Enhanced accuracy of kinetic information from CT-CPMG experiments by transverse rotating-frame spectroscopy

Studying micro to millisecond protein dynamics using simple amide 15N CEST experiments supplemented with major-state R2 and visible peak-position constraints

Over the last decade amide 15N CEST experiments have emerged as a popular tool to study protein dynamics that involves exchange between a 'visible' major state and sparsely populated 'invisible' minor states. Although initially introduced to study exchange between states that are in slow exchange with each other (typical exchange rates of, 10 to 400 s-1), they are now used to study interconversion between states on the intermediate to fast exchange timescale while still using low to moderate (5 to 350 Hz) 'saturating' B1 fields. The 15N CEST experiment is very sensitive to exchange as the exchange delay TEX can be quite long (~0.5 s) allowing for a large number of exchange events to occur making it a very powerful tool to detect minor sates populated ([Formula: see text]) to as low as 1%. When systems are in fast exchange and the 15N CEST data has to be described using a model that contains exchange, the exchange parameters are often poorly defined because the [Formula: see text] versus [Formula: see text] and [Formula: see text] versus exchange rate ([Formula: see text]) plots can be quite flat with shallow or no minima and the analysis of such 15N CEST data can lead to wrong estimates of the exchange parameters due to the presence of 'spurious' minima. Here we show that the inclusion of experimentally derived constraints on the intrinsic transverse relaxation rates and the inclusion of visible state peak-positions during the analysis of amide 15N CEST data acquired with moderate B1 values (~50 to ~350 Hz) results in convincing minima in the [Formula: see text] versus [Formula: see text] and the [Formula: see text] versus [Formula: see text] plots even when exchange occurs on the 100 μs timescale. The utility of this strategy is demonstrated on the fast-folding Bacillus stearothermophilus peripheral subunit binding domain that folds with a rate constant ~104 s-1. Here the analysis of 15N CEST data alone results in [Formula: see text] versus [Formula: see text] and [Formula: see text] versus [Formula: see text] plots that contain shallow minima, but the inclusion of visible-state peak positions and restraints on the intrinsic transverse relaxation rates of both states during the analysis of the 15N CEST data results in pronounced minima in the [Formula: see text] versus [Formula: see text] and [Formula: see text] versus [Formula: see text] plots and precise exchange parameters even in the fast exchange regime ([Formula: see text]~5). Using this strategy we find that the folding rate constant of PSBD is invariant (~10,500 s-1) from 33.2 to 42.9 °C while the unfolding rates (~70 to ~500 s-1) and unfolded state populations (~0.7 to ~4.3%) increase with temperature. The results presented here show that protein dynamics occurring on the 10 to 104 s-1 timescale can be studied using amide 15N CEST experiments.

Dynamical Models of Chemical Exchange in Nuclear Magnetic Resonance Spectroscopy

Chemical exchange line-broadening is an important phenomenon in nuclear magnetic resonance (NMR) spectroscopy, in which a nuclear spin experiences more than one magnetic environment as a result of chemical or conformational changes of a molecule. The dynamic process of chemical exchange strongly affects the sensitivity and resolution of NMR experiments, and increasingly provides a powerful probe of the inter-conversion between chemical and conformational states of proteins, nucleic acids, and other biological macromolecules. A simple and often used theoretical description of chemical exchange in NMR spectroscopy is based on an idealized two-state jump model (the random-phase or telegraph signal). However, chemical exchange can also be represented as a barrier-crossing event that can be modeled using chemical reaction rate theory. The time scale of crossing is determined by the barrier height, the temperature, and the dissipation modeled as collisional or frictional damping. This tutorial explores the connection between the NMR theory of chemical exchange line-broadening and strong-collision models for chemical kinetics in statistical mechanics. Theoretical modeling and numerical simulation are used to map the rate of barrier-crossing dynamics of a particle on a potential energy surface to the chemical exchange relaxation rate constant. By developing explicit models for the exchange dynamics, the tutorial aims to elucidate the underlying dynamical processes that give rise to the rich phenomenology of chemical exchange observed in NMR spectroscopy. Software for generating and analyzing the numerical simulations is provided in the form of Python and Fortran source codes.

