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Goodwin DL, Singh P, Foroozandeh M. Adaptive optimal control of entangled qubits. SCIENCE ADVANCES 2022; 8:eabq4244. [PMID: 36475803 PMCID: PMC9728963 DOI: 10.1126/sciadv.abq4244] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 04/24/2022] [Accepted: 11/02/2022] [Indexed: 06/17/2023]
Abstract
Developing fast, robust, and accurate methods for optimal control of quantum systems comprising interacting particles is one of the most active areas of current science. Although a valuable repository of algorithms is available for numerical applications in quantum control, the high computational cost is somewhat overlooked. Here, we present a fast and accurate optimal control algorithm for systems of interacting qubits, QOALA (quantum optimal control by adaptive low-cost algorithm), which is predicted to offer [Formula: see text](M2) speedup for an M-qubit system, compared to the state-of-the-art exact methods, without compromising overall accuracy of the optimal solution. The method is general and compatible with diverse Hamiltonian structures. The proposed approach uses inexpensive low-accuracy approximations of propagators far from the optimum, adaptively switching to higher accuracy, higher-cost propagators when approaching the optimum. In addition, the utilization of analytical Lie algebraic derivatives that do not require computationally expensive matrix exponential brings even better performance.
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Affiliation(s)
- David L. Goodwin
- Chemistry Research Laboratory, University of Oxford, Mansfield Road, Oxford OX1 3TA, UK
| | - Pranav Singh
- Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK
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2
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Blahut J, Brandl MJ, Pradhan T, Reif B, Tošner Z. Sensitivity-Enhanced Multidimensional Solid-State NMR Spectroscopy by Optimal-Control-Based Transverse Mixing Sequences. J Am Chem Soc 2022; 144:17336-17340. [PMID: 36074981 DOI: 10.1021/jacs.2c06568] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Recently, proton-detected magic-angle spinning (MAS) solid-state nuclear magnetic resonance (NMR) spectroscopy has become an attractive tool to study the structure and dynamics of insoluble proteins at atomic resolution. The sensitivity of the employed multidimensional experiments can be systematically improved when both transversal components of the magnetization are transferred simultaneously after an evolution period. The method of preservation of equivalent pathways has been explored in solution-state NMR; however, it does not find widespread application due to relaxation issues connected with increased molecular size. We present here for the first time heteronuclear transverse mixing sequences for correlation experiments at moderate and fast MAS frequencies. Optimal control allows to boost the signal-to-noise ratio (SNR) beyond the expected factor of 2 for each indirect dimension. In addition to the carbon-detected sensitivity-enhanced 2D NCA experiment, we present a novel proton-detected, doubly sensitivity-enhanced 3D hCANH pulse sequence for which we observe a 3-fold improvement in SNR compared to the conventional experimental implementation. The sensitivity gain turned out to be essential to unambiguously characterize a minor fibril polymorph of a human lambda-III immunoglobulin light chain protein that escaped detection so far.
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Affiliation(s)
- Jan Blahut
- Department of Chemistry, Faculty of Science, Charles University, Albertov 6, 12842 Prague, Czech Republic.,Institute of Organic Chemistry and Biochemistry of the CAS, Flemingovo nám. 2, 16610, Prague, Czech Republic
| | - Matthias J Brandl
- Bayerisches NMR Zentrum (BNMRZ) at Department Chemie, Technische Universität München (TUM), 85747 Garching, Germany
| | - Tejaswini Pradhan
- Bayerisches NMR Zentrum (BNMRZ) at Department Chemie, Technische Universität München (TUM), 85747 Garching, Germany
| | - Bernd Reif
- Bayerisches NMR Zentrum (BNMRZ) at Department Chemie, Technische Universität München (TUM), 85747 Garching, Germany.,Helmholtz-Zentrum München (HMGU), Deutsches Forschungszentrum für Gesundheit und Umwelt, 85764 Neuherberg, Germany
| | - Zdeněk Tošner
- Department of Chemistry, Faculty of Science, Charles University, Albertov 6, 12842 Prague, Czech Republic
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Ehni S, Koos MRM, Reinsperger T, Haller JD, Goodwin DL, Luy B. Concurrent J-evolving refocusing pulses. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2022; 336:107152. [PMID: 35189510 DOI: 10.1016/j.jmr.2022.107152] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/23/2021] [Revised: 01/06/2022] [Accepted: 01/25/2022] [Indexed: 06/14/2023]
Abstract
Conventional refocusing pulses are optimised for a single spin without considering any type of coupling. However, despite the fact that most couplings will result in undesired distortions, refocusing in delay-pulse-delay-type sequences with desired heteronuclear coherence transfer might be enhanced considerably by including coupling evolution into pulse design. We provide a proof of principle study for a Hydrogen-Carbon refocusing pulse sandwich with inherent J-evolution following the previously reported ICEBERG-principle with improved performance in terms of refocusing performance and/or overall effective coherence transfer time. Pulses are optimised using optimal control theory with a newly derived quality factor and z-controls as an efficient tool to speed up calculations. Pulses are characterised in theory and experiment and compared to conventional concurrent refocusing pulses, clearly showing an improvement for the J-evolving pulse sandwich. As a side-product, also efficient J-compensated resfocusing pulse sandwiches - termed BUBU pulses following the nomenclature of previous J-compensated BUBI and BEBEtr pulse sandwiches - have been optimised.
