1
|
Pell AJ. A method to calculate the NMR spectra of paramagnetic species using thermalized electronic relaxation. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2021; 326:106939. [PMID: 33744830 DOI: 10.1016/j.jmr.2021.106939] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/30/2020] [Revised: 02/06/2021] [Accepted: 02/08/2021] [Indexed: 06/12/2023]
Abstract
For paramagnetic species, it has been long understood that the hyperfine interaction between the unpaired electrons and the nucleus results in a nuclear magnetic resonance (NMR) peak that is shifted by a paramagnetic shift, rather than split by the coupling, due to an averaging of the electronic magnetic moment caused by electronic relaxation that is fast in comparison to the hyperfine coupling constant. However, although this feature of paramagnetic NMR has formed the basis of all theories of the paramagnetic shift, the precise theory and mechanism of the electronic relaxation required to predict this result has never been discussed, nor has the assertion been tested. In this paper, we show that the standard semi-classical Redfield theory of relaxation fails to predict a paramagnetic shift, as does any attempt to correct for the semi-classical theory using modifications such as the inhomogeneous master equation or Levitt-di Bari thermalization. In fact, only the recently-introduced Lindbladian theory of relaxation in magnetic resonance [J.Magn.Reson., 310, 106645 (2019)] is able to correctly predict the paramagnetic shift tensor and relaxation-induced linewidth in pNMR. Furthermore, this new formalism is able to predict the NMR spectra of paramagnetic species outside the high-temperature and weak-order limits, and is therefore also applicable to dynamic nuclear polarization. The formalism is tested by simulations of five case studies, which include Fermi-contact and spin-dipolar hyperfine couplings, g-anisotropy, zero-field splitting, high and low temperatures, and fast and slow electronic relaxation.
Collapse
Affiliation(s)
- Andrew J Pell
- Department of Materials and Environmental Chemistry, Stockholm University, Svänte Arrhenius väg 16 C, 106 91 Stockholm, Sweden; Centre de RMN Trés Hauts Champs de Lyon (UMR5082 CNRS/ENS-Lyon/Université Claude Bernard Lyon 1), Université de Lyon, 5 rue de la Doua, 69100 Villeurbanne, France.
| |
Collapse
|
2
|
Bengs C, Levitt MH. A master equation for spin systems far from equilibrium. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2020; 310:106645. [PMID: 31816583 DOI: 10.1016/j.jmr.2019.106645] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/17/2019] [Accepted: 11/08/2019] [Indexed: 05/25/2023]
Abstract
The quantum dynamics of spin systems is often treated by a differential equation known as the master equation, which describes the trajectories of spin observables such as magnetization components, spin state populations, and coherences between spin states. The master equation describes how a perturbed spin system returns to a state of thermal equilibrium with a finite-temperature environment. The conventional master equation, which has the form of an inhomogeneous differential equation, applies to cases where the spin system remains close to thermal equilibrium, which is well satisfied for a wide variety of magnetic resonance experiments conducted on thermally polarized spin systems at ordinary temperatures. However, the conventional inhomogeneous master equation may fail in the case of hyperpolarized spin systems, when the spin state populations deviate strongly from thermal equilibrium, and in general where there is a high degree of nuclear spin order. We highlight a simple case in which the inhomogeneous master equation clearly fails, and propose an alternative master equation based on Lindblad superoperators which avoids most of the deficiencies of previous proposals. We discuss the strengths and limitations of the various formulations of the master equation, in the context of spin systems which are far from thermal equilibrium. The method is applied to several problems in nuclear magnetic resonance and to spin-isomer conversion.
Collapse
Affiliation(s)
- Christian Bengs
- School of Chemistry, Southampton University, University Road, SO17 1BJ, UK.
| | - Malcolm H Levitt
- School of Chemistry, Southampton University, University Road, SO17 1BJ, UK.
| |
Collapse
|
3
|
Bengs C, Levitt MH. SpinDynamica: Symbolic and numerical magnetic resonance in a Mathematica environment. MAGNETIC RESONANCE IN CHEMISTRY : MRC 2018; 56:374-414. [PMID: 28809056 PMCID: PMC6001486 DOI: 10.1002/mrc.4642] [Citation(s) in RCA: 76] [Impact Index Per Article: 12.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2017] [Accepted: 08/03/2017] [Indexed: 05/11/2023]
Abstract
SpinDynamica is a set of Mathematica packages for performing numerical and symbolic analysis of a wide range of magnetic resonance experiments and phenomena. An overview of the SpinDynamica architecture and functionality is given, with some simple representative examples.
