1
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Toyama Y, Shimada I. Frequency selective coherence transfer NMR spectroscopy to study the structural dynamics of high molecular weight proteins. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2019; 304:62-77. [PMID: 31129430 DOI: 10.1016/j.jmr.2019.05.004] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/19/2019] [Revised: 05/05/2019] [Accepted: 05/14/2019] [Indexed: 06/09/2023]
Abstract
Multidimensional nuclear magnetic resonance (NMR) spectroscopy has enabled detailed characterizations of protein structures and dynamics that are closely linked to functions. However, it leads to a large sensitivity loss in applications to high molecular weight proteins, which is caused by spin relaxation during the frequency discrimination period in the indirect dimension. Here, we describe a selective coherence transfer scheme, which enables us to selectively observe 1H nuclei bonded to 15N or 13C nuclei with specified resonance frequencies. By utilizing this scheme, we achieved a 2.5- to 6-fold increase in signal height per unit of time with this scheme by avoiding the relaxation loss in the indirect dimension, as compared to the conventional two-dimensional heteronuclear correlation spectroscopy. We also demonstrated the effectiveness of this approach with applications to the membrane protein KirBac1.1, and characterized the functionally relevant conformational exchange process in both detergent micelles and a reconstituted membrane environment, corresponding to the apparent molecular masses of 220 kDa and 300 kDa, respectively.
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Affiliation(s)
- Yuki Toyama
- Graduate School of Pharmaceutical Sciences, The University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
| | - Ichio Shimada
- Graduate School of Pharmaceutical Sciences, The University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-0033, Japan.
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2
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Keeler EG, Fritzsching KJ, McDermott AE. Refocusing CSA during magic angle spinning rotating-frame relaxation experiments. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2018; 296:130-137. [PMID: 30253322 PMCID: PMC6512962 DOI: 10.1016/j.jmr.2018.09.004] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/06/2018] [Revised: 09/10/2018] [Accepted: 09/12/2018] [Indexed: 05/27/2023]
Abstract
We examine coherent evolution of spin-locked magnetization during magic-angle spinning (MAS), in the context of relaxation experiments designed to probe chemical exchange (rotating-frame relaxation (R1ρ)). Coherent evolution is expected in MAS based rotating-frame relaxation decay experiments if matching conditions are met (such as, ω1 = nωr) and if the chemical shielding anisotropy (CSA) is substantial. We show here using numerical simulations and experiments that even when such matching requirements are avoided (e.g., ω1 < 0.5ωr, ∼1.5ωr, >2.5ωr), coherent evolution of spin-locked magnetization with large CSA is still considerable. The coherent evolution has important consequences on the analysis of relaxation decay and the ability to extract accurate information of interest about dynamics. We present a pulse sequence that employs rotary echoes and refocuses CSA contributions, allowing for more sensitive measurement of rotating-frame relaxation with less interference from coherent evolution. In practice, the proposed pulse sequence, REfocused CSA Rotating-frame Relaxation (RECRR) is robust to carrier frequency offset, B1-field inhomogeneity, and slight miscalibrations of the refocusing pulses.
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Affiliation(s)
- Eric G Keeler
- Department of Chemistry, Columbia University, New York, NY 10027, United States
| | - Keith J Fritzsching
- Department of Chemistry, Columbia University, New York, NY 10027, United States
| | - Ann E McDermott
- Department of Chemistry, Columbia University, New York, NY 10027, United States.
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3
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Li JS, Ruths J, Glaser SJ. Exact broadband excitation of two-level systems by mapping spins to springs. Nat Commun 2017; 8:446. [PMID: 28874703 PMCID: PMC5585281 DOI: 10.1038/s41467-017-00441-7] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/12/2017] [Accepted: 06/27/2017] [Indexed: 11/24/2022] Open
Abstract
Designing accurate and high-fidelity broadband pulses is an essential component in conducting quantum experiments across fields from protein spectroscopy to quantum optics. However, constructing exact and analytic broadband pulses remains unsolved due to the nonlinearity and complexity of the underlying spin system dynamics. Here, we present a nontrivial dynamic connection between nonlinear spin and linear spring systems and show the surprising result that such nonlinear and complex pulse design problems are equivalent to designing controls to steer linear harmonic oscillators under optimal forcing. We derive analytic broadband π/2 and π pulses that perform exact, or asymptotically exact, excitation and inversion over a defined bandwidth, and also with bounded amplitude. This development opens up avenues for pulse sequence design and lays a foundation for understanding the control of two-level systems. Coherent control of two-level systems is crucial for achieving fidelity in spectroscopy and quantum computing, but inherent nonlinearities and parameter variation have, to date, required an approximate, numerical approach. Here, Li et al. show how to map a spin ensemble to a spring model so analytic pulses can be designed using linear methods.