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Affiliation(s)
- Sebastian Ehni
- Institute for Biological Interfaces 4 - Magnetic Resonance, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany; Institute of Organic Chemistry, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany; Bruker Biospin GmbH, Fällanden 8117, Switzerland
| | - Martin R M Koos
- Institute for Biological Interfaces 4 - Magnetic Resonance, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany; Pfizer Inc., Groton, CT 06340, USA; Department of Chemistry, Carnegie Mellon University, Pittsburgh, USA
| | - Tony Reinsperger
- Institute for Biological Interfaces 4 - Magnetic Resonance, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany; Institute of Organic Chemistry, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany; Bruker Biospin GmbH, Ettlingen 76275, Germany
| | - Jens D Haller
- Institute for Biological Interfaces 4 - Magnetic Resonance, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany; Institute of Organic Chemistry, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
| | - David L Goodwin
- Institute for Biological Interfaces 4 - Magnetic Resonance, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany; Chemistry Research Laboratory, University of Oxford, Mansfield Road, Oxford OX1 3TA, UK.
| | - Burkhard Luy
- Institute for Biological Interfaces 4 - Magnetic Resonance, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany; Institute of Organic Chemistry, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany.
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Tošner Z, Brandl MJ, Blahut J, Glaser SJ, Reif B. Maximizing efficiency of dipolar recoupling in solid-state NMR using optimal control sequences. SCIENCE ADVANCES 2021; 7:eabj5913. [PMID: 34644121 PMCID: PMC8514097 DOI: 10.1126/sciadv.abj5913] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/22/2021] [Accepted: 08/25/2021] [Indexed: 06/13/2023]
Abstract
Dipolar recoupling is a central concept in the nuclear magnetic resonance spectroscopy of powdered solids and is used to establish correlations between different nuclei by magnetization transfer. The efficiency of conventional cross-polarization methods is low because of the inherent radio frequency (rf) field inhomogeneity present in the magic angle spinning (MAS) experiments and the large chemical shift anisotropies at high magnetic fields. Very high transfer efficiencies can be obtained using optimal control–derived experiments. These sequences had to be optimized individually for a particular MAS frequency. We show that by adjusting the length and the rf field amplitude of the shaped pulse synchronously with sample rotation, optimal control sequences can be successfully applied over a range of MAS frequencies without the need of reoptimization. This feature greatly enhances their applicability on spectrometers operating at differing external fields where the MAS frequency needs to be adjusted to avoid detrimental resonance effects.
