Exploring the Higher Order Structure and Conformational Transitions in Insulin Microcrystalline Biopharmaceuticals by Proton-Detected Solid-State Nuclear Magnetic Resonance at Natural Abundance.

The integrity of a higher order structure (HOS) is an essential requirement to ensure the efficacy, stability, and safety of protein therapeutics. Solution-state nuclear magnetic resonance (NMR) occupies a unique niche as one of the most promising methods to access atomic-level structural information on soluble biopharmaceutical formulations. Another major class of drugs is poorly soluble, such as microcrystalline suspensions, which poses significant challenges for the characterization of the active ingredient in its native state. Here, we have demonstrated a solid-state NMR method for HOS characterization of biopharmaceutical suspensions employing a selective excitation scheme under fast magic angle spinning (MAS). The applicability of the method is shown on commercial insulin suspensions at natural isotopic abundance. Selective excitation aided with proton detection and non-uniform sampling (NUS) provides improved sensitivity and resolution. The enhanced resolution enabled us to demonstrate the first experimental evidence of a phenol-escaping pathway in insulin, leading to conformational transitions to different hexameric states. This approach has the potential to serve as a valuable means for meticulously examining microcrystalline biopharmaceutical suspensions, which was previously not attainable in their native formulation states and can be seamlessly extended to other classes of biopharmaceuticals such as mAbs and other microcrystalline proteins.

MODE: Multiply modulated frame technique, excitation and coherence transfer.

The study of modulated pulse (MODE pulse) approach for the application in NMR has been in the literature for over a decade. Although the method's purpose was initially to decouple the spins, its application can be extended to broadband excitation, inversion and coherence transfer between spins (TOCSY). In this paper, the experimental validation of the TOCSY experiment with the help of MODE pulse and how the coupling constant varies over different frames are shown. We demonstrate that the TOCSY with a higher MODE pulse will result in less coherence transfer even with the same RF-power, and a lower MODE pulse will require a larger RF-amplitude to achieve TOCSY over the same bandwidth. We also present a quantitative analysis of the error due to fast oscillating terms that can be neglected, giving the required results.

An improved algorithm for design of broadband excitation, inversion, and mixing pulse sequences by iterative optimization of phases: TOPS-2.

This paper presents an improved iterative algorithm (TOPS-2) for the design of broadband inversion, excitation and coherent transfer mixing sequence (TOCSY) pulses. The evolution of the Bloch vector is presented as a sequence of small constant flip angle pulses with varying phases and constant amplitude. This paper describes an improved algorithm for iterative optimization of piece-wise constant phases as we incorporate the quadratic terms in the propagators. In our iterative optimization we obtain a closed-form expression for each phase, and these phases are optimized sequentially using the new improved algorithm. This paper compares the simulation results of the TOPS vs TOPS-2 and shows that TOPS-2 perform better. Experimental validation of excitation and inversion TOPS-2 pulse sequence is performed with .5% H2O in 99.5% D2O, and experimental validation of TOPS-2 mixing (TOCSY) pulse sequence is done with 0.1% of Ethylbenzene (EB) in CDCl3 solvent.

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.

Chirp pulse sequences for broadband π rotation.

In this paper, we present various chirp pulse sequences for implementing a broadband π rotation, which can serve as an ideal refocusing pulse element in a spin echo pulse sequence. These sequences are composed of three pulse elements each of which do adiabatic passage at rate a or 2a in either backward or forward direction. Various possible combinations are considered and different variants are presented. They all implement a broadband π rotation. We present the theory of such composite chirp sequences along with simulations and experiments.

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.

Two pulse recoupling.

