Experimental approaches for NMR studies of side-chain dynamics in high-molecular-weight proteins

Protein dynamics detected by magic-angle spinning relaxation dispersion NMR

Magic-angle spinning (MAS) nuclear magnetic resonance (NMR) is establishing itself as a powerful method for the characterization of protein dynamics at the atomic scale. We discuss here how R1ρ MAS relaxation dispersion NMR can explore microsecond-to-millisecond motions. Progress in instrumentation, isotope labeling, and pulse sequence design has paved the way for quantitative analyses of even rare structural fluctuations. In addition to isotropic chemical-shift fluctuations exploited in solution-state NMR relaxation dispersion experiments, MAS NMR has a wider arsenal of observables, allowing to see motions even if the exchanging states do not differ in their chemical shifts. We demonstrate the potential of the technique for probing motions in challenging large enzymes, membrane proteins, and protein assemblies.

A "Steady-State" Relaxation Dispersion Nuclear Magnetic Resonance Experiment for Studies of Chemical Exchange in Degenerate 1H Transitions of Methyl Groups

Degenerate spin-systems consisting of magnetically equivalent nuclear spins, such as a ¹H₃ spin-system in selectively ¹³CH₃-labeled proteins, present considerable challenges for the design of Carr-Purcell-Meiboom-Gill (CPMG) relaxation dispersion NMR experiments to characterize chemical exchange on the micro-to-millisecond time-scale. Several approaches have been previously proposed for the elimination of deleterious artifacts observed in methyl ¹H CPMG relaxation dispersion profiles obtained for (¹³C)¹H₃ groups. We describe an alternative, experimentally simple solution and design a "steady-state" methyl ¹H CPMG scheme, where 90° or acute-angle (<90°) ¹H radiofrequency pulses are applied after each CPMG echo in-phase with methyl ¹H magnetization, resulting in the establishment of a "steady-state" for effective rates of magnetization decay. A simple computational procedure for quantitative analysis of the "steady-state" CPMG relaxation dispersion profiles is developed. The "steady-state" CPMG methodology is applied to two protein systems where exchange between major and minor species occurs in different regimes on the chemical shift time-scale.

Ion influence on surface water dynamics and proton exchange at protein surfaces - A unified model for transverse and longitudinal NMR relaxation dispersion

In all biologically relevant media, proteins interact in the presence of surrounding ions, and such interactions are water-mediated. Water molecules play a crucial role in the restructuring of proteins in solution and indeed in their biological activity. Surface water dynamics and proton exchange at protein surfaces is investigated here using NMR relaxometry, for two well-known globular proteins, lysozyme and bovine serum albumin, with particular attention to the role of surface ions. We present a unified model of surface water dynamics and proton exchange, accounting simultaneously for the observed longitudinal and transverse relaxation rates. The most notable effect of salt (0.1 M) concerns the slow surface water dynamics, related to rare water molecules embedded in energy wells on the protein surface. This response is protein-specific. On the other hand, the proton exchange time between labile protein-protons and water-protons at the protein surface seems to be very similar for the two proteins and is insensitive to the addition of salts at the concentration studied.

Functional control of a 0.5 MDa TET aminopeptidase by a flexible loop revealed by MAS NMR

Large oligomeric enzymes control a myriad of cellular processes, from protein synthesis and degradation to metabolism. The 0.5 MDa large TET2 aminopeptidase, a prototypical protease important for cellular homeostasis, degrades peptides within a ca. 60 Å wide tetrahedral chamber with four lateral openings. The mechanisms of substrate trafficking and processing remain debated. Here, we integrate magic-angle spinning (MAS) NMR, mutagenesis, co-evolution analysis and molecular dynamics simulations and reveal that a loop in the catalytic chamber is a key element for enzymatic function. The loop is able to stabilize ligands in the active site and may additionally have a direct role in activating the catalytic water molecule whereby a conserved histidine plays a key role. Our data provide a strong case for the functional importance of highly dynamic - and often overlooked - parts of an enzyme, and the potential of MAS NMR to investigate their dynamics at atomic resolution.

Mechanistic analysis by NMR spectroscopy: A users guide

A 'principles and practice' tutorial-style review of the application of solution-phase NMR in the analysis of the mechanisms of homogeneous organic and organometallic reactions and processes. This review of 345 references summarises why solution-phase NMR spectroscopy is uniquely effective in such studies, allowing non-destructive, quantitative analysis of a wide range of nuclei common to organic and organometallic reactions, providing exquisite structural detail, and using instrumentation that is routinely available in most chemistry research facilities. The review is in two parts. The first comprises an introduction to general techniques and equipment, and guidelines for their selection and application. Topics include practical aspects of the reaction itself, reaction monitoring techniques, NMR data acquisition and processing, analysis of temporal concentration data, NMR titrations, DOSY, and the use of isotopes. The second part comprises a series of 15 Case Studies, each selected to illustrate specific techniques and approaches discussed in the first part, including in situ NMR (^1/2H, ^10/11B, ¹³C, ¹⁵N, ¹⁹F, ²⁹Si, ³¹P), kinetic and equilibrium isotope effects, isotope entrainment, isotope shifts, isotopes at natural abundance, scalar coupling, kinetic analysis (VTNA, RPKA, simulation, steady-state), stopped-flow NMR, flow NMR, rapid injection NMR, pure shift NMR, dynamic nuclear polarisation, ¹H/¹⁹F DOSY NMR, and in situ illumination NMR.

Insights into the Cross Talk between Effector and Allosteric Lobes of KRAS from Methyl Conformational Dynamics

KRAS is the most frequently mutated RAS protein in cancer patients, and it is estimated that about 20% of the cancer patients in the United States carried mutant RAS proteins. To accelerate therapeutic development, structures and dynamics of RAS proteins had been extensively studied by various biophysical techniques for decades. Although 31P NMR studies revealed population equilibrium of the two major states in the active GMPPNP-bound form, more complex conformational dynamics in RAS proteins and oncogenic mutants subtly modulate the interactions with their downstream effectors. We established a set of customized NMR relaxation dispersion techniques to efficiently and systematically examine the ms-μs conformational dynamics of RAS proteins. This method allowed us to observe varying synchronized motions that connect the effector and allosteric lobes in KRAS. We demonstrated the role of conformational dynamics of KRAS in controlling its interaction with the Ras-binding domain of the downstream effector RAF1, the first kinase in the MAPK pathway. This allows one to explain, as well as to predict, the altered binding affinities of various KRAS mutants, which was neither previously reported nor apparent from the structural perspective.