Opportunities and Challenges of Backbone, Sidechain, and RDC Experiments to Study Membrane Protein Dynamics in a Detergent-Free Lipid Environment Using Solution State NMR

Whereas solution state NMR provided a wealth of information on the dynamics landscape of soluble proteins, only few studies have investigated membrane protein dynamics in a detergent-free lipid environment. Recent developments of smaller nanodiscs and other lipid-scaffolding polymers, such as styrene maleic acid (SMA), however, open new and promising avenues to explore the function-dynamics relationship of membrane proteins as well as between membrane proteins and their surrounding lipid environment. Favorably sized lipid-bilayer nanodiscs, established membrane protein reconstitution protocols and sophisticated solution NMR relaxation methods probing dynamics over a wide range of timescales will eventually reveal unprecedented lipid-membrane protein interdependencies that allow us to explain things we have not been able to explain so far. In particular, methyl group dynamics resulting from CEST, CPMG, ZZ exchange, and RDC experiments are expected to provide new and surprising insights due to their proximity to lipids, their applicability in large 100+ kDa assemblies and their simple labeling due to the availability of commercial precursors. This review summarizes the recent developments of membrane protein dynamics with a special focus on membrane protein dynamics in lipid-bilayer nanodiscs. Opportunities and challenges of backbone, side chain and RDC dynamics applied to membrane proteins are discussed. Solution-state NMR and lipid nanodiscs bear great potential to change our molecular understanding of lipid-membrane protein interactions.

Detection of chemical exchange in methyl groups of macromolecules

The zero- and double-quantum methyl TROSY Hahn-echo and the methyl ¹H-¹H dipole-dipole cross-correlation nuclear magnetic resonance experiments enable estimation of multiple quantum chemical exchange broadening in methyl groups in proteins. The two relaxation rate constants are established to be linearly dependent using molecular dynamics simulations and empirical analysis of experimental data. This relationship allows chemical exchange broadening to be recognized as an increase in the Hahn-echo relaxation rate constant. The approach is illustrated by analyzing relaxation data collected at three temperatures for E. coli ribonuclease HI and by analyzing relaxation data collected for different cofactor and substrate complexes of E. coli AlkB.

Chemical Exchange

The phenomenon of chemical or conformational exchange in NMR spectroscopy has enabled detailed characterization of time-dependent aspects of biomolecular function, including folding, molecular recognition, allostery, and catalysis, on timescales from microsecond to second. Importantly, NMR methods based on a variety of spin relaxation parameters have been developed that provide quantitative information on interconversion kinetics, thermodynamic properties, and structural features of molecular states populated to a fraction of a percent at equilibrium and otherwise unobservable by other NMR approaches. The ongoing development of more sophisticated experimental techniques and the necessity to apply these methods to larger and more complex molecular systems engenders a corresponding need for theoretical advances describing such techniques and facilitating data analysis in applications. This review surveys current aspects of the theory of chemical exchange, as utilized in ZZ-exchange; Hahn and Carr-Purcell-Meiboom-Gill (CPMG) spin-echo; and R_1ρ, chemical exchange saturation transfer (CEST), and dark state saturation transfer (DEST) spin-locking experiments. The review emphasizes theoretical results for kinetic topologies with more than two interconverting states, both to obtain compact analytical forms suitable for data analysis and to establish conditions for distinguishability between alternative kinetic schemes.

Structure and dynamics conspire in the evolution of affinity between intrinsically disordered proteins

In every established species, protein-protein interactions have evolved such that they are fit for purpose. However, the molecular details of the evolution of new protein-protein interactions are poorly understood. We have used nuclear magnetic resonance spectroscopy to investigate the changes in structure and dynamics during the evolution of a protein-protein interaction involving the intrinsically disordered CREBBP (CREB-binding protein) interaction domain (CID) and nuclear coactivator binding domain (NCBD) from the transcriptional coregulators NCOA (nuclear receptor coactivator) and CREBBP/p300, respectively. The most ancient low-affinity "Cambrian-like" [540 to 600 million years (Ma) ago] CID/NCBD complex contained less secondary structure and was more dynamic than the complexes from an evolutionarily younger "Ordovician-Silurian" fish ancestor (ca. 440 Ma ago) and extant human. The most ancient Cambrian-like CID/NCBD complex lacked one helix and several interdomain interactions, resulting in a larger solvent-accessible surface area. Furthermore, the most ancient complex had a high degree of millisecond-to-microsecond dynamics distributed along the entire sequences of both CID and NCBD. These motions were reduced in the Ordovician-Silurian CID/NCBD complex and further redistributed in the extant human CID/NCBD complex. Isothermal calorimetry experiments show that complex formation is enthalpically favorable and that affinity is modulated by a largely unfavorable entropic contribution to binding. Our data demonstrate how changes in structure and motion conspire to shape affinity during the evolution of a protein-protein complex and provide direct evidence for the role of structural, dynamic, and frustrational plasticity in the evolution of interactions between intrinsically disordered proteins.

