Unraveling motion in proteins by combining NMR relaxometry and molecular dynamics simulations: A case study on ubiquitin.

Nuclear magnetic resonance (NMR) relaxation experiments shine light onto the dynamics of molecular systems in the picosecond to millisecond timescales. As these methods cannot provide an atomically resolved view of the motion of atoms, functional groups, or domains giving rise to such signals, relaxation techniques have been combined with molecular dynamics (MD) simulations to obtain mechanistic descriptions and gain insights into the functional role of side chain or domain motion. In this work, we present a comparison of five computational methods that permit the joint analysis of MD simulations and NMR relaxation experiments. We discuss their relative strengths and areas of applicability and demonstrate how they may be utilized to interpret the dynamics in MD simulations with the small protein ubiquitin as a test system. We focus on the aliphatic side chains given the rigidity of the backbone of this protein. We find encouraging agreement between experiment, Markov state models built in the χ1/χ2 rotamer space of isoleucine residues, explicit rotamer jump models, and a decomposition of the motion using ROMANCE. These methods allow us to ascribe the dynamics to specific rotamer jumps. Simulations with eight different combinations of force field and water model highlight how the different metrics may be employed to pinpoint force field deficiencies. Furthermore, the presented comparison offers a perspective on the utility of NMR relaxation to serve as validation data for the prediction of kinetics by state-of-the-art biomolecular force fields.

Analytical Framework to Understand the Origins of Methyl Side-Chain Dynamics in Protein Assemblies.

Side-chain motions play an important role in understanding protein structure, dynamics, protein-protein, and protein-ligand interactions. However, our understanding of protein side-chain dynamics is currently limited by the lack of analytical tools. Here, we present a novel analytical framework employing experimental nuclear magnetic resonance (NMR) relaxation measurements at atomic resolution combined with molecular dynamics (MD) simulation to characterize with a high level of detail the methyl side-chain dynamics in insoluble protein assemblies, using amyloid fibrils formed by the prion HET-s. We use MD simulation to interpret experimental results, where rotameric hops, including methyl group rotation and χ1/χ2 rotations, cannot be completely described with a single correlation time but rather sample a broad distribution of correlation times, resulting from continuously changing local structure in the fibril. Backbone motion similarly samples a broad range of correlation times, from ∼100 ps to µs, although resulting from mostly different dynamic processes; nonetheless, we find that the backbone is not fully decoupled from the side-chain motion, where changes in side-chain dynamics influence backbone motion and vice versa. While the complexity of side-chain motion in protein assemblies makes it very challenging to obtain perfect agreement between experiment and simulation, our analytical framework improves the interpretation of experimental dynamics measurements for complex protein assemblies.

Analysis of the Dynamics of the Human Growth Hormone Secretagogue Receptor Reveals Insights into the Energy Landscape of the Molecule.

G protein-coupled receptors initiate signal transduction in response to ligand binding. Growth hormone secretagogue receptor (GHSR), the focus of this study, binds the 28 residue peptide ghrelin. While structures of GHSR in different states of activation are available, dynamics within each state have not been investigated in depth. We analyze long molecular dynamics simulation trajectories using "detectors" to compare dynamics of the apo and ghrelin-bound states yielding timescale-specific amplitudes of motion. We identify differences in dynamics between apo and ghrelin-bound GHSR in the extracellular loop 2 and transmembrane helices 5-7. NMR of the GHSR histidine residues reveals chemical shift differences in these regions. We evaluate timescale specific correlation of motions between residues of ghrelin and GHSR, where binding yields a high degree of correlation for the first 8 ghrelin residues, but less correlation for the helical end. Finally, we investigate the traverse of GHSR over a rugged energy landscape via principal component analysis.

The intriguing molecular dynamics of Cer[EOS] in rigid skin barrier lipid layers requires improvement of the model.