The measurement of relaxation rates of degenerate 1H transitions in methyl groups of proteins using acute angle radiofrequency pulses

A simple NMR experiment for the measurement of transverse relaxation rates of degenerate ¹H spins in ¹³CH₃ methyl groups of deuterated proteins, is described. The experiment relies on the use of acute-angle ¹H radio-frequency pulses, whereby a series of methyl ¹H R₂ decays is acquired with different values of the ¹H pulse flip-angle, which modulates the relative contributions of the slow- and fast-relaxing components of ¹H magnetization during the relaxation delay. These are subsequently analyzed simultaneously to extract the transverse relaxation rates of both components (R_S and R_F), along with the rate of cross-relaxation between these components, δ. The dipolar ¹H-¹H cross-correlated relaxation rate η = (R_F - R_S)/2 and the cross-relaxation rate δ, extracted from such acute-angle-pulse R₂ decay series are compared with those derived from well-established methodology that uses relaxation-violated methyl ¹H coherence transfer (so-called 'forbidden' experiments). Good agreement is achieved for the rates η derived from the two techniques, while slightly more accurate values of δ are obtained from analysis of acute-angle-pulse R₂ series. Recording of acute-angle-pulse R₂ series represents an attractive alternative to existing methodologies for quantifying methyl ¹H relaxation and dynamics of the methyl three-fold symmetry axis in selectively [¹³CH₃]-methyl-labeled, deuterated proteins - particularly so for very high-molecular-weight proteins, where the measurements of R_F rates or the build-up of methyl ¹H magnetization in relaxation-violated coherence transfer experiments, are problematic due to low sensitivity.

Comparative Analysis of Structural and Dynamical Features of Ribosome Upon Association With mRNA Reveals Potential Role of Ribosomal Proteins

Ribosomes play a critical role in maintaining cellular proteostasis. The binding of messenger RNA (mRNA) to the ribosome regulates kinetics of protein synthesis. To generate an understanding of the structural, mechanistic, and dynamical features of mRNA recognition in the ribosome, we have analysed mRNA-protein interactions through a structural comparison of the ribosomal complex in the presence and absence of mRNA. To do so, we compared the 3-Dimensional (3D) structures of components of the two assembly structures and analysed their structural differences because of mRNA binding, using elastic network models and structural network-based analysis. We observe that the head region of 30S ribosomal subunit undergoes structural displacement and subunit rearrangement to accommodate incoming mRNA. We find that these changes are observed in proteins that lie far from the mRNA-protein interface, implying allostery. Further, through perturbation response scanning, we show that the proteins S13, S19, and S20 act as universal sensors that are sensitive to changes in the inter protein network, upon binding of 30S complex with mRNA and other initiation factors. Our study highlights the significance of mRNA binding in the ribosome complex and identifies putative allosteric sites corresponding to alterations in structure and/or dynamics, in regions away from mRNA binding sites in the complex. Overall, our work provides fresh insights into mRNA association with the ribosome, highlighting changes in the interactions and dynamics of the ribosome assembly because of the binding.

Probing Side-Chain Dynamics in Proteins by NMR Relaxation of Isolated 13C Magnetization Modes in 13CH3 Methyl Groups

The dynamics of methyl-bearing side chains in proteins were probed by ¹³C relaxation measurements of a number of ¹³C magnetization modes in selectively ¹³CH₃-labeled methyl groups of proteins. We first show how ¹³C magnetization modes in a ¹³CH₃ spin-system can be isolated using acute-angle ¹H radio-frequency pulses. The parameters of methyl-axis dynamics, a measure of methyl-axis ordering (S_axis²) and the correlation time of fast local methyl-axis motions (τ_f), derived from ¹³C relaxation in ¹³CH₃ groups are compared with their counterparts obtained from ¹³C relaxation in ¹³CHD₂ methyl isotopomers. We show that in high-molecular-weight proteins, excellent correlations are obtained between the [¹³CHD₂]-derived S_axis² values and those extracted from relaxation of the ¹³C magnetization of the I = 1/2 manifold in ¹³CH₃ methyls. In smaller proteins, a certain degree of anticorrelation is observed between the S_axis² and τ_f values obtained from ¹³C relaxation of the I = 1/2 manifold magnetization in ¹³CH₃ methyls. These parameters can be partially decorrelated by inclusion in the analysis of relaxation data of the I = 3/2 manifold ¹³C magnetization.

Large Multidomain Protein NMR: HIV-1 Reverse Transcriptase Precursor in Solution

NMR studies of large proteins, over 100 kDa, in solution are technically challenging and, therefore, of considerable interest in the biophysics field. The challenge arises because the molecular tumbling of a protein in solution considerably slows as molecular mass increases, reducing the ability to detect resonances. In fact, the typical ¹H-¹³C or ¹H-¹⁵N correlation spectrum of a large protein, using a ¹³C- or ¹⁵N-uniformly labeled protein, shows severe line-broadening and signal overlap. Selective isotope labeling of methyl groups is a useful strategy to reduce these issues, however, the reduction in the number of signals that goes hand-in-hand with such a strategy is, in turn, disadvantageous for characterizing the overall features of the protein. When domain motion exists in large proteins, the domain motion differently affects backbone amide signals and methyl groups. Thus, the use of multiple NMR probes, such as ¹H, ¹⁹F, ¹³C, and ¹⁵N, is ideal to gain overall structural or dynamical information for large proteins. We discuss the utility of observing different NMR nuclei when characterizing a large protein, namely, the 66 kDa multi-domain HIV-1 reverse transcriptase that forms a homodimer in solution. Importantly, we present a biophysical approach, complemented by biochemical assays, to understand not only the homodimer, p66/p66, but also the conformational changes that contribute to its maturation to a heterodimer, p66/p51, upon HIV-1 protease cleavage.