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Affiliation(s)
- Jr-Shin Li
- Department of Electrical and Systems Engineering, Washington University in St Louis, St Louis, MO, 63130, USA.
| | - Justin Ruths
- Departments of Mechanical and Systems Engineering, University of Texas at Dallas, Richardson, TX, 75080, USA
| | - Steffen J Glaser
- Department of Chemistry, Technical University of Munich, 85747, Garching, Germany
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4
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Khaneja N. Cone separation, quadratic control systems and control of spin dynamics in the presence of decoherence. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2017; 375:rsta.2016.0214. [PMID: 28115611 DOI: 10.1098/rsta.2016.0214] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 12/02/2016] [Indexed: 06/06/2023]
Abstract
In this paper, we study some control problems related to the control of coupled spin dynamics in the presence of relaxation and decoherence in nuclear magnetic resonance spectroscopy. The decoherence is modelled through a master equation. We study some model problems, whereby, through an appropriate choice of state variables, the system is reduced to a control system, where the state enters linearly and controls quadratically. We study this quadratic control system. Study of this system gives us explicit bounds on how close a coupled spin system can be driven to its target state and how much coherence and polarization can be transferred between coupled spins. Optimal control for the quadratic control system can be understood as the separation of closed cones, and we show how the derived results on optimal efficiency can be interpreted in this formulation. Finally, we study some finite-time optimal control problems for the quadratic control system.This article is part of the themed issue 'Horizons of cybernetical physics'.
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Affiliation(s)
- Navin Khaneja
- Department of Electrical Engineering, IIT Bombay, Mumbai, Maharashtra 400076, India
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5
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Ehni S, Luy B. Robust INEPT and refocused INEPT transfer with compensation of a wide range of couplings, offsets, and B1-field inhomogeneities (COB3). JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2014; 247:111-117. [PMID: 25245402 DOI: 10.1016/j.jmr.2014.07.010] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/13/2014] [Revised: 07/14/2014] [Accepted: 07/15/2014] [Indexed: 06/03/2023]
Abstract
Following the two-step optimization procedure previously introduced with the COB-INEPT (Ehni and Luy, 2012), a corresponding inphase-to-antiphase transfer element with close to optimal transfer efficiencies over a coupling range comprising approximately J-6J has been derived. The hard pulse sequence length is only 5.5 ms for coupling constants within 125-750 Hz. Robustness with respect to an offset range of 37.5 kHz on carbon (corresponding to 250 ppm on a 600 MHz spectrometer) and 10 kHz on protons (16.6 ppm at 600 MHz) is achieved with corresponding BUBI and BURBOP broadband pulses. As the sequence achieves a three times higher upper limit of J-compensation compared to the COB-INEPT, we name the transfer element COB3-INEPT. Next to the description of optimization and pulse sequence details, the performance of the resulting element is demonstrated on a test sample and partially aligned sample with actual total couplings in the range of 134 Hz⩽(1)TCH⩽391 Hz. The sequence can also be used for inphase-to-antiphase transfer starting from carbon, where the upper limit of J-compensation is 6J for CH-groups, 3J for CH2-groups, and slightly less than 2J for CH3. Theoretical transfers and experimental verification for the different multiplicities in an refocused INEPT are given.
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Affiliation(s)
- Sebastian Ehni
- Institute of Organic Chemistry and Institute for Biological Interfaces, Karlsruhe Institute of Technology (KIT), Fritz-Haber-Weg 6, 76131 Karlsruhe, Germany
| | - Burkhard Luy
- Institute of Organic Chemistry and Institute for Biological Interfaces, Karlsruhe Institute of Technology (KIT), Fritz-Haber-Weg 6, 76131 Karlsruhe, Germany.