A guide to quantifying membrane protein dynamics in lipids and other native-like environments by solution-state NMR spectroscopy

Recent biochemical and technical developments permit residue-specific solution NMR measurements of membrane protein (MP) dynamics in lipidic and chaperone-bound environments. This is possible by combinations of improved sample preparations with suitable NMR relaxation experiments to correlate protein function to backbone dynamics on timescales from picoseconds to seconds, even for large MP-lipid assemblies above 100 kDa in molecular mass. Here, we introduce the basic concepts of different NMR relaxation experiments, individually sensitive to specific timescales. We discuss the general limitations of detergent environments and highlight the importance for native-like environments when studying MPs. We then review three practical studies of fast- and slow-timescale MP dynamics in lipid environments, as well as in a natively unfolded, chaperone-bound state. These examples illustrate the new avenues solution NMR spectroscopy is taking to investigate MP dynamics in native-like environments with atomic resolution.

Simultaneous determination of fast and slow dynamics in molecules using extreme CPMG relaxation dispersion experiments

Molecular dynamics play a significant role in how molecules perform their function. A critical method that provides information on dynamics, at the atomic level, is NMR-based relaxation dispersion (RD) experiments. RD experiments have been utilized for understanding multiple biological processes occurring at micro-to-millisecond time, such as enzyme catalysis, molecular recognition, ligand binding and protein folding. Here, we applied the recently developed high-power RD concept to the Carr-Purcell-Meiboom-Gill sequence (extreme CPMG; E-CPMG) for the simultaneous detection of fast and slow dynamics. Using a fast folding protein, gpW, we have shown that previously inaccessible kinetics can be accessed with the improved precision and efficiency of the measurement by using this experiment.

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.

Solution NMR views of dynamical ordering of biomacromolecules

BACKGROUND

To understand the mechanisms related to the 'dynamical ordering' of macromolecules and biological systems, it is crucial to monitor, in detail, molecular interactions and their dynamics across multiple timescales. Solution nuclear magnetic resonance (NMR) spectroscopy is an ideal tool that can investigate biophysical events at the atomic level, in near-physiological buffer solutions, or even inside cells.

SCOPE OF REVIEW

In the past several decades, progress in solution NMR has significantly contributed to the elucidation of three-dimensional structures, the understanding of conformational motions, and the underlying thermodynamic and kinetic properties of biomacromolecules. This review discusses recent methodological development of NMR, their applications and some of the remaining challenges.

MAJOR CONCLUSIONS

Although a major drawback of NMR is its difficulty in studying the dynamical ordering of larger biomolecular systems, current technologies have achieved considerable success in the structural analysis of substantially large proteins and biomolecular complexes over 1MDa and have characterised a wide range of timescales across which biomolecular motion exists. While NMR is well suited to obtain local structure information in detail, it contributes valuable and unique information within hybrid approaches that combine complementary methodologies, including solution scattering and microscopic techniques.

GENERAL SIGNIFICANCE

For living systems, the dynamic assembly and disassembly of macromolecular complexes is of utmost importance for cellular homeostasis and, if dysregulated, implied in human disease. It is thus instructive for the advancement of the study of the dynamical ordering to discuss the potential possibilities of solution NMR spectroscopy and its applications. This article is part of a Special Issue entitled "Biophysical Exploration of Dynamical Ordering of Biomolecular Systems" edited by Dr. Koichi Kato.

Characterization of Chemical Exchange Using Relaxation Dispersion of Hyperpolarized Nuclear Spins