Dynamics of Bacteriorhodopsin in the Dark-Adapted State from Solution Nuclear Magnetic Resonance Spectroscopy

To achieve efficient proton pumping in the light-driven proton pump bacteriorhodopsin (bR), the protein must be tightly coupled to the retinal to rapidly convert retinal isomerization into protein structural rearrangements. Methyl group dynamics of bR embedded in lipid nanodiscs were determined in the dark-adapted state, and were found to be mostly well ordered at the cytosolic side. Methyl groups in the M145A mutant of bR, which displays only 10 % residual proton pumping activity, are less well ordered, suggesting a link between side-chain dynamics on the cytosolic side of the bR cavity and proton pumping activity. In addition, slow conformational exchange, attributed to low frequency motions of aromatic rings, was indirectly observed for residues on the extracellular side of the bR cavity. This may be related to reorganization of the water network. These observations provide a detailed picture of previously undescribed equilibrium dynamics on different time scales for ground-state bR.

A distal regulatory region of a class I human histone deacetylase

Histone deacetylases (HDACs) are key enzymes in epigenetics and important drug targets in cancer biology. Whilst it has been established that HDACs regulate many cellular processes, far less is known about the regulation of these enzymes themselves. Here, we show that HDAC8 is allosterically regulated by shifts in populations between exchanging states. An inactive state is identified, which is stabilised by a range of mutations and resembles a sparsely-populated state in equilibrium with active HDAC8. Computational models show that the inactive and active states differ by small changes in a regulatory region that extends up to 28 Å from the active site. The regulatory allosteric region identified here in HDAC8 corresponds to regions in other class I HDACs known to bind regulators, thus suggesting a general mechanism. The presented results pave the way for the development of allosteric HDAC inhibitors and regulators to improve the therapy for several disease states.

Optimizing the α1B-adrenergic receptor for solution NMR studies

Sample preparation for NMR studies of G protein-coupled receptors faces special requirements: Proteins need to be stable for prolonged measurements at elevated temperatures, they should ideally be uniformly labeled with the stable isotopes ¹³C, ¹⁵N, and all carbon-bound protons should be replaced by deuterons. In addition, certain NMR experiments require protonated methyl groups in the presence of a perdeuterated background. All these requirements are most easily satisfied when using Escherichia coli as the expression host. Here we describe a workflow, starting from a temperature-stabilized mutant of the α_1B-adrenergic receptor, obtained using the CHESS methodology, into an even more stable species, in which flexible parts from termini were removed and the intracellular loop 3 (ICL3) was stabilized against proteolytic cleavage. The yield after purification corresponds to 1-2 mg/L of D₂O culture. The final purification step is ligand-affinity chromatography to ensure that only well-folded ligand-binding protein is isolated. Proper selection of detergent has a remarkable influence on the quality of NMR spectra. All optimization steps of sequence and detergent are monitored on a small scale by monitoring the melting temperature and long-term thermal stability to allow for screening of many conditions. The stabilized mutant of the α_1B-adrenergic receptor was additionally incorporated in nanodiscs, but displayed slightly inferior spectra compared to a sample in detergent micelles. Finally, both [¹⁵N,¹H]- as well as [¹³C,¹H]-HSQC spectra are shown highlighting the high quality of the final NMR sample. Importantly, the quality of [¹³C,¹H]-HSQC spectra indicates that the so prepared receptor could be used for studying side-chain dynamics.

Protein Dynamics revealed by NMR Relaxation Methods

Structural biology often focuses primarily on three-dimensional structures of biological macromolecules, deposited in the Protein Data Bank (PDB). This resource is a remarkable entity for the world-wide scientific and medical communities, as well as the general public, as it is a growing translation into three-dimensional space of the vast information in genomic databases, e.g. GENBANK. There is, however, significantly more to understanding biological function than the three-dimensional coordinate space for ground-state structures of biomolecules. The vast array of biomolecules experiences natural dynamics, interconversion between multiple conformational states, and molecular recognition and allosteric events that play out on timescales ranging from picoseconds to seconds. This wide range of timescales demands ingenious and sophisticated experimental tools to sample and interpret these motions, thus enabling clearer insight into functional annotation of the PDB. NMR spectroscopy is unique in its ability to sample this range of timescales at atomic resolution and in physiologically relevant conditions using spin relaxation methods. The field is constantly expanding to provide new creative experiments, to yield more detailed coverage of timescales, and to broaden the power of interpretation and analysis methods. This review highlights the current state of the methodology and examines the extension of analysis tools for more complex experiments and dynamic models. The future for understanding protein dynamics is bright, and these extended tools bring greater compatibility with developments in computational molecular dynamics, all of which will further our understanding of biological molecular functions. These facets place NMR as a key component in integrated structural biology.

Methyl TROSY spectroscopy: A versatile NMR approach to study challenging biological systems

A major goal in structural biology is to unravel how molecular machines function in detail. To that end, solution-state NMR spectroscopy is ideally suited as it is able to study biological assemblies in a near natural environment. Based on methyl TROSY methods, it is now possible to record high-quality data on complexes that are far over 100 kDa in molecular weight. In this review, we discuss the theoretical background of methyl TROSY spectroscopy, the information that can be extracted from methyl TROSY spectra and approaches that can be used to assign methyl resonances in large complexes. In addition, we touch upon insights that have been obtained for a number of challenging biological systems, including the 20S proteasome, the RNA exosome, molecular chaperones and G-protein-coupled receptors. We anticipate that methyl TROSY methods will be increasingly important in modern structural biology approaches, where information regarding static structures is complemented with insights into conformational changes and dynamic intermolecular interactions.

Probing the Broad Time Scale and Heterogeneous Conformational Dynamics in the Catalytic Core of the Arf-GAP ASAP1 via Methyl Adiabatic Relaxation Dispersion

Methyl-TROSY is one of the most powerful NMR spectroscopic tools for studying structures and conformational dynamics of large protein complexes in solution. In studying conformational dynamics, side chains usually display heterogeneous dynamics, including collective and local motions, that can be difficult to detect and analyze by conventional relaxation dispersion (RD) approaches. The combination of NH-based heteronuclear adiabatic relaxation dispersion (HARD) experiments and a geometric approximation (geoHARD) has been shown to have several advantages over conventional RD in revealing conformational dynamics over a broad time scale. Here, we demonstrate a new technique that has been developed to detect both heterogeneous and wide time scale conformational dynamics in the hydrophobic interior of large macromolecules utilizing methyl-geoHARD. It is shown that methyl-geoHARD will be feasible at ultrahigh magnetic fields (>1 GHz), when this technology becomes available. For the ZA domain of Arf-GAP ASAP1, with a global correlational time of 24 ns at 15 °C, a wide range of conformational dynamics (exhibiting chemical exchange rates (kex) between 102 and 105 s-1) are observed in the methyl groups of isoleucine, leucine, and valine. The dynamics include collective and independent local motions. Furthermore, portions of the collective motions have been confirmed by single-quantum Carr-Purcell-Meiboom-Gill (SQ-CPMG) RD experiments; however, motions outside of the detectable CPMG window (400-8000 s-1) cannot be accurately determined by SQ-CPMG experiments. The methyl-geoHARD experiment allows the dissection of heterogeneous conformational dynamics and pinpoints important motions that, potentially, can be correlated with important biological functions and recognition.

