Workshop Optimal Control in MAS solid-state NMR

Workshop motivation and introduction to our optimal control methods

tm-SPICE pulses for x to x transfer, TROP pulses for transverse mixing and sensitivity enhanced multidimensional spectra, combined and directed magnetization transfers for backbone assignments

"Using solid state NMR, membrane proteins can be studied in a lipid bilayer environment. The resulting spectra are often quite complex and suffer from spectral overlap. Therefore, often highly selective isotope labelling schemes are applied. Magnetization transfer steps in these sparsely labelled samples are difficult to optimize, especially when narrow conditions have to be met, due to the low signal-to-noise ratio in the 1D spectra. Here we show, for the case of moderate MAS frequencies at high B0-field, that such optimizations can be sped up significantly using optimal control pulses. We will also discuss the current limitations of these pulses in our applications."

"Proton-detected solid-state NMR spectroscopy has enabled the combined use of complex pulse sequences and short recycle delays, thereby granting both, high signal to noise per unit time and peak dispersion. As a consequence, proteins with high-molecular-weight asymmetric units have become amenable for solid-state NMR, both in terms of resonance assignment (including directly chemical-shift-derived aspects of NMR like secondary structure and chemical properties) as well as regarding the assessment of structure and dynamics. Here, I will report on the implementation of such strategies, in particular higher-dimensionality sequences, to help exceed the boundaries of high molecular weight in micro-crystalline enzymes. The talk will allow for discussion of the prospects and possible applications to facilitate future solid-state NMR on biomolecules and beyond."

Response functions of resonant circuits create ringing artefacts if their input changes rapidly. When physical limits of electromagnetic spectroscopies are explored, this creates two types of problems. Firstly, simulation: the system must be propagated accurately through every oscillatory transient, this may be computationally expensive. Secondly, optimal control optimisation: instrument response must be taken into account; it may be advantageous to design pulses that are resilient to instrumental distortions. At the root of both problems is the popular piecewise-constant approximation for control sequences; in magnetic resonance it has persisted since the earliest days. In this paper, we report an implementation and some benchmarks for simulation and optimal control routines that use more recent Lie-group methods. Those simulate and optimise control pulses that are piecewise-polynomial - easier to generate on modern hardware and more resilient to instrumental distortions. However, the basic mathematics of magnetic resonance simulation and optimal control does require an update.

1H-detected NMR under fast (above 50 kHz) MAS conditions offers sensitivity and resolution required for spectral analysis of complex biomolecules. To address the increasing ambiguity of protein backbone chemical shift assignment, resolution enhancement of multidimensional spectra is key. Inherently, RF schemes become increasingly more sophisticated, for example with extra pulses or decoupling schemes introduced into triple-resonance amide proton-detected 3D experiments. In this respect, we will also review recent alternative strategies including direct amide-to-amide correlations, high-dimensional approaches (up to 5Ds), shared-time spectral acquisition and side-chain to backbone correlations. We will present both simulated and experimental RF distributions in the coil, and discuss the impact of RF inhomogeneity on detection sensitivity and performance of various building blocks of complex correlation RF schemes such as CPs, hard and soft inversion pulses and specific recoupling schemes. We will additionally discuss which blocks could be optimised with respect to RF inhomogeneities using spin dynamics simulations in SIMPSON.

The analysis of multidimensional NMR spectra of macromolecules is considered to be a work-intensive task, which constitutes a bottleneck in NMR-driven structural biology research. Usually, it takes weeks or months of manual work to transform a set of raw NMR spectra into the protein structure model. Automation of this process is an open problem, formulated in the field about three decades ago. In this study, we addressed this challenge by combining deep learning with methods available in CYANA.
Our method, ARTINA, uses as input only protein sequence and set of 2D/3D/4D Fourier transformed NMR spectra, delivering as output: (a) cross-peak coordinates, (b) chemical shifts, (c) distance restraints, and (d) protein structure. The proposed technique works strictly without any human intervention, allowing to get (a), (b), (c) and/or (d) within hours after the completion of measurement.
ARTINA uses a deep residual neural network, trained on 675,324 diverse labelled examples, to identify and deconvolve cross-peaks in the spectrum. Detected signal coordinates undergo automated chemical shift assignment with FLYA, which is facilitated by a deep graph neural network. In the final step, ARTINA calculates 9 structure candidates with CYANA, and orders them by their expected quality using gradient boosted trees.
The method was tested on a 100-protein benchmark dataset (1329 2D/3D/4D NMR spectra), demonstrating its ability to solve structures with 1.44 A backbone median RMSD to the PDB reference, and to identify 91.36% correct NMR resonance assignments. ARTINA is publicly available to non-commercial users within the NMRtist platform.