Collapse
Affiliation(s)
- Christian Bengs
- School of ChemistryUniversity of SouthamptonSouthamptonSO17 1BJUK
| | | |
Collapse
|
4
|
Dumez JN, Butler MC, Emsley L. Numerical simulation of free evolution in solid-state nuclear magnetic resonance using low-order correlations in Liouville space. J Chem Phys 2010; 133:224501. [DOI: 10.1063/1.3505455] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
|
5
|
Nieuwkoop AJ, Wylie BJ, Franks WT, Shah GJ, Rienstra CM. Atomic resolution protein structure determination by three-dimensional transferred echo double resonance solid-state nuclear magnetic resonance spectroscopy. J Chem Phys 2010; 131:095101. [PMID: 19739873 DOI: 10.1063/1.3211103] [Citation(s) in RCA: 37] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We show that quantitative internuclear (15)N-(13)C distances can be obtained in sufficient quantity to determine a complete, high-resolution structure of a moderately sized protein by magic-angle spinning solid-state NMR spectroscopy. The three-dimensional ZF-TEDOR pulse sequence is employed in combination with sparse labeling of (13)C sites in the beta1 domain of the immunoglobulin binding protein G (GB1), as obtained by bacterial expression with 1,3-(13)C or 2-(13)C-glycerol as the (13)C source. Quantitative dipolar trajectories are extracted from two-dimensional (15)N-(13)C planes, in which approximately 750 cross peaks are resolved. The experimental data are fit to exact theoretical trajectories for spin clusters (consisting of one (13)C and several (15)N each), yielding quantitative precision as good as 0.1 A for approximately 350 sites, better than 0.3 A for another 150, and approximately 1.0 A for 150 distances in the range of 5-8 A. Along with isotropic chemical shift-based (TALOS) dihedral angle restraints, the distance restraints are incorporated into simulated annealing calculations to yield a highly precise structure (backbone RMSD of 0.25+/-0.09 A), which also demonstrates excellent agreement with the most closely related crystal structure of GB1 (2QMT, bbRMSD 0.79+/-0.03 A). Moreover, side chain heavy atoms are well restrained (0.76+/-0.06 A total heavy atom RMSD). These results demonstrate for the first time that quantitative internuclear distances can be measured throughout an entire solid protein to yield an atomic-resolution structure.
Collapse
Affiliation(s)
- Andrew J Nieuwkoop
- Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Avenue, Urbana, Illinois 61801, USA
| | | | | | | | | |
Collapse
|
6
|
Ladizhansky V. Homonuclear dipolar recoupling techniques for structure determination in uniformly 13C-labeled proteins. SOLID STATE NUCLEAR MAGNETIC RESONANCE 2009; 36:119-128. [PMID: 19729285 DOI: 10.1016/j.ssnmr.2009.07.003] [Citation(s) in RCA: 46] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/13/2009] [Accepted: 07/21/2009] [Indexed: 05/28/2023]
Abstract
In solid-state NMR magic angle spinning is often used to remove line broadening associated with anisotropic interactions, such as chemical shift anisotropy and dipolar couplings. Dipolar recoupling refers to sequences of pulses designed to reintroduce dipolar interactions that are otherwise averaged by magic angle spinning. One of the key applications of homonuclear (and heteronuclear) dipolar recoupling is for the purpose of protein structure determination. Recoupling experiments, originally designed for applications in spin-pair labeled samples, have been revised in recent years for applications in samples with extensive or uniform incorporation of isotopic labels. In these samples multiple internuclear distances can in principle be probed simultaneously, but the dipolar truncation effects (i.e. attenuation of the effects of weak couplings by strong ones) circumvent such measurements. In this article we review some of the recent developments in homonuclear recoupling methods that allow overcoming this problem.
Collapse
Affiliation(s)
- Vladimir Ladizhansky
- Department of Physics, University of Guelph, 50 Stone Road East, Guelph, Ontario, Canada.
| |
Collapse
|
7
|
Pileio G, Levitt MH. Theory of long-lived nuclear spin states in solution nuclear magnetic resonance. II. Singlet spin locking. J Chem Phys 2009; 130:214501. [DOI: 10.1063/1.3139064] [Citation(s) in RCA: 92] [Impact Index Per Article: 6.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
|
8
|
Skrynnikov NR. Asymmetric doublets in MAS NMR: coherent and incoherent mechanisms. MAGNETIC RESONANCE IN CHEMISTRY : MRC 2007; 45 Suppl 1:S161-73. [PMID: 18157846 DOI: 10.1002/mrc.2162] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/14/2023]
Abstract
It has been long noted that J-resolved doublets observed in solid-state MAS experiments are asymmetric. The asymmetry has been attributed to a coherent interference effect involving dipolar and CSA interactions. Recently, Bernd Reif and co-workers suggested that under fast MAS conditions the coherent portion of the effect is suppressed and it becomes possible to observe an incoherent mechanism reminiscent of TROSY. The researchers were able to observe the characteristic TROSY-type patterns in (15)N-(1)H(N) spectra of heavily deuterated protein samples (Chevlekov, Diehl, and Reif, previous article in this issue). In the present computer simulation study, we seek to obtain a unified picture of this phenomenon, including both coherent and incoherent aspects. The chosen model focuses on the (15)N-(1)H(N) pair from a polycrystalline sample subject to magic angle spinning. To mimic local dynamics, we assume that the corresponding peptide plane jumps between two orientations. The simulations demonstrate that this simple model reproduces both coherent and incoherent behavior, depending on the MAS speed and the time scale of local dynamics. Furthermore, semianalytical expressions can be derived for both coherent and incoherent (Redfield) limits. Of particular interest is the possibility to use solution-style Redfield results to probe internal protein motions, especially slower motions on the nanosecond time scale. Our simulations show that the differential relaxation measurement permits accurate determination of (15)N dipolar-CSA cross correlations already at moderately high MAS speed (ca 15 kHz).
