Exploring the limits of broadband excitation and inversion: II. Rf-power optimized pulses

Robust dual-angle T 1 measurement in magnetization transfer spectroscopy by time-optimal control

Magnetization transfer spectroscopy relies heavily on the robust determination ofT 1 relaxation times of nuclei participating in metabolic exchange. Challenges arise due to the use of surface RF coils for transmission (highB 1 + variation) and the broad resonance band of most X nuclei. These challenges are particularly pronounced when fastT 1 mapping methods, such as the dual-angle method, are employed. Consequently, in this work, we develop resonance offset andB 1 + robust excitation RF pulses for 31P magnetization transfer spectroscopy at 7T through ensemble-based time-optimal control. In our approach, we introduce a cost functional for designing robust pulses, incorporating the full Bloch equations as constraints, which are solved using symmetric operator splitting techniques. The optimal control design of the RF pulses developed demonstrates improved accuracy, desired phase properties, and reduced RF power when applied to dual-angleT 1 mapping, thereby improving the precision of exchange-rate measurements, as demonstrated in a preclinical in vivo study quantifying brain creatine kinase activity.

Hydrogen bond formation may enhance RDC-based discrimination of enantiomers

The distinction of enantiomers based on residual anisotropic parameters obtained by alignment in chiral poly-γ-benzyl-L-glutamate (PBLG) is among the strongest in high-resolution NMR spectroscopy. However, large variations in enantiodifferentiation among different solutes are frequently observed. One hypothesis is that the formation of hydrogen bonds between solute and PBLG is important for the distinction of enantiomers. With a small set of three almost spherical enantiomeric pairs, for which 1DCH residual dipolar couplings are measured, we address this issue in a systematic way: borneol contains a single functional group that can act as a hydrogen bond donor, camphor has a single group that may act as a hydrogen bond acceptor, and quinuclidinol can act as both hydrogen bond donor and acceptor. The results are unambiguous: although camphor shows low enantiodifferentiation with PBLG and alignment that can be predicted well by the purely steric TRAMITE approach, the distinction of enantiomers for the other enantiomeric pairs is significantly higher with alignment properties that must involve a specific interaction in addition to steric alignment.

Optimal control pulses for the 1.2-GHz (28.2-T) NMR spectrometers

The ability to measure nuclear magnetic resonance (NMR) spectra with a large sample volume is crucial for concentration-limited biological samples to attain adequate signal-to-noise (S/N) ratio. The possibility to measure with a 5-mm cryoprobe is currently absent at the 1.2-GHz NMR instruments due to the exceedingly high radio frequency power demands, which is four times compared to 600-MHz instruments. Here, we overcome the high-power demands by designing optimal control (OC) pulses with up to 20 times lower power requirements than currently necessary at a 1.2-GHz spectrometer. We show that multidimensional biomolecular NMR experiments constructed using these OC pulses can bestow improvement in the S/N ratio of up to 26%. With the expected power limitations of a 5-mm cryoprobe, we observe an enhancement in the S/N ratio of more than 240% using our OC sequences. This motivates the development of a cryoprobe with a larger volume than the current 3-mm cryoprobes.

Composite pulse combinations for chirp excitation

Composite pulses are the efficient method for broadband excitation to get control of the limitations of high field NMR, such as resonance offset effects with constraints on rf power that leads to signal intensity distortion. Phase-modulated chirp pulses are used as ordered composite pulse sequences in this paper as CHORUS sequence in a high-field NMR spectrometer (BRUKER 750 MHz) for broadband excitation. The composite pulse sequence applies chirp pulses with the forward and the reverse sweep mechanisms. A single excitation pulse combines adiabatic and non-adiabatic rotation, explained as a three-phase rotation, which leaves the magnetizing vectors to a non-uniform phase dispersion as a function of the offset frequency. One adiabatic refocusing pulse of the double sweep rate after the excitation pulse cannot satisfactorily compensate for the phase dispersion. Hence, composite self-refocussing CHORUS excitation pulse, with forward, reverse, and their combinations are used to remove the non-uniform phase dispersion generated due to offset resonance frequency. Four such combinations of composite pulses are produced with analytical explanation in this paper. MATLAB simulation results and experimental verification on the BRUKER 750 MHz NMR spectrometer of the composite pulses are also presented in this paper.

Band-selective universal 90° and 180° rotation pulses covering the aliphatic carbon chemical shift range for triple resonance experiments on 1.2 GHz spectrometers

Biomolecular NMR spectroscopy requires large magnetic field strengths for high spectral resolution. Today's highest fields comprise proton Larmor frequencies of 1.2 GHz and even larger field strengths are to be expected in the future. In protein triple resonance experiments, various carbon bandwidths need to be excited by selective pulses including the large aliphatic chemical shift range. When the spectrometer field strength is increased, the length of these pulses has to be decreased by the same factor, resulting in higher rf-amplitudes being necessary in order to cover the required frequency region. Currently available band-selective pulses like Q3/Q5 excite a narrow bandwidth compared to the necessary rf-amplitude. Because the maximum rf-power allowed in probeheads is limited, none of the selective universal rotation pulses reported so far is able to cover the full [Formula: see text]C aliphatic region on 1.2 GHz spectrometers. In this work, we present band-selective 90° and 180° universal rotation pulses (SURBOP90 and SURBOP180) that have a higher ratio of selective bandwidth to maximum rf-amplitude than standard pulses. Simulations show that these pulses perform better than standard pulses, e. g. Q3/Q5, especially when rf-inhomogeneity is taken into account. The theoretical and experimental performance is demonstrated in offset profiles and by implementing the SURBOP pulses in an HNCACB experiment at 1.2 GHz.