The paper describes a family of novel recoupling pulse sequences in magic angle spinning (MAS) solid state NMR, called two pulse recoupling. These pulse sequences can be employed for both homonuclear and heteronuclear recoupling experiments and are robust to dispersion in chemical shifts and rf-inhomogeneity. The homonuclear pulse sequence consists of a building block (π)ϕ(π)-ϕ where ϕ=π4n, and n is number of blocks in a rotor period. The recoupling block is made robust to rf-inhomogeneity by extending it to (π)ϕ(π)-ϕ(π)π+ϕ(π)π-ϕ. The heteronuclear recoupling pulse sequence consists of a building block [Formula: see text] and [Formula: see text] on channel I and S, where ϕ1=3π8n,ϕ2=π8n and n is number of blocks in a rotor period. The recoupling block is made robust to rf-inhomogeneity by extending it to [Formula: see text] and [Formula: see text] on two channels respectively. The recoupling pulse sequences mix the z magnetization. Experimental quantification of this method is shown for13Cα-13CO homonuclear recoupling in a sample of Glycine and 15N-13Cα heteronuclear recoupling in Alanine. Application of this method is demonstrated on a sample of tripeptide N-formyl-[U-13C,15N]-Met-Leu-Phe-OH (MLF). Compared to R-sequences (Levitt, 2002), these sequences are more robust to rf-inhomogeneity and give better sensitivity, as shown in Fig. 3.

Rf-inhomogeneity compensation using method of Fourier synthesis.

In this paper, we propose a new method for design of composite pulses that are robust to rf-amplitude (rf-inhomogeneity). We call this, the method of Fourier synthesis. The method is general enough to design excitation, inversion, refocusing or arbitary flip angle pulses that are robust to rf-amplitude. The method can be tailored to have amplitude selective excitation. We experimentally show rf-compensation over a order of magnitude (20db) variation in rf-amplitude. The method is expected to find use in invivo NMR studies using surface coils, where there is large dispersion in rf-amplitude over the sample.

Cone separation, quadratic control systems and control of spin dynamics in the presence of decoherence.

In this paper, we study some control problems related to the control of coupled spin dynamics in the presence of relaxation and decoherence in nuclear magnetic resonance spectroscopy. The decoherence is modelled through a master equation. We study some model problems, whereby, through an appropriate choice of state variables, the system is reduced to a control system, where the state enters linearly and controls quadratically. We study this quadratic control system. Study of this system gives us explicit bounds on how close a coupled spin system can be driven to its target state and how much coherence and polarization can be transferred between coupled spins. Optimal control for the quadratic control system can be understood as the separation of closed cones, and we show how the derived results on optimal efficiency can be interpreted in this formulation. Finally, we study some finite-time optimal control problems for the quadratic control system.This article is part of the themed issue 'Horizons of cybernetical physics'.

Four pulse recoupling.

The paper describes a family of novel recoupling pulse sequences in magic angle spinning (MAS) solid state NMR, called four pulse recoupling. These pulse sequences can be employed for both homonuclear and heteronuclear recoupling experiments and are robust to dispersion in chemical shifts and rf-inhomogeneity. The homonuclear pulse sequence consists of a building block π20°3π2ϕ°π2180°+ϕ°3π2180° where ϕ=πnϕ°=180°n, and n is number of blocks in a two rotor period. The heteronuclear recoupling pulse sequence consists of a building block [Formula: see text] and [Formula: see text] on channel I and S, where ϕ1=3π2n,ϕ2=π2n and n is number of blocks in a two rotor period. The recoupling pulse sequences mix the y magnetization. We show that four pulse recoupling is more broadband compared to three pulse recoupling [1]. Experimental quantification of this method is shown for 13Cα-13CO, homonuclear recoupling in a sample of Glycine and 15N-13Cα, heteronuclear recoupling in Alanine. Application of this method is demonstrated on a sample of tripeptide N-formyl-[U-13C,15N]-Met-Leu-Phe-OH (MLF).

Recoupling pulse sequences with constant phase increments.

