Atomic-Resolution Structural Dynamics in Crystalline Proteins from NMR and Molecular Simulation

Investigation of Protein Therapeutics in Frozen Conditions Using DNP MAS NMR: A Study on Pembrolizumab

The success of modern biopharmaceutical products depends on enhancing the stability of protein therapeutics. Freezing and thawing, which are common thermal stresses encountered throughout the lifecycle of drug substances, spanning protein production, formulation design, manufacturing, storage, and shipping, can impact this stability. Understanding the physicochemical and molecular behaviors of components in biological drug products at temperatures relevant to manufacturing and shipping is essential for assessing stability risks and determining appropriate storage conditions. This study focuses on the stability of high-concentration monoclonal antibody (mAb) pembrolizumab, the drug substance of Keytruda (Merck & Co., Inc., Rahway, NJ, United States), and its excipients in a frozen solution. By leveraging dynamic nuclear polarization (DNP), we achieve more than 100-fold signal enhancements in solid-state NMR (ssNMR), enabling efficient low-temperature (LT) analysis of pembrolizumab without isotopic enrichment. Through both ex situ and in situ ssNMR experiments conducted across a temperature range of 297 to 77 K, we provide insights into the stability of crystalline pembrolizumab under frozen conditions. Importantly, utilizing LT magic-angle spinning (MAS) probes allows us to study molecular dynamics in pembrolizumab from room temperature down to liquid nitrogen temperatures (<100 K). Our results demonstrate that valuable insights into protein conformation and dynamics, crystallinity, and the phase transformations of excipients during the freezing of the formulation matrix can be readily obtained for biological drug products. This study underscores the potential of LT-MAS ssNMR and DNP techniques for analyzing protein therapeutics and vaccines in frozen solutions.

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.

1H-Detected Biomolecular NMR under Fast Magic-Angle Spinning

Since the first pioneering studies on small deuterated peptides dating more than 20 years ago, 1H detection has evolved into the most efficient approach for investigation of biomolecular structure, dynamics, and interactions by solid-state NMR. The development of faster and faster magic-angle spinning (MAS) rates (up to 150 kHz today) at ultrahigh magnetic fields has triggered a real revolution in the field. This new spinning regime reduces the 1H-1H dipolar couplings, so that a direct detection of 1H signals, for long impossible without proton dilution, has become possible at high resolution. The switch from the traditional MAS NMR approaches with 13C and 15N detection to 1H boosts the signal by more than an order of magnitude, accelerating the site-specific analysis and opening the way to more complex immobilized biological systems of higher molecular weight and available in limited amounts. This paper reviews the concepts underlying this recent leap forward in sensitivity and resolution, presents a detailed description of the experimental aspects of acquisition of multidimensional correlation spectra with fast MAS, and summarizes the most successful strategies for the assignment of the resonances and for the elucidation of protein structure and conformational dynamics. It finally outlines the many examples where 1H-detected MAS NMR has contributed to the detailed characterization of a variety of crystalline and noncrystalline biomolecular targets involved in biological processes ranging from catalysis through drug binding, viral infectivity, amyloid fibril formation, to transport across lipid membranes.

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.

Protein structural dynamics by Magic-Angle Spinning NMR

Magic-Angle Spinning (MAS) Nuclear Magnetic Resonance (NMR) is a fast-developing technique, capable of complementing solution NMR, X-ray crystallography, and electron microscopy for the biophysical characterization of microcrystalline, poorly crystalline or disordered protein samples, such as enzymes, biomolecular assemblies, membrane-embedded systems or fibrils. Beyond structures, MAS NMR is an ideal tool for the investigation of dynamics, since it is unique in its ability to distinguish static and dynamic disorder, and to characterize not only amplitudes but also timescales of motion. Building on seminal work on model proteins, the technique is now ripe for widespread application in structural biology. This review briefly summarizes the recent evolutions in biomolecular MAS NMR and accounts for the growing number of systems where this spectroscopy has provided a description of conformational dynamics over the very last few years.