Pure shift amide detection in conventional and TROSY-type experiments of 13C,15N-labeled proteins

Large coupling networks in uniformly ¹³C,¹⁵N-labeled biomolecules induce broad multiplets that even in flexible proteins are frequently not recognized as such. The reason is that given multiplets typically consist of a large number of individual resonances that result in a single broad line, in which individual components are no longer resolved. We here introduce a real-time pure shift acquisition scheme for the detection of amide protons which is based on ¹³C-BIRD^r,X. As a result the full homo- and heteronuclear coupling network can be suppressed at low power leading to real singlets at substantially improved resolution and uncompromised sensitivity. The method is tested on a small globular and an intrinsically disordered protein (IDP) where the average spectral resolution is increased by a factor of ~ 2 and higher. Equally important, the approach works without saturation of water magnetization for solvent suppression and exchanging amide protons are not affected by saturation transfer.

Advanced design of MRI inversion pulses for inhomogeneous field conditions by optimal control

Non-selective inversion pulses find widespread use in MRI applications, where requirements on them are increasingly demanding. With the use of high and ultra-high field strength systems, robustness to Δ B 0 and B 1 + inhomogeneities, while tackling SAR and hardware limitations, has rapidly become important. In this work, we propose a time-optimal control framework for the optimization of Δ B 0 - and B 1 + -robust inversion pulses. Robustness is addressed by means of ensemble formulations, while allowing inclusion of hardware and energy limitations. The framework is flexible and performs excellently for various optimization goals. The optimization results are analyzed extensively in numerical experiments. Furthermore, they are validated, and compared with adiabatic RF pulses, in various phantom and in vivo measurements on a 3 T MRI system.

SORDOR pulses: expansion of the Böhlen-Bodenhausen scheme for low-power broadband magnetic resonance

A novel type of efficient broadband pulse, called second-order phase dispersion by optimised rotation (SORDOR), has recently been introduced. In contrast to adiabatic excitation, SORDOR-90 pulses provide effective transverse 90∘ rotations throughout their bandwidth, with a quadratic offset dependence of the phase in the x , y plane. Together with phase-matched SORDOR-180 pulses, this enables the Böhlen-Bodenhausen broadband refocusing approach for linearly frequency-swept pulses to be extended to any type of 90∘ /180∘ pulse-delay sequence. Example pulse shapes are characterised in theory and experiment, and an example application is given with a 19 F -PROJECT experiment for measuring relaxation times with reduced distortions due to J -coupling evolution.

Concurrent J-evolving refocusing pulses

Conventional refocusing pulses are optimised for a single spin without considering any type of coupling. However, despite the fact that most couplings will result in undesired distortions, refocusing in delay-pulse-delay-type sequences with desired heteronuclear coherence transfer might be enhanced considerably by including coupling evolution into pulse design. We provide a proof of principle study for a Hydrogen-Carbon refocusing pulse sandwich with inherent J-evolution following the previously reported ICEBERG-principle with improved performance in terms of refocusing performance and/or overall effective coherence transfer time. Pulses are optimised using optimal control theory with a newly derived quality factor and z-controls as an efficient tool to speed up calculations. Pulses are characterised in theory and experiment and compared to conventional concurrent refocusing pulses, clearly showing an improvement for the J-evolving pulse sandwich. As a side-product, also efficient J-compensated resfocusing pulse sandwiches - termed BUBU pulses following the nomenclature of previous J-compensated BUBI and BEBE^tr pulse sandwiches - have been optimised.

Application of Optimal Control Theory to Fourier Transform Ion Cyclotron Resonance

We study the application of Optimal Control Theory to Ion Cyclotron Resonance. We test the validity and the efficiency of this approach for the robust excitation of an ensemble of ions with a wide range of cyclotron frequencies. Optimal analytical solutions are derived in the case without any pulse constraint. A gradient-based numerical optimization algorithm is proposed to take into account limitation in the control intensity. The efficiency of optimal pulses is investigated as a function of control time, maximum amplitude and range of excited frequencies. A comparison with adiabatic and SWIFT pulses is done. On the basis of recent results in Nuclear Magnetic Resonance, this study highlights the potential usefulness of optimal control in Ion Cyclotron Resonance.

Chirped ordered pulses for ultra-broadband ESR spectroscopy

Recently, applications of swept-frequency pulses proved to be a useful approach to circumvent the problem of limited excitation bandwidth in pulsed ESR posed by conventional pulses. Here, we present a chirped excitation sequence, CHirped ORdered pulses for Ultra-broadband Spectroscopy (CHORUS), for ultra-broadband ESR spectroscopy. It will be demonstrated that the application of this sequence can address the problems of excitation non-uniformity and sensitivity to instrumental instabilities to a greater extent compared to the current state of the art. This sequence is highly promising for finding applications beyond single excitation in many ESR experiments. Theoretical and experimental results for the proposed method are presented along with calibration strategies for experimental implementation.

