Optimal control in NMR spectroscopy: Numerical implementation in SIMPSON

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.     

液体核磁共振中由分子间偶极耦合和分子内标量耦合共同作用后的谱图裂分模式

在高极化多自旋液体样品中,同时存在着分子间偶极（D）耦合和分子内标量（J）耦合,它们的共同作用产生了一些原来观测不到的分子间多量子相干信号。而且,信号的裂分模式与只存在J耦合的多自旋体系中观测到的多量子相干信号的裂分模式不同。本文从理论和实验上研究了这些禁阻的共振峰及其独特的裂分模式。为了比较验证,我们以I2S3+X自旋体系为例,结合使用选择和非选择性的射频脉冲序列来获得分子间双量子相干信号的五种裂分模式。进而归纳出对IpSq+Xk (p, q, k = 1, 2, 3,…)自旋体系普适的裂分模式规则。并指出,它们中如(1:0:-1)的裂分模式会放大J耦合裂分,使得J耦合常数的测量更精确,特别在J耦合常数很小或不均匀场中的J耦合常数的测量中具有诱人的应用前景。结果表明理论预测,计算机模拟和实验观测结果三者吻合的很好。     

Optimal control based NCO and NCA experiments for spectral assignment in biological solid-state NMR spectroscopy

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.     

Separation of 47Ti and 49Ti solid-state NMR lineshapes by static QCPMG experiments at multiple fields

Experimental procedures are proposed and demonstrated that separate the spectroscopic contribution from both (47)Ti and (49)Ti in solid-state nuclear magnetic resonance spectra. These take advantage of the different nuclear spin quantum numbers of these isotopes that lead to different "effective" radiofrequency fields for the central transition nutation frequencies when these nuclei occur in sites with a significant electric field gradient. Numerical simulations and solid-state NMR experiments were performed on the TiO(2) polymorphs anatase and rutile. For anatase, the separation of the two isotopes at high field (21.1T) facilitated accurate determination of the electric field gradient (EFG) and chemical shift anisotropy (CSA) tensors. This was accomplished by taking advantage of the quadrupolar interaction between the EFG at the titanium site and the different magnitudes of the nuclear quadrupole moments (Q) of the two isotopes. Rutile, having a larger quadrupolar coupling constant (C(Q)), was examined by (49)Ti-selective experiments at different magnetic fields to obtain spectra with different scalings of the two anisotropic tensors. A small chemical shielding anisotropy (CSA) of -30 ppm was determined.     

SPINEVOLUTION: a powerful tool for the simulation of solid and liquid state NMR experiments

Exact numerical simulations of NMR experiments are often required for the development of new techniques and for the extraction of structural and dynamic information from the spectra. Simulations of solid-state magic angle spinning (MAS) experiments can be particularly demanding both computationally and in terms of the programming required to carry them out, even if special simulation software is used. We recently developed a number of approaches that dramatically improve the efficiency and allow a high degree of automation of these computations. In the present paper, we describe SPINEVOLUTION, a highly optimized computer program that implements the new methodology. The algorithms used in the program will be described separately. Although particularly efficient for the simulation of experiments with complex pulse sequences and multi-spin systems in solids, SPINEVOLUTION is a versatile and easy to use tool for the simulation and optimization of virtually any NMR experiment. The performance of SPINEVOLUTION was compared with that of another recently developed NMR simulation package, SIMPSON. Benchmarked on a series of examples, SPINEVOLUTION was consistently found to be orders of magnitude faster. At the time of publication, the program is available gratis for non-commercial use.     