Multimodal Response to Copper Binding in Superoxide Dismutase Dynamics

Copper/zinc superoxide dismutase (SOD) is a homodimeric metalloenzyme that has been extensively studied as a benchmark for structure-function relationships in proteins, in particular because of its implication in the familial form of the neurodegenerative disease amyotrophic lateral sclerosis. Here, we investigate microcrystalline preparations of two differently metalated forms of SOD, namely, the fully mature functional Cu,Zn state and the E,Zn-SOD state in which the Cu site is empty. By using solid-state NMR with fast magic-angle spinning (MAS) at high magnetic fields (¹H Larmor frequency of 800-1000 MHz), we quantify motions spanning a dynamic range from ns to ms. We determine that metal ion uptake does not act as a rigidification element but as a switch redistributing motional processes on different time scales, with coupling of the dynamics of histidine side chains and those of remote key backbone elements of the protein.

Conformational Stability and Dynamics in Crystals Recapitulate Protein Behavior in Solution

A growing body of evidences has established that in many cases proteins may preserve most of their function and flexibility in a crystalline environment, and several techniques are today capable to characterize molecular properties of proteins in tightly packed lattices. Intriguingly, in the case of amyloidogenic precursors, the presence of transiently populated states (hidden to conventional crystallographic studies) can be correlated to the pathological fate of the native fold; the low fold stability of the native state is a hallmark of aggregation propensity. It remains unclear, however, to which extent biophysical properties of proteins such as the presence of transient conformations or protein stability characterized in crystallo reflect the protein behavior that is more commonly studied in solution. Here, we address this question by investigating some biophysical properties of a prototypical amyloidogenic system, β2-microglobulin in solution and in microcrystalline state. By combining NMR chemical shifts with molecular dynamics simulations, we confirmed that conformational dynamics of β2-microglobulin native state in the crystal lattice is in keeping with what observed in solution. A comparative study of protein stability in solution and in crystallo is then carried out, monitoring the change in protein secondary structure at increasing temperature by Fourier transform infrared spectroscopy. The increased structural order of the crystalline state contributes to provide better resolved spectral components compared to those collected in solution and crucially, the crystalline samples display thermal stabilities in good agreement with the trend observed in solution. Overall, this work shows that protein stability and occurrence of pathological hidden states in crystals parallel their solution counterpart, confirming the interest of crystals as a platform for the biophysical characterization of processes such as unfolding and aggregation.

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.

Molecular Dynamics Simulations of Macromolecular Crystals

The structures of biological macromolecules would not be known to their present extent without X-ray crystallography. Most simulations of globular proteins in solution begin by surrounding the crystal structure of the monomer in a bath of water molecules, but the standard simulation employing periodic boundary conditions is already close to a crystal lattice environment. With simple protocols, the same software and molecular models can perform simulations of the crystal lattice, including all asymmetric units and solvent to fill the box. Throughout the history of molecular dynamics, studies of crystal lattices have served to investigate the quality of the underlying force fields, correlate the simulated ensembles to experimental structure factors, and extrapolate the behavior in lattices to behavior in solution. Powerful new computers are enabling molecular simulations with greater realism and statistical convergence. Meanwhile, the advent of exciting new methods in crystallography, including femtosecond free-electron lasers and image reconstruction for time-resolved crystallography on slurries of small crystals, is expanding the range of structures accessible to X-ray diffraction. We review past fusions of simulations and crystallography, then look ahead to the ways that simulations of crystal structures will enhance structural biology in the future.

Simple and Robust Study of Backbone Dynamics of Crystalline Proteins Employing 1H-15N Dipolar Coupling Dispersion

We report a new solid-state multidimensional NMR approach based on the cross-polarization with variable-contact pulse sequence [ Paluch , P. ; Pawlak , T. ; Amoureux , J.-P. ; Potrzebowski , M. J. J. Magn. Reson. 233 , 2013 , 56 ], with ¹H inverse detection and very fast magic angle spinning (ν_R = 60 kHz), dedicated to the measurement of local molecular motions of ¹H-¹⁵N vectors. The introduced three-dimensional experiments, ¹H-¹⁵N-¹H and hCA(N)H, are particularly useful for the study of molecular dynamics of proteins and other complex structures. The applicability and power of this methodology have been revealed by employing as a model sample the GB-1 small protein doped with Na₂CuEDTA. The results clearly prove that the dispersion of ¹H-¹⁵N dipolar coupling constants well correlates with higher order structure of the protein. Our approach complements the conventional studies and offers a fast and reasonably simple method.

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.