Collapse
Affiliation(s)
- N R Skrynnikov
- Department of Chemistry, Purdue University, 560 Oval Drive, West Lafayette, IN 47907-2084, USA.
| |
Collapse
|
9
|
Wylie BJ, Sperling LJ, Rienstra CM. Isotropic chemical shifts in magic-angle spinning NMR spectra of proteins. Phys Chem Chem Phys 2007; 10:405-13. [PMID: 18174982 DOI: 10.1039/b710736f] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Here we examine the effect of magic-angle spinning (MAS) rate upon lineshape and observed peak position for backbone carbonyl (C') peaks in NMR spectra of uniformly-(13)C,15N-labeled (U-(13)C,15N) solid proteins. 2D N-C' spectra of U-(13)C,15N microcrystalline protein GB1 were acquired at six MAS rates, and the site-resolved C' lineshapes were analyzed by numerical simulations and comparison to spectra from a sparsely labeled sample (derived from 1,3-(13)C-glycerol). Spectra of the U-(13)C,15N sample demonstrate large variations in the signal-to-noise ratio and peak positions, which are absent in spectra of the sparsely labeled sample, in which most 13C' sites do not possess a directly bonded 13CA. These effects therefore are a consequence of rotational resonance, which is a well-known phenomenon. Yet the magnitude of this effect pertaining to chemical shift assignment has not previously been examined. To quantify these effects in high-resolution protein spectra, we performed exact numerical two- and four-spin simulations of the C' lineshapes, which reproduced the experimentally observed features. Observed peak positions differ from the isotropic shift by up to 1.0 ppm, even for MAS rates relatively far (a few ppm) from rotational resonance. Although under these circumstances the correct isotropic chemical shift values may be determined through simulation, systematic errors are minimized when the MAS rate is equivalent to approximately 85 ppm for 13C. This moderate MAS condition simplifies spectral assignment and enables data sets from different labeling patterns and spinning rates to be used most efficiently for structure determination.
Collapse
Affiliation(s)
- Benjamin J Wylie
- Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Avenue, Urbana, IL 61801, USA
| | | | | |
Collapse
|
10
|
Janik R, Peng X, Ladizhansky V. (13)C-(13)C distance measurements in U-(13)C, (15)N-labeled peptides using rotational resonance width experiment with a homogeneously broadened matching condition. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2007; 188:129-40. [PMID: 17644014 DOI: 10.1016/j.jmr.2007.06.005] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/13/2007] [Revised: 06/06/2007] [Accepted: 06/06/2007] [Indexed: 05/16/2023]
Abstract
In this publication, we introduce a version of the rotational resonance width experiment with a homogeneously broadened matching condition. The increase in the bandwidth is achieved by the reduction of the proton decoupling power during mixing, which results in the reduction of zero-quantum relaxation, and broadens the rotational resonance condition. We show that one can achieve recoupling of the carbonyl-aliphatic side chain dipolar interactions band selectively, while avoiding the recoupling of strongly interacting C'-Calpha and C'-Cbeta spin pairs. The attenuation of the multi-spin effects in the presence of short zero-quantum relaxation enables a two-spin approximation to be employed for the analysis of the experimental data. The systematic error introduced by this approximation is estimated by comparing the results with a three-spin simulation. The experiment is demonstrated in [U-(13)C,(15)N]N-acetyl-L-Val-L-Leu dipeptide, where 11 distances, ranging from 2.5 to 6 A, were measured.