Effective dipolar couplings determined by dipolar dephasing of double-quantum coherences

It is shown how homonuclear distances and homonuclear dipolar lattice sums between spin-1/2 nuclei can be measured by a pulsed solid-state NMR experiment under magic-angle spinning conditions. The presented technique is based on double-quantum coherence filtering. Instead of measuring a build-up of double-quantum coherence the pulse sequence is designed to dephase double-quantum coherence. This is achieved by exciting double-quantum coherence either with the help of the through-space dipolar coupling or the through-bond dipolar coupling while the dephasing relies on the through-space dipolar coupling as selected by a gamma-encoded pulse sequence from the C/R symmetry class. Since dephasing curves can be normalized on zero dephasing, it is possible to analyze the initial dephasing regime and hence determine dipolar lattice sums (effective dipolar couplings) in multiple-spin systems. A formula for the effective dipolar coupling is derived theoretically and validated by numerical calculations and experiments on crystalline model compounds for (13)C and (31)P spin systems. The double-quantum dephasing experiment can be combined with constant-time data sampling to compensate for relaxation effects, consequently only two experimental data points are necessary for a single distance measurement. The phase cycling overhead for the constant-time experiment is minimal because a short cogwheel phase cycle exists. A 2D implementation is demonstrated on [(13)C(3)]alanine.     

A 2D MAS solid-state NMR method to recover the amplified heteronuclear dipolar and chemical shift anisotropic interactions

A two-dimensional solid-state NMR method for the measurement of chemical shift anisotropy tensors of X nuclei (15N or 13C) from multiple sites of a polypeptide powder sample is presented. This method employs rotor-synchronized pi pulses to amplify the magnitude of the inhomogeneous X-CSA and 1H-X dipolar coupling interactions. A combination of on-resonance and magic angle rf irradiation of protons is used to vary the ratio of the magnitudes of the 1H-X dipolar and X-CSA interactions which are recovered under MAS, in addition to suppressing the 1H-1H dipolar interactions. The increased number of spinning sidebands in the recovered anisotropic interactions is useful to determine the CSA tensors accurately. The performance of this method is examined for powder samples of N-acetyl-(15)N-L-valine (NAV), N-acetyl-15N-L-valyl-15N-L-leucine (NAVL), and alpha-13C-L-leucine. The sources of experimental errors in the measurement of CSA tensors and the application of the pulse sequences under high-field fast MAS operations are discussed.     

Challenges in numerical simulations of solid-state NMR experiments: spin exchange pulse sequences

While simulations are essential for interpretation of solid-state NMR experiments, large spin systems involved in e.g. spin-diffusion experiments and/or dynamic effects like chemical exchange pose great challenges for the numerical simulations, where we typically want to include effects of finite pulses and other external manipulations in the simulation. In this paper, these topics are reviewed and addressed by simple numerical simulations. The numerical simulations comprise a 2-spin simulation of (2)H two-site jumps and a 332-spin simulation of a CHHC experiment for a small protein.     

Experimental aspects of multidimensional solid-state NMR correlation spectroscopy.

The experimental parameters critical for the implementation of multidimensional solid-state NMR experiments that incorporate heteronuclear spin exchange at the magic angle are discussed. This family of experiments is exemplified by the three-dimensional experiment that correlates the (1)H chemical shift, (1)H-(15)N dipolar coupling, and (15)N chemical shift frequencies. The broadening effects of the homonuclear (1)H-(1)H dipolar couplings are suppressed using flip-flop (phase- and frequency-switched) Lee-Goldburg irradiations in both the (1)H chemical shift and the (1)H-(15)N dipolar coupling dimensions. The experiments are illustrated using the (1)H and (15)N chemical shift and dipolar couplings in a single crystal of (15)N-acetylleucine.     

Efficient analysis of 51V solid-state MAS NMR spectra using genetic algorithms

A program for iterative fitting procedures to determine the NMR parameters from ⁵¹V solid-state MAS NMR spectra was developed. It contains options to use genetic algorithms and downhill-simplex optimizing procedures to extract the optimal parameter sets, which describe our spectra. As computational kernel the SIMPSON program is employed. Other kernels like SPINEVOLUTION are easily incorporable. The algorithms are checked for their suitability for the present optimization problem and optimal simulation conditions are determined, with the focus on minimal processing time. The procedure leads to a very good agreement between experimental and simulated spectra in a passable period of time. First results for spectra of model compounds for the active site of vanadium haloperoxidases are presented.     

