Compressed sensing

Compressed sensing

Crucial to studies of biomolecular systems are multidimensional NMR techniques. A significant limitation remains the time it takes to record such experiments to achieve sufficient resolution and sensitivity; this is a particular problem when studying large membrane proteins, which may have limited lifetimes. To support our work on membrane proteins, we also investigate new NMR methodologies. Sensitivity and resolution limitations may be overcome by sparse, or non-uniform sampling, i.e. recording only a subset of the full data matrix. To reconstruct such spectra, the discrete Fourier transform (DFT) can no longer be used. Recently compressed sensing (CS) has attracted considerable attention in information theory and we and others have demonstrated its suitability for reconstructing undersampled, high-resolution, multidimensional NMR spectra, suitable for studying large proteins.

An example showing part of a 3D ¹⁵N HSQC-NOESY experiment for residue Ala64 from sensory rhodopsin II (pSRII) comparing FT reconstruction and CS-IHT (iterative hard thresholding) reconstruction of a 40% sampled experiment (40 h equivalent experiment time) is shown below. The fidelity of the CS-reconstruction is apparent.

An example of CS ℓ₁-norm reconstruction of 22.8% sampled 3D HNCA and HN(CO)CA backbone experiments, used in assignment of the large membrane protein pSRII, which forms 70 kDa protein-detergent complexes is shown below. Experiment times were reduced from 386 h and 579 h to 88 h and 132 h for the HNCA and HN(CO)CA respectively.

We are researching new methods for reconstruction of undersampled data, and new applications of the CS methodology. Our algorithms are available in the 'Cambridge CS' processing package for easy processing of undersampled data. For more information see the compressed sensing pages and the following publications:

Compressed Sensing ℓ₁-Norm Minimisation in Multidimensional NMR Spectroscopy.
Mark J. Bostock, Daniel J. Holland and Daniel Nietlispach, from Fast NMR Data Acquisition - Beyond the Fourier Transform (RSC publishing) (2017)
(doi:10.1039/9781782628361-00267)

Compressed sensing reconstruction of undersampled 3D NOESY spectra: application to large membrane proteins.
Mark J. Bostock, Daniel J. Holland, Daniel Nietlispach, Journal of Biomolecular NMR (2012), 54, 15-32
(doi:10.1007/s10858-012-9643-4)

Fast multidimensional NMR spectroscopy using compressed sensing.
Daniel J. Holland, Mark J. Bostock, Lynn F. Gladden, Daniel Nietlispach, Angewandte Chemie International Edition (2011), 50,6548-6551
(doi:10.1002/anie.201100440)