Microsecond motions probed by near-rotary-resonance R1ρ15N MAS NMR experiments: the model case of protein overall-rocking in crystals

Solid-state near-rotary-resonance measurements of the spin-lattice relaxation rate in the rotating frame (R_1ρ) is a powerful NMR technique for studying molecular dynamics in the microsecond time scale. The small difference between the spin-lock (SL) and magic-angle-spinning (MAS) frequencies allows sampling very slow motions, at the same time it brings up some methodological challenges. In this work, several issues affecting correct measurements and analysis of ¹⁵N R_1ρ data are considered in detail. Among them are signal amplitude as a function of the difference between SL and MAS frequencies, "dead time" in the initial part of the relaxation decay caused by transient spin-dynamic oscillations, measurements under HORROR condition and proper treatment of the multi-exponential relaxation decays. The multiple ¹⁵N R_1ρ measurements at different SL fields and temperatures have been conducted in 1D mode (i.e. without site-specific resolution) for a set of four different microcrystalline protein samples (GB1, SH3, MPD-ubiquitin and cubic-PEG-ubiquitin) to study the overall protein rocking in a crystal. While the amplitude of this motion varies very significantly, its correlation time for all four sample is practically the same, 30-50 μs. The amplitude of the rocking motion correlates with the packing density of a protein crystal. It has been suggested that the rocking motion is not diffusive but likely a jump-like dynamic process.

Conformational dynamics in crystals reveal the molecular bases for D76N beta-2 microglobulin aggregation propensity

Spontaneous aggregation of folded and soluble native proteins in vivo is still a poorly understood process. A prototypic example is the D76N mutant of beta-2 microglobulin (β2m) that displays an aggressive aggregation propensity. Here we investigate the dynamics of β2m by X-ray crystallography, solid-state NMR, and molecular dynamics simulations to unveil the effects of the D76N mutation. Taken together, our data highlight the presence of minor disordered substates in crystalline β2m. The destabilization of the outer strands of D76N β2m accounts for the increased aggregation propensity. Furthermore, the computational modeling reveals a network of interactions with residue D76 as a keystone: this model allows predicting the stability of several point mutants. Overall, our study shows how the study of intrinsic dynamics in crystallo can provide crucial answers on protein stability and aggregation propensity. The comprehensive approach here presented may well be suited for the study of other folded amyloidogenic proteins.

The aggregation prone D76N beta-2 microglobulin mutant causes systemic amyloidosis. Here the authors combine crystallography, solid-state NMR, and computational studies and show that the D76N mutation increases protein dynamics and destabilizes the outer strands, which leads to an exposure of amyloidogenic parts explaining its aggregation propensity.

Internal protein motions in molecular-dynamics simulations of Bragg and diffuse X-ray scattering

Molecular-dynamics (MD) simulations of Bragg and diffuse X-ray scattering provide a means of obtaining experimentally validated models of protein conformational ensembles. This paper shows that compared with a single periodic unit-cell model, the accuracy of simulating diffuse scattering is increased when the crystal is modeled as a periodic supercell consisting of a 2 × 2 × 2 layout of eight unit cells. The MD simulations capture the general dependence of correlations on the separation of atoms. There is substantial agreement between the simulated Bragg reflections and the crystal structure; there are local deviations, however, indicating both the limitation of using a single structure to model disordered regions of the protein and local deviations of the average structure away from the crystal structure. Although it was anticipated that a simulation of longer duration might be required to achieve maximal agreement of the diffuse scattering calculation with the data using the supercell model, only a microsecond is required, the same as for the unit cell. Rigid protein motions only account for a minority fraction of the variation in atom positions from the simulation. The results indicate that protein crystal dynamics may be dominated by internal motions rather than packing interactions, and that MD simulations can be combined with Bragg and diffuse X-ray scattering to model the protein conformational ensemble.

Bringing diffuse X-ray scattering into focus

X-ray crystallography is experiencing a renaissance as a method for probing the protein conformational ensemble. The inherent limitations of Bragg analysis, however, which only reveals the mean structure, have given way to a surge in interest in diffuse scattering, which is caused by structure variations. Diffuse scattering is present in all macromolecular crystallography experiments. Recent studies are shedding light on the origins of diffuse scattering in protein crystallography, and provide clues for leveraging diffuse scattering to model protein motions with atomic detail.