先进固体NMR技术研究高分子结构与动力学

随着固体NMR理论和谱仪硬件技术的不断发展,近年来固体NMR技术在高分子多尺度结构与动力学研究领域中正发挥着越来越重要的作用. 多脉冲及高速魔角旋转（MAS）等质子高分辨技术的发展使得高灵敏度的¹H谱可有效地用于高分子化学结构与链间相互作用的检测;基于化学键（J-耦合）相关和通过空间（偶极耦合）相互作用的各种二维异核相关谱NMR新技术,使得复杂高分子的链结构得以严格解析. 基于MAS下同核和异核偶极-偶极相互作用、化学位移各向异性等各向异性相互作用重聚的系列新技术,使得研究者可在采用高分辨¹H或¹³C 检测信号的同时检测准静态下的各向异性相互作用,进而获得与之密切相关的结构和动力学信息. 通过质子偶极滤波技术可有效检测多相聚合物中的界面相与相区尺寸、高分子共混物中的相容性等问题. 在动力学的研究中,通过质子间自旋扩散的有效压制技术和化学位移各向异性的重聚,目前已经可以有效地获取链段上单个化学键的快速局域运动以及链段的超慢分子运动. 上述丰富的多尺度NMR技术可以使研究者在不同空间和时间尺度上对高分子聚合物的微观结构、相分离和动力学行为等进行详细的研究,进而阐明高分子微观结构与宏观性能的关联. 该文以固体NMR中最主要的2类核（¹H和¹³C）的检测技术为主线,简单介绍近年来固体NMR领域的一些最新研究进展及其在高分子结构和动力学研究中的应用.     

Insight into the CSA tensors of nucleobase carbons in RNA polynucleotides from solution measurements of residual CSA: towards new long-range orientational constraints

Using residual chemical shift anisotropies (RCSAs) measured in a weakly aligned stem-loop RNA, we examined the carbon chemical shift anisotropy (CSA) tensors of nucleobase adenine C2, pyrimidine C5 and C6, and purine C8. The differences between the measured RCSAs and the values back-calculated using three nucleobase carbon CSA sets [D. Stueber, D.M. Grant, 13C and 15N chemical shift tensors in adenosine, guanosine dihydrate, 2'-deoxythymidine, and cytidine, J. Am. Chem. Soc. 124 (2002) 10539-10551; D. Sitkoff, D.A. Case, Theories of chemical shift anisotropies in proteins and nucleic acids, Prog. NMR Spectrosc. 32 (1998) 165-190; R. Fiala, J. Czernek, V. Sklenar, Transverse relaxation optimized triple-resonance NMR experiments for nucleic acids, J. Biomol. NMR 16 (2000) 291-302] reported previously for mononucleotides (1.4 Hz) is significantly smaller than the predicted RCSA range (-10-10 Hz) but remains larger than the RCSA measurement uncertainty (0.8 Hz). Fitting of the traceless principal CSA values to the measured RCSAs using a grid search procedure yields a cytosine C5 CSA magnitude (CSAa=(3/2.(delta11(2)+delta22(2)+delta33(2)))1/2=173+/-21 ppm), which is significantly higher than the reported mononucleotide values (131-138 ppm) and a guanine C8 CSAa (148+/-13 ppm) that is in very good agreement with the mononucleotide value reported by solid-state NMR [134 ppm, D. Stueber, D.M. Grant, 13C and (15)N chemical shift tensors in adenosine, guanosine dihydrate, 2'-deoxythymidine, and cytidine, J. Am. Chem. Soc. 124 (2002) 10539-10551]. Owing to a unique sensitivity to directions normal to the base plane, the RCSAs can be translated into useful long-range orientational constraints for RNA structure determination even after allowing for substantial uncertainty in the nucleobase carbon CSA tensors.     