Omega-O-acyl ceramides such as 32-linoleoyloxydotriacontanoyl sphingosine (Cer[EOS]) are essential components of the lipid skin barrier, which protects our body from excessive water loss and the penetration of unwanted substances. These ceramides drive the lipid assembly to epidermal-specific long periodicity phase (LPP), structurally much different than conventional lipid bilayers. Here, we synthesized Cer[EOS] with selectively deuterated segments of the ultralong N-acyl chain or deuterated or 13C-labeled linoleic acid and studied their molecular behavior in a skin lipid model. Solid-state 2H NMR data revealed surprising molecular dynamics for the ultralong N-acyl chain of Cer[EOS] with increased isotropic motion toward the isotropic ester-bound linoleate. The sphingosine moiety of Cer[EOS] is also highly mobile at skin temperature, in stark contrast to the other LPP components, N-lignoceroyl sphingosine acyl, lignoceric acid, and cholesterol, which are predominantly rigid. The dynamics of the linoleic chain is quantitatively described by distributions of correlation times and using dynamic detector analysis. These NMR results along with neutron diffraction data suggest an LPP structure with alternating fluid (sphingosine chain-rich), rigid (acyl chain-rich), isotropic (linoleate-rich), rigid (acyl-chain rich), and fluid layers (sphingosine chain-rich). Such an arrangement of the skin barrier lipids with rigid layers separated with two different dynamic "fillings" i) agrees well with ultrastructural data, ii) satisfies the need for simultaneous rigidity (to ensure low permeability) and fluidity (to ensure elasticity, accommodate enzymes, or antimicrobial peptides), and iii) offers a straightforward way to remodel the lamellar body lipids into the final lipid barrier.

A method to construct the dynamic landscape of a bio-membrane with experiment and simulation.

Biomolecular function is based on a complex hierarchy of molecular motions. While biophysical methods can reveal details of specific motions, a concept for the comprehensive description of molecular dynamics over a wide range of correlation times has been unattainable. Here, we report an approach to construct the dynamic landscape of biomolecules, which describes the aggregate influence of multiple motions acting on various timescales and on multiple positions in the molecule. To this end, we use 13C NMR relaxation and molecular dynamics simulation data for the characterization of fully hydrated palmitoyl-oleoyl-phosphatidylcholine bilayers. We combine dynamics detector methodology with a new frame analysis of motion that yields site-specific amplitudes of motion, separated both by type and timescale of motion. In this study, we show that this separation allows the detailed description of the dynamic landscape, which yields vast differences in motional amplitudes and correlation times depending on molecular position.

Model-Free or Not?

Relaxation in nuclear magnetic resonance is a powerful method for obtaining spatially resolved, timescale-specific dynamics information about molecular systems. However, dynamics in biomolecular systems are generally too complex to be fully characterized based on NMR data alone. This is a familiar problem, addressed by the Lipari-Szabo model-free analysis, a method that captures the full information content of NMR relaxation data in case all internal motion of a molecule in solution is sufficiently fast. We investigate model-free analysis, as well as several other approaches, and find that model-free, spectral density mapping, LeMaster's approach, and our detector analysis form a class of analysis methods, for which behavior of the fitted parameters has a well-defined relationship to the distribution of correlation times of motion, independent of the specific form of that distribution. In a sense, they are all "model-free." Of these methods, only detectors are generally applicable to solid-state NMR relaxation data. We further discuss how detectors may be used for comparison of experimental data to data extracted from molecular dynamics simulation, and how simulation may be used to extract details of the dynamics that are not accessible via NMR, where detector analysis can be used to connect those details to experiments. We expect that combined methodology can eventually provide enough insight into complex dynamics to provide highly accurate models of motion, thus lending deeper insight into the nature of biomolecular dynamics.

How wide is the window opened by high-resolution relaxometry on the internal dynamics of proteins in solution?

The dynamics of molecules in solution is usually quantified by the determination of timescale-specific amplitudes of motions. High-resolution nuclear magnetic resonance (NMR) relaxometry experiments-where the sample is transferred to low fields for longitudinal (T1) relaxation, and back to high field for detection with residue-specific resolution-seeks to increase the ability to distinguish the contributions from motion on timescales slower than a few nanoseconds. However, tumbling of a molecule in solution masks some of these motions. Therefore, we investigate to what extent relaxometry improves timescale resolution, using the "detector" analysis of dynamics. Here, we demonstrate improvements in the characterization of internal dynamics of methyl-bearing side chains by carbon-13 relaxometry in the small protein ubiquitin. We show that relaxometry data leads to better information about nanosecond motions as compared to high-field relaxation data only. Our calculations show that gains from relaxometry are greater with increasing correlation time of rotational diffusion.

Experimental Characterization of the Hepatitis B Virus Capsid Dynamics by Solid-State NMR.

