Covariance 4D NMR

Synopsis

Elucidation of high-resolution protein structures by NMR spectroscopy requires a large number of distance constraints that are derived from nuclear Overhauser effects between protons (NOEs). Due to the high level of spectral overlap encountered in 2D NMR spectra of proteins, the measurement of high quality distance constraints requires higher dimensional NMR experiments. Although four-dimensional Fourier transform (FT) NMR experiments can provide the necessary kind of spectral information, the associated measurement times are often prohibitively long. Covariance NMR spectroscopy yields 2D spectra that exhibit along the indirect frequency dimension the same high resolution as along the direct dimension using minimal measurement time. The generalization of covariance NMR to 4D NMR spectroscopy presented here exploits the inherent symmetry of certain 4D NMR experiments and utilizes the trace metric between donor planes for the construction of a high-resolution spectral covariance matrix. The approach is demonstrated for a 4D 13C-edited NOESY experiment of ubiquitin. The 4D covariance spectrum narrows the line-widths of peaks strongly broadened in the FT spectrum due to the necessarily short number of increments collected, and it resolves otherwise overlapped cross peaks allowing for an increase in the number of NOE assignments to be made from a given dataset. At the same time there is no significant decrease in the positive predictive value of observing a peak as compared to the corresponding 4D Fourier transform spectrum. These properties make the 4D covariance method a potentially valuable tool for the structure determination of larger proteins and for high-throughput applications in structural biology.

Software

    Covar4D.m : Matlab script implementing covariance of 4D spectra in NMRPipe format.

    UBQnoesy4D.4covar.pipe : (Large file! 519 MB!) example data (courtesy of Daiwen Yang and coworkers): shared evolution 15N/13C 4D NOESY spectrum of Ubiquitin, processed using apodization functions tweaked for optimal performance of covariance processing.

    ubq_shifts.rl : chemical shift list (Sparky format) for Ubiquitin.

    README : a readme file.

Covar4D.m:

    Running Covar4D.m using the following command at the Matlab prompt: 
    
	Covar4D('UBQnoesy4D.4covar.pipe', 'UBQnoesy4D.covar', [240 275]);
    produces the following output files:

    UBQnoesy4D.4covar.pipe_svd_results.h5: Matlab HDF5 format file containing the singular value decomposition of the input spectrum.

    UBQnoesy4D.covar: the covariance spectrum produced by the Covar4D.m script (warning: this file > 4 GB in size).

    Copies of these files, as well as the 4D Ubiquitin NOESY as apodized for optimal viewing as an FT spectrum, are available from the Bruschweiler group upon request.

    The arguments for the Covar4D function are (1) the name of an input file containing a 4D spectrum in NMRPipe format, with the first two (w4,w3) dimensions being the acceptor dimensions and the last two dimensions (w2,w1) being the donor dimensions, (2) the name of the output file to which the covariance spectrum is to be written and (3) the range (in frequency domain increment indices for the direct -- first -- dimension) of the water line, which is removed (use [0 0] to not remove the water line). In addition to writing the indicated output file, this script also writes the singular value decomposition used to reconstruct the covariance result to a matlab HDF5 file named using the input file name followed by the extension _svd_results.h5; for further processing in Matlab, it is more convenient to read in the SVD and reconstruct portions of the covariance spectrum as needed than to read in the (very large) covariance spectrum.

    Acknowledgement

    This material is based upon work supported by the National Institute of Health under Grant No. RO1 GM066041.

    References

    [1] Snyder, D. A.; Zhang, F.; Brüschweiler, R. Covariance NMR in higher dimensions: application to 4D NOESY spectroscopy of proteins J Biomol NMR 39, 165-175 (2007)
    [2] Snyder, D. A.; Xu, Y.; Yang, D.; Brüschweiler, R. Resolution-Enhanced 4D 15N/13C NOESY Protein NMR Spectroscopy by Application of the Covariance Transform JACS in press (2007)


    Last modified: Nov. 2007