Collapse
Affiliation(s)
- Rafal Janik
- Department of Physics and Biophysics, Interdepartmental Group, University of Guelph, 50 Stone Road East, Guelph, Ontario, Canada N1G 2W1
| | | | | |
Collapse
|
11
|
Ramachandran R, Lewandowski JR, van der Wel PCA, Griffin RG. Multipole-multimode Floquet theory of rotational resonance width experiments: C13–C13 distance measurements in uniformly labeled solids. J Chem Phys 2006; 124:214107. [PMID: 16774398 DOI: 10.1063/1.2194905] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
A formal description of zero-quantum (ZQ) NMR processes using multipole-multimode Floquet theory is proposed for studying polarization transfer in magic angle spinning experiments. Specifically, we investigate the factors affecting the accuracy and precision of 13C-13C distance measurements that are based on ZQ-magnetization exchange processes in rotational resonance width experiments. With suitable examples drawn from measurements in N-acetyl-[U-13C,15N]-L-valine-L-leucine, we substantiate our approach and propose methods for improving the accuracy and reliability of such 13C-13C distance measurements in uniformly 13C, 15N-labeled solids. In addition, the theoretical model presented in this article provides a more general framework for describing relaxation phenomena involving multiple decay rate constants in zero-quantum processes.
Collapse
Affiliation(s)
- Ramesh Ramachandran
- Francis Bitter Magnet Laboratory, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | | | | | | |
Collapse
|
12
|
Ladizhansky V, Griffin RG. Band-selective carbonyl to aliphatic side chain 13C-13C distance measurements in U-13C,15N-labeled solid peptides by magic angle spinning NMR. J Am Chem Soc 2004; 126:948-58. [PMID: 14733572 DOI: 10.1021/ja037138c] [Citation(s) in RCA: 44] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We describe three-dimensional magic angle spinning NMR experiments that enable simultaneous band-selective measurement of the multiple distance constraints between carbonyl and side chain carbons in uniformly 13C,15N-labeled peptides. The approaches are designed to circumvent the dipolar truncation and to allow experimental separation of the multiple quantum (MQ) relaxation and dipolar effects. The pulse sequences employ the double quantum (DQ) rotational resonance in the tilted frame (R2TR) to perform selective polarization transfers that reintroduce the 13C'-13Cgamma,delta dipolar interactions. The scheme avoids recoupling of the strongly coupled C'-Calpha and C'-Cbeta spin pairs, therefore minimizing dipolar truncation effects. The experiment is performed in a constant time fashion as a function of the radio frequency irradiation intensity and measures the line shape of the DQ transition. The width and the intensity of this line shape are analyzed in terms of the DQ relaxation and dipolar coupling. The attenuation of the multispin effects in the presence of relaxation enables a two-spin approximation to be employed for the analysis of the experimental data. The systematic error introduced by this approximation is estimated by comparing the results with a three-spin simulation. The contributions of B1-inhomogeneity, CSA orientation effects, and the effects of inhomogeneous line broadening are also estimated. The experiments are demonstrated in model U-13C,15N-labeled peptides, N-acetyl-L-Val-L-Leu and N-formyl-L-Met-L-Leu-L-Phe, where 10 and 6 distances, ranging between 3 and 6 A, were measured, respectively.
Collapse
Affiliation(s)
- Vladimir Ladizhansky
- Department of Chemistry and Center for Magnetic Resonance, Francis Bitter Magnet Laboratory, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307, USA
| | | |
Collapse
|
13
|
Sonnenberg L, Luca S, Baldus M. Multiple-spin analysis of chemical-shift-selective (13C, 13C) transfer in uniformly labeled biomolecules. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2004; 166:100-110. [PMID: 14675825 DOI: 10.1016/j.jmr.2003.10.014] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
Chemical-shift-selective (13C, 13C) polarization transfer is analyzed in uniformly labeled biomolecules. It is shown that the spin system dynamics remain sensitive to the distance of interest and can be well reproduced within a quantum-mechanical multiple-spin analysis. These results lead to a general approach on how to describe chemical-shift-selective transfer in uniformly labeled systems. As demonstrated in the case of ubiquitin, this methodology can be used to detect long-range distance constraints in uniformly labeled proteins.
Collapse
Affiliation(s)
- Lars Sonnenberg
- Department for NMR-Based Structural Biology, Max-Planck-Institute for Biophysical Chemistry, 37077 Göttingen, Germany
| | | | | |
Collapse
|
14
|
Ramachandran R, Ladizhansky V, Bajaj VS, Griffin RG. 13C−13C Rotational Resonance Width Distance Measurements in Uniformly 13C-Labeled Peptides. J Am Chem Soc 2003; 125:15623-9. [PMID: 14664610 DOI: 10.1021/ja037761x] [Citation(s) in RCA: 52] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The rotational resonance width (R2W) experiment is a constant-time version of the rotational resonance (R2) experiment, in which the magnetization exchange is measured as a function of sample spinning frequency rather than the mixing time. The significant advantage of this experiment over conventional R2 is that both the dipolar coupling and the relaxation parameters can be independently and unambiguously extracted from the magnetization exchange profile. In this paper, we combine R2W with two-dimensional 13C-13C chemical shift correlation spectroscopy and demonstrate the utility of this technique for the site-specific measurement of multiple 13C-13C distances in uniformly labeled solids. The dipolar truncation effects, usually associated with distance measurements in uniformly labeled solids, are considerably attenuated in R2W experiments. Thus, R2W experiments are applicable to uniformly labeled biological systems. To validate this statement, multiple 13C-13C distances (in the range of 3-6 A) were determined in N-acetyl-[U-13C,15N]l-Val-l-Leu with an average precision of +/-0.5 A. Furthermore, the distance constraints extracted using a two-spin model agree well with the X-ray crystallographic data.