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6
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Göbl C, Madl T, Simon B, Sattler M. NMR approaches for structural analysis of multidomain proteins and complexes in solution. PROGRESS IN NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY 2014; 80:26-63. [PMID: 24924266 DOI: 10.1016/j.pnmrs.2014.05.003] [Citation(s) in RCA: 130] [Impact Index Per Article: 13.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/21/2014] [Accepted: 05/14/2014] [Indexed: 05/22/2023]
Abstract
NMR spectroscopy is a key method for studying the structure and dynamics of (large) multidomain proteins and complexes in solution. It plays a unique role in integrated structural biology approaches as especially information about conformational dynamics can be readily obtained at residue resolution. Here, we review NMR techniques for such studies focusing on state-of-the-art tools and practical aspects. An efficient approach for determining the quaternary structure of multidomain complexes starts from the structures of individual domains or subunits. The arrangement of the domains/subunits within the complex is then defined based on NMR measurements that provide information about the domain interfaces combined with (long-range) distance and orientational restraints. Aspects discussed include sample preparation, specific isotope labeling and spin labeling; determination of binding interfaces and domain/subunit arrangements from chemical shift perturbations (CSP), nuclear Overhauser effects (NOEs), isotope editing/filtering, cross-saturation, and differential line broadening; and based on paramagnetic relaxation enhancements (PRE) using covalent and soluble spin labels. Finally, the utility of complementary methods such as small-angle X-ray or neutron scattering (SAXS, SANS), electron paramagnetic resonance (EPR) or fluorescence spectroscopy techniques is discussed. The applications of NMR techniques are illustrated with studies of challenging (high molecular weight) protein complexes.
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Affiliation(s)
- Christoph Göbl
- Biomolecular NMR and Center for Integrated Protein Science Munich at Department Chemie, Technische Universität München, Garching, Germany
| | - Tobias Madl
- Biomolecular NMR and Center for Integrated Protein Science Munich at Department Chemie, Technische Universität München, Garching, Germany; Institute of Structural Biology, Helmholtz Zentrum München, Neuherberg, Germany; Institute of Molecular Biology, University of Graz, Graz, Austria.
| | - Bernd Simon
- European Molecular Biology Laboratory, Structural and Computational Biology Unit, Meyerhofstraße 1, 69117 Heidelberg, Germany
| | - Michael Sattler
- Biomolecular NMR and Center for Integrated Protein Science Munich at Department Chemie, Technische Universität München, Garching, Germany; Institute of Structural Biology, Helmholtz Zentrum München, Neuherberg, Germany.
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7
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Ehni S, Luy B. A systematic approach for optimizing the robustness of pulse sequence elements with respect to couplings, offsets, and B1-field inhomogeneities (COB). MAGNETIC RESONANCE IN CHEMISTRY : MRC 2012; 50 Suppl 1:S63-S72. [PMID: 23280662 DOI: 10.1002/mrc.3846] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/04/2012] [Revised: 06/21/2012] [Accepted: 06/21/2012] [Indexed: 06/01/2023]
Abstract
Robust experiments that cover a wide range of chemical shift offsets and J-couplings are highly desirable for a multitude of applications in small molecule NMR spectroscopy. Many attempts to improve individual aspects of the robustness of pulse sequence elements based on rational and numerical design have been reported, but a general optimization strategy to cover all necessary aspects for a fully robust sequence is still lacking. In this article, a viable optimization strategy is introduced that covers a defined range of couplings, offsets, and B(1)-field inhomogeneities (COB) in a time-optimal way. Individual components of the optimization strategy can be optimized in any adequate way. As an example for the COB approach, we present the (1)H -(13)C-COB-INEPT with transfer of approximately 99% over the full carbon and proton bandwidth and (1)J(CH) -couplings in the range of 120-250 Hz, which have been optimized using efficient algorithms derived from optimal control theory. The theoretical performance is demonstrated in a number of corresponding COB-HSQC experiments.
