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.     

A thermometer for nonspinning solid-state NMR spectroscopy

We discuss a method to determine temperature in a static NMR experiment from the temperature variation of the lead nitrate peak shift.     

AssignFit: a program for simultaneous assignment and structure refinement from solid-state NMR spectra

AssignFit is a computer program developed within the XPLOR-NIH package for the assignment of dipolar coupling (DC) and chemical shift anisotropy (CSA) restraints derived from the solid-state NMR spectra of protein samples with uniaxial order. The method is based on minimizing the difference between experimentally observed solid-state NMR spectra and the frequencies back calculated from a structural model. Starting with a structural model and a set of DC and CSA restraints grouped only by amino acid type, as would be obtained by selective isotopic labeling, AssignFit generates all of the possible assignment permutations and calculates the corresponding atomic coordinates oriented in the alignment frame, together with the associated set of NMR frequencies, which are then compared with the experimental data for best fit. Incorporation of AssignFit in a simulated annealing refinement cycle provides an approach for simultaneous assignment and structure refinement (SASR) of proteins from solid-state NMR orientation restraints. The methods are demonstrated with data from two integral membrane proteins, one α-helical and one β-barrel, embedded in phospholipid bilayer membranes.     

Selective averaging for high-resolution solid-state NMR spectroscopy of aligned samples

Solid-state NMR experiments benefit from being performed at high fields, and this is essential in order to obtain spectra with the resolution and sensitivity required for applications to protein structure determination in aligned samples. Since the amount of rf power that can be applied is limited, especially for aqueous protein samples, the most important pulse sequences suffer from bandwidth limitations resulting from the same spread in chemical shift frequencies that aids resolution. SAMPI4 is a pulse sequence that addresses these limitations. It yields separated local field spectra with narrower and more uniform linewidths over the entire spectrum than the currently used PISEMA and SAMMY experiments. In addition, it is much easier to set up on commercial spectrometers and can be incorporated as a building block into other multidimensional pulse sequences. This is illustrated with a two-dimensional HETCOR experiment, where it is crucial to transfer polarization from the amide protons to their directly bonded nitrogens over a wide range of chemical shift frequencies. A quantum-mechanical treatment of the spin Hamiltonians under high-power rf pulses is presented which gives the scaling factor for SAMPI4 as well as the durations of the rf pulses to achieve optimal decoupling.     

High-resolution solid-state NMR spectroscopy as a tool for investigation of enantioselective inclusion complexation

In this paper, we showed the application of solid state-NMR (SS NMR) spectroscopy in structural studies of chiral compounds employing sample of (E)-1-diphenylphosphinoylpent-3-en-2-ol 1 as a model compound. Racemate of 1 was fully characterized by NMR techniques (both in liquid and solid phase) and X-ray crystallography. Theoretical calculations employing the GIAO approach were used to explain the influence of hydrogen bonding on 31P NMR shielding parameter in racemate. Enantioselective inclusion complexation (EIC) method with TADDOL as host molecule was applied to separate of enantiomers. The formation of host-guest complex and decomplexation procedure was monitored by means of the SS NMR. The liquid-state NMR, due to similarity of 13C and 31P spectral parameters was not able to distinguish racemate from enantiomer. In the solid phase, owing to distinction of hydrogen bonding and molecular packing in the crystal lattice, racemate and enantiomers were easy recognized by NMR spectroscopy.     

Multidimensional solid-state NMR spectroscopy of plant cell walls

Plant biomass has become an important source of bio-renewable energy in modern society. The molecular structure of plant cell walls is difficult to characterize by most atomic-resolution techniques due to the insoluble and disordered nature of the cell wall. Solid-state NMR (SSNMR) spectroscopy is uniquely suited for studying native hydrated plant cell walls at the molecular level with chemical resolution. Significant progress has been made in the last five years to elucidate the molecular structures and interactions of cellulose and matrix polysaccharides in plant cell walls. These studies have focused on primary cell walls of growing plants in both the dicotyledonous and grass families, as represented by the model plants Arabidopsis thaliana, Brachypodium distachyon, and Zea mays. To date, these SSNMR results have shown that 1) cellulose, hemicellulose, and pectins form a single network in the primary cell wall; 2) in dicot cell walls, the protein expansin targets the hemicellulose-enriched region of the cellulose microfibril for its wall-loosening function; and 3) primary wall cellulose has polymorphic structures that are distinct from the microbial cellulose structures. This article summarizes these key findings, and points out future directions of investigation to advance our fundamental understanding of plant cell wall structure and function.     

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.     

