Observing the overall rocking motion of a protein in a crystal

Antigen presentation of post-translationally modified peptides in major histocompatibility complexes

T cells of the adaptive immune system recognize pathogens and malignantly transformed cells through a process called antigen presentation. During this process, peptides are displayed on major histocompatibility complex (MHC) class I and II molecules. Self-reactive T cells are typically removed or suppressed during T-cell development and through peripheral tolerance mechanisms, ensuring that only T cells recognizing peptides that are either absent or present in low abundance under normal conditions remain. This selective process allows T cells to respond to peptides derived from foreign proteins while ignoring those from self-proteins. However, T cells can also respond to peptides derived from proteins that have undergone post-translational modifications (PTMs). Over 200 different PTMs have been described, and while they are essential for protein function, localization and stability, their dysregulation is often associated with disease conditions. PTMs can affect the proteolytic processing of proteins and prevent MHC binding, thereby changing the repertoire of peptides presented on MHC molecules. However, it is also increasingly evident that many peptides presented on MHC molecules carry PTMs, which can alter their immunogenicity. As a result, the presentation of post-translationally modified peptides by MHC molecules plays a significant role in various diseases, as well as autoimmune disorders and allergies. This review will provide an overview of the impact of PTMs on antigen presentation and their implications for immune recognition and disease.

Ubiquitin's Conformational Heterogeneity as Discerned by Nuclear Magnetic Resonance Spectroscopy

Visualizing a protein's molecular motions has been a long standing topic of research in the biophysics community. Largely this has been done by exploiting nuclear magnetic resonance spectroscopy (NMR), and arguably no protein's molecular motions have been better characterized by NMR than that of ubiquitin (Ub), a 76 amino acid polypeptide essential in ubiquitination-a key regulatory system within cells. Herein, we discuss ubiquitin's conformational plasticity as visualized, at atomic resolution, by more than 35 years of NMR work. In our discussions we point out the differences between data acquired in vitro, ex vivo, as well as in vivo and stress the need to investigate Ub's conformational plasticity in more biologically representative backgrounds.

Native Cellular Membranes Facilitate Channel Activity of MscL by Enhancing Slow Collective Motions of Its Transmembrane Helices

Mechanosensitive channels of large conductance (MscL) serve as a mechanoelectrical valve of cells in response to the membrane tension. The influence of membrane environments on the MscL channel activity and the underlying mechanism remains unclear. Herein, we developed a new sample preparation protocol that allows for the detection of high-quality 1H-detected solid-state NMR spectra of MscL in cellular membranes, enabling site-specific analysis of its dynamics. Dipolar order parameters and spin relaxation rates are measured for 51 residues of MscL in synthetic and native membranes. The dynamics data reveal that while MscL maintains a similar rigidity in both membrane environments, it exhibits enhanced slow collective motions in the native cellular membranes. Molecular dynamics simulations demonstrate the critical role of slow motions in the mechanosensitivity of MscL by promoting protein-membrane interactions. This study examines atomic-resolution dynamics of a membrane-protein in cellular membranes and provides novel insights into the functional significance of membrane-protein dynamics.

Slow global motions in biosolids studied by the deuteron stimulated echo NMR experiment

Recent 15N R1ρ-relaxation studies have shown that proteins in the solid state undergo slow, low amplitude global motion in the sub-millisecond time range. This range is at the edge of the time window for R1ρ experiments and, therefore, the motional parameters obtained by this method are not precise or reliable. In this paper, we present a 2H stimulated echo study of this type of molecular dynamics. The 2H stimulated echo experiments on a static sample allow for direct measurement of the correlation function in the time range of 10-6-10-1 s, making them well suited to study this type of molecular mobility. We have conducted a detailed analytical and numerical comparison of the correlation functions obtained from the relaxation and stimulated echo experiments, which are generally different. We have identified conditions and algorithms that enable a direct comparison of the relaxation and stimulated echo experimental results. Using the protein GB1 in the form of a lyophilized powder, we have demonstrated that 15N R1ρ-relaxation and 2H stimulated echo experiments yield essentially the same slow-motion correlation function. Surprisingly, this type of motion is observed not only in the protein sample but also in the tripeptide and single amino acid solid samples. The comparison of data measured in these three samples at different temperatures led us to conclude that this slow motion is, in fact, ultrasonic phonons, which seem to be inherent to all rigid biological solids.

