Two-Dimensional Correlation NMR Spectroscopy

In most cases, for useful and reliable information to be extracted from NMR spectra, the individual resonances must be resolved. In one-dimensional (1D) NMR (direct detection only), the resolution of resonances relies on their chemical shift separation being larger than their line widths, which, for many types of samples, cannot always be the case. For proteins, it is common for hundreds of resonances of a given nuclear species (e.g.1_H, 13_C, 15_{N) to be present, leading to crowded spectra in which many resonances are likely to}

overlap. An indispensable tool for studying such samples is the two dimensional (2D) correlation experiment, in which resonances are dispersed across two frequency dimensions.28,116 _{Depending on the choice of frequency dimensions, this has the effect of}

decreasing the likelihood that resonances overlap, as well as, as we shall discuss, offering additional information compared to a 1D experiment.

A 2D correlation experiment consists of a minimum of 4 basic stages: preparation, evolution, mixing and detection (see Figure 2.7c). In the first instance, magnetisation (i.e. coherence) is generated on the nuclear species of interest, usually by either a single π/2 pulse or (more commonly for 13_{C or} 15_{N) via CP from protons.}

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influence of isotropic chemical shift for a time t1, before the mixing period where this

magnetisation is transferred to different nuclei. This may be to nuclei of a different species (e.g. by CP) or to others of the same species, and is achieved by using r.f. pulses and delays to reintroduce interactions such as dipolar couplings (which have been averaged by MAS) in a process called recoupling. This transfer of magnetisation can to some extent be controlled by careful choice of the recoupling scheme (see §3.2), but will in general occur between nuclei close in space. The final signal is detected in the same manner as in a 1D experiment, and the entire sequence is repeated for increasing values of t1 that sample the oscillatory behaviour during evolution. In this way the detected

signal is amplitude-modulated by the evolution earlier in the pulse sequence and therefore contains chemical shift information about both nuclear sites:

_(2.59) where and are the transverse relaxation times for the t₁ (evolution/indirect detection) and t2 (direct detection) periods respectively.

2D experiments that correlate the chemical shifts of different nuclear sites in this manner are a staple of biological NMR, often forming the basis for more elaborate experiments, and as such this technique is used often throughout this thesis. Depending on the recoupling method employed, an experiment can be designed to correlate chosen nuclei that neighbour each other, giving information about molecular structure and for peak assignment.94 _{Note that because the coherence that evolves during t}

1 does not

necessarily have to be single-quantum coherence (whereas detection during t2 requires

single-quantum coherence), the 2D method also offers the ability to observe multiple- quantum coherences. Experiments that excite and correlate double- (or higher) with single-quantum coherences for the same nuclei are a common and powerful tool in many fields of SSNMR because of their ability to help resolve broad resonances,117-119 _although

the efficiency of exciting higher-order coherences can be relatively low.

For a 1D experiment, the total experimental time is simply the length of the pulse sequence (including recycle delay) multiplied by the number of scans. Because acquisition of 2D data requires the repetition of the entire pulse sequence for multiple values of t1,

the total time scale for a 2D experiment is many times longer than an equivalent 1D experiment. The experimental time scales with the spectral width in the indirect

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dimension, as this is inversely proportional to the time separation between t1 increments

(resulting in more t₁ increments over the same total t₁ time). The spectral width is often defined by the chemical shift range of observed resonances. Choosing the number of t1

increments for a given spectral width is then often a balance between the experimental time and the resolution required (as the maximum t₁ time defines the minimum line width observable in the corresponding Fourier-transformed F1 dimension). The overall

sensitivity of an experiment is also impacted by the efficiency of the mixing step – depending on the mixing scheme used and the experimental conditions, only a fraction of the original polarisation may be recovered at the end, so many more scans may be required to offset these losses. Because losses are cumulative, in general the more steps in a pulse sequence, the lower its overall efficiency and the lower the final signal to noise.

To produce a spectrum (with dimensions F1 and F2 for the indirect and direct

dimensions respectively), Fourier transforms are performed in each dimension. A Fourier transform in the t2 dimension gives

_{. (2.60)} Here and in all that follows, and represent the absorptive and dispersive lineshapes, respectively, centred at frequencies ±Ω in the F dimension. To ensure absorptive lineshapes are obtained, a so-called hypercomplex Fourier transform is performed, whereby the signal is separated into its real and imaginary parts prior to performing the Fourier transform in F₁. For the real part,

(2.61)

For the imaginary part,

(2.62)

This process therefore yields four different lineshapes – absorptive in both dimensions, dispersive in F1 only, dispersive in F2 only and dispersive in both dimensions. However,

there is no sign discrimination for Ω in the F1 dimension – each of the four terms

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A commonly-employed technique to restore this discrimination is the “States” method120_{. In this scheme, two experiments are performed per t}

1 increment, with

appropriate pulse phases (during the preparation stage) such that during evolution, the signals in each instance are π/2 out of phase with each other. Two signals are therefore recorded: one with sine modulation and the other with cosine modulation. As above, we first apply Fourier transforms in the t2 dimension:

_{(2.63) (2.64)} Taking the real parts only and applying Fourier transforms in the t₁ dimension gives

(2.65)

(2.66)

Finally, taking the difference of the real part of and the imaginary part of gives

(2.67)

i.e. the desired absorptive lineshape at (+Ω, +Ω) only. Peaks are found at the chemical shift of the first nucleus in the F₁ dimension, and the second nucleus (due to mixing) in the F2 dimension, leading to correlations.

A second popular method for returning sign discrimination, known as “time- proportional phase incrementation” (TPPI)121_{, relies on linearly incrementing the phase}

of the preparation stage by π/2 every t1 slice, with the t1 increment halved. For many of

the experiments performed for this thesis, a hybrid method known as “States-TPPI”122

was used. This is based on the States method outlined above but instead of resetting the phase after every two experiments (i.e. 0, π/2, 0, π/2...), the phase is incremented linearly

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(i.e. 0, π/2, π, 3π/2...) as in the TPPI method. This has the result that every other t1 point

is negative, but traditionally this method was much simpler to programme a spectrometer to carry out.