A novel spectrally selective fat saturation pulse design with robustness to B0 and B1 inhomogeneities: A demonstration on 3D T1-weighted breast MRI at 3 T

PURPOSE

Spectrally selective fat saturation (FatSat) sequence is commonly used to suppress signal from adipose tissue. Conventional SINC-shaped pulses are sensitive to B₀ off-resonance and B₁⁺ offset. Uniform fat saturation with large spatial coverage is especially challenging for the body and breast MRI. The aim of this study is to develop spectrally selective FatSat pulses that offer more immunity to B₀/B₁⁺ field inhomogeneities than SINC pulses and evaluate them in bilateral breast imaging at 3 T.

MATERIALS AND METHODS

Optimized composite pulses (OCP) were designed based on the optimal control theory with robustness to a targeted B₀/ B₁⁺ conditions. OCP pulses also allows flexible flip angles to meet different requirements. Comparisons with the vendor-provided SINC pulses were conducted by numerical simulation and in vivo scans using a 3D T₁-weighted (T₁w) gradient-echo (GRE) sequence with coverage of the whole-breast.

RESULTS

Simulation revealed that OCP pulses yielded almost half of the transition band and much less sensitivity to B₁⁺ inhomogeneity compared to SINC pulses with B₀ off-resonance within ±200 Hz and B₁⁺ scale error within ±0.3 (P < 0.001). Across five normal subjects, OCP FatSat pulses produced 25-41% lower residual fat signals (P < 0.05) with 27-36% less spatial variation (P < 0.05) than SINC.

CONCLUSION

In contrast to conventional SINC-shaped pulses, the newly designed OCP FatSat pulses mitigated challenges of wide range of B₀/ B₁⁺ field inhomogeneities and achieved more uniform fat suppression in bilateral breast T₁w imaging at 3 T.

Power of Pure Shift HαCα Correlations: A Way to Characterize Biomolecules under Physiological Conditions

Intrinsically disordered proteins (IDPs) constitute an important class of biomolecules with high flexibility. Atomic-resolution studies for these molecules are essentially limited to NMR spectroscopy, which should be performed under physiological pH and temperature to populate relevant conformational ensembles. In this context, however, fundamental problems arise with established triple resonance NMR experiments: high solvent accessibility of IDPs promotes water exchange, which disfavors classical amide ¹H-detection, while ¹³C-detection suffers from significantly reduced sensitivity. A favorable alternative, the conventional detection of nonexchangeable ¹Hα, so far resulted in broad signals with insufficient resolution and sensitivity. To overcome this, we introduce here a selective Hα,Cα-correlating pure shift detection scheme, the selective Hα,Cα-HSQC (SHACA-HSQC), using extensive hetero- and homonuclear decoupling applicable to aqueous samples (≥90% H₂O) and tested on small molecules and proteins. SHACA-HSQC spectra acquired on IDPs provide uncompromised resolution and sensitivity (up to fivefold increased S/N compared to the standard ¹H,¹³C-HSQC), as shown for resonance distinction and unambiguous assignment on the disordered transactivation domain of the tumor suppressor p53, α-synuclein, and folded ubiquitin. The detection scheme can be implemented in any ¹Hα-detected triple resonance experiment and may also form the basis for the detection of isotope-labeled markers in biological studies or compound libraries.

On the use of frequency-swept pulses and pulses designed with optimal control theory for the acquisition of ultra-wideline NMR spectra

Frequency-swept (FS) pulses, such as wideband uniform-rate smooth-truncation (WURST) pulses, have found much success for the acquisition of ultra-wideline (UW) solid-state NMR spectra. In this preliminary study, new pulses and pulse sequences are explored in simulation and experimentally for several nuclei exhibiting UWNMR powder patterns under static conditions, including ¹¹⁹Sn (I = 1/2), ¹⁹⁵Pt (I = 1/2), ²H (I = 1), and ⁷¹Ga (I = 3/2). First, hyperbolic secant (HS) and tanh/tan (THT) pulses are tested and implemented as excitation and refocusing pulses in spin-echo and Carr-Purcell/Meiboom Gill (CPMG)-type sequences, and shown to have comparable performances to analogous WURST pulses. Second, optimal control theory (OCT) is utilized for the design of new Optimal Control Theory Optimized Broadband Excitation and Refocusing (OCTOBER) pulses, using carefully parameterized WURST, THT, and HS pulses as starting points. Some of the new OCTOBER pulses used in spin-echo sequences are capable of efficient broadband excitation and refocusing, in some cases resulting in spectra with increased signal enhancements over those obtained in experiments using conventional FS pulses. Finally, careful consideration of the spin dynamics of several systems, by monitoring of the time evolution of the density matrix via the Liouville-von Neumann equation and analysis of the time-resolved Fourier transforms of the pulses, lends insight into the underlying mechanisms of the FS and OCTOBER pulses. This is crucial for understanding their performance in terms of generating uniformly excited patterns of high signal intensity, and for identifying trends that may offer pathways to generalized parameterization and/or new pulse shapes.