MAS NMR experiments of corynebacterial cell walls: Complementary 1H- and CPMAS CryoProbe-enhanced 13C-detected experiments

Bacterial cell walls are gigadalton-large cross-linked polymers with a wide range of motional amplitudes, including rather rigid as well as highly flexible parts. Magic-angle spinning NMR is a powerful method to obtain atomic-level information about intact cell walls. Here we investigate sensitivity and information content of different homonuclear 13C13C and heteronuclear 1H15N, 1H13C and 15N13C correlation experiments. We demonstrate that a CPMAS CryoProbe yields ca. 8-fold increased signal-to-noise over a room-temperature probe, or a ca. 3-4-fold larger per-mass sensitivity. The increased sensitivity allowed to obtain high-resolution spectra even on intact bacteria. Moreover, we compare resolution and sensitivity of 1H MAS experiments obtained at 100 kHz vs. 55 kHz. Our study provides useful hints for choosing experiments to extract atomic-level details on cell-wall samples.

Analytical approaches for assessing protein structure in protein-rich food: A comprehensive review

This review focuses on changes in nutrition and functional properties of protein-rich foods, primarily attributed to alterations in protein structures. We provide a comprehensive overview and comparison of commonly used laboratory methods for protein structure identification, aiming to offer readers a convenient understanding of these techniques. The review covers a range of detection technologies employed in food protein analysis and conducts an extensive comparison to identify the most suitable method for various proteins. While these techniques offer distinct advantages for protein structure determination, the inherent complexity of food matrices presents ongoing challenges. Further research is necessary to develop and enhance more robust detection methods to improve accuracy in protein conformation and structure analysis.

Fast collective motions of backbone in transmembrane α helices are critical to water transfer of aquaporin

Fast collective motions are widely present in biomolecules, but their functional relevance remains unclear. Herein, we reveal that fast collective motions of backbone are critical to the water transfer of aquaporin Z (AqpZ) by using solid-state nuclear magnetic resonance (ssNMR) spectroscopy and molecular dynamics (MD) simulations. A total of 212 residue site-specific dipolar order parameters and 158 15N spin relaxation rates of the backbone are measured by combining the 13C- and 1H-detected multidimensional ssNMR spectra. Analysis of these experimental data by theoretic models suggests that the small-amplitude (~10°) collective motions of the transmembrane α helices on the nanosecond-to-microsecond timescales are dominant for the dynamics of AqpZ. The MD simulations demonstrate that these collective motions are critical to the water transfer efficiency of AqpZ by facilitating the opening of the channel and accelerating the water-residue hydrogen bonds renewing in the selectivity filter region.

gmXtal: Cooking Crystals with GROMACS

Molecular dynamics (MD) simulations are routinely performed of biomolecules in solution, because this is their native environment. However, the structures used in such simulations are often obtained with X-ray crystallography, which provides the atomic coordinates of the biomolecule in a crystal environment. With the advent of free electron lasers and time-resolved techniques, X-ray crystallography can now also access metastable states that are intermediates in a biochemical process. Such experiments provide additional data, which can be used, for example, to optimize MD force fields. Doing so requires that the simulation of the biomolecule is also performed in the crystal environment. However, in contrast to simulations of biomolecules in solution, setting up a crystal is challenging. In particular, because not all solvent molecules are resolved in X-ray crystallography, adding a suitable number of solvent molecules, such that the properties of the crystallographic unit cell are preserved in the simulation, can be difficult and typically is a trial-and-error based procedure requiring manual interventions. Such interventions preclude high throughput applications. To overcome this bottleneck, we introduce gmXtal, a tool for setting up crystal simulations for MD simulations with GROMACS. With the information from the protein data bank (rcsb.org) gmXtal automatically (i) builds the crystallographic unit cell; (ii) sets the protonation of titratable residues; (iii) builds missing residues that were not resolved experimentally; and (iv) adds an appropriate number of solvent molecules to the system. gmXtal is available as a standalone tool https://gitlab.com/pbuslaev/gmxtal .

X-ray Crystallography Module in MD Simulation Program Amber 2023. Refining the Models of Protein Crystals

The MD simulation package Amber offers an attractive platform to refine crystallographic structures of proteins: (i) state-of-the-art force fields help to regularize protein coordinates and reconstruct the poorly diffracting elements of the structure, such as flexible loops; (ii) MD simulations restrained by the experimental diffraction data provide an effective strategy to optimize structural models of protein crystals, including explicitly modeled interstitial solvent as well as crystal contacts. Here, we present the new crystallography module xray, released as a part of the Amber 2023 package. This module contains functions to calculate and scale structure factors (including the contributions from bulk solvent), evaluate the maximum-likelihood-type crystallographic potential, and compute its derivative forces. The X-ray functionality of Amber no longer relies on external dependencies so that the full advantage of GPU acceleration can be taken. This makes it possible to refine in a short time hundreds of crystal models, including supercell models comprised of multiple unit cells. The new automated Amber-based refinement procedure leads to an appreciable improvement in Rfree (in some cases, by as much as 0.067) as well as MolProbity scores.