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Affiliation(s)
- Zdeněk Tošner
- Department of Chemistry, Faculty of Science, Charles University, Albertov 6, 12842 Prague, Czech Republic
| | - Matthias J. Brandl
- Bayerisches NMR Zentrum (BNMRZ) at Department Chemie, Technische Universität München (TUM), 85747 Garching, Germany
| | - Jan Blahut
- Department of Chemistry, Faculty of Science, Charles University, Albertov 6, 12842 Prague, Czech Republic
| | - Steffen J. Glaser
- Bayerisches NMR Zentrum (BNMRZ) at Department Chemie, Technische Universität München (TUM), 85747 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, D-80799 München, Germany
| | - Bernd Reif
- Bayerisches NMR Zentrum (BNMRZ) at Department Chemie, Technische Universität München (TUM), 85747 Garching, Germany
- Helmholtz Zentrum München (HMGU), Deutsches Forschungszentrum für Gesundheit und Umwelt, 85764 Neuherberg, Germany
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Kharkov B, Strouk L, Skinner TE, Jerschow A. Optimal control RF pulses for excitation and suppression of NMR signals in a conductive medium. J Chem Phys 2018; 149:034201. [DOI: 10.1063/1.5031154] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Boris Kharkov
- Department of Chemistry, New York University, 100 Washington Sq. East, New York, New York 10003, USA
- Laboratory of Biomolecular NMR, St. Petersburg State University, St. Petersburg 199034, Russia
| | - Leonard Strouk
- Department of Chemistry, New York University, 100 Washington Sq. East, New York, New York 10003, USA
| | - Thomas E. Skinner
- Department of Physics, Wright State University, Dayton, Ohio 45435, USA
| | - Alexej Jerschow
- Department of Chemistry, New York University, 100 Washington Sq. East, New York, New York 10003, USA
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Maximov II, Vinding MS, Tse DHY, Nielsen NC, Shah NJ. Real-time 2D spatially selective MRI experiments: Comparative analysis of optimal control design methods. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2015; 254:110-120. [PMID: 25863895 DOI: 10.1016/j.jmr.2015.03.003] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/09/2014] [Revised: 03/12/2015] [Accepted: 03/13/2015] [Indexed: 06/04/2023]
Abstract
There is an increasing need for development of advanced radio-frequency (RF) pulse techniques in modern magnetic resonance imaging (MRI) systems driven by recent advancements in ultra-high magnetic field systems, new parallel transmit/receive coil designs, and accessible powerful computational facilities. 2D spatially selective RF pulses are an example of advanced pulses that have many applications of clinical relevance, e.g., reduced field of view imaging, and MR spectroscopy. The 2D spatially selective RF pulses are mostly generated and optimised with numerical methods that can handle vast controls and multiple constraints. With this study we aim at demonstrating that numerical, optimal control (OC) algorithms are efficient for the design of 2D spatially selective MRI experiments, when robustness towards e.g. field inhomogeneity is in focus. We have chosen three popular OC algorithms; two which are gradient-based, concurrent methods using first- and second-order derivatives, respectively; and a third that belongs to the sequential, monotonically convergent family. We used two experimental models: a water phantom, and an in vivo human head. Taking into consideration the challenging experimental setup, our analysis suggests the use of the sequential, monotonic approach and the second-order gradient-based approach as computational speed, experimental robustness, and image quality is key. All algorithms used in this work were implemented in the MATLAB environment and are freely available to the MRI community.
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Affiliation(s)
- Ivan I Maximov
- Institute of Neuroscience and Medicine 4, Forschungszentrum Jülich GmbH, 52425 Jülich, Germany.
| | - Mads S Vinding
- Center for Insoluble Protein Structures (inSPIN), Interdisciplinary Nanoscience Center (iNANO) and Department of Chemistry, Aarhus University, DK-8000 Aarhus, Denmark.