Floquet theory uses a Fourier series expansion of the time-dependent Hamiltonian to transform the Hamiltonian into a time-independent representation. The price to pay for this transformation is the transition from a finite-dimensional to an infinite-dimensional Hilbert space. Today, Floquet theory is often used in combination with analytical operator-based van Vleck perturbation theory to generate effective time-independent Hamiltonians.
We present a modified Floquet framework that uses a continuous frequency space to describe and design solid-state NMR experiments using time-dependent Hamiltonians. The approach is similar to the well established Floquet treatment for NMR, but is not restricted to periodic Hamiltonians and allows the design of experiments in a reverse fashion. The framework is based on perturbation theory on a continuous Fourier space, which leads to effective, i.e. time-independent, Hamiltonians. This continuous Floquet approach simplifies the description of sequences with effective fields and correctly describes the finite width of resonance conditions for pulse sequences with finite mixing time.
It allows, in certain cases, the back calculation of the pulse scheme from the desired effective Hamiltonian as a function of spin-system parameters. We show as an example how to back calculate the radio-frequency irradiation in the MIRROR experiment from the desired chemical-shift offset behavior of the sequence. It also enables us to optimize pulse sequences based on effective Hamiltonians without requiring the use of density-operator simulations. We will show first preliminary applications to frequency-selective recoupling in solid-state NMR under MAS.

Paramagnetic materials exhibit solid-state NMR spectra with very large shifts and shift anisotropies. In addition enhanced relaxation results in short coherence lifetimes, meaning that signals decay rapidly following excitation. The broad fast-relaxing resonances are difficult to excite and observe. This presentation explores the ways in which these problems can be addressed, including fast MAS, fast signal averaging, and broadband adiabatic pulse schemes. We explore the different adiabatic pulse schemes that can be used, and, using a broad range of materials as test subjects, how these pulses can be incorporated into more complex 2D experiments for both spin 1/2 and quadrupolar nuclei.

The switch from the traditional MAS NMR approaches with 13C and 15N detection to 1H has accelerated the site-specific analysis of complex immobilised biological systems and opened the way to samples of higher molecular weight and available in limited amounts. We will take the moves from a critical analysis of recent literature data, share our first results on a prototype Bruker 0.4mm probe capable of rates exceeding 150 kHz and discuss the expected impact of fast MAS on resolution and sensitivity of different biomolecular NMR experiments.

Magic-angle spinning NMR probes need to fulfill various technical requirements. Apart from RF capabilities for spin excitation and detection with high efficiency and homogeneity at multiple frequencies, sample spinning speeds on the order of 10-100 kHz need to be attainable, often at given temperatures beyond the ambient range. Secondary aspects indirectly linked to performance are producibility and usability, which are relevant for efficient production of diverse probe portfolios and for the general accessibility of MAS NMR, respectively. Substantial advances in probe instrumentation have been made in all above fields over the last decades. However, physical and engineering limitations are quite diverse across the requirements, and some requirements are interlinked. An overview of these requirements will be given, along with an insight into theoretical and practical limitations, recent achievements, the current state of technology and an outlook into future advances.

Single-vector effective Hamiltonian theory (SV-EHT) and exact effective Hamiltonian theory (EEHT) methods are described for analysis and design of advanced magnetic resonance experiments. These tools provide highly accurate/exact descriptions of effective Hamiltonians with detailed information on linear and bilinear components and their interplay in experiments for coherence/polarization transfer in presence of large offsets. The complementarity and use of SV-EHT and EEHT is demonstrated for liquid-state NMR isotropic mixing and solid-state NMR dipolar recoupling focusing on offset behavior, delicate aspects of resonance formation, and multiple-spin effective Hamiltonian/density operator evolution based on single-spin analysis.

MAS NMR is an essential method to gain insights into dynamics at the atomic scale, independently of the protein size. In this presentation I show recent applications to studies of dynamics.
In one part I will decipher how large-scale motion within a half-megadalton enzyme complex can be detected and quantified using MAS NMR methods, and how these are linked to an apparently allosteric network across the protein.
In a second part, I will dwell onto details of side chain motion; in particular, I will investigate how aromatic rings flip in different types of protein assemblies: globular proteins in a crystal, amyloid fibers and large oligomeric proteins. The results shed light onto the packing of aromatic rings within a protein interior and with other molecules.

The ultrafast MAS regime ( ~50-100 kHz) brings opportunities and challenges. Recent developments in pulse sequences will be discussed that apply to the ultrafast MAS regime, such as selective proton recouping, torsion angle determination, and diagonal suppression. These new developments will be highlighted in applications to biological solid-state NMR, in particular, for atomic resolution structure determination of membrane proteins and proteins that mis-fold and aggregate on membranes.

no abstract given