Protein dynamics detected by magic-angle spinning relaxation dispersion NMR

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

Nuclear spin diffusion under fast magic-angle spinning in solid-state NMR

Solid-state nuclear spin diffusion is the coherent and reversible process through which spin order is transferred via dipolar couplings. With the recent increases in magic-angle spinning (MAS) frequencies and magnetic fields becoming routinely applied in solid-state nuclear magnetic resonance, understanding how the increased 1H resolution obtained affects spin diffusion is necessary for interpretation of several common experiments. To investigate the coherent contributions to spin diffusion with fast MAS, we have developed a low-order correlation in Liouville space model based on the work of Dumez et al. (J. Chem. Phys. 33, 224501, 2010). Specifically, we introduce a new method for basis set selection, which accounts for the resonance-offset dependence at fast MAS. Furthermore, we consider the necessity of including chemical shift, both isotropic and anisotropic, in the modeling of spin diffusion. Using this model, we explore how different experimental factors change the nature of spin diffusion. Then, we show case studies to exemplify the issues that arise in using spin diffusion techniques at fast spinning. We show that the efficiency of polarization transfer via spin diffusion occurring within a deuterated and 100% back-exchanged protein sample at 60 kHz MAS is almost entirely dependent on resonance offset. We additionally identify temperature-dependent magnetization transfer in beta-aspartyl L-alanine, which could be explained by the influence of an incoherent relaxation-based nuclear Overhauser effect.

Integrated Assessment of the Structure and Dynamics of Solid Proteins

Understanding macromolecular function, interactions, and stability hinges on detailed assessment of conformational ensembles. For solid proteins, accurate elucidation of the spatial aspects of dynamics at physiological temperatures is limited by the qualitative character or low abundance of solid-state nuclear magnetic resonance internuclear distance information. Here, we demonstrate access to abundant proton-proton internuclear distances for integrated structural biology and chemistry with unprecedented accuracy. Apart from highest-resolution single-state structures, the exact distances enable molecular dynamics (MD) ensemble simulations orchestrated by a dense network of experimental interproton distance boundaries gathered in the context of their physical lattices. This direct embedding of experimental ensemble distances into MD will provide access to representative, atomic-level spatial details of conformational dynamics in supramolecular assemblies, crystalline and lipid-embedded proteins, and beyond.

Simulating diffraction photographs based on molecular dynamics trajectories of a protein crystal: a new option to examine structure-solving strategies in protein crystallography

A molecular dynamics (MD)-based pipeline has been designed and implemented to emulate the entire process of collecting diffraction photographs and calculating crystallographic structures of proteins from them. Using a structure of lysozyme solved in-house, a supercell comprising 125 (5 × 5 × 5) crystal unit cells containing a total of 1000 protein molecules and explicit interstitial solvent was constructed. For this system, two 300 ns MD trajectories at 298 and 250 K were recorded. A series of snapshots from these trajectories were then used to simulate a fully realistic set of diffraction photographs, which were further fed into the standard pipeline for structure determination. The resulting structures show very good agreement with the underlying MD model not only in terms of coordinates but also in terms of B factors; they are also consistent with the original experimental structure. The developed methodology should find a range of applications, such as optimizing refinement protocols to solve crystal structures and extracting dynamics information from diffraction data or diffuse scattering.

Aromatic ring flips in differently packed ubiquitin protein crystals from MAS NMR and MD

Probing the dynamics of aromatic side chains provides important insights into the behavior of a protein because flips of aromatic rings in a protein's hydrophobic core report on breathing motion involving a large part of the protein. Inherently invisible to crystallography, aromatic motions have been primarily studied by solution NMR. The question how packing of proteins in crystals affects ring flips has, thus, remained largely unexplored. Here we apply magic-angle spinning NMR, advanced phenylalanine 1H-13C/2H isotope labeling and MD simulation to a protein in three different crystal packing environments to shed light onto possible impact of packing on ring flips. The flips of the two Phe residues in ubiquitin, both surface exposed, appear remarkably conserved in the different crystal forms, even though the intermolecular packing is quite different: Phe4 flips on a ca. 10-20 ns time scale, and Phe45 are broadened in all crystals, presumably due to µs motion. Our findings suggest that intramolecular influences are more important for ring flips than intermolecular (packing) effects.