| | - Desmond H Y Tse
- Institute of Neuroscience and Medicine 4, Forschungszentrum Jülich GmbH, 52425 Jülich, Germany
| | - Niels Chr Nielsen
- Center for Insoluble Protein Structures (inSPIN), Interdisciplinary Nanoscience Center (iNANO) and Department of Chemistry, Aarhus University, DK-8000 Aarhus, Denmark
| | - N Jon Shah
- Institute of Neuroscience and Medicine 4, Forschungszentrum Jülich GmbH, 52425 Jülich, Germany; Department of Neurology, Faculty of Medicine, RWTH Aachen University, JARA, 52074 Aachen, Germany
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7
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Tošner Z, Andersen R, Stevensson B, Edén M, Nielsen NC, Vosegaard T. Computer-intensive simulation of solid-state NMR experiments using SIMPSON. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2014; 246:79-93. [PMID: 25093693 DOI: 10.1016/j.jmr.2014.07.002] [Citation(s) in RCA: 115] [Impact Index Per Article: 11.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/27/2014] [Revised: 07/08/2014] [Accepted: 07/13/2014] [Indexed: 06/03/2023]
Abstract
Conducting large-scale solid-state NMR simulations requires fast computer software potentially in combination with efficient computational resources to complete within a reasonable time frame. Such simulations may involve large spin systems, multiple-parameter fitting of experimental spectra, or multiple-pulse experiment design using parameter scan, non-linear optimization, or optimal control procedures. To efficiently accommodate such simulations, we here present an improved version of the widely distributed open-source SIMPSON NMR simulation software package adapted to contemporary high performance hardware setups. The software is optimized for fast performance on standard stand-alone computers, multi-core processors, and large clusters of identical nodes. We describe the novel features for fast computation including internal matrix manipulations, propagator setups and acquisition strategies. For efficient calculation of powder averages, we implemented interpolation method of Alderman, Solum, and Grant, as well as recently introduced fast Wigner transform interpolation technique. The potential of the optimal control toolbox is greatly enhanced by higher precision gradients in combination with the efficient optimization algorithm known as limited memory Broyden-Fletcher-Goldfarb-Shanno. In addition, advanced parallelization can be used in all types of calculations, providing significant time reductions. SIMPSON is thus reflecting current knowledge in the field of numerical simulations of solid-state NMR experiments. The efficiency and novel features are demonstrated on the representative simulations.
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Affiliation(s)
- Zdeněk Tošner
- Center for Insoluble Protein Structures (inSPIN), Interdisciplinary Nanoscience Center (iNANO) and Department of Chemistry, Aarhus University, Gustav Wieds Vej 14, DK-8000 Aarhus C, Denmark; NMR Laboratory, Department of Chemistry, Faculty of Science, Charles University in Prague, Hlavova 8, CZ-128 43, Czech Republic.
| | - Rasmus Andersen
- Center for Insoluble Protein Structures (inSPIN), Interdisciplinary Nanoscience Center (iNANO) and Department of Chemistry, Aarhus University, Gustav Wieds Vej 14, DK-8000 Aarhus C, Denmark
| | - Baltzar Stevensson
- Physical Chemistry Division, Department of Materials and Environmental Chemistry, Arrhenius Laboratory, Stockholm University, SE-106 91 Stockholm, Sweden
| | - Mattias Edén
- Physical Chemistry Division, Department of Materials and Environmental Chemistry, Arrhenius Laboratory, Stockholm University, SE-106 91 Stockholm, Sweden
| | - Niels Chr Nielsen
- Center for Insoluble Protein Structures (inSPIN), Interdisciplinary Nanoscience Center (iNANO) and Department of Chemistry, Aarhus University, Gustav Wieds Vej 14, DK-8000 Aarhus C, Denmark.
| | - Thomas Vosegaard
- Center for Insoluble Protein Structures (inSPIN), Interdisciplinary Nanoscience Center (iNANO) and Department of Chemistry, Aarhus University, Gustav Wieds Vej 14, DK-8000 Aarhus C, Denmark.
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8
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Kumar P, Malinovskaya SA, Sola IR, Malinovsky VS. Selective creation of maximum coherence in multi-level Λ system. Mol Phys 2014. [DOI: 10.1080/00268976.2013.809166] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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9
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Low-power broadband homonuclear dipolar recoupling without decoupling: Double-quantum 13C NMR correlations at very fast magic-angle spinning. Chem Phys Lett 2012. [DOI: 10.1016/j.cplett.2012.07.053] [Citation(s) in RCA: 28] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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10
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de Fouquieres P, Schirmer SG, Glaser SJ, Kuprov I. Second order gradient ascent pulse engineering. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2011; 212:412-417. [PMID: 21885306 DOI: 10.1016/j.jmr.2011.07.023] [Citation(s) in RCA: 32] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/17/2011] [Revised: 07/22/2011] [Accepted: 07/28/2011] [Indexed: 05/31/2023]
Abstract
We report some improvements to the gradient ascent pulse engineering (GRAPE) algorithm for optimal control of spin ensembles and other quantum systems. These include more accurate gradients, convergence acceleration using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton algorithm as well as faster control derivative calculation algorithms. In all test systems, the wall clock time and the convergence rates show a considerable improvement over the approximate gradient ascent.