Protein plasticity and dynamics are important aspects of their function. Here we use solid-state NMR to experimentally characterize the dynamics of the 3.5 MDa hepatitis B virus (HBV) capsid, assembled from 240 copies of the Cp149 core protein. We measure both T 1 and T 1ρ relaxation times, which we use to establish detectors on the nanosecond and microsecond timescale. We compare our results to those from a 1 microsecond all-atom Molecular Dynamics (MD) simulation trajectory for the capsid. We show that, for the constituent residues, nanosecond dynamics are faithfully captured by the MD simulation. The calculated values can be used in good approximation for the NMR-non-detected residues, as well as to extrapolate into the range between the nanosecond and microsecond dynamics, where NMR has a blind spot at the current state of technology. Slower motions on the microsecond timescale are difficult to characterize by all-atom MD simulations owing to computational expense, but are readily accessed by NMR. The two methods are, thus, complementary, and a combination thereof can reliably characterize motions covering correlation times up to a few microseconds.

Reducing bias in the analysis of solution-state NMR data with dynamics detectors.

Nuclear magnetic resonance (NMR) is sensitive to dynamics on a wide range of correlation times. Recently, we have shown that analysis of relaxation rates via fitting to a correlation function with a small number of exponential terms could yield a biased characterization of molecular motion in solid-state NMR due to limited sensitivity of experimental data to certain ranges of correlation times. We introduced an alternative approach based on "detectors" in solid-state NMR, for which detector responses characterize motion for a range of correlation times and reduce potential bias resulting from the use of simple models for the motional correlation functions. Here, we show that similar bias can occur in the analysis of solution-state NMR relaxation data. We have thus adapted the detector approach to solution-state NMR, specifically separating overall tumbling motion from internal motions and accounting for contributions of chemical exchange to transverse relaxation. We demonstrate that internal protein motions can be described with detectors when the overall motion and the internal motions are statistically independent. We illustrate the detector analysis on ubiquitin with typical relaxation data sets recorded at a single high magnetic field or at multiple high magnetic fields and compare with results of model-free analysis. We also compare our methodology to LeMaster's method of dynamics analysis.

Localized and Collective Motions in HET-s(218-289) Fibrils from Combined NMR Relaxation and MD Simulation.

Nuclear magnetic resonance (NMR) relaxation data and molecular dynamics (MD) simulations are combined to characterize the dynamics of the fungal prion HET-s(218-289) in its amyloid form. NMR data is analyzed with the dynamics detector method, which yields timescale-specific information. An analogous analysis is performed on MD trajectories. Because specific MD predictions can be verified as agreeing with the NMR data, MD was used for further interpretation of NMR results: for the different timescales, cross-correlation coefficients were derived to quantify the correlation of the motion between different residues. Short timescales are the result of very local motions, while longer timescales are found for longer-range correlated motion. Similar trends on ns- and µs-timescales suggest that µs motion in fibrils is the result of motion correlated over many fibril layers.

Setting the magic angle for fast magic-angle spinning probes.

Fast magic-angle spinning, coupled with 1H detection is a powerful method to improve spectral resolution and signal to noise in solid-state NMR spectra. Commercial probes now provide spinning frequencies in excess of 100 kHz. Then, one has sufficient resolution in the 1H dimension to directly detect protons, which have a gyromagnetic ratio approximately four times larger than 13C spins. However, the gains in sensitivity can quickly be lost if the rotation angle is not set precisely. The most common method of magic-angle calibration is to optimize the number of rotary echoes, or sideband intensity, observed on a sample of KBr. However, this typically uses relatively low spinning frequencies, where the spinning of fast-MAS probes is often unstable, and detection on the 13C channel, for which fast-MAS probes are typically not optimized. Therefore, we compare the KBr-based optimization of the magic angle with two alternative approaches: optimization of the splitting observed in 13C-labeled glycine-ethylester on the carbonyl due to the Cα-C' J-coupling, or optimization of the H-N J-coupling spin echo in the protein sample itself. The latter method has the particular advantage that no separate sample is necessary for the magic-angle optimization.

Correction to: Characterization of fibril dynamics on three timescales by solid-state NMR.