Real-time pure shift measurements for uniformly isotope-labeled molecules using X-selective BIRD homonuclear decoupling

We introduce a novel selective inversion element for chunked homonuclear decoupling that combines isotope selection via BIRD-filtering with band-selective inversion on the X-heteronucleus and allows efficient real-time decoupling of homonuclear and heteronuclear couplings. It is especially suitable for uniformly isotope-labeled compounds. We discuss in detail the inversion element based on band-selective refocusing on the X-nuclei (BASEREX), highlighting in particular the role of appropriate band-selective shaped refocusing pulses and the application of broadband X-pulses for an effective BIRD^d element during homodecoupling. The approach is experimentally verified and studied in detail using uniformly ¹³C-labeled glucose and a uniformly ¹⁵N,¹³C-labeled amino acid mixture.

Improved ultra-broadband chirp excitation

The design and application of ultra-broadband excitation pulses have been among the most interesting and timely areas in NMR and EPR methodology in recent years, due especially to advances in hardware design in EPR, the advent and popularity of high- and ultrahigh-field NMR, and the application of numerical methods like optimal control theory to the design and optimization of radiofrequency pulses and pulse sequences. In this communication, we present a short, robust, and flexible version of the CHORUS family of constant-phase, very broadband excitation sequences. We demonstrate that more than 0.5 MHz excitation with uniform amplitudes and phases can be achieved with this excitation sequence.

ASAP-HSQC-TOCSY for fast spin system identification and extraction of long-range couplings

Based on Ernst-angle-type excitation and Acceleration by Sharing Adjacent Polarization (ASAP), a fast HSQC-TOCSY experiment is introduced. In the approach, the DIPSI-2 isotropic mixing period of the ASAP-HSQC is simply shifted, which provides a TOCSY period without additional application of rf-energy. The ASAP-HSQC-TOCSY allows the acquisition of a conventional 2D in about 30 s. Alternatively, it allows the acquisition of highly carbon-resolved spectra (several Hz digital resolution) on the order of minutes. An ASAP-HSQC-TOCSY-IPAP variant, finally, allows the sign-sensitive extraction of heteronuclear long-range coupling constants from a pair of highly resolved spectra in less than an hour. Pulse sequences, several example spectra, and a discussion of results are given.

Using optimal control methods with constraints to generate singlet states in NMR

A method is proposed for optimizing the performance of the APSOC (Adiabatic-Passage Spin Order Conversion) technique, which can be exploited in NMR experiments with singlet spin states. In this technique magnetization-to-singlet conversion (and singlet-to-magnetization conversion) is performed by using adiabatically ramped RF-fields. Optimization utilizes the GRAPE (Gradient Ascent Pulse Engineering) approach, in which for a fixed search area we assume monotonicity to the envelope of the RF-field. Such an approach allows one to achieve much better performance for APSOC; consequently, the efficiency of magnetization-to-singlet conversion is greatly improved as compared to simple model RF-ramps, e.g., linear ramps. We also demonstrate that the optimization method is reasonably robust to possible inaccuracies in determining NMR parameters of the spin system under study and also in setting the RF-field parameters. The present approach can be exploited in other NMR and EPR applications using adiabatic switching of spin Hamiltonians.

Boosting the NMR Assignment of Carbohydrates with Clean In-Phase Correlation Experiments

Novel CLIP-COSY based homo- and heteronuclear correlation experiments are reported for the rapid, semi-automated NMR assignment of small to medium-sized molecules. The homonuclear CLIP-COSY and corresponding relayed experiments employ the perfect-echo based mixing sequence for in-phase coherence transfer between directly and/or indirectly coupled proton spins. The combined analysis of the resulting CLIP-COSY and relayed spectra made it possible to easily track down, layer by layer, the proton-proton connectivity network. In larger molecules the narrow chemical shift range of protons may, however, compromise the efficacy of the homonuclear correlation based assignment strategy. To overcome this limitation, an HSQC variant of the CLIP-COSY experiment has now been devised. Combined treatment of HSQC-CLIP-COSY (relayed) and standard HSQC spectra facilitates simultaneous and semi-automatic assignment of ¹ H and ¹³ C resonances of medium-sized molecules, such as pentasaccharides. The recently introduced PSYCHE broadband homonuclear decoupling scheme has been also implemented into the devised homo- and heteronuclear CLIP-COSY based experiments, resulting in fully decoupled high-resolution pure-shift correlation spectra.

Cooperative broadband spin echoes through optimal control

The Hahn echo sequence is one of the most common building blocks in magnetic resonance, consisting of an excitation pulse and a refocusing pulse. Conventional approaches to improve the performance of echo experiments focused on the optimization of individual pulses, compensating their own imperfections. Here we present an approach to concurrently design both pulses such that they also compensate each others imperfections. The fact that for such cooperative pulses the individual pulses do not need to be perfect provides additional degrees of freedom, resulting in improved overall Hahn echo performance. Single-scan cooperative pulses are compared to conventional approaches by simulations as well as experiments.