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Affiliation(s)
- P de Fouquieres
- Centre for Quantum Computation, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
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11
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Saalwächter K, Lange F, Matyjaszewski K, Huang CF, Graf R. BaBa-xy16: robust and broadband homonuclear DQ recoupling for applications in rigid and soft solids up to the highest MAS frequencies. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2011; 212:204-15. [PMID: 21803622 DOI: 10.1016/j.jmr.2011.07.001] [Citation(s) in RCA: 63] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/18/2011] [Revised: 06/28/2011] [Accepted: 07/01/2011] [Indexed: 05/18/2023]
Abstract
We here present a substantially improved version of the popular Back-to-Back (BaBa) homonuclear double-quantum (DQ) MAS recoupling pulse sequence. By combining the original pulse sequence with a virtual π pulse train with xy-16 phase cycling along with time-reversed DQ reconversion, a truly broadband and exceptionally robust pulse sequence is obtained. The sequence has moderate radio-frequency power requirements, amounting to only one 360° nutation per rotor cycle, it is robust with respect to rf power and tune-up errors, and its broadband performance increases with increasing spinning frequency, here tested up to 63 kHz. The experiment can be applied to many spin-1/2 nuclei in rigid solids with substantial frequency offsets and CSAs, which is demonstrated on the example of 31P NMR of a magnesium ultraphosphate, comparing experimental data with multi-spin simulations, and we also show simulations addressing the performance in 13C NMR of bio(macro)molecules. 1H-based studies of polymer dynamics are highlighted for the example of a rigid solid with strongly anisotropic mobility, represented by a polymer inclusion compound, and for the example of soft materials with weak residual dipole-dipole couplings, represented by homogeneous and inhomogeneous elastomers. We advocate the use of normalized (relaxation-corrected) DQ build-up curves for a quantitative assessment of weak average dipole-dipole couplings and even distributions thereof.
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Affiliation(s)
- Kay Saalwächter
- Institut für Physik-NMR, Martin-Luther-Universität Halle-Wittenberg, Betty-Heimann-Str. 7, D-06120 Halle, Germany.
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13
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Gopinath T, Traaseth NJ, Mote K, Veglia G. Sensitivity enhanced heteronuclear correlation spectroscopy in multidimensional solid-state NMR of oriented systems via chemical shift coherences. J Am Chem Soc 2010; 132:5357-63. [PMID: 20345172 PMCID: PMC3328406 DOI: 10.1021/ja905991s] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We present new sensitivity enhanced schemes for heteronuclear correlation spectroscopy (HETCOR) in solid-state NMR of oriented systems. These schemes will enhance the sensitivity of the HETCOR by 40% for the two-dimensional experiments (SE-HETCOR) and up to 180% for the 3D HETCOR-separated local field version (SE-PISEMAI-HETCOR). The signal enhancement is demonstrated for a single crystal of ((15)N)N-acetylleucine and the integral membrane protein sarcolipin oriented in lipid bicelles. These methods will significantly reduce the time needed to acquire multidimensional experiments for membrane proteins oriented in magnetically or mechanically aligned lipid bilayers as well as liquid crystalline materials.