In our recent publication (Smith et al., J Biomol NMR 65:171-191, 2016) on the dynamics of HET-s(218-289), we reported on page 176, that calculation of solid-state NMR R1ρ rate constants using analytical equations based on Redfield theory (Kurbanov et al., J Chem Phys 135:184104:184101-184109, 2011) failed when the correlation time of motion becomes too long.

Optimized "detectors" for dynamics analysis in solid-state NMR.

Relaxation in nuclear magnetic resonance (NMR) results from stochastic motions that modulate anisotropic NMR interactions. Therefore, measurement of relaxation-rate constants can be used to characterize molecular-dynamic processes. The motion is often characterized by Markov processes using an auto-correlation function, which is assumed to be a sum of multiple decaying exponentials. We have recently shown that such a model can lead to severe misrepresentation of the real motion, when the real correlation function is more complex than the model. Furthermore, multiple distributions of motion may yield the same set of dynamics data. Therefore, we introduce optimized dynamics "detectors" to characterize motions which are linear combinations of relaxation-rate constants. A detector estimates the average or total amplitude of motion for a range of motional correlation times. The information obtained through the detectors is less specific than information obtained using an explicit model, but this is necessary because the information contained in the relaxation data is ambiguous, if one does not know the correct motional model. On the other hand, if one has a molecular dynamics trajectory, one may calculate the corresponding detector responses, allowing direct comparison to experimental NMR dynamics analysis. We describe how to construct a set of optimized detectors for a given set of relaxation measurements. We then investigate the properties of detectors for a number of different data sets, thus gaining an insight into the actual information content of the NMR data. Finally, we show an example analysis of ubiquitin dynamics data using detectors, using the DIFRATE software.

Because the Light is Better Here: Correlation-Time Analysis by NMR Spectroscopy.

Relaxation data in NMR spectra are often used for dynamics analysis, by modeling motion in the sample with a correlation function consisting of one or more decaying exponential terms, each described by an order parameter, and a correlation time. This method has its origins in the Lipari-Szabo model-free approach, which originally considered overall tumbling plus one internal motion and was later expanded to several internal motions. Considering several of these cases in the solid state it is found that if the real motion is more complex than the assumed model, model fitting is biased towards correlation times where the relaxation data are most sensitive. This leads to unexpected distortions in the resulting dynamics description. Therefore dynamics detectors should be used, which characterize different ranges of correlation times and can help in the analysis of protein motion without assuming a specific model of the correlation function.

INFOS: spectrum fitting software for NMR analysis.

Software for fitting of NMR spectra in MATLAB is presented. Spectra are fitted in the frequency domain, using Fourier transformed lineshapes, which are derived using the experimental acquisition and processing parameters. This yields more accurate fits compared to common fitting methods that use Lorentzian or Gaussian functions. Furthermore, a very time-efficient algorithm for calculating and fitting spectra has been developed. The software also performs initial peak picking, followed by subsequent fitting and refinement of the peak list, by iteratively adding and removing peaks to improve the overall fit. Estimation of error on fitting parameters is performed using a Monte-Carlo approach. Many fitting options allow the software to be flexible enough for a wide array of applications, while still being straightforward to set up with minimal user input.

Partially-deuterated samples of HET-s(218-289) fibrils: assignment and deuterium isotope effect.

Fast magic-angle spinning and partial sample deuteration allows direct detection of 1H in solid-state NMR, yielding significant gains in mass sensitivity. In order to further analyze the spectra, 1H detection requires assignment of the 1H resonances. In this work, resonance assignments of backbone HN and Hα are presented for HET-s(218-289) fibrils, based on the existing assignment of Cα, Cß, C', and N resonances. The samples used are partially deuterated for higher spectral resolution, and the shifts in resonance frequencies of Cα and Cß due to the deuterium isotope effect are investigated. It is shown that the deuterium isotope effect can be estimated and used for assigning resonances of deuterated samples in solid-state NMR, based on known resonances of the protonated protein.

Gd(iii) and Mn(ii) complexes for dynamic nuclear polarization: small molecular chelate polarizing agents and applications with site-directed spin labeling of proteins.