The PROSECCO server for chemical shift predictions in ordered and disordered proteins

The chemical shifts measured in solution-state and solid-state nuclear magnetic resonance (NMR) are powerful probes of the structure and dynamics of protein molecules. The exploitation of chemical shifts requires methods to correlate these data with the protein structures and sequences. We present here an approach to calculate accurate chemical shifts in both ordered and disordered proteins using exclusively the information contained in their sequences. Our sequence-based approach, protein sequences and chemical shift correlations (PROSECCO), achieves the accuracy of the most advanced structure-based methods in the characterization of chemical shifts of folded proteins and improves the state of the art in the study of disordered proteins. Our analyses revealed fundamental insights on the structural information carried by NMR chemical shifts of structured and unstructured protein states.

Slow conformational exchange and overall rocking motion in ubiquitin protein crystals

Proteins perform their functions in solution but their structures are most frequently studied inside crystals. Here we probe how the crystal packing alters microsecond dynamics, using solid-state NMR measurements and multi-microsecond MD simulations of different crystal forms of ubiquitin. In particular, near-rotary-resonance relaxation dispersion (NERRD) experiments probe angular backbone motion, while Bloch–McConnell relaxation dispersion data report on fluctuations of the local electronic environment. These experiments and simulations reveal that the packing of the protein can significantly alter the thermodynamics and kinetics of local conformational exchange. Moreover, we report small-amplitude reorientational motion of protein molecules in the crystal lattice with an ~3–5° amplitude on a tens-of-microseconds time scale in one of the crystals, but not in others. An intriguing possibility arises that overall motion is to some extent coupled to local dynamics. Our study highlights the importance of considering the packing when analyzing dynamics of crystalline proteins.

X-ray crystallography is the main method for protein structure determination. Here the authors combine solid-state NMR measurements and molecular dynamics simulations and show that crystal packing alters the thermodynamics and kinetics of local conformational exchange as well as overall rocking motion of protein molecules in the crystal lattice.

HIV-1 Capsid Function Is Regulated by Dynamics: Quantitative Atomic-Resolution Insights by Integrating Magic-Angle-Spinning NMR, QM/MM, and MD

HIV-1 CA capsid protein possesses intrinsic conformational flexibility, which is essential for its assembly into conical capsids and interactions with host factors. CA is dynamic in the assembled capsid, and residues in functionally important regions of the protein undergo motions spanning many decades of time scales. Chemical shift anisotropy (CSA) tensors, recorded in magic-angle-spinning NMR experiments, provide direct residue-specific probes of motions on nano- to microsecond time scales. We combined NMR, MD, and density-functional-theory calculations, to gain quantitative understanding of internal backbone dynamics in CA assemblies, and we found that the dynamically averaged 15N CSA tensors calculated by this joined protocol are in remarkable agreement with experiment. Thus, quantitative atomic-level understanding of the relationships between CSA tensors, local backbone structure, and motions in CA assemblies is achieved, demonstrating the power of integrating NMR experimental data and theory for characterizing atomic-resolution dynamics in biological systems.

Studying Dynamics by Magic-Angle Spinning Solid-State NMR Spectroscopy: Principles and Applications to Biomolecules

Magic-angle spinning solid-state NMR spectroscopy is an important technique to study molecular structure, dynamics and interactions, and is rapidly gaining importance in biomolecular sciences. Here we provide an overview of experimental approaches to study molecular dynamics by MAS solid-state NMR, with an emphasis on the underlying theoretical concepts and differences of MAS solid-state NMR compared to solution-state NMR. The theoretical foundations of nuclear spin relaxation are revisited, focusing on the particularities of spin relaxation in solid samples under magic-angle spinning. We discuss the range of validity of Redfield theory, as well as the inherent multi-exponential behavior of relaxation in solids. Experimental challenges for measuring relaxation parameters in MAS solid-state NMR and a few recently proposed relaxation approaches are discussed, which provide information about time scales and amplitudes of motions ranging from picoseconds to milliseconds. We also discuss the theoretical basis and experimental measurements of anisotropic interactions (chemical-shift anisotropies, dipolar and quadrupolar couplings), which give direct information about the amplitude of motions. The potential of combining relaxation data with such measurements of dynamically-averaged anisotropic interactions is discussed. Although the focus of this review is on the theoretical foundations of dynamics studies rather than their application, we close by discussing a small number of recent dynamics studies, where the dynamic properties of proteins in crystals are compared to those in solution.

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.

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.