Chemical exchange phenomena are ubiquitous in macromolecules, which undergo conformational change or ligand complexation. NMR relaxation dispersion (RD) spectroscopy based on a Carr-Purcell-Meiboom-Gill pulse sequence is widely applied to identify the exchange and measure the lifetime of intermediate states on the millisecond time scale. Advances in hyperpolarization methods improve the applicability of NMR spectroscopy when rapid acquisitions or low concentrations are required, through an increase in signal strength by several orders of magnitude. Here, we demonstrate the measurement of chemical exchange from a single aliquot of a ligand hyperpolarized by dissolution dynamic nuclear polarization (D-DNP). Transverse relaxation rates are measured simultaneously at different pulsing delays by dual-channel ¹⁹F NMR spectroscopy. This two-point measurement is shown to allow the determination of the exchange term in the relaxation rate expression. For the ligand 4-(trifluoromethyl)benzene-1-carboximidamide binding to the protein trypsin, the exchange term is found to be equal within error limits in neutral and acidic environments from D-DNP NMR spectroscopy, corresponding to a pre-equilibrium of trypsin deprotonation. This finding illustrates the capability for determination of binding mechanisms using D-DNP RD. Taking advantage of hyperpolarization, the ligand concentration in the exchange measurements can reach on the order of tens of μM and protein concentration can be below 1 μM, i.e., conditions typically accessible in drug discovery.

Ligand-Mediated Folding of the OmpA Periplasmic Domain from Acinetobacter baumannii

The periplasmic domain of OmpA from Acinetobacter baumannii (AbOmpA-PD) binds to diaminopimelate and anchors the outer membrane to the peptidoglycan layer in the cell wall. Although the crystal structure of AbOmpA-PD with its ligands has been reported, the mechanism of ligand-mediated folding of AbOmpA remains elusive. Here, we report that in vitro refolded apo-AbOmpA-PD in the absence of ligand exists as a mixture of two partially folded forms in solution: mostly unfolded (apo-state I) and hololike (apo-state II) states. Binding of the diaminopimelate or glycine ligand induced complete folding of AbOmpA-PD. The apo-state I was highly flexible and contained some secondary structural elements, whereas the apo-state II closely resembled the holo-state in terms of both structure and backbone dynamics, except for the ligand-binding region. ¹⁵N-relaxation-dispersion analyses for apo-state II revealed substantial motion on a millisecond timescale of residues in the H3 helix near the ligand-binding site, with this motion disappearing upon ligand binding. These results provide an insight into the ligand-mediated folding mechanism of AbOmpA-PD in solution.

Recent advances in measuring the kinetics of biomolecules by NMR relaxation dispersion spectroscopy

Protein function can be modulated or dictated by the amplitude and timescale of biomolecular motion, therefore it is imperative to study protein dynamics. Nuclear Magnetic Resonance (NMR) spectroscopy is a powerful technique capable of studying timescales of motion that range from those faster than molecular reorientation on the picosecond timescale to those that occur in real-time. Across this entire regime, NMR observables can report on the amplitude of atomic motion, and the kinetics of atomic motion can be ascertained with a wide variety of experimental techniques from real-time to milliseconds and several nanoseconds to picoseconds. Still a four orders of magnitude window between several nanoseconds and tens of microseconds has remained elusive. Here, we highlight new relaxation dispersion NMR techniques that serve to cover this "hidden-time" window up to hundreds of nanoseconds that achieve atomic resolution while studying the molecule under physiological conditions.

Non-uniform sampling of NMR relaxation data

The use of non-uniform sampling of NMR spectra may give significant reductions in the data acquisition time. For quantitative experiments such as the measurement of spin relaxation rates, non-uniform sampling is however not widely used as inaccuracies in peak intensities may lead to errors in the extracted dynamic parameters. By systematic reducing the coverage of the Nyquist grid of (15)N Carr-Purcell-Meiboom-Gill (CPMG) relaxation dispersion datasets for four different proteins and performing a full data analysis of the resulting non-uniform sampled datasets, we have compared the performance of the multi-dimensional decomposition and iterative re-weighted least-squares algorithms in reconstructing spectra with accurate peak intensities. As long as a single fully sampled spectrum is included in a series of otherwise non-uniform sampled two-dimensional spectra, multi-dimensional decomposition reconstructs the non-uniform sampled spectra with high accuracy. For two of the four analyzed datasets, a coverage of only 20% results in essentially the same results as the fully sampled data. As exemplified by other data, such a low coverage is in general not enough to produce reliable results. We find that a coverage level not compromising the final results can be estimated by recording a single full two-dimensional spectrum and reducing the spectrum quality in silico.

Speeding-up exchange-mediated saturation transfer experiments by Fourier transform

Protein motions over various time scales are crucial for protein function. NMR relaxation dispersion experiments play a key role in explaining these motions. However, the study of slow conformational changes with lowly populated states remained elusive. The recently developed exchange-mediated saturation transfer experiments allow the detection and characterization of such motions, but require extensive measurement time. Here we show that, by making use of Fourier transform, the total acquisition time required to measure an exchange-mediated saturation transfer profile can be reduced by twofold in case that one applies linear prediction. In addition, we demonstrate that the analytical solution for R1ρ experiments can be used for fitting the exchange-mediated saturation transfer profile. Furthermore, we show that simultaneous analysis of exchange-mediated saturation transfer profiles with two different radio-frequency field strengths is required for accurate and precise characterization of the exchange process and the exchanging states.