Collapse
Affiliation(s)
- Ramesh Ramachandran
- Francis Bitter Magnet Laboratory and Department of Chemistry, Massachusetts Institute of Technology, Cambridge, MA 02139-4307, USA
| | | | | | | |
Collapse
|
15
|
|
16
|
Carravetta M, Schmedt auf der Günne J, Levitt MH. Enhanced triple-quantum excitation in 13C magic-angle spinning NMR. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2003; 162:443-453. [PMID: 12810030 DOI: 10.1016/s1090-7807(03)00059-4] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
We describe a new method for exciting triple-quantum coherences in 13C-labelled powder samples under MAS. The proposed method combines selective double-quantum excitation with rotational resonance and frequency-selective composite pulses. The spin dynamics of this new method are described theoretically. Numerical calculations of the spin dynamics are compared to experimental results on fully 13C-labelled L-alanine. The observed triple-quantum filtering efficiency is around 10% for the most intense spectral peak. The method is also demonstrated on other fully 13C-labelled compounds, including a uniformly 13C-labelled amino acid.
Collapse
|
17
|
Rienstra CM, Hohwy M, Mueller LJ, Jaroniec CP, Reif B, Griffin RG. Determination of multiple torsion-angle constraints in U-(13)C,(15)N-labeled peptides: 3D (1)H-(15)N-(13)C-(1)H dipolar chemical shift NMR spectroscopy in rotating solids. J Am Chem Soc 2002; 124:11908-22. [PMID: 12358535 DOI: 10.1021/ja020802p] [Citation(s) in RCA: 104] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We demonstrate constraint of peptide backbone and side-chain conformation with 3D (1)H-(15)N-(13)C-(1)H dipolar chemical shift, magic-angle spinning NMR experiments. In these experiments, polarization is transferred from (15)N[i] by ramped SPECIFIC cross polarization to the (13)C(alpha)[i], (13)C(beta)[i], and (13)C(alpha)[i - 1] resonances and evolves coherently under the correlated (1)H-(15)N and (1)H-(13)C dipolar couplings. The resulting set of frequency-labeled (15)N(1)H-(13)C(1)H dipolar spectra depend strongly upon the molecular torsion angles phi[i], chi1[i], and psi[i - 1]. To interpret the data with high precision, we considered the effects of weakly coupled protons and differential relaxation of proton coherences via an average Liouvillian theory formalism for multispin clusters and employed average Hamiltonian theory to describe the transfer of (15)N polarization to three coupled (13)C spins ((13)C(alpha)[i], (13)C(beta)[i], and (13)C(alpha)[i - 1]). Degeneracies in the conformational solution space were minimized by combining data from multiple (15)N(1)H-(13)C(1)H line shapes and analogous data from other 3D (1)H-(13)C(alpha)-(13)C(beta)-(1)H (chi1), (15)N-(13)C(alpha)-(13)C'-(15)N (psi), and (1)H-(15)N[i]-(15)N[i + 1]-(1)H (phi, psi) experiments. The method is demonstrated here with studies of the uniformly (13)C,(15)N-labeled solid tripeptide N-formyl-Met-Leu-Phe-OH, where the combined data constrains a total of eight torsion angles (three phi, three chi1, and two psi): phi(Met) = -146 degrees, psi(Met) = 159 degrees, chi1(Met) = -85 degrees, phi(Leu) = -90 degrees, psi(Leu) = -40 degrees, chi1(Leu) = -59 degrees, phi(Phe) = -166 degrees, and chi1(Phe) = 56 degrees. The high sensitivity and dynamic range of the 3D experiments and the data analysis methods provided here will permit immediate application to larger peptides and proteins when sufficient resolution is available in the (15)N-(13)C chemical shift correlation spectra.