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Affiliation(s)
- Sebastian Ehni
- Institute of Organic Chemistry and Institute for Biological Interfaces, Karlsruhe Institute of Technology, Fritz-Haber-Weg 6, 76131 Karlsruhe, Germany
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8
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Skinner TE, Gershenzon NI, Nimbalkar M, Bermel W, Luy B, Glaser SJ. New strategies for designing robust universal rotation pulses: application to broadband refocusing at low power. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2012; 216:78-87. [PMID: 22325853 DOI: 10.1016/j.jmr.2012.01.005] [Citation(s) in RCA: 37] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/20/2011] [Revised: 01/10/2012] [Accepted: 01/13/2012] [Indexed: 05/12/2023]
Abstract
Optimizing pulse performance often requires a compromise between maximizing signal amplitude and minimizing spectral phase errors. We consider methods for the de novo design of universal rotation pulses, applied specifically but not limited to refocusing pulses. Broadband inversion pulses that rotate all magnetization components 180° about a given fixed axis are necessary for refocusing and mixing in high-resolution NMR spectroscopy. The relative merits of various methodologies for generating pulses suitable for broadband refocusing are considered. The de novo design of 180° universal rotation pulses (180(UR)(°)) using optimal control can provide improved performance compared to schemes which construct refocusing pulses as composites of existing pulses. The advantages of broadband universal rotation by optimized pulses (BURBOP) are most evident for pulse design that includes tolerance to RF inhomogeneity or miscalibration. Nearly ideal refocusing is possible over a resonance offset range of ± 170% relative to the nominal pulse B(1) field, concurrent with tolerance to B(1) inhomogeneity/miscalibration of ± 33%. We present new modifications of the optimal control algorithm that incorporate symmetry principles (S-BURBOP) and relax conservative limits on peak RF pulse amplitude for short time periods that pose no threat to the probe. We apply them to generate a set of low-power 180(BURBOP)(°) pulses suitable for widespread use in (13)C spectroscopy on the majority of available probes. A quantitative measure for the reduced spectral phase error provided by these symmetry principles is also derived. For pulses designed according to this symmetry, refocusing phase errors are virtually eliminated upon application of EXORCYCLE or an equivalent G-180(S-BURBOP)(°)-G gradient sandwich, independent of resonance offset and RF inhomogeneity. The magnitude of the refocused component is not significantly compromised in achieving such ideal phase performance.
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Affiliation(s)
- Thomas E Skinner
- Physics Department, Wright State University, Dayton, OH 45435, USA.
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9
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Liu Y, Prestegard JH. Multi-dimensional NMR without coherence transfer: minimizing losses in large systems. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2011; 212:289-98. [PMID: 21835658 PMCID: PMC3183249 DOI: 10.1016/j.jmr.2011.07.007] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/08/2011] [Revised: 06/25/2011] [Accepted: 07/08/2011] [Indexed: 05/31/2023]
Abstract
Most multi-dimensional solution NMR experiments connect one dimension to another using coherence transfer steps that involve evolution under scalar couplings. While experiments of this type have been a boon to biomolecular NMR the need to work on ever larger systems pushes the limits of these procedures. Spin relaxation during transfer periods for even the most efficient (15)N-(1)H HSQC experiments can result in more than an order of magnitude loss in sensitivity for molecules in the 100 kDa range. A relatively unexploited approach to preventing signal loss is to avoid coherence transfer steps entirely. Here we describe a scheme for multi-dimensional NMR spectroscopy that relies on direct frequency encoding of a second dimension by multi-frequency decoupling during acquisition, a technique that we call MD-DIRECT. A substantial improvement in sensitivity of (15)N-(1)H correlation spectra is illustrated with application to the 21 kDa ADP ribosylation factor (ARF) labeled with (15)N in all alanine residues. Operation at 4°C mimics observation of a 50 kDa protein at 35°C.