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.

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 T₁ 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.

Biophysical and biochemical properties of PHGDH revealed by studies on PHGDH inhibitors

The rate-limiting serine biogenesis enzyme PHGDH is overexpressed in cancers. Both serine withdrawal and genetic/pharmacological inhibition of PHGDH have demonstrated promising tumor-suppressing activities. However, the enzyme properties of PHGDH are not well understood and the discovery of PHGDH inhibitors is still in its infancy. Here, oridonin was identified from a natural product library as a new PHGDH inhibitor. The crystal structure of PHGDH in complex with oridonin revealed a new allosteric site. The binding of oridonin to this site reduced the activity of the enzyme by relocating R54, a residue involved in substrate binding. Mutagenesis studies showed that PHGDH activity was very sensitive to cysteine mutations, especially those in the substrate binding domain. Conjugation of oridonin and other reported covalent PHGDH inhibitors to these sites will therefore inhibit PHGDH. In addition to being inhibited enzymatically, PHGDH can also be inhibited by protein aggregation and proteasome-mediated degradation. Several tested PHGDH cancer mutants showed altered enzymatic activity, which can be explained by protein structure and stability. Overall, the above studies present new biophysical and biochemical insights into PHGDH and may facilitate the future design of PHGDH inhibitors.

Deuteration for High-Resolution Detection of Protons in Protein Magic Angle Spinning (MAS) Solid-State NMR

Proton detection developed in the last 20 years as the method of choice to study biomolecules in the solid state. In perdeuterated proteins, proton dipolar interactions are strongly attenuated, which allows yielding of high-resolution proton spectra. Perdeuteration and backsubstitution of exchangeable protons is essential if samples are rotated with MAS rotation frequencies below 60 kHz. Protonated samples can be investigated directly without spin dilution using proton detection methods in case the MAS frequency exceeds 110 kHz. This review summarizes labeling strategies and the spectroscopic methods to perform experiments that yield assignments, quantitative information on structure, and dynamics using perdeuterated samples. Techniques for solvent suppression, H/D exchange, and deuterium spectroscopy are discussed. Finally, experimental and theoretical results that allow estimation of the sensitivity of proton detected experiments as a function of the MAS frequency and the external B₀ field in a perdeuterated environment are compiled.

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.

On the vibrational free energy of hydrated proteins

When the hydration shell of a protein is filled with at least 0.6 gram of water per gram of protein, a significant anti-correlation between the vibrational free energy and the potential energy of energy-minimized conformers is observed. This means that low potential energy, well-hydrated, protein conformers tend to be more rigid than high-energy ones. On the other hand, in the case of CASP target 624, when its hydration shell is filled, a significant energy gap is observed between the crystal structure and the best conformers proposed during the prediction experiment, strongly suggesting that including explicit water molecules may help identifying unlikely conformers among good-looking ones.

Solid-state NMR spectroscopy

Solid-state nuclear magnetic resonance (NMR) spectroscopy is an atomic-level method used to determine the chemical structure, three-dimensional structure, and dynamics of solids and semi-solids. This Primer summarizes the basic principles of NMR as applied to the wide range of solid systems. The fundamental nuclear spin interactions and the effects of magnetic fields and radiofrequency pulses on nuclear spins are the same as in liquid-state NMR. However, because of the anisotropy of the interactions in the solid state, the majority of high-resolution solid-state NMR spectra is measured under magic-angle spinning (MAS), which has profound effects on the types of radiofrequency pulse sequences required to extract structural and dynamical information. We describe the most common MAS NMR experiments and data analysis approaches for investigating biological macromolecules, organic materials, and inorganic solids. Continuing development of sensitivity-enhancement approaches, including 1H-detected fast MAS experiments, dynamic nuclear polarization, and experiments tailored to ultrahigh magnetic fields, is described. We highlight recent applications of solid-state NMR to biological and materials chemistry. The Primer ends with a discussion of current limitations of NMR to study solids, and points to future avenues of development to further enhance the capabilities of this sophisticated spectroscopy for new applications.

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.