The paper studies a family of recoupling pulse sequences in magic angle spinning (MAS) solid state NMR, that are characterized by constant phase increments at regular intervals. These pulse sequences can be employed for both homonuclear and heteronuclear recoupling experiments and are robust to dispersion in chemical shifts and rf-inhomogeneity. The homonuclear pulse sequence consists of a building block [Formula: see text] , where ϕ(p)=p(n-1)πn, where n is number of blocks in a rotor period and p=0,1,2,…. The pulse sequence repeats itself every rotor period when n is odd and every two rotor period when n is even. The heteronuclear recoupling pulse sequence consists of a building block [Formula: see text] and [Formula: see text] on channel I and S, where ϕ1(p)=p(2n-3)π2n,ϕ2(p)=p(2n-1)π2n and n is number of blocks in a rotor period. The recoupling pulse sequences mix the z magnetization. Experimental quantification of this method is shown for (13)Cα-(13)CO, homonuclear recoupling in a sample of Glycine and (15)N-(13)Cα, heteronuclear recoupling in Alanine. Application of this method is demonstrated on a sample of tripeptide N-formyl-[U-(13)C,(15)N]- Met-Leu-Phe-OH (MLF).

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.

Three pulse recoupling and phase jump matching.

The paper describes a family of novel recoupling pulse sequences, called three pulse recoupling. These pulse sequences can be employed for both homonuclear and heteronuclear recoupling experiments and are robust to dispersion in chemical shifts and rf-inhomogeneity. These recoupling pulse sequences can be used in design of two-dimensional solid state NMR experiments that use powdered dephased antiphase coherence (γ preparation) to encode chemical shifts in the indirect dimension. Both components of this chemical shift encoded gamma-prepared states can be refocused into inphase coherence by a recoupling element. This helps to achieve sensitivity enhancement in 2D NMR experiments by quadrature detection.

Accurate measurements of ¹³C-¹³C distances in uniformly ¹³C-labeled proteins using multi-dimensional four-oscillating field solid-state NMR spectroscopy.

Application of sets of (13)C-(13)C internuclear distance restraints constitutes a typical key element in determining the structure of peptides and proteins by magic-angle-spinning solid-state NMR spectroscopy. Accurate measurements of the structurally highly important (13)C-(13)C distances in uniformly (13)C-labeled peptides and proteins, however, pose a big challenge due to the problem of dipolar truncation. Here, we present novel two-dimensional (2D) solid-state NMR experiments capable of extracting distances between carbonyl ((13)C') and aliphatic ((13)C(aliphatic)) spins with high accuracy. The method is based on an improved version of the four-oscillating field (FOLD) technique [L. A. Straasø, M. Bjerring, N. Khaneja, and N. C. Nielsen, J. Chem. Phys. 130, 225103 (2009)] which circumvents the problem of dipolar truncation, thereby offering a base for accurate extraction of internuclear distances in many-spin systems. The ability to extract reliable accurate distances is demonstrated using one- and two-dimensional variants of the FOLD experiment on uniformly (13)C,(15)N-labeled-L-isoleucine. In a more challenging biological application, FOLD 2D experiments are used to determine a large number of (13)C'-(13)C(aliphatic) distances in amyloid fibrils formed by the SNNFGAILSS fibrillating core of the human islet amyloid polypeptide with uniform (13)C,(15)N-labeling on the FGAIL fragment.

A new broadband homonuclear mixing pulse for NMR with low applied power.

Broadband homonuclear mixing pulses with low radiofrequency power are essential for NMR spectroscopy of proteins and small molecules, especially for emerging applications in high field NMR. We have analytically designed a mixing pulse with high bandwidth-to-power ratio, using our recently developed multi-frame method. Here, we compare the new pulse, NF4 (mixing in the fourth nutating frame), to the best currently available sequence, focusing on the low-power regime. We use simulations and experiments to compare the two pulses' relaxation properties and bandwidth, and demonstrate that NF4 has approximately 1.35 times higher bandwidth, with similar effective relaxation. Therefore, NF4 is a good choice for broadband homonuclear mixing, particularly when the available radiofrequency power is limited.

Pulse design for broadband correlation NMR spectroscopy by multi-rotating frames.

We present a method for designing radio-frequency (RF) pulses for broadband or multi-band isotropic mixing at low power, suitable for protein NMR spectroscopy. These mixing pulses are designed analytically, rather than by numerical optimization, by repeatedly constructing new rotating frames of reference. We show how pulse parameters can be chosen frame-by-frame to systematically reduce the effective chemical shift bandwidth, but maintain most of the effective J-coupling strength. The effective Hartmann-Hahn mixing condition is then satisfied in a multi-rotating frame of reference. This design method yields multi-band and broadband mixing pulses at low RF power. In particular, the ratio of RF power to mixing bandwidth for these pulses is lower than for existing mixing pulses, such as DIPSI and FLOPSY. Carbon-carbon TOCSY experiments at low RF power support our theoretical analysis.