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Affiliation(s)
- Yizhou Liu
- Complex Carbohydrate Research Center, The University of Georgia, Athens, GA 30602, USA
| | - James H. Prestegard
- Complex Carbohydrate Research Center, The University of Georgia, Athens, GA 30602, USA
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10
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Ruths J, Li JS. A multidimensional pseudospectral method for optimal control of quantum ensembles. J Chem Phys 2011; 134:044128. [PMID: 21280708 DOI: 10.1063/1.3541253] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In our previous work, we have shown that the pseudospectral method is an effective and flexible computation scheme for deriving pulses for optimal control of quantum systems. In practice, however, quantum systems often exhibit variation in the parameters that characterize the system dynamics. This leads us to consider the control of an ensemble (or continuum) of quantum systems indexed by the system parameters that show variation. We cast the design of pulses as an optimal ensemble control problem and demonstrate a multidimensional pseudospectral method with several challenging examples of both closed and open quantum systems from nuclear magnetic resonance spectroscopy in liquid. We give particular attention to the ability to derive experimentally viable pulses of minimum energy or duration.
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Affiliation(s)
- Justin Ruths
- Department of Electrical and Systems Engineering, Washington University in St. Louis, St. Louis, Missouri 63130 USA
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11
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Optimal pulse design in quantum control: a unified computational method. Proc Natl Acad Sci U S A 2011; 108:1879-84. [PMID: 21245345 DOI: 10.1073/pnas.1009797108] [Citation(s) in RCA: 92] [Impact Index Per Article: 7.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Many key aspects of control of quantum systems involve manipulating a large quantum ensemble exhibiting variation in the value of parameters characterizing the system dynamics. Developing electromagnetic pulses to produce a desired evolution in the presence of such variation is a fundamental and challenging problem in this research area. We present such robust pulse designs as an optimal control problem of a continuum of bilinear systems with a common control function. We map this control problem of infinite dimension to a problem of polynomial approximation employing tools from geometric control theory. We then adopt this new notion and develop a unified computational method for optimal pulse design using ideas from pseudospectral approximations, by which a continuous-time optimal control problem of pulse design can be discretized to a constrained optimization problem with spectral accuracy. Furthermore, this is a highly flexible and efficient numerical method that requires low order of discretization and yields inherently smooth solutions. We demonstrate this method by designing effective broadband π/2 and π pulses with reduced rf energy and pulse duration, which show significant sensitivity enhancement at the edge of the spectrum over conventional pulses in 1D and 2D NMR spectroscopy experiments.
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12
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O’Dell LA, Ratcliffe CI. Crystal Structure Based Design of Signal Enhancement Schemes for Solid-State NMR of Insensitive Half-Integer Quadrupolar Nuclei. J Phys Chem A 2010; 115:747-52. [DOI: 10.1021/jp111531e] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Luke A. O’Dell
- Steacie Institute for Molecular Sciences, National Research Council, 100 Sussex Drive, Ottawa, K1A 0R6, Ontario, Canada
| | - Christopher I. Ratcliffe
- Steacie Institute for Molecular Sciences, National Research Council, 100 Sussex Drive, Ottawa, K1A 0R6, Ontario, Canada
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13
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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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14
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Lee JS, Regatte RR, Jerschow A. Optimal excitation of (23)Na nuclear spins in the presence of residual quadrupolar coupling and quadrupolar relaxation. J Chem Phys 2010; 131:174501. [PMID: 19895019 DOI: 10.1063/1.3253970] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Optimal control theory is applied for designing pulse sequences to optimally excite a spin-3/2 system with residual quadrupolar coupling in the presence of quadrupolar relaxation. A homogeneous form of the master equation is constructed to simulate the dynamics of the spin system, and a general optimization procedure with a homogeneous form of the equation of motion is described. The optimized pulses are tested with (23)Na NMR, and their performance is compared with that of pulses optimized in the absence of relaxation.
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Affiliation(s)
- Jae-Seung Lee
- Department of Chemistry, New York University, New York, New York 10003, USA
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15
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Jones DH, Cellitti SE, Hao X, Zhang Q, Jahnz M, Summerer D, Schultz PG, Uno T, Geierstanger BH. Site-specific labeling of proteins with NMR-active unnatural amino acids. JOURNAL OF BIOMOLECULAR NMR 2010; 46:89-100. [PMID: 19669620 DOI: 10.1007/s10858-009-9365-4] [Citation(s) in RCA: 56] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/26/2009] [Accepted: 07/17/2009] [Indexed: 05/19/2023]
Abstract
A large number of amino acids other than the canonical amino acids can now be easily incorporated in vivo into proteins at genetically encoded positions. The technology requires an orthogonal tRNA/aminoacyl-tRNA synthetase pair specific for the unnatural amino acid that is added to the media while a TAG amber or frame shift codon specifies the incorporation site in the protein to be studied. These unnatural amino acids can be isotopically labeled and provide unique opportunities for site-specific labeling of proteins for NMR studies. In this perspective, we discuss these opportunities including new photocaged unnatural amino acids, outline usage of metal chelating and spin-labeled unnatural amino acids and expand the approach to in-cell NMR experiments.