Collapse
Affiliation(s)
- Chad M Rienstra
- Department of Chemistry, Center for Magnetic Resonance, Francis Bitter Magnet Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | | | | | | | | | | |
Collapse
|
18
|
Brinkmann A, Schmedt auf der Günne J, Levitt MH. Homonuclear zero-quantum recoupling in fast magic-angle spinning nuclear magnetic resonance. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2002; 156:79-96. [PMID: 12081445 DOI: 10.1006/jmre.2002.2525] [Citation(s) in RCA: 40] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
Solid-state magic-angle-spinning NMR pulse sequences which implement zero-quantum homonuclear dipolar recoupling are designed with the assistance of symmetry theory. The pulse sequences are compensated on a short time scale by the use of composite pulses and on a longer time scale by the use of supercycles. (13)C dipolar recoupling is demonstrated in powdered organic solids at high spinning frequencies. The new sequences are compared to existing pulse sequences by means of numerical simulations. Experimental two-dimensional magnetization exchange spectra are shown for [U-(13)C]-L-tyrosine.
Collapse
Affiliation(s)
- Andreas Brinkmann
- Division of Physical Chemistry, Arrhenius Laboratory, Stockholm University, Stockholm, 10691, Sweden
| | | | | |
Collapse
|
19
|
Goobes G, Vega S. Improved narrowband dipolar recoupling for homonuclear distance measurements in rotating solids. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2002; 154:236-251. [PMID: 11846581 DOI: 10.1006/jmre.2001.2463] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
Recovery of the magnetic dipolar interaction between nuclei bearing the same gyromagnetic ratio in rotating solids can be promoted by synchronous rf irradiation. Determination of the dipolar interaction strength can serve as a tool for structural elucidation in polycrystalline powders. Spinning frequency dependent narrow-band (nb) RFDR and SEDRA experiments are utilized as simple techniques for the determination of dipolar interactions between the nuclei in coupled homonuclear spin pairs. The magnetization exchange and coherence dephasing due to a fixed number of rotor-synchronously applied pi-pulses is monitored at spinning frequencies in the vicinity of the rotational resonance (R(2)) conditions. The powder nbRFDR and nbSEDRA decay curves of spin magnetizations and coherences, respectively, as a function of the spinning frequency can be measured and analyzed using simple rate equations providing a quantitative measure of the dipolar coupling. The effects of the phenomenological relaxation parameters in these rate equations are discussed and an improved methodology is suggested for analyzing nbRFDR data for small dipolar couplings. The distance between the labeled nuclei in the 1,3-(13)C(2)-hydroxybutyric acid molecule is rederived using existing nbRFDR results and the new simulation procedure. A nbSEDRA experiment has been performed successfully on a powder sample of singly labeled 1-(13)C-L-leucine measuring the dipolar interaction between the labeled carboxyl carbon and the natural abundant beta-carbon. Both narrowband techniques are employed for the determination of the nuclear distances between the side-chain carbons of leucine and its carbonyl carbon in a tripeptide Leu-Gly-Phe that is singly (13)C-labeled at the leucine carbonyl carbon position.
Collapse
Affiliation(s)
- G Goobes
- Department of Chemical Physics, Weizmann Institute of Science, Rehovot, 76100, Israel
| | | |
Collapse
|
20
|
Carravetta M, Edén M, Johannessen OG, Luthman H, Verdegem PJ, Lugtenburg J, Sebald A, Levitt MH. Estimation of carbon-carbon bond lengths and medium-range internuclear distances by solid-state nuclear magnetic resonance. J Am Chem Soc 2001; 123:10628-38. [PMID: 11673994 DOI: 10.1021/ja016027f] [Citation(s) in RCA: 96] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We describe magic-angle-spinning NMR methods for the accurate determination of internuclear dipole-dipole couplings between homonuclear spins-(1/2) in the solid state. The new sequences use symmetry principles to treat the effect of magic-angle sample-rotation and resonant radio frequency fields. The pulse-sequence symmetries generate selection rules which reduce the interference of undesirable interactions and improve the robustness of the pulse sequences with respect to chemical shift anisotropies. We show that the pulse sequences may be used to estimate distances between 13C spins in organic solids, including bond lengths in systems with large chemical shift anisotropies, such as conjugated systems. For bond-length measurements, the precision of the method is +/-2 pm with a systematic overestimate of the internuclear distance by 3 +/- 1 pm. The method is expected to be a useful tool for investigating structural changes in macromolecules.