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Affiliation(s)
- T. Gopinath
- Department of Biochemistry, Molecular Biology, and Biophysics, University of Minnesota, Minneapolis, MN 55455
| | | | - Kaustubh Mote
- Department of Biochemistry, Molecular Biology, and Biophysics, University of Minnesota, Minneapolis, MN 55455
| | - Gianluigi Veglia
- Department of Biochemistry, Molecular Biology, and Biophysics, University of Minnesota, Minneapolis, MN 55455
- Department of Chemistry, University of Minnesota, Minneapolis, MN 55455
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O'Dell LA, Harris KJ, Schurko RW. Optimized excitation pulses for the acquisition of static NMR powder patterns from half-integer quadrupolar nuclei. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2010; 203:156-166. [PMID: 20060763 DOI: 10.1016/j.jmr.2009.12.016] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/24/2009] [Revised: 11/27/2009] [Accepted: 12/15/2009] [Indexed: 05/28/2023]
Abstract
Various amplitude- and phase-modulated excitation pulses for the observation of static NMR powder patterns from half-integer quadrupolar nuclei have been generated using the optimal control routines implemented in SIMPSON 2.0. Such pulses are capable of both excitation of the central transition and signal enhancement by population transfer from the satellites. Enhancements in excess of 100% have been achieved for the central transition of the spin-3/2 (87)Rb nucleus compared with a selective pi/2 pulse. These pulses are shown to be relatively insensitive to changes in RF power and transmitter offsets, and can achieve a more uniform signal enhancement than double-frequency sweeps (DFS), resulting in more accurate spectral lineshapes. We also investigate the possibility of "calibration-free" optimized pulses for general use on half-integer quadrupoles with unknown interaction parameters. Such pulses could prove extremely useful for studying low abundance or insensitive nuclei for which experimental optimization of the DFS scheme may be difficult. We demonstrate that a pulse optimized for an arbitrary spin-3/2 system can function well on multiple samples, and can also excite the central transition of higher spin numbers, albeit with a smaller enhancement. The mechanism by which these optimized pulses achieve the signal enhancement is highly complex and, unlike DFS, involves a non-linear excitation of the satellite transition manifold, as well as the generation and manipulation of significant multiple-quantum coherences.
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Affiliation(s)
- Luke A O'Dell
- Department of Chemistry and Biochemistry, University of Windsor, Windsor, Ont, Canada
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15
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Maximov II, Salomon J, Turinici G, Nielsen NC. A smoothing monotonic convergent optimal control algorithm for nuclear magnetic resonance pulse sequence design. J Chem Phys 2010; 132:084107. [DOI: 10.1063/1.3328783] [Citation(s) in RCA: 32] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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16
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Neves JL, Heitmann B, Khaneja N, Glaser SJ. Heteronuclear decoupling by optimal tracking. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2009; 201:7-17. [PMID: 19695913 DOI: 10.1016/j.jmr.2009.07.024] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/10/2009] [Revised: 07/19/2009] [Accepted: 07/25/2009] [Indexed: 05/28/2023]
Abstract
The problem to design efficient heteronuclear decoupling sequences is studied using optimal control methods. A generalized version of the gradient ascent engineering (GRAPE) algorithm is presented that makes it possible to design complex non-periodic decoupling sequences which are characterized by tens of thousands of pulse sequence parameters. In contrast to conventional approaches based on average Hamiltonian theory, the concept of optimal tracking is used: a pulse sequence is designed that steers the evolution of an ensemble of spin systems such that at a series of time points, a specified trajectory of the density operator is tracked as closely as possible. The approach is demonstrated for the case of low-power heteronuclear decoupling in the liquid state for in vivo applications. Compared to conventional sequences, significant gains in decoupling efficiency and robustness with respect to offset and inhomogeneity of the radio-frequency field were found in simulations and experiments.
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Affiliation(s)
- Jorge L Neves
- Department of Chemistry, Technische Universität München, 85747 Garching, Germany
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17
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Nielsen AB, Bjerring M, Nielsen JT, Nielsen NC. Symmetry-based dipolar recoupling by optimal control: Band-selective experiments for assignment of solid-state NMR spectra of proteins. J Chem Phys 2009; 131:025101. [DOI: 10.1063/1.3157737] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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18
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Tosner Z, Vosegaard T, Kehlet C, Khaneja N, Glaser SJ, Nielsen NC. Optimal control in NMR spectroscopy: numerical implementation in SIMPSON. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2009; 197:120-34. [PMID: 19119034 DOI: 10.1016/j.jmr.2008.11.020] [Citation(s) in RCA: 108] [Impact Index Per Article: 7.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/13/2008] [Revised: 11/19/2008] [Accepted: 11/23/2008] [Indexed: 05/17/2023]
Abstract
We present the implementation of optimal control into the open source simulation package SIMPSON for development and optimization of nuclear magnetic resonance experiments for a wide range of applications, including liquid- and solid-state NMR, magnetic resonance imaging, quantum computation, and combinations between NMR and other spectroscopies. Optimal control enables efficient optimization of NMR experiments in terms of amplitudes, phases, offsets etc. for hundreds-to-thousands of pulses to fully exploit the experimentally available high degree of freedom in pulse sequences to combat variations/limitations in experimental or spin system parameters or design experiments with specific properties typically not covered as easily by standard design procedures. This facilitates straightforward optimization of experiments under consideration of rf and static field inhomogeneities, limitations in available or desired rf field strengths (e.g., for reduction of sample heating), spread in resonance offsets or coupling parameters, variations in spin systems etc. to meet the actual experimental conditions as close as possible. The paper provides a brief account on the relevant theory and in particular the computational interface relevant for optimization of state-to-state transfer (on the density operator level) and the effective Hamiltonian on the level of propagators along with several representative examples within liquid- and solid-state NMR spectroscopy.
