Introduction

The covariance spectrum C [1] is determined using the mixed time-frequency domain data S, C=(S^TS)^1/2, where S is the N₁ x N₂ mixed time-frequency domain matrix after Fourier transform along the detection dimension t₂. The matrix square-root can be efficiently determined by singular value composition [2,3].

Results and Discussion

Fig. 1 Aliphatic proton region of TOCSY NMR spectra of the 1 mM antamanide peptide in CDCl₃ at 800 MHz proton frequency and 300 K using TPPI-States along the indirect dimension.

An advantage of covariance spectrum over traditional 2D FT is that the indirect dimension is not required to be sampled with a time increment that fulfills the Nyquist theorem, 1/(spectral width).  Importantly, if N₁ is to be minimized to achieve maximal speed up, undersampling in t₁ can be advantageous by probing a wider range of t₁ evolution times, which allows better discrimination between true and spurious correlations involving differentially spaced resonances.

The conventional FT spectrum obtained from the time-domain data of the same size (N₁=48) shows severe line broadening along the indirect dimension ω₁, and thus is unsuitable for simple analysis. The covariance spectrum has the same high resolution along both dimensions by definition. Comparison with the 2D FT spectrum with 2048 increments reveals, however, the presence of extra peaks reflecting the onset of poor sampling effects due to the small size of the dataset. These effects can be removed by a masking scheme. Spectral masking is based on two criteria. Application of the resulting mask to the covariance spectrum leads to the spectrum that is essentially void of false peaks while most of the true peaks are present.

Conclusions

The enhanced covariance method presented here provides high-resolution 2D spectra from minimal t₁ datasets. The undersampling and cross-validation schemes represent powerful means to suppress spurious correlations. Only few weak peaks that are present in the full 2D FT spectrum are absent in the masked covariance spectrum. The scheme thereby offers substantial savings of measurement time for TOCSY- and COSY-type spectra experiments. The approach is readily applicable to high-throughput screening such as in metabolomics.

Acknowledgements

We thank Dr. David Snyder for discussion. This work is supported by NIH (GRANT GM066041).

References

[1]   Brüschweiler, R., et al., J. Chem. Phys., 120, 5253-5260 (2004).

[2]   Brüschweiler, R., J. Chem. Phys., 121, 409-414 (2004).

[3]   Trbovic, N. et al., J. Magn. Reson., 171, 277-283 (2005).