Broadband RF-amplitude-dependent flip angle pulses with linear phase slope

Pulse sequences in NMR spectroscopy sometimes require the application of pulses with effective flip angles different from 90° and 180°. Previously (Magn. Reson. Chem. 2015, 53, 886-893), offset-compensated broadband excitation pulses with RF-amplitude-dependent effective flip angles (RADFA) were introduced that are applicable in such cases. However, especially RF-amplitude-restricted RADFA pulses turned out to perform not as good as desired in terms of achievable bandwidths. Here, a class of RF-amplitude-restricted RADFA pulses with linear phase slope is introduced that allows excitation over much larger bandwidths with better performance. In this theoretical work, the basic principle of the pulse class is explained, their physical limits explored, and their properties, also compared with other pulse classes, discussed in detail. Copyright © 2017 John Wiley & Sons, Ltd.

An optimal control approach to design entire relaxation dispersion experiments

A general approach is introduced to optimize experiments for the analysis of spin systems in the presence of chemical exchange. Rather than optimizing individual pulse sequence elements, such as refocusing pulses, entire relaxation dispersion sequences are optimized in the form of a single shaped pulse. This is achieved by defining a performance index that is only based on the remaining signal after the relaxation dispersion sequence for a range of exchange, relaxation, offset, and rf inhomogeneity parameters. The approach is demonstrated by optimizing energy-limited broadband relaxation dispersion sequences that closely approach the overall effect of ideal CPMG sequences. As illustrated both theoretically and experimentally, significant improvements are found compared to standard amplitude or energy-limited CPMG sequences.

Chirp excitation

The paper describes the design of broadband chirp excitation pulses. We first develop a three stage model for understanding chirp excitation in NMR. We then show how a chirp π pulse can be used to refocus the phase of the chirp excitation pulse. The resulting magnetization still has some phase dispersion in it. We show how a combination of two chirp π pulses instead of one can be used to eliminate this dispersion, leaving behind a small residual phase dispersion. The excitation pulse sequence presented here allows exciting arbitrary large bandwidths without increasing the peak rf-amplitude. Experimental excitation profiles for the residual HDO signal in a sample of 99.5% D₂O are displayed as a function of resonance offset. Although methods presented in this paper have appeared elsewhere, we present complete analytical treatment that elucidates the working of these methods.

Improvements, extensions, and practical aspects of rapid ASAP-HSQC and ALSOFAST-HSQC pulse sequences for studying small molecules at natural abundance

Previously we introduced two novel NMR experiments for small molecules, the so-called ASAP-HSQC and ALSOFAST-HSQC (Schulze-Sünninghausen et al., 2014), which allow the detection of heteronuclear one-bond correlations in less than 30s at natural abundance. We propose an improved symmetrized pulse scheme of the basic experiment to minimize artifact intensities and the combination with non-uniform sampling to enable the acquisition of conventional HSQC spectra in as short as a couple of seconds and extremely ¹³C-resolved spectra in less than ten minutes. Based on steady state investigations, a first estimate to relative achievable signal intensities with respect to conventional, ASAP-, and ALSOFAST-HSQC experiments is given. In addition, we describe several extensions to the basic pulse schemes, like a multiplicity-edited version, a revised symmetrized CLIP-ASAP-HSQC, an ASAP-/ALSOFAST-HSQC sequence with broadband BIRD-based ¹H,¹H decoupling, and a symmetrized sequence optimized for water suppression. Finally, RF-power considerations with respect to the high duty cycle of the experiments are given.

Perspectives of shaped pulses for EPR spectroscopy

This article describes current uses of shaped pulses, generated by an arbitrary waveform generator, in the field of EPR spectroscopy. We show applications of sech/tanh and WURST pulses to dipolar spectroscopy, including new pulse schemes and procedures, and discuss the more general concept of optimum-control-based pulses for applications in EPR spectroscopy. The article also describes a procedure to correct for experimental imperfections, mostly introduced by the microwave resonator, and discusses further potential applications and limitations of such pulses.

Ultra broadband NMR spectroscopy using multiple rotating frame technique

The paper describes the design of broadband excitation and inversion pulses by method of multiple rotating frame technique. The ideal situation for perfect excitation and inversion is to have no chemical shift offset and thereby everything on resonance. However, when chemical shifts span a wide range, this condition is not realized. We achieve this condition using a multiply modulated rf-field, whose effect can be understood by progressing into multiple frames. As we progress through the frames, the ratio of chemical shift dispersion to strength of static rf-field decreases, resulting in a final frame, where there is negligible chemical shift as compared to the effective rf-field and we get good excitation and inversion. Increasing the number of frames, increases excitation bandwidth and the ratio of bandwidth to rms excitation amplitude. We show, in principle, it is possible to excite arbitrary large bandwidth for a given rms rf-amplitude by increasing the number of frames. The time of excitation increases linearly with the bandwidth when we keep the rms rf-amplitude constant. Experimental demonstration of proposed method is presented on (1)H excitation over a bandwidth of 52 kHz with a rms amplitude of 10 kHz. Increasing the frames increases excitation bandwidth for same rms amplitude of 10 kHz. Experimental spectra obtained from 100%(13)C labeled arginine shows uniform excitation over the entire carbon spectra, obtained with a 8-frame pulse sequence.