Aromatic Ring Dynamics, Thermal Activation, and Transient Conformations of a 468 kDa Enzyme by Specific 1H-13C Labeling and Fast Magic-Angle Spinning NMR

Aromatic residues are located at structurally important sites of many proteins. Probing their interactions and dynamics can provide important functional insight but is challenging in large proteins. Here, we introduce approaches to characterize the dynamics of phenylalanine residues using ¹H-detected fast magic-angle spinning (MAS) NMR combined with a tailored isotope-labeling scheme. Our approach yields isolated two-spin systems that are ideally suited for artifact-free dynamics measurements, and allows probing motions effectively without molecular weight limitations. The application to the TET2 enzyme assembly of ∼0.5 MDa size, the currently largest protein assigned by MAS NMR, provides insights into motions occurring on a wide range of time scales (picoseconds to milliseconds). We quantitatively probe ring-flip motions and show the temperature dependence by MAS NMR measurements down to 100 K. Interestingly, favorable line widths are observed down to 100 K, with potential implications for DNP NMR. Furthermore, we report the first ¹³C R_1ρ MAS NMR relaxation-dispersion measurements and detect structural excursions occurring on a microsecond time scale in the entry pore to the catalytic chamber and at a trimer interface that was proposed as the exit pore. We show that the labeling scheme with deuteration at ca. 50 kHz MAS provides superior resolution compared to 100 kHz MAS experiments with protonated, uniformly ¹³C-labeled samples.

Characterising side chains in large proteins by protonless 13C-detected NMR spectroscopy

Side chains cover protein surfaces and are fundamental to processes as diverse as substrate recognition, protein folding and enzyme catalysis. However, characterisation of side-chain motions has so far been restricted to small proteins and methyl-bearing side chains. Here we present a class of methods, based on ¹³C-detected NMR spectroscopy, to more generally quantify motions and interactions of side chains in medium-to-large proteins. A single, uniformly isotopically labelled sample is sufficient to characterise the side chains of six different amino acid types. Side-chain conformational dynamics on the millisecond time-scale can be quantified by incorporating chemical exchange saturation transfer (CEST) into the presented methods, whilst long-range ¹³C-¹³C scalar couplings reporting on nanosecond to millisecond motions can be quantified in proteins as large as 80 kDa. The presented class of methods promises characterisation of side-chain behaviour at a level that has so far been reserved for the protein backbone.

Analysis of side-chain motions by NMR has so far been restricted to small proteins and methyl-bearing side chains. Here, the authors present NMR methods based on ¹³C direct detection of highly deuterated protein samples that yield sharp and well-resolved signals and allow the characterisation of side-chain conformational dynamics of six different amino acid types in medium-to-large proteins.

Structure determination of supra-molecular assemblies by solid-state NMR: Practical considerations

In the cellular environment, biomolecules assemble in large complexes which can act as molecular machines. Determining the structure of intact assemblies can reveal conformations and inter-molecular interactions that are only present in the context of the full assembly. Solid-state NMR (ssNMR) spectroscopy is a technique suitable for the study of samples with high molecular weight that allows the atomic structure determination of such large protein assemblies under nearly physiological conditions. This review provides a practical guide for the first steps of studying biological supra-molecular assemblies using ssNMR. The production of isotope-labeled samples is achievable via several means, which include recombinant expression, cell-free protein synthesis, extraction of assemblies directly from cells, or even the study of assemblies in whole cells in situ. Specialized isotope labeling schemes greatly facilitate the assignment of chemical shifts and the collection of structural data. Advanced strategies such as mixed, diluted, or segmental subunit labeling offer the possibility to study inter-molecular interfaces. Detailed and practical considerations are presented with respect to first setting up magic-angle spinning (MAS) ssNMR experiments, including the selection of the ssNMR rotor, different methods to best transfer the sample and prepare the rotor, as well as common and robust procedures for the calibration of the instrument. Diagnostic spectra to evaluate the resolution and sensitivity of the sample are presented. Possible improvements that can reduce sample heterogeneity and improve the quality of ssNMR spectra are reviewed.

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.

Measurement of 15N longitudinal relaxation rates in 15NH4+ spin systems to characterise rotational correlation times and chemical exchange

Many chemical and biological processes rely on the movement of monovalent cations and an understanding of such processes can therefore only be achieved by characterising the dynamics of the involved ions. It has recently been shown that 15N-ammonium can be used as a proxy for potassium to probe potassium binding in bio-molecules such as DNA quadruplexes and enzymes. Moreover, equations have been derived to describe the time-evolution of 15N-based spin density operator elements of 15NH4+ spin systems. Herein NMR pulse sequences are derived to select specific spin density matrix elements of the 15NH4+ spin system and to measure their longitudinal relaxation in order to characterise the rotational correlation time of the 15NH4+ ion as well as report on chemical exchange events of the 15NH4+ ion. Applications to 15NH4+ in acidic aqueous solutions are used to cross-validate the developed pulse sequence while measurements of spin-relaxation rates of 15NH4+ bound to a 41kDa domain of the bacterial Hsp70 homologue DnaK are presented to show the general applicability of the derived pulse sequence. The rotational correlation time obtained for 15N-ammonium bound to DnaK is similar to the correlation time that describes the rotation about the threefold axis of a methyl group. The methodology presented here provides, together with the previous theoretical framework, an important step towards characterising the motional properties of cations in macromolecular systems.