Relaxation-induced dipolar exchange with recoupling (RIDER) distortions in CODEX experiments

Chemical shift anisotropy (CSA) and dipolar CODEX (Cenralband Only Detection of EXchange) experiments enable abundant quantitative information on the reorientation of the CSA and dipolar tensors to be obtained on millisecond-second timescales. At the same time, proper performance of the experiments and data analysis can often be a challenge since CODEX is prone to some interfering effects that may lead to incorrect interpretation of the experimental results. One of the most important such effects is RIDER (relaxation-induced dipolar exchange with recoupling). It appears due to the dipolar interaction of the observed X nuclei with some other nuclei, which causes an apparent decay in the mixing time dependence of the signal intensity reflecting not molecular motion, but spin flips of the adjacent nuclei. This may hamper obtaining correct values of the parameters of molecular mobility. In this contribution we consider in detail the reasons why the RIDER distortions remain even under decoupling conditions and propose measures to eliminate them. That is, we suggest (1) using an additional Z filter between the cross-polarization (CP) section and the CODEX recoupling blocks that suppresses the interfering anti-phase coherence responsible for the X -H RIDER and (2) recording only the cosine component of the CODEX signal since it is less prone to the RIDER distortions in comparison to the sine component. The experiments were conducted on rigid model substances as well as microcrystalline 2 H /  15 N-enriched proteins (GB1 and SH3) with a partial back-exchange of labile protons. Standard CSA and dipolar CODEX experiments reveal a fast-decaying component in the mixing time dependence of 15 N nuclei in proteins, which can be misinterpreted as a slow overall protein rocking motion. However, the RIDER-free experimental setup provides flat mixing time dependences, meaning that the studied proteins do not undergo global motions on the millisecond timescale.

Recent advances in solid-state relaxation dispersion techniques

This review describes two rotating-frame (R_1ρ) relaxation dispersion methods, namely the Bloch-McConnell Relaxation Dispersion and the Near-rotary Resonance Relaxation Dispersion, which enable the study of microsecond time-scale conformational fluctuations in the solid state using magic-angle-spinning nuclear magnetic resonance spectroscopy. The goal is to provide the reader with key ideas, experimental descriptions, and practical considerations associated with R_1ρ measurements that are needed for analyzing relaxation dispersion and quantifying conformational exchange. While the focus is on protein motion, many presented concepts can be equally well adapted to study the microsecond time-scale dynamics of other bio- (e.g. lipids, polysaccharides, nucleic acids), organic (e.g. pharmaceutical compounds), or inorganic molecules (e.g., metal organic frameworks). This article summarizes the essential contributions made by recent theoretical and experimental solid-state NMR studies to our understanding of protein motion. Here we discuss recent advances in fast MAS applications that enable the observation and atomic level characterization of sparsely populated conformational states which are otherwise inaccessible for other experimental methods. Such high-energy states are often associated with protein functions such as molecular recognition, ligand binding, or enzymatic catalysis, as well as with disease-related properties such as misfolding and amyloid formation.

Molecular dynamics simulation of the heart type fatty acid binding protein in a crystal environment

Crystallographic data comes from a space-time average over all the unit cells within the crystal, so dynamic phenomena do not contribute significantly to the diffraction data. Many efforts have been made to reconstitute the movement of the macromolecules and explore the microstates that the confined proteins can adopt in the crystalline network. We explored different strategies to simulate a heart fatty acid binding protein (H-FABP) crystal by means of Molecular Dynamics (MD) simulations. We evaluate the effect of introducing restraints according to experimental isotropic B-factors and we analyzed the H-FABP motions in the crystal using Principal Component Analysis (PCA), isotropic and anisotropic B-factors. We compared the behavior of the protein simulated in the crystal confinement versus in solution, and we observed the effect of that confinement in the mobility of the protein residues. Restraining one-third of Cα atoms based on experimental B-factors produce lower B-factors than simulations without restraints, showing that the position restraint of the atoms with the lowest experimental B-factor is a good strategy to maintain the geometry of the crystal with an obvious decrease in the degrees of motion of the protein. PCA shows that, as position restraint reduces the conformational space explored by the system, the motion of the crystal is better recovered, for an essential subspace of the same size, in the simulations without restraints. Restraining only one Cα seems to be a good balance between giving flexibility to the system and preserving its structure. Communicated by Ramaswamy H. Sarma.

High mobility of lattice molecules and defects during the early stage of protein crystallization

Protein crystals are expected to be useful not only for their molecular structure analysis but also as functional materials due to their unique properties. Although the generation and the propagation of defects during crystallization play critical roles in the final properties of protein crystals, the dynamics of these processes are poorly understood. By time-resolved liquid-cell transmission electron microscopy, we observed that nanosized crystal defects are surprisingly mobile during the early stages of the crystallization of a lysozyme as a model protein. This highly dynamic behavior of defects reveals that the lattice molecules are mobile throughout the crystal structure. Moreover, the disappearance of the defects indicated that intermolecular bonds can break and reform rapidly with little energetic cost, as reported in theoretical studies. All these findings are in marked contrast to the generally accepted notion that crystal lattices are rigid with very limited mobility of individual lattice molecules.