CLIP-ASAP-HSQC for fast and accurate extraction of one-bond couplings from isotropic and partially aligned molecules

Fast measurement of heteronuclear one-bond couplings, a class of NMR parameters valuable for structure elucidation, is highly desirable, especially if samples undergo chemical reactions or dynamic processes are observed. Methods presented so far face severe limitations in terms of resolution, accessible bandwidth, and sensitivity. We present the CLean InPhase-Acceleration by Sharing Adjacent Polarization-HSQC (CLIP-ASAP-HSQC) pulse sequence that allows fast acquisition of spectra with clean inphase multiplets in about 25 s. The performance in terms of accurate extraction of one-bond couplings is demonstrated on three test samples including partially aligned molecules.

Broadband excitation pulses with variable RF amplitude-dependent flip angle (RADFA)

Pulse sequences in NMR spectroscopy sometimes require the adjustment of effective flip angles with respect to experiment-specific or sample-specific parameters. Here, we present a quality factor for efficient optimization of offset-compensated broadband excitation pulses with RF amplitude-dependent effective flip angles (RADFA). After proof of principle, physical limits of RF amplitude-restricted and RF power-restricted broadband RADFA pulses are explored and corresponding pulse shapes and performances characterized in detail.

Robust INEPT and refocused INEPT transfer with compensation of a wide range of couplings, offsets, and B1-field inhomogeneities (COB3)

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.

Direct optimization of signal-to-noise ratio of CPMG-like sequences in inhomogeneous fields

The performance of the standard CPMG sequence in inhomogeneous fields can be improved with the use of broadband excitation and refocusing pulses. In previous work we have developed short composite broadband refocusing pulses together with practical excitation pulses to realize such performance gains, and quantified them using the ratio of signal to noise power (SNR). In this work we systematically explore the performance of refocusing pulses as a function of the overall pulse length up to ten times the length of the regular 180° pulse. This is in the regime of non-adiabatic pulses. We introduce a new performance functional for numerical pulse optimization that directly maximizes SNR and study the effect of symmetry constraints on the pulses. We find that for the optimal pulses, the SNR per asymptotic echo increases with pulse length but, for typical echo spacings, the SNR per unit time is maximized for refocusing pulses that are between two and four times longer than the duration of the standard rectangular 180° pulse. The performance is limited by the control bandwidth and the inability of finding the global maximum. The best performance was obtained with symmetric phase-alternating (SPA) refocusing pulses optimized with our novel performance functional. To test them in the CPMG sequence, we also developed axis-matching excitation (AMEX) pulses for use with these SPA refocusing pulses and tested the new AMEX-SPA sequences experimentally in a grossly inhomogeneous field, observing excellent agreement with the theoretical expectations. One of these sequences produced over 4.5 times higher SNR per asymptotic echo and 3.9 times higher SNR per unit time than the standard CPMG sequence with the same instantaneous RF power level. We also found that the new sequences are at least as robust to changes in the RF field strength as the standard CPMG sequence.

Comparison of 1H-19F two-dimensional NMR scalar coupling correlation pulse sequences

The effectiveness of hetero-COSY, HETCOR, HMQC, and HSQC two-dimensional NMR pulse sequences for detection of (19)F-(1)H correlations by scalar coupling was evaluated on monofluorinated and polyfluorinated test compounds. All four of these sequences were effective in observing (1)H-(19)F correlations, using either (19) F or (1)H as the observe nucleus. All four sequences were amenable, to some degree, to adjustment to observe larger or smaller couplings preferentially. A 1/2J echo filter was effectively applied to remove artifacts from (2)JFF strong coupling. The HETCOR experiments afforded the best overall combination of sensitivity, resolution and selectivity for JHF.

Homonuclear BIRD-decoupled spectra for measuring one-bond couplings with highest resolution: CLIP/CLAP-RESET and constant-time-CLIP/CLAP-RESET

Heteronuclear one-bond couplings are of interest for various aspects of structural analysis of small organic molecules, including for example the distinction of axial and equatorial protons or the use of RDCs as angular constraints. Such couplings are most easily measured from pure doublets in HSQC-type spectra. Recently, the fully decoupled RESET HSQC experiment was reported and several other so-called pure-shift methods followed that allow for the removal of splittings due to homonuclear scalar interactions in one and two-dimensional NMR. In this work we present broadband homonuclear decoupled CLIP/CLAP-RESET experiments based on an isotope-selective BIRD filter element using a recently reported improved version of Zangger-Sterk data chunking. The concatenated FIDs result in multiplets in which most homonuclear splittings are removed while the heteronuclear one-bond couplings are retained. Couplings can be extracted in an IPAP fashion without scaling of subspectra by the use of optimized coherence transfer elements like the COB-INEPT. The method leads to complete homonuclear decoupling for CH groups and CH3 groups in isotropic samples, but leaves residual splittings with antiphase contributions for e.g. CH2 groups due to (2)JHH coupling evolution that is not affected by the BIRD element. For this case we present a constant-time version of the proposed BIRD decoupling scheme with full homonuclear decoupling. In addition, the effects of strong coupling are discussed. Strong coupling artifacts cannot be circumvented, but the proposed experiments allow their distinct recognition.