Protein folding by NMR

Protein folding is a highly complex process proceeding through a number of disordered and partially folded nonnative states with various degrees of structural organization. These transiently and sparsely populated species on the protein folding energy landscape play crucial roles in driving folding toward the native conformation, yet some of these nonnative states may also serve as precursors for protein misfolding and aggregation associated with a range of devastating diseases, including neuro-degeneration, diabetes and cancer. Therefore, in vivo protein folding is often reshaped co- and post-translationally through interactions with the ribosome, molecular chaperones and/or other cellular components. Owing to developments in instrumentation and methodology, solution NMR spectroscopy has emerged as the central experimental approach for the detailed characterization of the complex protein folding processes in vitro and in vivo. NMR relaxation dispersion and saturation transfer methods provide the means for a detailed characterization of protein folding kinetics and thermodynamics under native-like conditions, as well as modeling high-resolution structures of weakly populated short-lived conformational states on the protein folding energy landscape. Continuing development of isotope labeling strategies and NMR methods to probe high molecular weight protein assemblies, along with advances of in-cell NMR, have recently allowed protein folding to be studied in the context of ribosome-nascent chain complexes and molecular chaperones, and even inside living cells. Here we review solution NMR approaches to investigate the protein folding energy landscape, and discuss selected applications of NMR methodology to studying protein folding in vitro and in vivo. Together, these examples highlight a vast potential of solution NMR in providing atomistic insights into molecular mechanisms of protein folding and homeostasis in health and disease.

Sensitive proton-detected solid-state NMR spectroscopy of large proteins with selective CH3 labelling: application to the 50S ribosome subunit

Solid-state NMR spectroscopy allows the characterization of the structure, interactions and dynamics of insoluble and/or very large proteins. Sensitivity and resolution are often major challenges for obtaining atomic-resolution information, in particular for very large protein complexes. Here we show that the use of deuterated, specifically CH3-labelled proteins result in significant sensitivity gains compared to previously employed CHD2 labelling, while line widths increase only marginally. We apply this labelling strategy to a 468 kDa-large dodecameric aminopeptidase, TET2, and the 1.6 MDa-large 50S ribosome subunit of Thermus thermophilus.

Site-Specific Internal Motions in GB1 Protein Microcrystals Revealed by 3D ²H-¹³C-¹³C Solid-State NMR Spectroscopy

(2)H quadrupolar line shapes deliver rich information about protein dynamics. A newly designed 3D (2)H-(13)C-(13)C solid-state NMR magic angle spinning (MAS) experiment is presented and demonstrated on the microcrystalline β1 immunoglobulin binding domain of protein G (GB1). The implementation of (2)H-(13)C adiabatic rotor-echo-short-pulse-irradiation cross-polarization (RESPIRATION CP) ensures the accuracy of the extracted line shapes and provides enhanced sensitivity relative to conventional CP methods. The 3D (2)H-(13)C-(13)C spectrum reveals (2)H line shapes for 140 resolved aliphatic deuterium sites. Motional-averaged (2)H quadrupolar parameters obtained from the line-shape fitting identify side-chain motions. Restricted side-chain dynamics are observed for a number of polar residues including K13, D22, E27, K31, D36, N37, D46, D47, K50, and E56, which we attribute to the effects of salt bridges and hydrogen bonds. In contrast, we observe significantly enhanced side-chain flexibility for Q2, K4, K10, E15, E19, N35, N40, and E42, due to solvent exposure and low packing density. T11, T16, and T17 side chains exhibit motions with larger amplitudes than other Thr residues due to solvent interactions. The side chains of L5, V54, and V29 are highly rigid because they are packed in the core of the protein. High correlations were demonstrated between GB1 side-chain dynamics and its biological function. Large-amplitude side-chain motions are observed for regions contacting and interacting with immunoglobulin G (IgG). In contrast, rigid side chains are primarily found for residues in the structural core of the protein that are absent from protein binding and interactions.

Kinetic Cooperativity in Human Pancreatic Glucokinase Originates from Millisecond Dynamics of the Small Domain

The hallmark of glucokinase (GCK), which catalyzes the phosphorylation of glucose during glycolysis, is its kinetic cooperativity, whose understanding at atomic detail has remained open since its discovery over 40 years ago. Herein, by using kinetic CPMG NMR spectroscopic data for 17 isoleucine side chains distributed over all parts of GCK, we show that the origin of kinetic cooperativity is rooted in intramolecular protein dynamics. Residues of glucose-free GCK located in the small domain displayed distinct exchange behavior involving multiple conformers that are substantially populated (p>17 %) with a kex  value of 509±51 s(-1) , whereas in the glucose-bound form these exchange processes were quenched. This exchange behavior directly competes with the enzymatic turnover rate at physiological glucose concentrations, thereby generating the sigmoidal rate dependence that defines kinetic cooperativity.

NMR studies of dynamic biomolecular conformational ensembles

Multidimensional heteronuclear NMR approaches can provide nearly complete sequential signal assignments of isotopically enriched biomolecules. The availability of assignments together with measurements of spin relaxation rates, residual spin interactions, J-couplings and chemical shifts provides information at atomic resolution about internal dynamics on timescales ranging from ps to ms, both in solution and in the solid state. However, due to the complexity of biomolecules, it is not possible to extract a unique atomic-resolution description of biomolecular motions even from extensive NMR data when many conformations are sampled on multiple timescales. For this reason, powerful computational approaches are increasingly applied to large NMR data sets to elucidate conformational ensembles sampled by biomolecules. In the past decade, considerable attention has been directed at an important class of biomolecules that function by binding to a wide variety of target molecules. Questions of current interest are: "Does the free biomolecule sample a conformational ensemble that encompasses the conformations found when it binds to various targets; and if so, on what time scale is the ensemble sampled?" This article reviews recent efforts to answer these questions, with a focus on comparing ensembles obtained for the same biomolecules by different investigators. A detailed comparison of results obtained is provided for three biomolecules: ubiquitin, calmodulin and the HIV-1 trans-activation response RNA.