Robust and efficient 19F heteronuclear dipolar decoupling using refocused continuous-wave rf irradiation.

Refocused continuous wave (rCW) decoupling is presented as an efficient and robust means to obtain well-resolved magic-angle-spinning solid-state NMR spectra of low-γ spins, such as (13)C dipolar coupled to fluorine. The rCW decoupling sequences, recently introduced for (1)H decoupling, are very robust towards large isotropic and anisotropic shift ranges as often encountered for (19)F spins. In rCW decoupling, the so-called refocusing pulses inserted into the CW irradiation eliminate critical residual second- and third-order dipolar coupling and dipolar-coupling against chemical shielding anisotropy cross-terms in the effective Hamiltonian through time-reversal (i.e. refocusing). As important additional assets, the rCW decoupling sequences are robust towards variations in rf amplitudes, operational at low to high spinning speeds, and easy to set-up for optimal performance experimentally. These aspects are demonstrated analytically/numerically and experimentally in comparison to state-of-the-art decoupling sequences such as TPPM, SPINAL-64, and frequency-swept variants of these.

Refocused continuous-wave decoupling: a new approach to heteronuclear dipolar decoupling in solid-state NMR spectroscopy.

A novel strategy for heteronuclear dipolar decoupling in magic-angle spinning solid-state nuclear magnetic resonance (NMR) spectroscopy is presented, which eliminates residual static high-order terms in the effective Hamiltonian originating from interactions between oscillating dipolar and anisotropic shielding tensors. The method, called refocused continuous-wave (rCW) decoupling, is systematically established by interleaving continuous wave decoupling with appropriately inserted rotor-synchronized high-power π refocusing pulses of alternating phases. The effect of the refocusing pulses in eliminating residual effects from dipolar coupling in heteronuclear spin systems is rationalized by effective Hamiltonian calculations to third order. In some variants the π pulse refocusing is supplemented by insertion of rotor-synchronized π/2 purging pulses to further reduce the residual dipolar coupling effects. Five different rCW decoupling sequences are presented and their performance is compared to state-of-the-art decoupling methods. The rCW decoupling sequences benefit from extreme broadbandedness, tolerance towards rf inhomogeneity, and improved potential for decoupling at relatively low average rf field strengths. In numerical simulations, the rCW schemes clearly reveal superior characteristics relative to the best decoupling schemes presented so far, which we to some extent also are capable of demonstrating experimentally. A major advantage of the rCW decoupling methods is that they are easy to set up and optimize experimentally.

Homonuclear decoupling for liquid-state NMR.

We present a solution to the problem of decoupling of a homonuclear two-spin system having weak isotropic scalar coupling. We describe non-selective pulse sequences that create an effective field perpendicular to the coupling interaction over a broad range of chemical shifts, with a magnitude proportional to the chemical shifts. Effective decoupling is achieved when the difference in chemical shifts imprinted on the perpendicular field is sufficiently larger than the coupling between the spins. The proposed methods scale down the chemical shifts. The pulse sequences may be useful in various applications in nuclear magnetic resonance spectroscopy.

Control aspects of quantum computing using pure and mixed states.

Steering quantum dynamics such that the target states solve classically hard problems is paramount to quantum simulation and computation. And beyond, quantum control is also essential to pave the way to quantum technologies. Here, important control techniques are reviewed and presented in a unified frame covering quantum computational gate synthesis and spectroscopic state transfer alike. We emphasize that it does not matter whether the quantum states of interest are pure or not. While pure states underly the design of quantum circuits, ensemble mixtures of quantum states can be exploited in a more recent class of algorithms: it is illustrated by characterizing the Jones polynomial in order to distinguish between different (classes of) knots. Further applications include Josephson elements, cavity grids, ion traps and nitrogen vacancy centres in scenarios of closed as well as open quantum systems.