Rapid heteronuclear single quantum correlation NMR spectra at natural abundance

A novel NMR experiment, the so-called ASAP-HSQC, is introduced that allows the detection of heteronuclear one-bond correlations in less than 30 s on small molecules at natural abundance without compromises in sweep width, resolution or spectral quality. Equally, the experiment allows a significant increase in digital resolution or a moderate senstitivity enhancement in the same overall experiment time compared to a conventional HSQC. The gain is a consequence of keeping all unused proton magnetization along z during acquisition, so that the previously reported ASAP and ALSOFAST approaches can be transferred from HMQC to HSQC-type experiments. Next to basic and broadband pulse sequences, a characterization of the sequence with respect to minimum measurement time, sensitivity gain, and advantages in resolution compared to state-of-the-art experiments is given.

Axis-matching excitation pulses for CPMG-like sequences in inhomogeneous fields

The performance of the standard CPMG sequence in inhomogeneous fields can be improved with the use of broadband excitation and refocusing pulses. Here we introduce a new class of excitation pulses, so-called axis-matching excitation pulses, that optimize the response for a given refocusing pulse. These new excitation pulses are tailored to the refocusing pulses and take their imperfections into account. Rather than generating purely transverse magnetization, these pulses are designed to generate magnetization pointing along the axis of the effective rotation of the refocusing cycle. This approach maximizes the CPMG component and minimizes the CP component of the signal. Replacing a standard 90° pulse with a new excitation pulse matched to the 180° refocusing pulse increases the signal bandwidth and improves the echo amplitudes by 30% in inhomogeneous fields in comparison to the standard CPMG sequence. Larger gains are obtained with more advanced refocusing pulses. Recent work demonstrated that it is possible to increase the signal to noise ratio (SNR) of individual echoes by more than a factor of 1.5 (in power units) without increasing the duration or amplitude of the refocusing pulses. This was achieved by replacing the standard 180° refocusing pulse by a short phase alternating pulse and the standard 90° excitation pulse by a broadband excitation pulse. We show here that with suitable axis-matching excitation pulses, the SNR further increases by over a factor of 2. We discuss the underlying theory and present several practical implementations of purely phase modulated axis-matching excitation pulses for a number of different refocusing pulses that were derived using methods of optimal control. To gain the full benefit of these new excitation pulses, it is essential to replace the standard phase cycling scheme based on 180° phase shifts by a new scheme involving phase inversion. We tested the new pulses experimentally and observe excellent agreement with the theoretical expectations. We also demonstrate that an additional benefit of axis-matching excitation pulses is the decrease of the transient that appears in the amplitudes of the first few echoes, thus enabling better measurements of short relaxation times.

BEBE(tr) and BUBI: J-compensated concurrent shaped pulses for 1H-13C experiments

Shaped pulses designed for broadband excitation, inversion and refocusing are important tools in modern NMR spectroscopy to achieve robust pulse sequences especially in heteronuclear correlation experiments. A large variety of mostly computer-optimized pulse shapes exist for different desired bandwidths, available rf-field strengths, and tolerance to B1-inhomogeneity. They are usually derived for a single spin 1/2, neglecting evolution due to J-couplings. While pulses with constant resulting phase are selfcompensated for heteronuclear coupling evolution as long as they are applied exclusively on a single nucleus, the situation changes for concurrently applied pulse shapes. Using the example of a (1)H,(13)C two spin system, two J-compensated pulse pairs for the application in INEPT-type transfer elements were optimized: a point-to-point pulse sandwich called BEBE(tr), consisting of a broadband excitation and time-reversed excitation pulse, and a combined universal rotation and point-to-point pulse pair called BUBI, which acts as a refocusing pulse on (1)H and a corresponding inversion pulse on (13)C. After a derivation of quality factors and optimization protocols, a theoretical and experimental comparison with conventionally derived BEBOP, BIBOP, and BURBOP-180° pulses is given. While the overall transfer efficiency of a single pulse pair is only reduced by approximately 0.1%, resulting transfer to undesired coherences is reduced by several percent. In experiments this can lead to undesired phase distortions for pairs of uncompensated pulse shapes and even differences in signal intensities of 5-10% in HSQC and up to 68% in more complex COB-HSQC experiments.

