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IPASS: error tolerant NMR backbone resonance assignment by linear programming
, 2009
"... Abstract. The automation of the entire NMR protein structure determination process requires a superior error tolerant backbone resonance assignment method. Although a variety of assignment approaches have been developed, none works well on noisy automatically picked peaks. IPASS is proposed as a nov ..."
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Abstract. The automation of the entire NMR protein structure determination process requires a superior error tolerant backbone resonance assignment method. Although a variety of assignment approaches have been developed, none works well on noisy automatically picked peaks. IPASS is proposed as a novel integer linear programming (ILP) based assignment method. In order to reduce size of the problem, IPASS employs probabilistic spin system typing based on chemical shifts and secondary structure predictions. Furthermore, IPASS extracts connectivity information from the interresidue information and the 15 Nedited NOESY peaks which are then used to fix reliable fragments. The experimental results demonstrate that IPASS significantly outperforms the previous assignment methods on the synthetic data sets. It achieves an average of 99 % precision and 96 % recall on the synthesized spin systems, and an average of 96 % precision and 90 % recall on the synthesized peak lists. When applied on automatically picked peaks from experimentally derived data sets, it achieves an average precision and recall of 78 % and 67%, respectively. In contrast, the next best method, MARS, achieved an average precision and recall of 50 % and 40%, respectively. Availability: IPASS is available upon request, and the web server for IPASS is under construction.
Fast ℓ1 Minimization by Iterative Thresholding for Multidimensional NMR Spectroscopy
, 2007
"... Fast multidimensional NMR is important in chemical shift assignment and for studying structures of large proteins. We present the first method which takes advantage of the sparsity of the wavelet representation of the NMR spectra and reconstructs the spectra from partial random measurements of its f ..."
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Cited by 3 (0 self)
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Fast multidimensional NMR is important in chemical shift assignment and for studying structures of large proteins. We present the first method which takes advantage of the sparsity of the wavelet representation of the NMR spectra and reconstructs the spectra from partial random measurements of its free induction decay (FID) by solving the following optimization problem: min ‖x‖1 subject to ‖y − SF T W T x‖ 2 ≤ ɛ, wherey is a given n × 1 observation vector, S a random sampling operator, F denotes the Fourier transform, and W an orthogonal 2D wavelet transform. The matrix A = SF T W T is a given n × p matrix such that n<p. This problem can be solved by generalpurpose solvers; however, these can be prohibitively expensive in largescale applications. In the settings of interest, the underlying solution is sparse with a few nonzeros. We show here that for large practical systems, a good approximation to the sparsest solution is obtained by iterative thresholding algorithms running much more rapidly than general solvers. We demonstrate the applicability of our approach to fast multidimensional NMR spectroscopy. Our main practical result estimates a fourfold reduction in sampling and experiment time without loss of resolution while maintaining sensitivity for a wide range of existing settings. Our results maintain the quality of the peak list of the reconstructed signal which is the key deliverable used in protein structure determination.
Abstract Polar Fourier transforms of radially sampled NMR data
, 2006
"... Radial sampling of the NMR time domain has recently been introduced to speed up data collection significantly. Here, we show that radially sampled data can be processed directly using Fourier transforms in polar coordinates. We present a comprehensive theoretical analysis of the discrete polar Fouri ..."
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Cited by 1 (0 self)
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Radial sampling of the NMR time domain has recently been introduced to speed up data collection significantly. Here, we show that radially sampled data can be processed directly using Fourier transforms in polar coordinates. We present a comprehensive theoretical analysis of the discrete polar Fourier transform, and derive the consequences of its application to radially sampled data using linear response theory. With adequate sampling, the resulting spectrum using a polar Fourier transform is indistinguishable from conventionally processed spectra with Cartesian sampling. In the case of undersampling in azimuth—the condition that provides significant savings in measurement time—the correct spectrum is still produced, but with limited distortion of the baseline away from the peaks, taking the form of a summation of highorder Bessel functions. Finally, we describe an intrinsic connection between the polar Fourier transform and the filtered backprojection method that has recently been introduced to process projectionreconstruction NOESY data. Direct polar Fourier transformation holds great potential for producing quantitatively accurate spectra from radially sampled NMR data.
Research Article Fast ℓ1 Minimization by Iterative Thresholding for Multidimensional NMR Spectroscopy
"... Fast multidimensional NMR is important in chemical shift assignment and for studying structures of large proteins. We present the first method which takes advantage of the sparsity of the wavelet representation of the NMR spectra and reconstructs the spectra from partial random measurements of its f ..."
Abstract
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Fast multidimensional NMR is important in chemical shift assignment and for studying structures of large proteins. We present the first method which takes advantage of the sparsity of the wavelet representation of the NMR spectra and reconstructs the spectra from partial random measurements of its free induction decay (FID) by solving the following optimization problem: min ‖x‖1 subject to ‖y − SF T W T x‖ 2 ≤ ɛ, wherey is a given n × 1 observation vector, S a random sampling operator, F denotes the Fourier transform, and W an orthogonal 2D wavelet transform. The matrix A = SF T W T is a given n × p matrix such that n<p. This problem can be solved by generalpurpose solvers; however, these can be prohibitively expensive in largescale applications. In the settings of interest, the underlying solution is sparse with a few nonzeros. We show here that for large practical systems, a good approximation to the sparsest solution is obtained by iterative thresholding algorithms running much more rapidly than general solvers. We demonstrate the applicability of our approach to fast multidimensional NMR spectroscopy. Our main practical result estimates a fourfold reduction in sampling and experiment time without loss of resolution while maintaining sensitivity for a wide range of existing settings. Our results maintain the quality of the peak list of the reconstructed signal which is the key deliverable used in protein structure determination. Copyright © 2007 Iddo Drori. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1.