Investigating protein conformational energy landscapes and atomic resolution dynamics from NMR dipolar couplings: a review

Nuclear magnetic resonance spectroscopy is exquisitely sensitive to protein dynamics. In particular inter-nuclear dipolar couplings, that become measurable in solution when the protein is dissolved in a dilute liquid crystalline solution, report on all conformations sampled up to millisecond timescales. As such they provide the opportunity to describe the Boltzmann distribution present in solution at atomic resolution, and thereby to map the conformational energy landscape in unprecedented detail. The development of analytical methods and approaches based on numerical simulation and their application to numerous biologically important systems is presented.

Observing the overall rocking motion of a protein in a crystal

The large majority of three-dimensional structures of biological macromolecules have been determined by X-ray diffraction of crystalline samples. High-resolution structure determination crucially depends on the homogeneity of the protein crystal. Overall ‘rocking' motion of molecules in the crystal is expected to influence diffraction quality, and such motion may therefore affect the process of solving crystal structures. Yet, so far overall molecular motion has not directly been observed in protein crystals, and the timescale of such dynamics remains unclear. Here we use solid-state NMR, X-ray diffraction methods and μs-long molecular dynamics simulations to directly characterize the rigid-body motion of a protein in different crystal forms. For ubiquitin crystals investigated in this study we determine the range of possible correlation times of rocking motion, 0.1–100 μs. The amplitude of rocking varies from one crystal form to another and is correlated with the resolution obtainable in X-ray diffraction experiments.

Small-amplitude overall motion of molecules in crystals limits the achievable resolution in X-ray diffraction, yet little is known about its exact nature. Here, the authors obtain NMR, XRD and MD data from three different crystal forms of a protein (ubiquitin) to gain insight into amplitude and timescale of such motions.

Unraveling the complexity of protein backbone dynamics with combined (13)C and (15)N solid-state NMR relaxation measurements

Typically, protein dynamics involve a complex hierarchy of motions occurring on different time scales between conformations separated by a range of different energy barriers. NMR relaxation can in principle provide a site-specific picture of both the time scales and amplitudes of these motions, but independent relaxation rates sensitive to fluctuations in different time scale ranges are required to obtain a faithful representation of the underlying dynamic complexity. This is especially pertinent for relaxation measurements in the solid state, which report on dynamics in a broader window of time scales by more than 3 orders of magnitudes compared to solution NMR relaxation. To aid in unraveling the intricacies of biomolecular dynamics we introduce (13)C spin-lattice relaxation in the rotating frame (R1ρ) as a probe of backbone nanosecond-microsecond motions in proteins in the solid state. We present measurements of (13)C'R1ρ rates in fully protonated crystalline protein GB1 at 600 and 850 MHz (1)H Larmor frequencies and compare them to (13)C'R1, (15)N R1 and R1ρ measured under the same conditions. The addition of carbon relaxation data to the model free analysis of nitrogen relaxation data leads to greatly improved characterization of time scales of protein backbone motions, minimizing the occurrence of fitting artifacts that may be present when (15)N data is used alone. We also discuss how internal motions characterized by different time scales contribute to (15)N and (13)C relaxation rates in the solid state and solution state, leading to fundamental differences between them, as well as phenomena such as underestimation of picosecond-range motions in the solid state and nanosecond-range motions in solution.

Molecular modeling as a predictive tool for the development of solid dispersions

In this study molecular modeling is introduced as a novel approach for the development of pharmaceutical solid dispersions. A computational model based on quantum mechanical (QM) calculations was used to predict the miscibility of various drugs in various polymers by predicting the binding strength between the drug and dimeric form of the polymer. The drug/polymer miscibility was also estimated by using traditional approaches such as Van Krevelen/Hoftyzer and Bagley solubility parameters or Flory-Huggins interaction parameter in comparison to the molecular modeling approach. The molecular modeling studies predicted successfully the drug-polymer binding energies and the preferable site of interaction between the functional groups. The drug-polymer miscibility and the physical state of bulk materials, physical mixtures, and solid dispersions were determined by thermal analysis (DSC/MTDSC) and X-ray diffraction. The produced solid dispersions were analyzed by X-ray photoelectron spectroscopy (XPS), which confirmed not only the exact type of the intermolecular interactions between the drug-polymer functional groups but also the binding strength by estimating the N coefficient values. The findings demonstrate that QM-based molecular modeling is a powerful tool to predict the strength and type of intermolecular interactions in a range of drug/polymeric systems for the development of solid dispersions.