Manipulating Solid-State Intramolecular Motion toward Controlled Fluorescence Patterns

Molecules have limited mobility in the solid state because of the strong intermolecular interactions, and therefore, applications based on solid-state molecular motions are seldom explored. Herein, by manipulating the solid-state intramolecular motion of tetraphenylethylene (TPE) in a crystallizing polymer matrix, controlled fluorescent patterns with information storage and encoding functionality are developed. The intramolecular mobility of TPE can not only affect the fluorescence intensity but also determine the photocyclization activity, which can be tuned by surrounding polymer rigidity. The soft amorphous region in the semicrystalline polymer facilitates the intramolecular motion to achieve weak blue emission and high photocyclization activity, whereas the rigid crystalline phase restricts the intramolecular motion to give intense blue emission and low photoreactivity. Meanwhile, in the process of crystallization, the dynamic movement of the polymer chain in the crystal growth boundary layer further accelerates the intramolecular motions of TPE, allowing enhanced photoreactivity across crystalline and amorphous regions. The motion-dominated fluorescence allows TPE as a smart molecular robot to generate desired fluorescent patterns triggered by polymer crystallization. Our findings provide a correlation between microscopic molecular motions and macroscopic optical signals.

Liquid-like and rigid-body motions in molecular-dynamics simulations of a crystalline protein

To gain insight into crystalline protein dynamics, we performed molecular-dynamics (MD) simulations of a periodic 2 × 2 × 2 supercell of staphylococcal nuclease. We used the resulting MD trajectories to simulate X-ray diffraction and to study collective motions. The agreement of simulated X-ray diffraction with the data is comparable to previous MD simulation studies. We studied collective motions by analyzing statistically the covariance of alpha-carbon position displacements. The covariance decreases exponentially with the distance between atoms, which is consistent with a liquidlike motions (LLM) model, in which the protein behaves like a soft material. To gain finer insight into the collective motions, we examined the covariance behavior within a protein molecule (intraprotein) and between different protein molecules (interprotein). The interprotein atom pairs, which dominate the overall statistics, exhibit LLM behavior; however, the intraprotein pairs exhibit behavior that is consistent with a superposition of LLM and rigid-body motions (RBM). Our results indicate that LLM behavior of global dynamics is present in MD simulations of a protein crystal. They also show that RBM behavior is detectable in the simulations but that it is subsumed by the LLM behavior. Finally, the results provide clues about how correlated motions of atom pairs both within and across proteins might manifest in diffraction data. Overall, our findings increase our understanding of the connection between molecular motions and diffraction data and therefore advance efforts to extract information about functionally important motions from crystallography experiments.

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.

Microsecond Protein Dynamics from Combined Bloch-McConnell and Near-Rotary-Resonance R1p Relaxation-Dispersion MAS NMR

Studying protein dynamics on microsecond-to-millisecond (μs-ms) time scales can provide important insight into protein function. In magic-angle-spinning (MAS) NMR, μs dynamics can be visualized by R 1 ρ rotating-frame relaxation dispersion experiments in different regimes of radio-frequency field strengths: at low RF field strength, isotropic-chemical-shift fluctuation leads to "Bloch-McConnell-type" relaxation dispersion, while when the RF field approaches rotary resonance conditions bond angle fluctuations manifest as increased R 1 ρ rate constants ("Near-Rotary-Resonance Relaxation Dispersion", NERRD). Here we explore the joint analysis of both regimes to gain comprehensive insight into motion in terms of geometric amplitudes, chemical-shift changes, populations and exchange kinetics. We use a numerical simulation procedure to illustrate these effects and the potential of extracting exchange parameters, and apply the methodology to the study of a previously described conformational exchange process in microcrystalline ubiquitin.