Bringing dynamic molecular machines into focus by methyl-TROSY NMR

Large macromolecular assemblies, so-called molecular machines, are critical to ensuring proper cellular function. Understanding how proper function is achieved at the atomic level is crucial to advancing multiple avenues of biomedical research. Biophysical studies often include X-ray diffraction and cryo-electron microscopy, providing detailed structural descriptions of these machines. However, their inherent flexibility has complicated an understanding of the relation between structure and function. Solution NMR spectroscopy is well suited to the study of such dynamic complexes, and continued developments have increased size boundaries; insights into function have been obtained for complexes with masses as large as 1 MDa. We highlight methyl-TROSY (transverse relaxation optimized spectroscopy) NMR, which enables the study of such large systems, and include examples of applications to several cellular machines. We show how this emerging technique contributes to an understanding of cellular function and the role of molecular plasticity in regulating an array of biochemical activities.

Temperature dependence of internal motions of protein side-chain NH3(+) groups: insight into energy barriers for transient breakage of hydrogen bonds

Although charged side chains play important roles in protein function, their dynamic properties are not well understood. Nuclear magnetic resonance methods for investigating the dynamics of lysine side-chain NH3(+) groups were established recently. Using this methodology, we have studied the temperature dependence of the internal motions of the lysine side-chain NH3(+) groups that form ion pairs with DNA phosphate groups in the HoxD9 homeodomain-DNA complex. For these NH3(+) groups, we determined order parameters and correlation times for bond rotations and reorientations at 15, 22, 28, and 35 °C. The order parameters were found to be virtually constant in this temperature range. In contrast, the bond-rotation correlation times of the NH3(+) groups were found to depend strongly on temperature. On the basis of transition state theory, the energy barriers for NH3(+) rotations were analyzed and compared to those for CH3 rotations. Enthalpies of activation for NH3(+) rotations were found to be significantly higher than those for CH3 rotations, which can be attributed to the requirement of hydrogen bond breakage. However, entropies of activation substantially reduce the overall free energies of activation for NH3(+) rotations to a level comparable to those for CH3 rotations. This entropic reduction in energy barriers may accelerate molecular processes requiring hydrogen bond breakage and play a kinetically important role in protein function.

Heteronuclear transverse and longitudinal relaxation in AX4 spin systems: application to (15)N relaxations in (15)NH4(+)

The equations that describe the time-evolution of transverse and longitudinal (15)N magnetisations in tetrahedral ammonium ions, (15)NH4(+), are derived from the Bloch-Wangsness-Redfield density operator relaxation theory. It is assumed that the relaxation of the spin-states is dominated by (1) the intra-molecular (15)N-(1)H and (1)H-(1)H dipole-dipole interactions and (2) interactions of the ammonium protons with remote spins, which also include the contribution to the relaxations that arise from the exchange of the ammonium protons with the bulk solvent. The dipole-dipole cross-correlated relaxation mechanisms between each of the (15)N-(1)H and (1)H-(1)H interactions are explicitly taken into account in the derivations. An application to (15)N-ammonium bound to a 41kDa domain of the protein DnaK is presented, where a comparison between experiments and simulations show that the ammonium ion rotates rapidly within its binding site with a local correlation time shorter than approximately 1ns. The theoretical framework provided here forms the basis for further investigations of dynamics of AX4 spin systems, with ammonium ions in solution and bound to proteins of particular interest.

NMR approaches for structural analysis of multidomain proteins and complexes in solution

NMR spectroscopy is a key method for studying the structure and dynamics of (large) multidomain proteins and complexes in solution. It plays a unique role in integrated structural biology approaches as especially information about conformational dynamics can be readily obtained at residue resolution. Here, we review NMR techniques for such studies focusing on state-of-the-art tools and practical aspects. An efficient approach for determining the quaternary structure of multidomain complexes starts from the structures of individual domains or subunits. The arrangement of the domains/subunits within the complex is then defined based on NMR measurements that provide information about the domain interfaces combined with (long-range) distance and orientational restraints. Aspects discussed include sample preparation, specific isotope labeling and spin labeling; determination of binding interfaces and domain/subunit arrangements from chemical shift perturbations (CSP), nuclear Overhauser effects (NOEs), isotope editing/filtering, cross-saturation, and differential line broadening; and based on paramagnetic relaxation enhancements (PRE) using covalent and soluble spin labels. Finally, the utility of complementary methods such as small-angle X-ray or neutron scattering (SAXS, SANS), electron paramagnetic resonance (EPR) or fluorescence spectroscopy techniques is discussed. The applications of NMR techniques are illustrated with studies of challenging (high molecular weight) protein complexes.

Monitoring side-chain dynamics of proteins using (2)H relaxation

Nuclear magnetic resonance (NMR) is a powerful technique capable of monitoring a wide range of motions in proteins on a per residue basis. A variety of (2)H relaxation experiments have been developed for monitoring side-chain methyl group motions on the picosecond-nanosecond timescale. These experiments enable determination of the order parameter, S (2) axis, which reports on the rigidity of the C-CH3 bond for side-chain methyl groups. The application of a commonly used subset of these experiments is described in this chapter. It is intended to serve as a practical guide to investigators interested in monitoring side-chain motions.

Experiments for the editing of singlet peaks and simplification of ¹H NMR spectra of complex mixtures

A 1D NMR singlet filtered experiment (s-filter) is presented for the clean editing of singlets peaks in crowded ¹H NMR spectra. The experiment affords a clean editing of singlet peaks and weak coupled signals ((n)JHH < 3 Hz), while the remaining multiplets peaks are strongly attenuated to a factor over 90% of its original intensity. The experiment provided a useful simplification of the typically congested ¹H NMR spectra of foodstuffs, and the edited signals retained most of the sensitivity and quantitativity. The versatility of the s-filter scheme permitted its easy incorporation as excitation building block into other 1D and 2D experiments, providing a further editing of the singlet responses. The combination of the 1D s-filter experiment and difference spectroscopy provided a 1D reverse singlet filtered experiment (s-filter(rev)) for the clean editing of multiplet peaks and strong suppression of singlets. The experiments proposed could be valuable to facilitate the detection and/or quantification of target compounds in complex mixtures of metabolites.