The virtual NMR spectrometer: a computer program for efficient simulation of NMR experiments involving pulsed field gradients

This paper presents a software program, the Virtual NMR Spectrometer, for computer simulation of multichannel, multidimensional NMR experiments on user-defined spin systems. The program is capable of reproducing most features of the modern NMR experiment, including homo- and heteronuclear pulse sequences, phase cycling, pulsed field gradients, and shaped pulses. Two different approaches are implemented to simulate the effect of pulsed field gradients on coherence selection, an explicit calculation of all coherence transfer pathways, and an effective approximate method using integration over multiple positions in the sample. The applications of the Virtual NMR Spectrometer are illustrated using homonuclear COSY and DQF COSY experiments with gradient selection, heteronuclear HSQC, and TROSY. The program uses an intuitive graphical user interface, which resembles the appearance and operation of a real spectrometer. A translator is used to allow the user to design pulse sequences with the same programming language used in the actual experiment on a real spectrometer. The Virtual NMR Spectrometer is designed as a useful tool for developing new NMR experiments and for tuning and adjusting the experimental setup for existing ones prior to running costly NMR experiments, in order to reduce the setup time on a real spectrometer. It will also be a useful aid for learning the general principles of magnetic resonance and contemporary innovations in NMR pulse sequence design.     

Sensitivity and resolution enhancement in solid-state NMR spectroscopy of bicelles

Magnetically aligned bicelles are becoming attractive model membranes to investigate the structure, dynamics, geometry, and interaction of membrane-associated peptides and proteins using solution- and solid-state NMR experiments. Recent studies have shown that bicelles are more suitable than mechanically aligned bilayers for multidimensional solid-state NMR experiments. In this work, we describe experimental aspects of the natural abundance (13)C and (14)N NMR spectroscopy of DMPC/DHPC bicelles. In particular, approaches to enhance the sensitivity and resolution and to quantify radio-frequency heating effects are presented. Sensitivity of (13)C detection using single pulse excitation, conventional cross-polarization (CP), ramp-CP, and NOE techniques are compared. Our results suggest that the proton decoupling efficiency of the FLOPSY pulse sequence is better than that of continuous wave decoupling, TPPM, SPINAL, and WALTZ sequences. A simple method of monitoring the water proton chemical shift is demonstrated for the measurement of sample temperature and calibration of the radio-frequency-induced heating in the sample. The possibility of using (14)N experiments on bicelles is also discussed.     

The in-situ solid-state NMR spectroscopy investigation of alcoholic lactose suspensions

The polymorphic forms of lactose in alcoholic suspensions have been determined by ¹³C CP-MAS NMR spectroscopy, employing hand-made glass inserts. Suspensions of alpha lactose monohydrate (Lα·H₂O) with particle size between 2 and 200 μm were prepared by 24 h reflux or by storage for 28 d in anhydrous ethanol without agitation. These suspensions were compared to an ethanolic sub-micron lactose suspension provided by a 3 M Health Care (Loughborough). The ¹³C CP-MAS NMR spectra indicated that Lα·H₂O dehydrated to stable anhydrous alpha lactose polymorph (Lα_S) whilst suspended in ethanol. In addition, strong ethanol ¹³C resonances were observed for some samples, indicating a liquid–solid interaction between the ethanol and lactose surface. Replacement of ethanol with anhydrous methanol, n-butanol and 3-methylbutan-2-ol implied that the solvent mediated dehydration of Lα·H₂O to Lα_S occurs as a result of sterically controlled interactions.     

A comparison of NCO and NCA transfer methods for biological solid-state NMR spectroscopy

Three different techniques (adiabatic passage Hartman-Hahn cross-polarization, optimal control designed pulses, and EXPORT) are compared for transferring (15)N magnetization to (13)C in solid-state NMR experiments under magic-angle-spinning conditions. We demonstrate that, in comparison to adiabatic passage Hartman-Hahn cross-polarization, optimal control transfer pulses achieve similar or better transfer efficiencies for uniformly-(13)C,(15)N labeled samples and are generally superior for samples with non-uniform labeling schemes (such as 1,3- and 2-(13)C glycerol labeling). In addition, the optimal control pulses typically use substantially lower average RF field strengths and are more robust with respect to experimental variation and RF inhomogeneity. Consequently, they are better suited for demanding samples.     

NMR difference probe: a dual-coil probe for NMR difference spectroscopy

A unique probe designed to acquire nuclear magnetic resonance difference spectra of two samples is presented. The NMR Difference Probe contains two sample coils in a resonant circuit that switches between parallel excitation and serial acquisition to cancel common signals such as solvent peaks and impurities. Two samples containing a common analyte, acetonitrile, were used to demonstrate signal cancellation in a difference spectrum collected with a single pulse experiment. The cancellation was over 96% effective. The approach described has applications in the areas of solvent subtraction and spectral simplification.     

SIMQUADNMR: a program for simulation and interpretation of multiple quantum-filtered NMR spectra of quadrupolar nuclei

In this paper, we present a computer program which simulates NMR multiple quantum-filtered spectra of quadrupolar nuclei as a function of physical parameters, of the type of experiment and experimental conditions. The program works by solving relaxation theory equations for the given system, and it can be useful in order to plan the ideal conditions to set up specific experiments or to give a physical interpretation of experimental results. The program allows to independently follow the dependence of individual coherences and relaxation rates as a function of up to 50 parameters regarding the physical properties of the system under investigation, sample conditions and instrumental setup making it an helpful tool also for teaching purposes.