Ensemble MD simulations restrained via crystallographic data: accurate structure leads to accurate dynamics

Currently, the best existing molecular dynamics (MD) force fields cannot accurately reproduce the global free-energy minimum which realizes the experimental protein structure. As a result, long MD trajectories tend to drift away from the starting coordinates (e.g., crystallographic structures). To address this problem, we have devised a new simulation strategy aimed at protein crystals. An MD simulation of protein crystal is essentially an ensemble simulation involving multiple protein molecules in a crystal unit cell (or a block of unit cells). To ensure that average protein coordinates remain correct during the simulation, we introduced crystallography-based restraints into the MD protocol. Because these restraints are aimed at the ensemble-average structure, they have only minimal impact on conformational dynamics of the individual protein molecules. So long as the average structure remains reasonable, the proteins move in a native-like fashion as dictated by the original force field. To validate this approach, we have used the data from solid-state NMR spectroscopy, which is the orthogonal experimental technique uniquely sensitive to protein local dynamics. The new method has been tested on the well-established model protein, ubiquitin. The ensemble-restrained MD simulations produced lower crystallographic R factors than conventional simulations; they also led to more accurate predictions for crystallographic temperature factors, solid-state chemical shifts, and backbone order parameters. The predictions for (15) N R1 relaxation rates are at least as accurate as those obtained from conventional simulations. Taken together, these results suggest that the presented trajectories may be among the most realistic protein MD simulations ever reported. In this context, the ensemble restraints based on high-resolution crystallographic data can be viewed as protein-specific empirical corrections to the standard force fields.

Access to Cα backbone dynamics of biological solids by 13C T1 relaxation and molecular dynamics simulation

We introduce a labeling scheme for magic angle spinning (MAS) solid-state NMR that is based on deuteration in combination with dilution of the carbon spin system. The labeling strategy achieves spectral editing by simplification of the HαCα and aliphatic side chain spectral region. A reduction in both proton and carbon spin density in combination with fast spinning (≥50 kHz) is essential to retrieve artifact-free (13)C-R1 relaxation data for aliphatic carbons. We obtain good agreement between the NMR experimental data and order parameters extracted from a molecular dynamics (MD) trajectory, which indicates that carbon based relaxation parameters can yield complementary information on protein backbone as well as side chain dynamics.

Slow motions in microcrystalline proteins as observed by MAS-dependent 15N rotating-frame NMR relaxation

(15)N NMR relaxation rate R1ρ measurements reveal that a substantial fraction of residues in the microcrystalline chicken alpha-spectrin SH3 domain protein undergoes dynamics in the μs-ms timescale range. On the basis of a comparison of 2D site-resolved with 1D integrated (15)N spectral intensities, we demonstrate that the significant fraction of broad signals in the 2D spectrum exhibits the most pronounced slow mobility. We show that (15)N R1ρ's in proton-diluted protein samples are practically free from the coherent spin-spin contribution even at low MAS rates, and thus can be analysed quantitatively. Moderate MAS rates (10-30 kHz) can be more advantageous in comparison with the rates >50-60 kHz when slow dynamics are to be identified and quantified by means of R1ρ experiments.

Dynamics in the solid-state: perspectives for the investigation of amyloid aggregates, membrane proteins and soluble protein complexes

Aggregates formed by amyloidogenic peptides and proteins and reconstituted membrane protein preparations differ significantly in terms of the spectral quality that they display in solid-state NMR experiments. Structural heterogeneity and dynamics can both in principle account for that observation. This perspectives article aims to point out challenges and limitations, but also potential opportunities in the investigation of these systems.

Internal protein dynamics on ps to μs timescales as studied by multi-frequency (15)N solid-state NMR relaxation