Indirect use of deuterium in solution NMR studies of protein structure and hydrogen bonding

A description of the utility of deuteration in protein NMR is provided with an emphasis on quantitative evaluation of the effects of deuteration on a number of NMR parameters of proteins: (1) chemical shifts, (2) scalar coupling constants, (3) relaxation properties (R1 and R2 rates) of nuclei directly attached to one or more deuterons as well as protons of methyl groups in a highly deuterated environment, (4) scalar relaxation of 15N and 13C nuclei in 15N-D and 13C-D spin systems as a measure of hydrogen bonding strength, and (5) NOE-based applications of deuteration in NMR studies of protein structure. The discussion is restricted to the 'indirect' use of deuterium in the sense that the description of NMR parameters and properties of the nuclei affected by nearby deuterons (15N, 13C, 1H) is provided rather than those of deuterium itself.

A NMR experiment for simultaneous correlations of valine and leucine/isoleucine methyls with carbonyl chemical shifts in proteins

A methyl-detected 'out-and-back' NMR experiment for obtaining simultaneous correlations of methyl resonances of valine and isoleucine/leucine residues with backbone carbonyl chemical shifts, SIM-HMCM(CGCBCA)CO, is described. The developed pulse-scheme serves the purpose of convenience in recording a single data set for all Ile(δ1), Leu(δ) and Val(γ) (ILV) methyl positions instead of acquiring two separate spectra selective for valine or leucine/isoleucine residues. The SIM-HMCM(CGCBCA)CO experiment can be used for ILV methyl assignments in moderately sized protein systems (up to ~100 kDa) where the backbone chemical shifts of (13)C(α), (13)Cβ and (13)CO are known from prior NMR studies and where some losses in sensitivity can be tolerated for the sake of an overall reduction in NMR acquisition time.

Selective isotope labelling of leucine residues by using α-ketoacid precursor compounds

You can have one without the other: A new metabolic precursor compound can selectively introduce (13)C and (2)H patterns at leucine residues in proteins in cell-based expression systems without interfering with valine metabolism. The protocol provides selectively labelled macromolecules well suited for probing structure and dynamics in high-molecular-weight proteins by NMR spectroscopy.

Estimating side-chain order in [U-2H;13CH3]-labeled high molecular weight proteins from analysis of HMQC/HSQC spectra

A simple approach for quantification of methyl-containing side-chain mobility in high molecular weight methyl-protonated, uniformly deuterated proteins is described, based on the measurement of peak intensities in methyl (1)H-(13)C HMQC and HSQC correlation maps and relaxation rates of slowly decaying components of methyl (1)H-(13)C multiple-quantum coherences. A strength of the method is that [U-(2)H;(13)CH3]-labeled protein samples are required that are typically available at an early stage of any analysis. The utility of the methodology is demonstrated with applications to three protein systems ranging in molecular weight from 82 to 670 kDa. Although the approach is only semiquantitative, a high correlation between order parameters extracted via this scheme and other more established methods is nevertheless demonstrated.

Observation and relaxation properties of individual fast-relaxing proton transitions in [¹³CH₃]-methyl-labeled, deuterated proteins

A pair of NMR experiments is developed for separation of individual fast-relaxing transitions in (13)CH(3) methyl groups of methyl-protonated, highly deuterated proteins, and the measurement of their relaxation rates. Intra-methyl (1)H-(1)H/(1)H-(13)C dipole-dipole cross-correlated spin relaxation that differentiates the rates of the fast-relaxing transitions depending on the state of (13)C spins, is measured in the selectively [(13)CH(3)]-methyl-labeled, deuterated ubiquitin at 10, 27, and 40°C. In contrast with previous observations, the (1)H-(1)H/(1)H-(13)C cross-correlated relaxation rates measured from relaxation rates of single-quantum proton transitions serve as good measures of side-chain order even in proteins with global rotational correlation times significantly less than 10 ns.

Estimating side-chain order in methyl-protonated, perdeuterated proteins via multiple-quantum relaxation violated coherence transfer NMR spectroscopy

Relaxation violated coherence transfer NMR spectroscopy (Tugarinov et al. in J Am Chem Soc 129:1743-1750, 2007) is an established experimental tool for quantitative estimation of the amplitudes of side-chain motions in methyl-protonated, highly deuterated proteins. Relaxation violated coherence transfer experiments monitor the buildup of methyl proton multiple-quantum coherences that can be created in magnetically equivalent spin-systems as long as their transverse magnetization components relax with substantially different rates. The rate of this build-up is a reporter of the methyl-bearing side-chain mobility. Although the build-up of multiple-quantum (1)H coherences is monitored in these experiments, the decay of the methyl signal during relaxation delays occurs when methyl proton magnetization is in a single-quantum state. We describe a relaxation violated coherence transfer approach where the relaxation of multiple-quantum (1)H-(13)C methyl coherences during the relaxation delay period is quantified. The NMR experiment and the associated fitting procedure that models the time-dependence of the signal build-up, are applicable to the characterization of side-chain order in [(13)CH(3)]-methyl-labeled, highly deuterated protein systems up to ~100 kDa in molecular weight. The feasibility of extracting reliable measures of side-chain order is experimentally verified on methyl-protonated, perdeuterated samples of an 8.5-kDa ubiquitin at 10°C and an 82-kDa Malate Synthase G at 37°C.

Determining protein dynamics from ¹⁵N relaxation data by using DYNAMICS

Motions are essential for protein function, and knowledge of protein dynamics is a key to our understanding the mechanisms underlying protein folding and stability, ligand recognition, allostery, and catalysis. In the last two decades, NMR relaxation measurements have become a powerful tool for characterizing backbone and side chain dynamics in complex biological macromolecules such as proteins and nucleic acids. Accurate analysis of the experimental data in terms of motional parameters is an essential prerequisite for developing physical models of motions to paint an adequate picture of protein dynamics. Here, I describe in detail how to use the software package DYNAMICS that was developed for accurate characterization of the overall tumbling and local dynamics in a protein from nuclear spin-relaxation rates measured by NMR. Step-by-step instructions are provided and illustrated through an analysis of (15)N relaxation data for protein G.