Mechanistic Insights into Microsecond Time-Scale Motion of Solid Proteins Using Complementary 15N and 1H Relaxation Dispersion Techniques

NMR relaxation dispersion methods provide a holistic way to observe microsecond time-scale protein backbone motion both in solution and in the solid state. Different nuclei (¹H and ¹⁵N) and different relaxation dispersion techniques (Bloch-McConnell and near-rotary-resonance) give complementary information about the amplitudes and time scales of the conformational dynamics and provide comprehensive insights into the mechanistic details of the structural rearrangements. In this paper, we exemplify the benefits of the combination of various solution- and solid-state relaxation dispersion methods on a microcrystalline protein (α-spectrin SH3 domain), for which we are able to identify and model the functionally relevant conformational rearrangements around the ligand recognition loop occurring on multiple microsecond time scales. The observed loop motions suggest that the SH3 domain exists in a binding-competent conformation in dynamic equilibrium with a sterically impaired ground-state conformation both in solution and in crystalline form. This inherent plasticity between the interconverting macrostates is compatible with a conformational-preselection model and provides new insights into the recognition mechanisms of SH3 domains.

What Drives 15N Spin Relaxation in Disordered Proteins? Combined NMR/MD Study of the H4 Histone Tail

Backbone (¹⁵N) NMR relaxation is one of the main sources of information on dynamics of disordered proteins. Yet, we do not know very well what drives ¹⁵N relaxation in such systems, i.e., how different forms of motion contribute to the measurable relaxation rates. To address this problem, we have investigated, both experimentally and via molecular dynamics simulations, the dynamics of a 26-residue peptide imitating the N-terminal portion of the histone protein H4. One part of the peptide was found to be fully flexible, whereas the other part features some transient structure (a hairpin stabilized by hydrogen bonds). The following motional modes proved relevant for ¹⁵N relaxation. 1) Sub-picosecond librations attenuate relaxation rates according to S² ∼0.85-0.90. 2) Axial peptide-plane fluctuations along a stretch of the peptide chain contribute to relaxation-active dynamics on a fast timescale (from tens to hundreds of picoseconds). 3) φ/ψ backbone jumps contribute to relaxation-active dynamics on both fast (from tens to hundreds of picoseconds) and slow (from hundreds of picoseconds to a nanosecond) timescales. The major contribution is from polyproline II (PPII) ↔ β transitions in the Ramachandran space; in the case of glycine residues, the major contribution is from PPII ↔ (β) ↔ rPPII transitions, in which rPPII is the mirror-image (right-handed) version of the PPII geometry, whereas β geometry plays the role of an intermediate state. 4) Reorientational motion of certain (sufficiently long-lived) elements of transient structure, i.e., rotational tumbling, contributes to slow relaxation-active dynamics on ∼1-ns timescale (however, it is difficult to isolate this contribution). In conclusion, recent advances in the area of force-field development have made it possible to obtain viable Molecular Dynamics models of protein disorder. After careful validation against the experimental relaxation data, these models can provide a valuable insight into mechanistic origins of spin relaxation in disordered peptides and proteins.

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.

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.

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.

Localizing Conformational Hinges by NMR: Where Do Hepatitis B Virus Core Proteins Adapt for Capsid Assembly?

The hepatitis B virus (HBV) icosahedral nucleocapsid is assembled from 240 chemically identical core protein molecules and, structurally, comprises four groups of symmetrically nonequivalent subunits. We show here that this asymmetry is reflected in solid-state NMR spectra of the capsids, in which peak splitting is observed for a subset of residues. We compare this information to dihedral angle variations from available 3D structures and also to computational predictions of "dynamic" domains and molecular hinges. We find that although, at the given resolution, dihedral angles variations directly obtained from the X-ray structures are not precise enough to be interpreted, the chemical-shift information from NMR correlates, and interestingly goes beyond, information from bioinformatics approaches. Our study reveals the high sensitivity with which NMR can detect the residues allowing the subtle conformational adaptations needed in lattice formation. Our findings are important for understanding the formation and modulation of protein assemblies in general.

Dynamics and Interactions of a 29 kDa Human Enzyme Studied by Solid-State NMR

Solid-state NMR has been employed for characterization of a broad range of biomacromolecules and supramolecular assemblies. However, because of limitations in sensitivity and resolution, the size of the individual monomeric units has rarely exceeded 15 kDa. As such, enzymes, which are often more complex and comprise long peptide chains, have not been easily accessible, even though manifold desirable information could potentially be provided by solid-state NMR studies. Here, we demonstrate that more than 1200 backbone and side-chain chemical shifts can be reliably assessed from minimal sample quantities for a 29 kDa human enzyme of the carbonic anhydrase family, giving access to its backbone dynamics and intermolecular interactions with a small-molecule inhibitor. The possibility of comprehensive assessment of enzymes in this molecular-weight regime without molecular-tumbling-derived limitations enables the study of residue-specific properties important for their mode of action as well as for pharmacological interference in this and many other enzymes.

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.