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Affiliation(s)
- David H Jones
- Genomics Institute of the Novartis Research Foundation, San Diego, CA 92121-1125, USA
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16
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Li JS, Ruths J, Stefanatos D. A pseudospectral method for optimal control of open quantum systems. J Chem Phys 2009; 131:164110. [PMID: 19894930 DOI: 10.1063/1.3253796] [Citation(s) in RCA: 31] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In this paper, we present a unified computational method based on pseudospectral approximations for the design of optimal pulse sequences in open quantum systems. The proposed method transforms the problem of optimal pulse design, which is formulated as a continuous-time optimal control problem, to a finite-dimensional constrained nonlinear programming problem. This resulting optimization problem can then be solved using existing numerical optimization suites. We apply the Legendre pseudospectral method to a series of optimal control problems on open quantum systems that arise in nuclear magnetic resonance spectroscopy in liquids. These problems have been well studied in previous literature and analytical optimal controls have been found. We find an excellent agreement between the maximum transfer efficiency produced by our computational method and the analytical expressions. Moreover, our method permits us to extend the analysis and address practical concerns, including smoothing discontinuous controls as well as deriving minimum-energy and time-optimal controls. The method is not restricted to the systems studied in this article and is applicable to optimal manipulation of both closed and open quantum systems.
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Affiliation(s)
- Jr-Shin Li
- Department of Electrical and Systems Engineering, Washington University in St. Louis, St. Louis, Missouri 63130, USA.
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17
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Lee JS, Regatte RR, Jerschow A. Selective detection of ordered sodium signals by a jump-and-return pulse sequence. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2009; 200:126-9. [PMID: 19596211 DOI: 10.1016/j.jmr.2009.06.015] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/24/2009] [Revised: 06/18/2009] [Accepted: 06/18/2009] [Indexed: 05/08/2023]
Abstract
A simple pulse sequence, derived from the shaped pulse optimally exciting the central transition of a spin 3/2, can be used to selectively detect ordered sodium with a given quadrupolar coupling. The pulse sequence consists of two pulses with opposite phases and separated by a delay, called a quadrupolar jump-and-return (QJR) sequence. This QJR sequence is tested with a phantom made of sodium ions in bacteriophage and in aqueous solution and its feasibility for contrast modification based on the quadrupolar coupling is demonstrated.
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Affiliation(s)
- Jae-Seung Lee
- Department of Chemistry, New York University, New York, NY 10003, USA
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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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Lee JS, Regatte RR, Jerschow A. Optimal nuclear magnetic resonance excitation schemes for the central transition of a spin 3/2 in the presence of residual quadrupolar coupling. J Chem Phys 2009; 129:224510. [PMID: 19071931 DOI: 10.1063/1.3036005] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Optimal control theory is applied for enhancing the intensity of the central peak of a spin 3/2 signal in the presence of a residual quadrupolar coupling. While a maximum enhancement is always possible in the regime omega(rf) << omega(Q) via the use of modulated and shaped pulses, the intermediate rf-power regime omega(rf)-omega(Q) does not admit simple solutions based on intuition. In this work we present optimized shaped pulses that have been derived using an optimization algorithm based on optimal control and test these with (23)Na NMR in this regime. In addition to enhancing the intensity of the central transition signal, the satellite peaks can be effectively suppressed, which is a useful feature for the implementation in (23)Na imaging sequences.