A comprehensive analysis of the dynamics of the SH3 domain of chicken alpha-spectrin is presented, based upon (15)N T1 and on- and off-resonance T1ρ relaxation times obtained on deuterated samples with a partial back-exchange of labile protons under a variety of the experimental conditions, taking explicitly into account the dipolar order parameters calculated from (15)N-(1)H dipole-dipole couplings. It is demonstrated that such a multi-frequency approach enables access to motional correlation times spanning about 6 orders of magnitude. We asses the validity of different motional models based upon orientation autocorrelation functions with a different number of motional components. We find that for many residues a "two components" model is not sufficient for a good description of the data and more complicated fitting models must be considered. We show that slow motions with correlation times on the order of 1-10 μs can be determined reliably in spite of rather low apparent amplitudes (below 1 %), and demonstrate that the distribution of the protein backbone mobility along the time scale axis is pronouncedly non-uniform and non-monotonic: two domains of fast (τ < 10(-10) s) and intermediate (10(-9) s < τ < 10(-7) s) motions are separated by a gap of one order of magnitude in time with almost no motions. For slower motions (τ > 10(-6) s) we observe a sharp ~1 order of magnitude decrease of the apparent motional amplitudes. Such a distribution obviously reflects different nature of backbone motions on different time scales, where the slow end may be attributed to weakly populated "excited states." Surprisingly, our data reveal no clearly evident correlations between secondary structure of the protein and motional parameters. We also could not notice any unambiguous correlations between motions in different time scales along the protein backbone emphasizing the importance of the inter-residue interactions and the cooperative nature of protein dynamics.

Amplitudes and time scales of picosecond-to-microsecond motion in proteins studied by solid-state NMR: a critical evaluation of experimental approaches and application to crystalline ubiquitin

Solid-state NMR provides insight into protein motion over time scales ranging from picoseconds to seconds. While in solution state the methodology to measure protein dynamics is well established, there is currently no such consensus protocol for measuring dynamics in solids. In this article, we perform a detailed investigation of measurement protocols for fast motions, i.e. motions ranging from picoseconds to a few microseconds, which is the range covered by dipolar coupling and relaxation experiments. We perform a detailed theoretical investigation how dipolar couplings and relaxation data can provide information about amplitudes and time scales of local motion. We show that the measurement of dipolar couplings is crucial for obtaining accurate motional parameters, while systematic errors are found when only relaxation data are used. Based on this realization, we investigate how the REDOR experiment can provide such data in a very accurate manner. We identify that with accurate rf calibration, and explicit consideration of rf field inhomogeneities, one can obtain highly accurate absolute order parameters. We then perform joint model-free analyses of 6 relaxation data sets and dipolar couplings, based on previously existing, as well as new data sets on microcrystalline ubiquitin. We show that nanosecond motion can be detected primarily in loop regions, and compare solid-state data to solution-state relaxation and RDC analyses. The protocols investigated here will serve as a useful basis towards the establishment of a routine protocol for the characterization of ps-μs motions in proteins by solid-state NMR.

Advances in solid-state relaxation methodology for probing site-specific protein dynamics

Dynamics are intimately linked to protein stability and play a crucial role in important biological processes, such as ligand binding, allosteric regulation, protein folding, signaling, and enzymatic catalysis. Solid-state NMR relaxation measurements allow researchers to determine the amplitudes, time scales, and under favorable conditions, directionality of motions at atomic resolution over the entire range of dynamic processes from picoseconds to milliseconds. Because this method allows researchers to examine both the amplitudes and time scales of motions in this range, they can link different tiers of protein motions in protein energy landscapes. As a result, scientists can better understand the relationships between protein motions and functions. Such studies are possible both with the primary targets of solid-state NMR studies, such as amyloid fibrils, membrane proteins, or other heterogeneous systems, and others that researchers typically study by solution NMR and X-ray crystallography. In addition, solid-state NMR, with the absence of tumbling in solution, eliminates the intrinsic size limitation imposed by slow tumbling of large proteins. Thus, this technique allows researchers to characterize interdomain and intermolecular interactions in large complexes at the atomic scale. In this Account, we discuss recent advances in solid-state relaxation methodology for studying widespread site-specific protein dynamics. We focus on applications involving magic angle spinning, one of the primary methods used in high-resolution solid-state NMR. We give an overview of challenges and solutions for measuring (15)N and (13)C spin-lattice relaxation (R1) to characterize fast picosecond-nanosecond motions, spin-lattice in the rotating frame (R1ρ), and other related relaxation rates for characterization of picosecond-millisecond protein motions. In particular, we discuss the problem of separating incoherent effects caused by random motions from coherent effects arising from incomplete averaging of orientation-dependent NMR interactions. We mention a number of quantitative studies of protein dynamics based on solid-state relaxation measurements. Finally, we discuss the potential use of relaxation measurements for extracting the directionality of motions. Using the (15)N and (13)C R1 and R1ρ measurements, we illustrate the backbone and side-chain dynamics in the protein GB1 and comment on this emerging dynamic picture within the context of data from solution NMR measurements and simulations.