Resolution Enhancement of 4D NOESY Data via Covariance Processing

David A. Snyder, Fengli Zhang, and Rafael Brüschweiler
Department of Chemistry and Biochemistry, Florida State University and National High Magnetic Field Laboratory (NHMFL), Tallahassee, FL

Summary

Covariance NMR is a technique which, either following or in lieu of a Fourier Transform of a multi-dimensional NMR spectrum, allows for the indirect dimension to achieve the same nominal resolution and spectral width as the direct dimension. A matrix square root operation or, alternatively, the use of a singular value decomposition in implementation of the covariance transformation, suppresses spectral artefacts.[1] Covariance processing has already been successfully applied in the analysis of 2D NOESY, TOCSY and COSY spectra.[2,3,4] Here we demonstrate how 4D covariance NMR provides substantial resolution enhancement to 4D NOESY spectra.[5] Covariance NMR resolves additional cross peaks, some arising from long-range constraints, from otherwise overlapped regions of a 4D FT NOESY spectrum.

Representation of a 4D NOESY Spectrum


Associated with each donor carbon/proton (w1, w2) pair is an acceptor plane: a signal at a particular location (w3, w4) within the acceptor plane indicates an NOE between the proton of the donor pair with the proton of the acceptor carbon/proton (w3, w4) pair.



Transposing the view shown above leads to a representation of the 4D NOESY spectrum as a plane of donor planes, each associated with an acceptor (w3, w4) carbon/proton pair. As a guide through this transposition, a fixed (w3, w4) location in each acceptor plane is painted red; these points comprise a particular donor plane which is painted red in the view shown on the right.

Schematic Diagram of 4D Covariance NMR


4D NOESY: Experiment and Simulation

Experimental:
  • Uniformly 13C-labeled Ubiquitin
  • Dimension order: Cdonor, Hdonor, Cacceptor, Hacceptor
  • (N1, N2, N3, N4) = (8, 32, 16, 1024), Linear prediction to (16, 64, 32, 1024) complex points
  • All data measured at 298 K on an 800 MHz Bruker Spectrometer
    • Simulated Data
  • Predict intensity of signal (accounting for overlap and finite resolution) at each (w1, w2, w3, w4) point, where the (w1, w2) and (w3, w4) pairs range over the known C & H chemical shift values for Ubiquitin

    Resolution Enhancement of Experimental Data via 4D Covariance NMR
    A. Portion of the FT acceptor plane to the V5CG1/HG1 donor pair of Ubiquitin
    B. Portion of the FT donor plane orthogonal to the acceptor plane of A at the filled orange square
    C-D. Acceptor (C) and donor (D) planes after covariance transformation: covariance NMR maintains the acceptor plane resolution, with which it also endows the donor plane
    4D Covariance NMR resolves a peak in the lower resolution 4D FT spectrum into multiple distinct peaks: (1) V5HG1/I13HA, (2) I13HG2/HA, and (3) V26HG1/K27HA and L8HD2/L8HA, both centered in other planes

    Demonstration of Resolution Recovery by Covariance NMR using Simulated Data


    Covariance NMR Resolves Peak Overlap


    A. Portion of the 4D covariance NMR acceptor plane associated with the T9, T22 and T55 CG2/HG2 donor pairs showing peaks from the (1) T55HG2/S20HA, (2) T9HG2/HA and (3) T9HG2/HB proton pairs.
    B. Portion of the 4D covariance NMR donor plane associated with the S20CA/HA acceptor pair – i.e. orthogonal to the acceptor plane shown in A at peak (1) – verifying that peak (1) is indeed a local maximum in the 4D covariance spectrum, as is (4), arising from the T22HG2/S20HA proton pair
    C-D. Mutually orthogonal acceptor (C) and donor (D) FT planes, corresponding to the covariance planes shown in A-B.
    E-F. Mutually orthogonal donor (E) and acceptor (F) FT planes symmetric to the planes shown in C-D.

    Neither feature (1) nor its symmetric feature (1') is a local maximum in the 4D FT spectrum: the FT spectrum does not allow for the identification of the T55HG2/S20HA NOE, readily identifiable in the covariance spectrum

    Conclusions

    4D Covariance NMR:
  • Provides substantial resolution enhancement of 4D NOESY spectra
  • Resolves highly overlapped NOESY cross peaks
  • Enables one to use tighter tolerances for more reliable assignments
  • Increases the utility of 4D NOESY data in iterative structure calculation

    Acknowledgments

    The authors thank Dr. Wolfgang Bermel for helpful discussions and acknowledge the support of NIH Grant R01-GM066041

    References

    [1] N. Trbovic, S. Smirnov, F. Zhang, and R. Brüschweiler, J. Magn. Reson. 171, 277-283 (2004)
    [2] R. Brüschweiler and F. Zhang, J. Chem. Phys. 120, 5253-5260 (2004)
    [3] R. Brüschweiler, J. Chem. Phys. 121, 409-414 (2004)
    [4] Y. Chen, F. Zhang, W. Bermel, and R. Brüschweiler, J. Am. Chem. Soc., 128, 15564-15565 (2006)
    [5] G.M. Clore, L.E. Kay, A. Bax and A.M. Gronenborn, Biochemistry, 30, 12-18 (1991)
    Department of Chemistry and Biochemistry, Dittmer Building, Room 217, Florida State University, Tallahassee, FL 32306
    Phone: (850) 644-1768 / Fax: (850) 644-8281
    National High Magnetic Field Laboratory, Room B234, 1800 E. Paul Dirac Drive, Tallahassee, FL 32310