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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

High-field 13C dynamic nuclear polarization with a radical mixture.

We report direct (13)C dynamic nuclear polarization at 5 T under magic-angle spinning (MAS) at 82 K using a mixture of monoradicals with narrow EPR linewidths. We show the importance of optimizing both EPR linewidth and electron relaxation times by studying direct DNP of (13)C using SA-BDPA and trityl radical, and achieve (13)C enhancements above 600. This new approach may be best suited for dissolution DNP and for studies of (1)H depleted biological and other nonprotonated solids.

Observation of strongly forbidden solid effect dynamic nuclear polarization transitions via electron-electron double resonance detected NMR.

We present electron paramagnetic resonance experiments for which solid effect dynamic nuclear polarization transitions were observed indirectly via polarization loss on the electron. This use of indirect observation allows characterization of the dynamic nuclear polarization (DNP) process close to the electron. Frequency profiles of the electron-detected solid effect obtained using trityl radical showed intense saturation of the electron at the usual solid effect condition, which involves a single electron and nucleus. However, higher order solid effect transitions involving two, three, or four nuclei were also observed with surprising intensity, although these transitions did not lead to bulk nuclear polarization--suggesting that higher order transitions are important primarily in the transfer of polarization to nuclei nearby the electron. Similar results were obtained for the SA-BDPA radical where strong electron-nuclear couplings produced splittings in the spectrum of the indirectly observed solid effect conditions. Observation of high order solid effect transitions supports recent studies of the solid effect, and suggests that a multi-spin solid effect mechanism may play a major role in polarization transfer via DNP.

Dynamic nuclear polarization with a water-soluble rigid biradical.

A new biradical polarizing agent, bTbtk-py, for dynamic nuclear polarization (DNP) experiments in aqueous media is reported. The synthesis is discussed in light of the requirements of the optimum, theoretical, biradical system. To date, the DNP NMR signal enhancement resulting from bTbtk-py is the largest of any biradical in the ideal glycerol/water solvent matrix, ε = 230. EPR and X-ray crystallography are used to characterize the molecule and suggest approaches for further optimizing the biradical distance and relative orientation.

Water-soluble narrow-line radicals for dynamic nuclear polarization.

The synthesis of air-stable, highly water-soluble organic radicals containing a 1,3-bis(diphenylene)-2-phenylallyl (BDPA) core is reported. A sulfonated derivative, SA-BDPA, retains the narrow electron paramagnetic resonance linewidth (<30 MHz at 5 T) of the parent BDPA in highly concentrated glycerol/water solutions (40 mM), which enables its use as polarizing agent for solid effect dynamic nuclear polarization (SE DNP). A sensitivity enhancement of 110 was obtained in high-field magic-angle-spinning (MAS) NMR experiments. The ease of synthesis and high maximum enhancements obtained with the BDPA-based radicals constitute a major advance over the trityl-type narrow-line polarization agents.