1.1. Accelerating Multi-Dimensional NMR
Multi-dimensional NMR spectroscopy is an essential tool in chemistry and structural biology. Recent efforts to improve on the methodology target its main weaknesses: low sensitivity and long time requirements. Continuous innovations in NMR hardware (e.g. higher magnetic field strengths, cryogenically cooled probe circuits and preamplifiers,1 and the upcoming very promising hyper-polarization techniques2, 3) have alleviated the basic sensitivity bottleneck for many NMR applications. Given sufficient physical sensitivity, the time required for a multi-dimensional NMR experiment is mostly determined by two factors: 1) the number of indirect time increments, which grows exponentially with the number of dimensions and 2) the coherence selection process. Presently, there are a number of different approaches to reduce total experiment times by acquiring the same information in less time. Prominent examples are sparse-sampling techniques,4 single-scan multi-dimensional NMR,5 and relaxation optimization as, for example, in fast heteronuclear single quantum coherence (FHSQC) schemes.6
Our goal is improving the overall acquisition efficiency by reducing the total number of acquisitions required. At the same time information is retained, which is often discarded prematurely in today’s routine pulse sequences, either by gradient defocusing during evolution, or by linear combination during acquisition. We strive to increase the coherence selection efficiency in phase cycling7 based on concepts by Ivchenko et al.8 They obtained pure-phase 2D spectra of solids by different linear combinations of phase-shifted N- and P-type spectra derived from a single raw data set. Previously we used cogwheel multiplex-phase cycles in homonuclear 2D correlation spectra.9 Multiplex-quadrature detection (MQD) is introduced herein as a way to accelerate common multi-dimensional NMR experiments, in particular heteronuclear correlation experiments, utilizing the nested multiplex-phase cycling.
1.2. Quadrature Detection in the Indirect Dimensions
Quadrature detection in the indirect dimensions is an important prerequisite to obtain pure-phase spectra. It can usually be achieved either by the States method,10 that is, acquiring a pair of free induction decays (FID) with and without a relative 90° phase shift between the excitation and mixing blocks, or by acquiring separate echo and anti-echo FIDs (N/P-selection),11 with subsequent linear combination. Many variants of these schemes have been developed over time,11, 12 like time proportional phase incrementation (TPPI),13 States-TPPI,14 and echo/anti-echo (EA)-TPPI. Essentially they can all be traced back to one of the two basic schemes. The minimum total number of 1D FIDs, ntot, required to obtain a phase-sensitive N-dimensional NMR spectrum, is thus determined by the length of the basic phase cycle M and the numbers of points ni required to achieve the desired resolution in each indirect dimension as shown in Equation (1):
The factor 2N−1 is due to the quadrature detection requiring acquisition of one pair of FIDs (either sine and cosine modulated or echo and anti-echo) for each time increment in each indirect dimension.
Echo/anti-echo based schemes can be implemented easily by applying pulsed field gradients during evolution15 requiring only two FIDs per time increment but at the cost of irreversibly defocusing the complimentary component in each transient, that is, discarding 50 % of useful signal, thus losing ca. 30 % of the per scan signal-to-noise ratio. In the quest for ultimate sensitivity and efficiency we focus on generally applicable approaches and therefore exclude methods with gradients during evolution times. It is noteworthy, that in conventional implementations of phase-cycled experiments, such waste of potentially useful information is also common, since the FIDs from individual steps are often co-added immediately. Sensitivity improvement techniques as introduced by Kay et al.16 alleviate the sensitivity loss in experiments with gradients during evolution for some multi-dimensional heteronuclear experiments. But since the same modifications can also be applied to the corresponding phase-cycled correlation experiments,17 the MQD gain in per-scan sensitivity, as outlined below, can also be applied to these sensitivity improved experiments.
Typically multi-dimensional heteronuclear chemical-shift correlation experiments in NMR, like the ones most frequently used for bio-macromolecules, consist of an excitation block followed by a series of single-quantum coherence evolution periods connected by mixing sequences tailored to the specific information sought. Herein we focus on the common type of experiment, where multiple single-quantum evolution times occur. Apart from the specific requirements of the mixing blocks, the basic conventional phase cycle derives from a two-step phase alternation for each indirect dimension to suppress axial peaks, which adversely affect spectral quality even when pushed to the edges of the respective indirect dimensions by use of TPPI.13 A 180° phase change of the pulse or block preceding an evolution period is applied in concert with receiver phase inversion in order to suppress the pathway through coherence order zero, which causes axial peaks in the respective dimension, such as seen in cases of non-perfect 90° pulses or fast relaxation, for example, in paramagnetic proteins.18 As outlined above, to achieve quadrature separation usually, for each increment of each indirect dimension, two FIDs with 90° shifted relative phases of the coherence-transfer pulses are acquired separately. In the original TPPI method13 this doubling of recorded transients is masked by a virtual doubling of the spectral width, which however has the same overall effect of doubling the experiment duration. Thus, excluding gradient selection during evolution periods for the reasons given above, the minimum total number of acquired transients in an N-dimensional NMR experiment scales with 4N−1 (that is 2N−1 for the basic axial peak suppression phase cycle, which is included in M in Equation (1), times 2N−1, for the quadrature detection). The decrease of ntot described in Section 2 corresponds to reducing the factor 2N−1×M by merging coherence selection and quadrature separation in a multiplex manner.