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Affiliation(s)
- Jae-Seung Lee
- Department of Chemistry, New York University, New York, New York 10003, USA
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20
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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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21
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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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22
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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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23
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Luy B. NMR-spektroskopische Messungen an einem Megadalton-Proteinkomplex. Angew Chem Int Ed Engl 2007. [DOI: 10.1002/ange.200701093] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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24
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Affiliation(s)
- Burkhard Luy
- Department Chemie, LS OC II, Technische Universität München, Lichtenbergstrasse 4, 85747 Garching, Germany.
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25
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Kobzar K, Luy B. Spin state selective Hadamard encoding during transfer periods using multiple selective CW-HCP. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2007; 186:228-37. [PMID: 17392000 DOI: 10.1016/j.jmr.2007.03.004] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/13/2007] [Revised: 03/01/2007] [Accepted: 03/03/2007] [Indexed: 05/14/2023]
Abstract
Hadamard spectroscopy today represents an alternative to conventional Fourier transform spectroscopy. The selective inversion of several narrow frequency bands is typically achieved by taylored inversion pulses in place of t1-evolution periods. However, band-selective inversion can also be achieved during coherence transfer steps, thereby shortening the period during which the magnetization is in the transverse plane. Using CW heteronuclear cross polarization (CW-HCP) as an example for highly selective coherence transfer, the implementation of Hadamard encoding within a transfer step is presented. Transfer characteristics, the preparation of multiple frequency selective CW-HCP and the possibility of acquiring spin state selective spectra are discussed in detail. The theoretical results are verified on two examples involving a cyclic pentapeptide and ubiquitin.
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Affiliation(s)
- Kyryl Kobzar
- Department Chemie, Organische Chemie II, Technische Universität München, Lichtenbergstrasse 4, D-85747 Garching, Germany
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26
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Valentine ER, Ferrage F, Massi F, Cowburn D, Palmer AG. Joint composite-rotation adiabatic-sweep isotope filtration. JOURNAL OF BIOMOLECULAR NMR 2007; 38:11-22. [PMID: 17353973 PMCID: PMC2290856 DOI: 10.1007/s10858-006-9131-9] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/10/2006] [Revised: 11/28/2006] [Accepted: 11/29/2006] [Indexed: 05/14/2023]
Abstract
Joint composite-rotation adiabatic-sweep isotope filters are derived by combining the composite-rotation [Stuart AC et al. (1999) J Am Chem Soc 121: 5346-5347] and adiabatic-sweep [Zwahlen C et al. (1997) J Am Chem Soc 119:6711-6721; Kupce E, Freeman R (1997) J Magn Reson 127:36-48] approaches. The joint isotope filters have improved broadband filtration performance, even for extreme values of the one-bond (1)H-(13)C scalar coupling constants in proteins and RNA molecules. An average Hamiltonian analysis is used to describe evolution of the heteronuclear scalar coupling interaction during the adiabatic sweeps within the isotope filter sequences. The new isotope filter elements permit improved selective detection of NMR resonance signals originating from (1)H spins attached to an unlabeled natural abundance component of a complex in which the other components are labeled with (13)C and (15)N isotopes.
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Affiliation(s)
- Elizabeth R Valentine
- Department of Biochemistry and Molecular Biophysics, Columbia University, 630 West 168th Street, New York, NY 10032, USA
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27
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Tosner Z, Glaser SJ, Khaneja N, Nielsen NC. Effective Hamiltonians by optimal control: Solid-state NMR double-quantum planar and isotropic dipolar recoupling. J Chem Phys 2006; 125:184502. [PMID: 17115760 DOI: 10.1063/1.2366703] [Citation(s) in RCA: 34] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We report the use of optimal control algorithms for tailoring the effective Hamiltonians in nuclear magnetic resonance (NMR) spectroscopy through sophisticated radio-frequency (rf) pulse irradiation. Specifically, we address dipolar recoupling in solid-state NMR of powder samples for which case pulse sequences offering evolution under planar double-quantum and isotropic mixing dipolar coupling Hamiltonians are designed. The pulse sequences are constructed numerically to cope with a range of experimental conditions such as inhomogeneous rf fields, spread of chemical shifts, the intrinsic orientation dependencies of powder samples, and sample spinning. While the vast majority of previous dipolar recoupling sequences are operating through planar double-or zero-quantum effective Hamiltonians, we present here not only improved variants of such experiments but also for the first time homonuclear isotropic mixing sequences which transfers all I(x), I(y), and I(z) polarizations from one spin to the same operators on another spin simultaneously and with equal efficiency. This property may be exploited to increase the signal-to-noise ratio of two-dimensional experiments by a factor of square root 2 compared to conventional solid-state methods otherwise showing the same efficiency. The sequences are tested numerically and experimentally for a powder of (13)C(alpha),(13)C(beta)-L-alanine and demonstrate substantial sensitivity gains over previous dipolar recoupling experiments.
