielding solely clean absorption mode signals.
PMS can be applied to an arbitrary number of indirect dimensions of a multi-dimensional experiment. For example, (c+1,c−1)-PMS of K+1 chemical shiftsα0, α1,…αK with phase errors Φ0, Φ1,…ΦK (Supporting Information I.4.1) yields a purely absorptive peak at (α0, α1,… αK) with relative intensity ΠKj=0 cosΦj, while the quad peak intensities are proportional to cosΦj for every +αj and to sinΦj for every −αj in the peak coordinates. PMS can likewise be applied to an arbitrary sub-set of the chemical shift evolution periods jointly sampled in GFT NMR. For example, joint (c+1,c−1)-PMS of K+1 chemical shiftsα0,α1,…αK (Supporting Information I.4.2) yields a peak at the desired linear combination of chemical shifts with relative intensity of ΠKj=0 cosΦj, while peaks located at different linear combinations of shifts exhibit intensities proportional to cosΦj for all αj for which the sign of the chemical shift in the linear combination does not change, and proportional to sinΦj for all αj for which the sign in the linear combination does change. Hence, PMS converts dispersive GFT NMR peak components into both quad and ‘cross-talk’ peaks. For a given sub-spectrum, the latter peaks are located at linear combinations of chemical shifts which are detected in the other sub-spectra. Furthermore, arbitrary combinations of time domain sampling schemes can be employed in multidimensional NMR, including GFT NMR (Supporting Information I.4.3).
Clean absorption mode data acquisition leads to a reduction of the signal maximum [and therefore the signal-to-noise ratio (S/N)] relative to a hypothetical absorptive signal by a factor of cosΦ (see above). It is therefore advantageous to employ the commonly used repertoire[1–5] of techniques to avoid phase corrections, so that only residual dispersive components have to be removed. For routine applications, however, the reduction in S/N is then hardly significant: assuming that residual phase errors are |Φ| < 15°, one obtains a reduction of < 3.4%. Moreover, the superposition of a dispersive component on an absorptive peak in a conventionally acquired spectrum likewise reduces the signal maximum. As a result, the actual loss for |Φ| < 15° is < 1.7% (Supporting Information II, Figure S1).
(c+1,c−1)-PMS and (c+3,c−3)-PMS are unique since they yield clean absorption mode spectra (Figure 1) with the same measurement time as is required for ‘States’ acquisition. Whenever the quad peaks (and cross talk peaks in GFT NMR), which exhibit a relative intensity proportional to sinΦ, emerge in otherwise empty spectral regions, they evidently do not interfere with spectral analysis and there is no need for their removal [when in doubt, (c+0,c−2)-PMS and (c−0,c+2)-PMS allows one to identify quad peaks since they are purely dispersive]. Furthermore, sensitivity limited data acquisition[6c] is often desirable (e.g., with an average S/N ~ 5). For |Φ| < 15°, sinΦ < 0.26 implies that quad and cross-talk peaks exhibit intensities ~1.25 times the noise level, so that they are within the noise.
Suppression of axial peaks and residual solvent peaks is routinely accomplished using a two-step phase cycle.[1a,2a] In particular when studying molecules which exhibit resonances close those of the solvent line (e.g. 1Hα resonances of proteins dissolved in 1H2O) such additional suppression of the solvent line is most often required. DPMS schemes can be readily concatenated with the two-step cycle (Supporting Information I.5), that is, DPMS spectra can be acquired with the same measurement as a conventional 2-step phase cycled NMR experiment. In solid state NMR,[2b] artifact suppression relies primarily on phase cycling, and such concatenation of (multiple) DPMS and phase cycles enables one to obtain clean absorption mode spectra without investment of additional spectrometer time.
NMR spectra were acquired for 13C,15N-labeled 8 kDa protein CaR178. First, (c+1,c−1)-, (c+0,c−2)-PMS, and corresponding DPMS was implemented and tested for 2D [13C,1H]-HSQC. The implementation of non-constant time ‘backward-sampling’ required introduction of an additional 180° 13C radio-frequency (r.f.) pulse (Supporting Information III, Figure S2). As theory predicts, PMS and DPMS remove dispersive components and yield clean absorption mode spectra(Figure S3)without a phase correction.
(c+1,c−1)-PMS and (c+1,c−1,c+3,c−3)-DPMS was then employed for simultaneous constant-time 2D [13Caliphatic/13Caromatic,1H]-HSQC in which aromatic signals are folded. Since frequency labeling was accomplished in a constant-time manner, no r.f. pulses had to be added to the pulse scheme. The phase errors of the folded aromatic signals cannot be corrected after conventional data acquisition, [1a] but are eliminated with PMS (Figures 2, S4).
Multiple (c+1,c−1,c+3,c−3)-DPMS was exemplified for 3D HC(C)H total correlation spectroscopy (TOCSY). The 13C–13C isotropic mixing introduces phase errors along ω1(13C) which cannot be entirely removed by existing techniques. Moreover, in hetero-nuclear resolved NMR spectra comprising 1H-1H planes with intense diagonal peaks [e.g. HC(C)H TOCSY], even small phase errors impede identification of cross peaks close to the diagonal. Since 1H and 13C frequency labeling was accomplished in a semi constant-time manner, no r.f. pulses had to be added to the pulse scheme. Comparison with the conventionally acquired spectrum shows elimination of dispersive components in both indirect dimensions (Figures 3, S5).
To exemplify multiple (c+1,c−1,c+3,c−3)-DPMS for GFT NMR, it was employed for (4,3)D CαβCα(CO)NHN[7b] in both the 13Cαβ and 13Cα shift evolution periods. Since frequency labeling was accomplished in a constant-time manner, [2,7b] no r.f. pulses had to be added to the pulse scheme. [7b] Comparison with standard GFT NMR shows elimination of dispersive components in the GFT-dimension (Figures 4, S6). Importantly, only PMS can eliminate entirely dispersive components in GFT-based projection NMR.[7–11]
Dispersive components shift peak maxima (Supporting Information II). For example, in routinely acquired (4,3)D CαβCα(CO)NHN,[7b] signals exhibit full widths at half height of ΔνFWHH ~140 Hz in the GFT dimension. Since phase errors up to about ±15° are observed, maxima are shifted by up to about ±10 Hz (~±0.07 ppm at 600 MHz 1H resonance frequency) and the precision of chemical shift measurements is reduced accordingly.
Clean absorption mode NMR spectra are most amenable to automated peak ‘picking’ and the resulting increased precision of shift measurements also increases the efficiency of automated resonance assignment of NMR spectra. This is because chemical shift matching tolerances can be reduced. Moreover, the enhanced spectral resolution promises to be of particular value for systems exhibiting very high chemical shift degeneracy such as (partially) unfolded or membrane proteins.
Taken together, clean absorption mode NMR data acquisition enables one to also remove dispersive components arising from phase errors which cannot be removed by a zero- or first-order phase correction. Hence, such data acquisition resolves a longstanding challenge of both conventional[1a,2] and GFT-based projection NMR,[7–11] and promises to broadly impact on NMR data acquisition protocols for science and engineering.
NMR spectra were acquired for 13C,15N-labeled 8 kDa protein CaR178, a target of the Northeast Structural Genomics Consortium (http://www.nesg.org), on a Varian INOVA 600 spectrometer equipped with a cryogenic probe at 25 °C, and processed as described in the Supporting Information (section IV).
This work was supported by NSF (MCB 0416899 and MCB 0817857) and NIH (P50 GM62413-01). We thank Drs. T. Acton and G. T. Montelione, Rutgers University, for providing the sample of protein CaR178.