(13)C chemical shift and (13)C-(14)N dipolar coupling tensors determined by (13)C rotary resonance solid-state NMR

This work explores the utility of simple rotary resonance experiments for the determination of the magnitude and orientation of (13)C chemical shift tensors relative to one or more (13)C--(14)N internuclear axes from (13)C magic-angle-spinning NMR experiments. The experiment relies on simultaneous recoupling of the anisotropic (13)C chemical shift and (13)C--(14)N dipole--dipole coupling interactions using 2D rotary resonance NMR with RF irradiation on the (13)C spins only. The method is demonstrated by experiments and numerical simulations for the (13)C(alpha) spins in powder samples of L-alanine and glycine with (13)C in natural abundance. To investigate the potential of the experiment for determination of relative/absolute tensor orientations and backbone dihedral angles in peptides, the influence from long-range dipolar coupling to sequential (14)N spins in a peptide chain ((14)N(i)--(13)C(alpha)(i)--(14)N(i+1) and (14)N(i+1)--(13)C'(i)--(14)N(i) three-spin systems) as well as residual quadrupolar-dipolar coupling cross-terms is analyzed numerically.     

液体多脉冲及二维FT-NMR实验的乘积算符描述的计算机模拟

本文报道了利用乘积算符方法分析多脉冲及二维FT-NMR实验的模拟程序PROPER-MT.该程序对分析弱耦合I_mS_n(I=1/2;S=(1)/2;1 ≤ m十n<4)自旋体系实验脉冲序列是普遍适用的;它可给出实验过程中体系任何时刻算符的解析表达式.用PROPER-MT程序对一些典型的多脉冲及二维FT-NMR实验进行了模拟,特别对多量子滤波及多自旋滤波脉冲序列进行了分析计算,得到了预期的结果.     

Quadrupolar and Chemical Shift Tensors Characterized by 2D Multiple-Quantum NMR Spectroscopy

The present work discusses a new 2D NMR method for characterizing the principal values and relative orientations of the electric field gradient and the chemical shift tensors of half-integer quadrupolar sites. The technique exploits the different contributions that quadrupolar and shielding interactions impart on the evolution of multiple-quantum and of single-quantum coherences, in order to obtain 2D powder lineshapes that are highly sensitive to these nuclear spin coupling parameters. Different spinning variants of this experiment were assayed, but it was concluded that a static version can yield the highest sensitivity to the values of the principal components and to the relative geometries of the local coupling tensors. It was found that correlating the central transition evolution with the highest available order of the spin coherence was also helpful for maximizing this spectral information. Good agreement between data obtained on ⁸⁷Rb (S = ) and ⁵⁹Co (S = ) samples and ideal theoretical lineshape predictions of this experiment was obtained, provided that heterogeneities in the multiple-quantum excitation and conversion processes were suitably accounted by procedures similar to those described in the spin- multiple-quantum NMR literature.     

Spinning Sidebands in Slow-Magic-Angle-Spinning NMR Spectra Arising from TightlyJ-Coupled Spin Pairs

Complex spinning sidebands are observed in magic-angle-spinning (MAS) NMR spectra arising from isolated tightlyJ-coupled spin pairs under slow spinning conditions. Such spinning sidebands are sensitive to the magnitude and relative orientation of the chemical-shift tensors, the dipolar-coupling tensor, and the sign of the indirect spin–spin (J) coupling. We show that it is possible to extract information concerning such NMR parameters from an analysis of the observed spinning sidebands. As an example, numerical simulations are carried out to reproduce observed³¹P MAS NMR spectra of a phosphole tetramer (1) ando-bis(diphenylphosphino)benzene (2), so that invaluable information concerning the orientations of the phosphorus chemical-shift tensors and the sign ofJ(³¹P,³¹P) can be deduced. Simulations are carried out by numerically evaluating the spin-density matrix of the spin system.     

The magnetic structure on the ground state of the equilateral triangular spin tube

The ground state of the frustrated equilateral triangular spin tube CsCrF₄ is still hidden behind a veil though NMR spectrum broaden into 2 T at low temperature. In order to investigate the spin structure in an ordered state by ¹⁹F-NMR, we have determined the anisotropic hyperfine coupling tensors for each three fluorine sites in the paramagnetic state. The measurement field was raised up to 10 T to achieve highest resolution. The preliminary analysis using the obtained hyperfine tensors has shown that the archetypal 120°-type structure in ab-plane does not accord with the NMR spectra of ordered state.