Probing side-chain dynamics in proteins by the measurement of nine deuterium relaxation rates per methyl group

We demonstrate the feasibility of the measurement of up to nine deuterium spin relaxation rates in 13CHD2 and 13CH2D methyl isotopomers of small proteins. In addition to five measurable 2H relaxation rates in a 13CH2D methyl group (Millet, O.; Muhandiram, D. R.; Skrynnikov, N. R.; Kay, L. E. J. Am. Chem. Soc. 2002, 124, 6439-48), the measurement of additional four rates of (nearly) single-exponentially decaying magnetization terms in methyl groups of the 13CHD2 variety is reported. Consistency relationships between 2H spin relaxation rates measured in the two different types of methyl groups are derived and verified experimentally for a subset of methyl-containing side chains in the protein ubiquitin. A detailed comparison of methyl-bearing side-chain dynamics parameters obtained from relaxation measurements in 13CH2D and 13CHD2 methyls of ubiquitin at 10, 27, and 40 °C reveals that transverse 2H relaxation rates in 13CHD2 groups are reliable and accurate reporters of the amplitudes of methyl 3-fold axis motions (S(axis)2) for protein molecules with global molecular tumbling times τ(C) >~9 ns. For smaller molecules, simple correction of transverse 2H relaxation rates in 13CHD2 groups is sufficient for the derivation of robust measures of order. Residue-specific distributions of S(axis)2 are consistent with atomic-detail molecular dynamics (MD) results. Both 13CHD2- and 13CH2D-derived S(axis)2 values are in good overall agreement with those obtained from 1 μs MD simulations at all the three temperatures, although some differences in the site-specific temperature dependence between MD- and 2H-relaxation-derived S(axis)2 values are observed.

An optimized relaxation-based coherence transfer NMR experiment for the measurement of side-chain order in methyl-protonated, highly deuterated proteins

Relaxation violated coherence transfer NMR spectroscopy has emerged as a powerful experimental tool for the quantitative measurement of amplitudes of motion of methyl containing side-chains. Typically, the experiments, performed on proteins that are highly deuterated and methyl-protonated, monitor the build-up of methyl (1)H double-quantum magnetization. Because all three protons in a methyl group are degenerate, such coherences can only result from differential relaxation of transverse magnetization components, which in turn reflect the extent and time-scale of motion of the methyl probe [Tugarinov, V., Sprangers, R.; Kay, L.E. J. Am. Chem. Soc. 2007, 129, 1743-1750]. We show here that a 50% gain in the sensitivity of the experiment can be achieved through selection of (1)H triple-quantum coherence, thereby significantly increasing the utility of the approach. A theoretical treatment rationalizes the sensitivity gain that is subsequently verified through experiment. The utility of the methodology is demonstrated on a number of proteins, including the 360 kDa α(7)α(7) "half-proteasome".

Structure-based prediction of methyl chemical shifts in proteins

Protein methyl groups have recently been the subject of much attention in NMR spectroscopy because of the opportunities that they provide to obtain information about the structure and dynamics of proteins and protein complexes. With the advent of selective labeling schemes, methyl groups are particularly interesting in the context of chemical shift based protein structure determination, an approach that to date has exploited primarily the mapping between protein structures and backbone chemical shifts. In order to extend the scope of chemical shifts for structure determination, we present here the CH3Shift method of performing structure-based predictions of methyl chemical shifts. The terms considered in the predictions take account of ring current, magnetic anisotropy, electric field, rotameric type, and dihedral angle effects, which are considered in conjunction with polynomial functions of interatomic distances. We show that the CH3Shift method achieves an accuracy in the predictions that ranges from 0.133 to 0.198 ppm for (1)H chemical shifts for Ala, Thr, Val, Leu and Ile methyl groups. We illustrate the use of the method by assessing the accuracy of side-chain structures in structural ensembles representing the dynamics of proteins.

Dynamics of lysine side-chain amino groups in a protein studied by heteronuclear 1H−15N NMR spectroscopy

Despite their importance in macromolecular interactions and functions, the dynamics of lysine side-chain amino groups in proteins are not well understood. In this study, we have developed the methodology for the investigations of the dynamics of lysine NH3(+) groups by NMR spectroscopy and computation. By using 1H−15N heteronuclear correlation experiments optimized for 15NH3(+) moieties, we have analyzed the dynamic behavior of individual lysine NH3(+) groups in human ubiquitin at 2 °C and pH 5. We modified the theoretical framework developed previously for CH3 groups and used it to analyze 15N relaxation data for the NH3(+) groups. For six lysine NH3(+) groups out of seven in ubiquitin, we have determined model-free order parameters, correlation times for bond rotation, and reorientation of the symmetry axis occurring on a pico- to nanosecond time scale. From CPMG relaxation dispersion experiment for lysine NH3(+) groups, slower dynamics occurring on a millisecond time scale have also been detected for Lys27. The NH3(+) groups of Lys48, which plays a key role as the linkage site in ubiquitination for proteasomal degradation, was found to be highly mobile with the lowest order parameter among the six NH3(+) groups analyzed by NMR. We compared the experimental order parameters for the lysine NH3(+) groups with those from a 1 μs molecular dynamics simulation in explicit solvent and found good agreement between the two. Furthermore, both the computer simulation and the experimental correlation times for the bond rotations of NH3(+) groups suggest that their hydrogen bonding is highly dynamic with a subnanosecond lifetime. This study demonstrates the utility of combining NMR experiment and simulation for an in-depth characterization of the dynamics of these functionally most important side-chains of ubiquitin.

Selective detection of ¹³CHD₂ signals from a mixture of ¹³CH₃/¹³CH₂D/¹³CHD₂ methyl isotopomers in proteins

In NMR spectra of partially deuterated proteins methyl correlations are commonly observed as a combination of signals from ¹³CH₃, ¹³CH₂D and ¹³CHD₂ isotopomers. In a number of NMR applications, methyl groups of the ¹³CHD₂ variety are targeted because of their AX-like character and concomitant simplification of the involved relaxation mechanisms. Although complete elimination of signals from ¹³CH₂D methyl groups can be easily achieved in such applications, if the magnetization is not transferred through deuterium nuclei, efficient suppression of usually stronger ¹³CH₃ peaks is more problematic. A pair of simple pulse-scheme elements are presented that achieve almost complete suppression of ¹³CH₃ signals in the mixtures of ¹³CH₃/¹³CH₂D/¹³CHD₂ methyl isotopomers of small proteins at the expense of a moderate (∼20-to-40%) reduction in intensities of the targeted ¹³CHD₂ groups. The approaches described are based purely on scalar coupling (¹J(CH)) evolution properties of different ¹³C and ¹H transitions within ¹³CH₃ spin-systems and are superior to magnetization transfer through deuterons with respect to sensitivity of the detected ¹³CHD₂ methyl signals.