The Fantastic Four: A plug 'n' play set of optimal control pulses for enhancing NMR spectroscopy

We present highly robust, optimal control-based shaped pulses designed to replace all 90° and 180° hard pulses in a given pulse sequence for improved performance. Special attention was devoted to ensuring that the pulses can be simply substituted in a one-to-one fashion for the original hard pulses without any additional modification of the existing sequence. The set of four pulses for each nucleus therefore consists of 90° and 180° point-to-point (PP) and universal rotation (UR) pulses of identical duration. These 1ms pulses provide uniform performance over resonance offsets of 20kHz ((1)H) and 35kHz ((13)C) and tolerate reasonably large radio frequency (RF) inhomogeneity/miscalibration of ±15% ((1)H) and ±10% ((13)C), making them especially suitable for NMR of small-to-medium-sized molecules (for which relaxation effects during the pulse are negligible) at an accessible and widely utilized spectrometer field strength of 600MHz. The experimental performance of conventional hard-pulse sequences is shown to be greatly improved by incorporating the new pulses, each set referred to as the Fantastic Four (Fanta4).

A systematic approach for optimizing the robustness of pulse sequence elements with respect to couplings, offsets, and B1-field inhomogeneities (COB)

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.

Exploring the limits of broadband 90° and 180° universal rotation pulses

90° and 180° universal rotation (UR) pulses are two of the most important classes of pulses in modern NMR spectroscopy. This article presents a systematic study characterizing the achievable performance of these pulses as functions of bandwidth, pulse length, and tolerance to B(1)-field inhomogeneity/miscalibration. After an evaluation of different quality factors employed in pulse design algorithms based on optimal control theory, resulting pulses are discussed in detail with a special focus on pulse symmetry. The vast majority of resulting BURBOP (broadband universal rotations by optimal control) pulses are either fully symmetric or have one symmetric and one antisymmetric Cartesian rf component, where the importance of the first symmetry has not been demonstrated yet and the latter one matches the symmetry that results from a previously derived construction principle of universal rotation pulses out of point-to-point pulses [3]. Optimized BURBOP pulses are shown to perform better than previously reported UR pulses, resulting in shorter pulse durations for the same quality of broadband rotations. From a comparison of qualities of effective universal rotations, we find that the application of a single optimal refocusing pulse matches or improves the performance of two consecutive inversion pulses in INEPT-like pulse sequence elements of the same total duration.

Tailored real-time scaling of heteronuclear couplings

Heteronuclear couplings are a valuable source of molecular information, which is measured from the multiplet splittings of an NMR spectrum. Radiofrequency irradiation on one coupled nuclear spin allows to modify the effective coupling constant, scaling down the multiplet splittings in the spectrum observed at the resonance frequency of the other nuclear spin. Such decoupling sequences are often used to collapse a multiplet into a singlet and can therefore simplify NMR spectra significantly. Continuous-wave (cw) decoupling has an intrinsic non-linear offset dependence of the scaling of the effective J-coupling constant. Using optimal control pulse optimization, we show that virtually arbitrary off-resonance scaling of the J-coupling constant can be achieved. The new class of tailored decoupling pulses is named SHOT (Scaling of Heteronuclear couplings by Optimal Tracking). Complementing cw irradiation, SHOT pulses offer an alternative approach of encoding chemical shift information indirectly through off-resonance decoupling, which however makes it possible for the first time to achieve linear J scaling as a function of offset frequency. For a simple mixture of eight aromatic compounds, it is demonstrated experimentally that a 1D-SHOT {(1)H}-(13)C experiment yields comparable information to a 2D-HSQC and can give full assignment of all coupled spins.

Measurement of ¹⁵N relaxation rates in perdeuterated proteins by TROSY-based methods

While extracting dynamics parameters from backbone (15)N relaxation measurements in proteins has become routine over the past two decades, it is increasingly recognized that accurate quantitative analysis can remain limited by the potential presence of systematic errors associated with the measurement of (15)N R(1) and R(2) or R(1ρ) relaxation rates as well as heteronuclear (15)N-{(1)H} NOE values. We show that systematic errors in such measurements can be far larger than the statistical error derived from either the observed signal-to-noise ratio, or from the reproducibility of the measurement. Unless special precautions are taken, the problem of systematic errors is shown to be particularly acute in perdeuterated systems, and even more so when TROSY instead of HSQC elements are used to read out the (15)N magnetization through the NMR-sensitive (1)H nucleus. A discussion of the most common sources of systematic errors is presented, as well as TROSY-based pulse schemes that appear free of systematic errors to the level of <1 %. Application to the small perdeuterated protein GB3, which yields exceptionally high S/N and therefore is an ideal test molecule for detection of systematic errors, yields relaxation rates that show considerably less residue by residue variation than previous measurements. Measured R(2)'/R(1)' ratios fit an axially symmetric diffusion tensor with a Pearson's correlation coefficient of 0.97, comparable to fits obtained for backbone amide RDCs to the Saupe matrix.

Optimal control design of band-selective excitation pulses that accommodate relaxation and RF inhomogeneity

Existing optimal control protocols for mitigating the effects of relaxation and/or RF inhomogeneity on broadband pulse performance are extended to the more difficult problem of designing robust, refocused, frequency selective excitation pulses. For the demanding case of T(1) and T(2) equal to the pulse length, anticipated signal losses can be significantly reduced while achieving nearly ideal frequency selectivity. Improvements in performance are the result of allowing residual unrefocused magnetization after applying relaxation-compensated selective excitation by optimized pulses (RC-SEBOPs). We demonstrate simple pulse sequence elements for eliminating this unwanted residual signal.