Visualizing transient dark states by NMR spectroscopy

Myriad biological processes proceed through states that defy characterization by conventional atomic-resolution structural biological methods. The invisibility of these 'dark' states can arise from their transient nature, low equilibrium population, large molecular weight, and/or heterogeneity. Although they are invisible, these dark states underlie a range of processes, acting as encounter complexes between proteins and as intermediates in protein folding and aggregation. New methods have made these states accessible to high-resolution analysis by nuclear magnetic resonance (NMR) spectroscopy, as long as the dark state is in dynamic equilibrium with an NMR-visible species. These methods - paramagnetic NMR, relaxation dispersion, saturation transfer, lifetime line broadening, and hydrogen exchange - allow the exploration of otherwise invisible states in exchange with a visible species over a range of timescales, each taking advantage of some unique property of the dark state to amplify its effect on a particular NMR observable. In this review, we introduce these methods and explore two specific techniques - paramagnetic relaxation enhancement and dark state exchange saturation transfer - in greater detail.

Chemical exchange in biomacromolecules: past, present, and future

The perspective reviews quantitative investigations of chemical exchange phenomena in proteins and other biological macromolecules using NMR spectroscopy, particularly relaxation dispersion methods. The emphasis is on techniques and applications that quantify the populations, interconversion kinetics, and structural features of sparsely populated conformational states in equilibrium with a highly populated ground state. Applications to folding, molecular recognition, catalysis, and allostery by proteins and nucleic acids are highlighted.

Improved NMR experiments with ¹³C-isotropic mixing for assignment of aromatic and aliphatic side chains in labeled proteins

Three improved ¹³C-spinlock experiments for side chain assignments of isotope labelled proteins in liquid state are presented. These are based on wide bandwidth spinlock techniques that have become possible with contemporary cryogenic probes. The first application, the H(C(ali)C(aro))H-TOCSY, is an HCCH-TOCSY in which all CHn moieties of a protein are detected in a single experiment, including the aromatic ones. This enables unambiguous assignment of aromatic and aliphatic amino acids in a single, highly sensitive experiment. In the second application, the ¹³C-detected C(all)-TOCSY, magnetization transfer comprises all carbons--aliphatic, aromatic as well as the carbonyl carbons--making the complete carbon assignment possible using one spectrum only. Thirdly, the frequently used HC(CCO)NH experiment was redesigned by replacing the long C-carbonyl refocused INEPT transfer step by direct ¹³C-¹³C-TOCSY magnetization transfer from side chain carbons to the backbone carbonyls. The resulting HC(CCO)NH experiment minimizes relaxation losses because it is shorter and represents a more sensitive alternative particularly for larger proteins. The performance of the experiments is demonstrated on isotope labeled proteins up to the size of 43 kDa.

Measuring dynamic and kinetic information in the previously inaccessible supra-τ(c) window of nanoseconds to microseconds by solution NMR spectroscopy

Nuclear Magnetic Resonance (NMR) spectroscopy is a powerful tool that has enabled experimentalists to characterize molecular dynamics and kinetics spanning a wide range of time-scales from picoseconds to days. This review focuses on addressing the previously inaccessible supra-tc window (defined as τ(c) < supra-τ(c) < 40 μs; in which tc is the overall tumbling time of a molecule) from the perspective of local inter-nuclear vector dynamics extracted from residual dipolar couplings (RDCs) and from the perspective of conformational exchange captured by relaxation dispersion measurements (RD). The goal of the first section is to present a detailed analysis of how to extract protein dynamics encoded in RDCs and how to relate this information to protein functionality within the previously inaccessible supra-τ(c) window. In the second section, the current state of the art for RD is analyzed, as well as the considerable progress toward pushing the sensitivity of RD further into the supra-τ(c) scale by up to a factor of two (motion up to 25 μs). From the data obtained with these techniques and methodology, the importance of the supra-τ(c) scale for protein function and molecular recognition is becoming increasingly clearer as the connection between motion on the supra-τ(c) scale and protein functionality from the experimental side is further strengthened with results from molecular dynamics simulations.