Collapse
Affiliation(s)
- M Carravetta
- Physical Chemistry Division, Stockholm University, S-106 91 Stockholm, Sweden
| | | | | | | | | | | | | | | |
Collapse
|
21
|
Brinkmann A, Levitt MH. Symmetry principles in the nuclear magnetic resonance of spinning solids: Heteronuclear recoupling by generalized Hartmann–Hahn sequences. J Chem Phys 2001. [DOI: 10.1063/1.1377031] [Citation(s) in RCA: 187] [Impact Index Per Article: 8.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
22
|
Filip C, Filip X, Bertmer M, Demco DE, Blümich B. Dipolar and J encoded DQ MAS spectra under rotational resonance. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2001; 150:184-193. [PMID: 11384179 DOI: 10.1006/jmre.2001.2331] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
A two-dimensional (2D) double-quantum (DQ) experiment under rotational resonance (R(2)) conditions is introduced for evaluating dipolar couplings in rotating solids. The contributions from the R(2)-recoupled dipolar interaction and the J coupling can be conveniently separated in the resulting 2D R(2)-DQ spectrum, so that the unknown dipolar coupling can readily be extracted, provided that the values of the involved J coupling constants are known. Since the measured parameters are integral intensity ratios between suitably chosen absorption peaks in the 2D spectrum, the proposed method is characterized by a reduced sensitivity to relaxation parameters. The effect of rotor-modulated terms, including chemical shift anisotropy, is efficiently averaged out by synchronizing the excitation/reconversion time with the rotor period. All of these features are demonstrated theoretically by the example of two model systems, namely, isolated spin-pairs and a three-spin system. The results of the theoretical models are applied to both (13)C and (1)H nuclei to extract dipolar couplings in uniformly (13)C labeled L-alanine and a crosslinked natural rubber.
Collapse
Affiliation(s)
- C Filip
- Institute for Technical Chemistry and Macromolecular Chemistry, RWTH Aachen, Worringerweg 1, D-52074 Aachen, Germany
| | | | | | | | | |
Collapse
|
23
|
Karlsson T, Hughes CE, Schmedt auf der Günne J, Levitt MH. Double-quantum excitation in the NMR of spinning solids by pulse-assisted rotational resonance. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2001; 148:238-247. [PMID: 11237629 DOI: 10.1006/jmre.2000.2243] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
We describe a new technique for double-quantum excitation in magic-angle-spinning NMR of powdered solids. The technique is designed to efficiently excite double-quantum coherence in the vicinity of a rotational resonance condition. The offset from rotational resonance allows the double-quantum filtered signals to be observed with high resolution and sensitivity. The method uses rotational excitation of zero-quantum coherence, assisted by radiofrequency pulse cycles. The zero-quantum coherence is converted into double-quantum coherence by a frequency-selective inversion sequence. Experiments on [(13)C(2), (15)N]-glycine demonstrate a double-quantum filtering efficiency of approximately 41% at a sample rotation frequency of 8.300 kHz, which is 1.600 kHz away from the n = 1 rotational resonance. We achieve 32% double-quantum filtering efficiency at a spinning frequency of 9.250 kHz, which is 2.550 kHz away from rotational resonance.
Collapse
Affiliation(s)
- T Karlsson
- Division of Physical Chemistry, Stockholm University, S-106 91 Stockhom, Sweden
| | | | | | | |
Collapse
|
24
|
Antzutkin ON, Levitt MH. Coherence transfer signals in the rotational resonance NMR of a spinning single crystal. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2000; 147:147-151. [PMID: 11042058 DOI: 10.1006/jmre.2000.2169] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
A recent analysis of rotational resonance lineshapes (M. Helmle et al., J. Magn. Reson. 140, 379-403, 1999) predicted the existence of coherence transfer signals, which are generated by mechanically induced coherence transfer during the detection process. These signals correspond to the generation of observable coherences at spin sites that have no magnetization at the beginning of the observation interval but which acquire coherence while the detection is underway. The coherence transfer signals disappear for powder samples in conventional magic-angle-spinning solid-state NMR experiments. In this Communication, we report the successful detection of coherence transfer signals in rotor-synchronized experiments performed on a single crystal of [1,2-(13)C(2)]glycine. Copyright 2000 Academic Press.
Collapse
Affiliation(s)
- ON Antzutkin
- Division of Inorganic Chemistry, Lulea University of Technology, Lulea, S-971 87, Sweden
| | | |
Collapse
|
25
|
Goobes G, Boender GJ, Vega S. Spinning-frequency-dependent narrowband RF-driven dipolar recoupling. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2000; 146:204-219. [PMID: 10968974 DOI: 10.1006/jmre.2000.2126] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
Dipolar recoupling techniques of homonuclear spin pairs are commonly used for distance or orientation measurements in solids. Accurate measurements are interfered with by broadening mechanisms. In this publication narrowband RF-driven dipolar recoupling magnetization exchange experiments are performed as a function of the spinning frequency to reduce the effect of zero-quantum T(2) relaxation. To enhance the exchange of magnetization between the coupled spins, a fixed number of rotor-synchronous pi-pulses are applied at spinning frequencies approaching the rotational resonance (R(2)) conditions. The analysis of the powder averaged dipolar decay curves of the spin magnetizations as a function of the spinning frequency provides a quantitative measure of the dipolar coupling. An effective Hamiltonian for this experiment is derived, taking into account all chemical shift parameters of the spins. The length of the nbRFDR mixing time and the number of rotor cycles per pi-pulse are optimized by numerical simulations for sensitive probing of the dipolar coupling strength. The zero-quantum T(2) relaxation time can easily be taken into account in the data analysis, because the overall exchange time is almost constant in these experiments. Spinning-frequency-dependent nbRFDR experiments near the m = 1 and m = 2 R(2) condition are shown for doubly (13)C-labeled hydroxybutyric acid. Copyright 2000 Academic Press.