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Affiliation(s)
- Zdenek Tosner
- Center for Insoluble Protein Structures (inSPIN), Interdisciplinary Nanoscience Center (iNANO), University of Aarhus, Aarhus C, Denmark.
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19
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Maximov II, Tošner Z, Nielsen NC. Optimal control design of NMR and dynamic nuclear polarization experiments using monotonically convergent algorithms. J Chem Phys 2008; 128:184505. [DOI: 10.1063/1.2903458] [Citation(s) in RCA: 77] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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McNeill SA, Gor'kov PL, Struppe J, Brey WW, Long JR. Optimizing ssNMR experiments for dilute proteins in heterogeneous mixtures at high magnetic fields. MAGNETIC RESONANCE IN CHEMISTRY : MRC 2007; 45 Suppl 1:S209-20. [PMID: 18157844 DOI: 10.1002/mrc.2146] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/15/2023]
Abstract
Solid-state NMR spectroscopy at high magnetic fields is proving to be an effective technique in structural biology, particularly for proteins which are not amenable to traditional X-ray and solution NMR approaches. Several parameters can be selected to provide optimal sensitivity, improve sample stability, and ensure biological relevance for ssNMR measurements on protein samples. These include selection of sample conditions, NMR probe design, and design of pulse experiments. Here, we demonstrate and evaluate several engineering and experimental approaches for pursuing measurements on dilute proteins in heterogeneous mixtures.
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Affiliation(s)
- Seth A McNeill
- Department of Biochemistry and Molecular Biology, McKnight Brain Institute, University of Florida, Gainesville, FL 32610, USA
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Hansen JØ, Kehlet C, Bjerring M, Vosegaard T, Glaser SJ, Khaneja N, Nielsen NC. Optimal control based design of composite dipolar recoupling experiments by analogy to single-spin inversion pulses. Chem Phys Lett 2007. [DOI: 10.1016/j.cplett.2007.08.072] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Kehlet C, Bjerring M, Sivertsen AC, Kristensen T, Enghild JJ, Glaser SJ, Khaneja N, Nielsen NC. Optimal control based NCO and NCA experiments for spectral assignment in biological solid-state NMR spectroscopy. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2007; 188:216-30. [PMID: 17681479 DOI: 10.1016/j.jmr.2007.06.011] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/02/2007] [Revised: 06/02/2007] [Accepted: 06/07/2007] [Indexed: 05/16/2023]
Abstract
We present novel pulse sequences for magic-angle-spinning solid-state NMR structural studies of (13)C,(15)N-isotope labeled proteins. The pulse sequences have been designed numerically using optimal control procedures and demonstrate superior performance relative to previous methods with respect to sensitivity, robustness to instrumental errors, and band-selective excitation profiles for typical biological solid-state NMR applications. Our study addresses specifically (15)N to (13)C coherence transfers being important elements in spectral assignment protocols for solid-state NMR structural characterization of uniformly (13)C,(15)N-labeled proteins. The pulse sequences are analyzed in detail and their robustness towards spin system and external experimental parameters are illustrated numerically for typical (15)N-(13)C spin systems under high-field solid-state NMR conditions. Experimentally the methods are demonstrated by 1D (15)N-->(13)C coherence transfer experiments, as well as 2D and 3D (15)N,(13)C and (15)N,(13)C,(13)C chemical shift correlation experiments on uniformly (13)C,(15)N-labeled ubiquitin.
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Affiliation(s)
- Cindie Kehlet
- Center for Insoluble Protein Structures (inSPIN), Interdisciplinary Nanoscience Center (iNANO), University of Aarhus, Langelandsgade 140, DK-8000, Aarhus C, Denmark
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