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Affiliation(s)
- Zdenek Tosner
- Center for Insoluble Protein Structures (inSPIN), Interdisciplinary Nanoscience Center (iNANO), University of Aarhus, DK-8000 Aarhus C, Denmark
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28
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Abstract
Three-dimensional structure determination of small proteins and oligonucleotides by solution NMR is established. With the development of novel NMR and labeling techniques, structure determination is now feasible for proteins with a molecular mass of up to approximately 100 kDa and RNAs of up to 35 kDa. Beyond these molecular masses special techniques and approaches are required for applying NMR as a multiprobe method for structural investigations of proteins and RNAs. It is the aim of this review to summarize the NMR techniques and approaches available to advance the molecular mass limit of NMR both for proteins (up to 1 MDa) and RNAs (up to 100 kDa). Physical pictures of the novel techniques, their experimental applications, as well as labeling and assignment strategies are discussed and accompanied by future perspectives.
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Affiliation(s)
- Andreas G Tzakos
- MRC Laboratory of Molecular Biology, Cambridge CB2 2QH, United Kingdom
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29
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Kehlet C, Vosegaard T, Khaneja N, Glaser SJ, Nielsen NC. Low-power homonuclear dipolar recoupling in solid-state NMR developed using optimal control theory. Chem Phys Lett 2005. [DOI: 10.1016/j.cplett.2005.08.061] [Citation(s) in RCA: 35] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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30
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Vosegaard T, Kehlet C, Khaneja N, Glaser SJ, Nielsen NC. Improved Excitation Schemes for Multiple-Quantum Magic-Angle Spinning for Quadrupolar Nuclei Designed Using Optimal Control Theory. J Am Chem Soc 2005; 127:13768-9. [PMID: 16201779 DOI: 10.1021/ja054035g] [Citation(s) in RCA: 33] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We have investigated the use of optimal control theory for the design of improved multiple-quantum excitation schemes for the popular multiple-quantum magic-angle spinning NMR experiment for quadrupolar nuclei with half-integer quadrupolar spin. The advantage of the new low-power experiments, termed OCFASTER, is demonstrated by sensitivity improvements approaching 50% for 87Rb in RbClO4 and RbNO3 as compared to FASTER and standard strong-pulse excitation schemes.
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Affiliation(s)
- Thomas Vosegaard
- Center for Insoluble Protein Structures (inSPIN), University of Aarhus, DK-8000 Aarhus C, Denmark.
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31
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Frueh DP, Ito T, Li JS, Wagner G, Glaser SJ, Khaneja N. Sensitivity enhancement in NMR of macromolecules by application of optimal control theory. JOURNAL OF BIOMOLECULAR NMR 2005; 32:23-30. [PMID: 16041480 DOI: 10.1007/s10858-005-3592-0] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/06/2004] [Accepted: 02/16/2005] [Indexed: 05/03/2023]
Abstract
NMR of macromolecules is limited by large transverse relaxation rates. In practice, this results in low efficiency of coherence transfer steps in multidimensional NMR experiments, leading to poor sensitivity and long acquisition times. The efficiency of coherence transfer can be maximized by design of relaxation optimized pulse sequences using tools from optimal control theory. In this paper, we demonstrate that this approach can be adopted for studies of large biological systems, such as the 800 kDa chaperone GroEL. For this system, the 1H-15N coherence transfer module presented here yields an average sensitivity enhancement of 20-25% for cross-correlated relaxation induced polarization transfer (CRIPT) experiments.
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Affiliation(s)
- Dominique P Frueh
- Department of Biological Chemistry and Molecular Pharmacology, Harvard Medical School, Boston, MA 02115, USA
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