Collapse
Affiliation(s)
- G Goobes
- Department of Chemical Physics, Weizmann Institute of Science, Rehovot, 76100, Israel
| | | | | |
Collapse
|
26
|
Bryce DL, Wasylishen RE. Dipolar-Chemical Shift and Rotational Resonance 13C NMR Studies of the Carboxyl−Methylene Carbon Spin Pair in Solid Phenylacetic Acid and Potassium Hydrogen Bisphenylacetate. J Phys Chem A 2000. [DOI: 10.1021/jp0013661] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- David L. Bryce
- Department of Chemistry, Dalhousie University, Halifax, Nova Scotia, Canada, B3H 4J3
| | | |
Collapse
|
27
|
Karlsson T, Edén M, Luthman H, Levitt MH. Efficient double-quantum excitation in rotational resonance NMR. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2000; 145:95-107. [PMID: 10873500 DOI: 10.1006/jmre.2000.2080] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
We present a new technique for double-quantum excitation in magic-angle-spinning solid-state NMR. The method involves (i) preparation of nonequilibrium longitudinal magnetization; (ii) mechanical excitation of zero-quantum coherence by spinning the sample at rotational resonance, and (iii) phase-coherent conversion of the zero-quantum coherence into double-quantum coherence by frequency-selective spin inversion. The double-quantum coherence is converted into observable magnetization by reversing the excitation process, followed by a pi/2 pulse. The method is technically simple, does not require strong RF fields, and is feasible at high spinning frequencies. In [(13)C(2),(15)N]-glycine, with an internuclear (13)C-(13)C distance of 0.153 nm, we achieve a double-quantum filtering efficiency of approximately 56%. In [11, 20-(13)C(2)]-all-E-retinal, with an internuclear (13)C-(13)C distance of 0.296 nm, we obtain approximately 45% double-quantum filtering efficiency.
Collapse
Affiliation(s)
- T Karlsson
- Division of Physical Chemistry, Stockholm University, Stockholm, S-106 91, Sweden
| | | | | | | |
Collapse
|
28
|
Brinkmann A, Edén M, Levitt MH. Synchronous helical pulse sequences in magic-angle spinning nuclear magnetic resonance: Double quantum recoupling of multiple-spin systems. J Chem Phys 2000. [DOI: 10.1063/1.481458] [Citation(s) in RCA: 177] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
29
|
Ernst M, Zimmermann H, Meier BH. A simple model for heteronuclear spin decoupling in solid-state NMR. Chem Phys Lett 2000. [DOI: 10.1016/s0009-2614(99)01423-2] [Citation(s) in RCA: 42] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
|
30
|
Dusold S, Maisel H, Sebald A. Magnitudes and orientations of interaction tensors determined from rotational resonance MAS NMR lineshapes of a four-(13)C-spin system. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 1999; 141:78-90. [PMID: 10527746 DOI: 10.1006/jmre.1999.1865] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
Possibilities and limitations of iterative lineshape fitting approaches for the complete determination of magnitudes and orientations of NMR interaction tensors in a four-(13)C-spin system from MAS NMR experiments are investigated. The availability of fast and numerically accurate computational methods is an important prerequisite. The model compound chosen for this investigation is the monoammonium salt of maleic acid. Various selectively and fully (13)C-labeled versions of this compound permit a stepwise reduction of the number of unknown parameters, necessary to fully describe the four-(13)C-spin system in the uniformly (13)C-labeled maleate moiety. This stepwise procedure allows one to monitor reliability and accuracy of multiparameter fits of the four-(13)C-spin system itself, as well as to characterize limitations and requirements for such fitting procedures. Satisfactory (1)H-decoupling performance is an essential experimental requirement; TPPM decoupling yields n = 1, 2 rotational resonance (13)C MAS NMR lineshapes suitable for analysis by iterative lineshape fitting methods. It is demonstrated that assumptions about "typical" chemical shielding tensor orientations, even if not deviating much from the real orientations, lead to severe errors in internuclear distance determinations. Copyright 1999 Academic Press.
Collapse
Affiliation(s)
- S Dusold
- Bayerisches Geoinstitut, Universitat Bayreuth, Bayreuth, D-95440, Germany
| | | | | |
Collapse
|