We investigate complexes of two paramagnetic metal ions Gd3+ and Mn2+ to serve as polarizing agents for solid-state dynamic nuclear polarization (DNP) of 1H, 13C, and 15N at magnetic fields of 5, 9.4, and 14.1 T. Both ions are half-integer high-spin systems with a zero-field splitting and therefore exhibit a broadening of the mS = -1/2 ↔ +1/2 central transition which scales inversely with the external field strength. We investigate experimentally the influence of the chelator molecule, strong hyperfine coupling to the metal nucleus, and deuteration of the bulk matrix on DNP properties. At small Gd-DOTA concentrations the narrow central transition allows us to polarize nuclei with small gyromagnetic ratio such as 13C and even 15N via the solid effect. We demonstrate that enhancements observed are limited by the available microwave power and that large enhancement factors of >100 (for 1H) and on the order of 1000 (for 13C) can be achieved in the saturation limit even at 80 K. At larger Gd(iii) concentrations (≥10 mM) where dipolar couplings between two neighboring Gd3+ complexes become substantial a transition towards cross effect as dominating DNP mechanism is observed. Furthermore, the slow spin-diffusion between 13C and 15N, respectively, allows for temporally resolved observation of enhanced polarization spreading from nuclei close to the paramagnetic ion towards nuclei further removed. Subsequently, we present preliminary DNP experiments on ubiquitin by site-directed spin-labeling with Gd3+ chelator tags. The results hold promise towards applications of such paramagnetically labeled proteins for DNP applications in biophysical chemistry and/or structural biology.

Characterization of fibril dynamics on three timescales by solid-state NMR.

A multi-timescale analysis of the backbone dynamics of HET-s (218-289) fibrils is described based on multiple site-specific R 1 and R 1ρ data sets and S (2) measurements via REDOR for most backbone (15)N and (13)Cα nuclei. (15)N and (13)Cα data are fitted with motions at three timescales. Slow motion is found, indicating a global fibril motion. We further investigate the effect of (13)C-(13)C transfer in measurement of (13)Cα R 1. Finally, we show that it is necessary to go beyond the Redfield approximation for slow motions in order to obtain accurate numerical values for R 1ρ.

Protein resonance assignment at MAS frequencies approaching 100 kHz: a quantitative comparison of J-coupling and dipolar-coupling-based transfer methods.

We discuss the optimum experimental conditions to obtain assignment spectra for solid proteins at magic-angle spinning (MAS) frequencies around 100 kHz. We present a systematic examination of the MAS dependence of the amide proton T 2' times and a site-specific comparison of T 2' at 93 kHz versus 60 kHz MAS frequency. A quantitative analysis of transfer efficiencies of building blocks, as they are used for typical 3D experiments, was performed. To do this, we compared dipolar-coupling and J-coupling based transfer steps. The building blocks were then combined into 3D experiments for sequential resonance assignment, where we evaluated signal-to-noise ratio and information content of the different 3D spectra in order to identify the best assignment strategy. Based on this comparison, six experiments were selected to optimally assign the model protein ubiquitin, solely using spectra acquired at 93 kHz MAS. Within 3 days of instrument time, the required spectra were recorded from which the backbone resonances have been assigned to over 96%.

Dynamic nuclear polarization of (1)H, (13)C, and (59)Co in a tris(ethylenediamine)cobalt(III) crystalline lattice doped with Cr(III).

The study of inorganic crystalline materials by solid-state NMR spectroscopy is often complicated by the low sensitivity of heavy nuclei. However, these materials often contain or can be prepared with paramagnetic dopants without significantly affecting the structure of the crystalline host. Dynamic nuclear polarization (DNP) is generally capable of enhancing NMR signals by transferring the magnetization of unpaired electrons to the nuclei. Therefore, the NMR sensitivity in these paramagnetically doped crystals might be increased by DNP. In this paper we demonstrate the possibility of efficient DNP transfer in polycrystalline samples of [Co(en)3Cl3]2·NaCl·6H2O (en = ethylenediamine, C2H8N2) doped with Cr(III) in varying concentrations between 0.1 and 3 mol %. We demonstrate that (1)H, (13)C, and (59)Co can be polarized by irradiation of Cr(III) with 140 GHz microwaves at a magnetic field of 5 T. We further explain our findings on the basis of electron paramagnetic resonance spectroscopy of the Cr(III) site and analysis of its temperature-dependent zero-field splitting, as well as the dependence of the DNP enhancement factor on the external magnetic field and microwave power. This first demonstration of DNP transfer from one paramagnetic metal ion to its diamagnetic host metal ion will pave the way for future applications of DNP in paramagnetically doped materials or metalloproteins.