Protein crystal lattices are dynamic assemblies: the role of conformational entropy in the protein condensed phase

Until recently, the occurrence of conformational entropy in protein crystal contacts was considered to be a very unlikely event. A study based on the most accurately refined protein structures demonstrated that side-chain conformational entropy and static disorder might be common in protein crystal lattices. The present investigation uses structures refined using ensemble refinement to show that although paradoxical, conformational entropy is likely to be the major factor in the emergence and integrity of the protein condensed phase. This study reveals that the role of shape entropy and local entropic forces expands beyond the onset of crystallization. For the first time, the complete pattern of intermolecular interactions by protein atoms in crystal lattices is presented, which shows that van der Waals interactions dominate in crystal formation.

New applications of solid-state NMR in structural biology

Various recent developments in solid-state nuclear magnetic resonance (ssNMR) spectroscopy have enabled an array of new insights regarding the structure, dynamics, and interactions of biomolecules. In the ever more integrated world of structural biology, ssNMR studies provide structural and dynamic information that is complementary to the data accessible by other means. ssNMR enables the study of samples lacking a crystalline lattice, featuring static as well as dynamic disorder, and does so independent of higher-order symmetry. The present study surveys recent applications of biomolecular ssNMR and examines how this technique is increasingly integrated with other structural biology techniques, such as (cryo) electron microscopy, solution-state NMR, and X-ray crystallography. Traditional ssNMR targets include lipid bilayer membranes and membrane proteins in a lipid bilayer environment. Another classic application has been in the area of protein misfolding and aggregation disorders, where ssNMR has provided essential structural data on oligomers and amyloid fibril aggregates. More recently, the application of ssNMR has expanded to a growing array of biological assemblies, ranging from non-amyloid protein aggregates, protein–protein complexes, viral capsids, and many others. Across these areas, multidimensional magic angle spinning (MAS) ssNMR has, in the last decade, revealed three-dimensional structures, including many that had been inaccessible by other structural biology techniques. Equally important insights in structural and molecular biology derive from the ability of MAS ssNMR to probe information beyond comprehensive protein structures, such as dynamics, solvent exposure, protein–protein interfaces, and substrate–enzyme interactions.

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.

Hydrogen bond strength in membrane proteins probed by time-resolved 1H-detected solid-state NMR and MD simulations

¹H-detected solid-state NMR in combination with ¹H/²D exchange steps allows for the direct identification of very strong hydrogen bonds in membrane proteins. On the example of the membrane-embedded potassium channel KcsA, we quantify the longevity of such very strong hydrogen bonds by combining time-resolved ¹H-detected solid-state NMR experiments and molecular dynamics simulations. In particular, we show that the carboxyl-side chain of the highly conserved residue Glu51 is involved in ultra-strong hydrogen bonds, which are fully-water-exposed and yet stable for weeks. The astonishing stability of these hydrogen bonds is important for the structural integrity of potassium channels, which we further corroborate by computational studies.

Mollib: a molecular and NMR data analysis software

Mollib is a software framework for the analysis of molecular structures, properties and data with an emphasis on data collected by NMR. It uses an open source model and a plugin framework to promote community-driven development of new and enhanced features. Mollib includes tools for the automatic retrieval and caching of protein databank (PDB) structures, the hydrogenation of biomolecules, the analysis of backbone dihedral angles and hydrogen bonds, and the fitting of residual dipolar coupling (RDC) and residual anisotropic chemical shift (RACS) data. In this article, we release version 1.0 of mollib and demonstrate its application to common molecular and NMR data analyses.

Protein conformational dynamics studied by 15N and 1H R1ρ relaxation dispersion: Application to wild-type and G53A ubiquitin crystals

Solid-state NMR spectroscopy can provide site-resolved information about protein dynamics over many time scales. Here we combine protein deuteration, fast magic-angle spinning (~45-60kHz) and proton detection to study dynamics of ubiquitin in microcrystals, and in particular a mutant in a region that undergoes microsecond motions in a β-turn region in the wild-type protein. We use ¹⁵N R_1ρ relaxation measurements as a function of the radio-frequency (RF) field strength, i.e. relaxation dispersion, to probe how the G53A mutation alters these dynamics. We report a population-inversion of conformational states: the conformation that in the wild-type protein is populated only sparsely becomes the predominant state. We furthermore explore the potential to use amide-¹H R_1ρ relaxation to obtain insight into dynamics. We show that while quantitative interpretation of ¹H relaxation remains beyond reach under the experimental conditions, due to coherent contributions to decay, one may extract qualitative information about flexibility.

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.