Motional displacements in proteins: The origin of wave-vector-dependent values

Differences between calcium rich and depleted alpha-lactalbumin investigated by molecular dynamics simulations and incoherent neutron scattering

We present a study comparing atomic motional amplitudes in calcium rich and depleted alpha-lactalbumin. The investigations were performed by elastic incoherent neutron scattering (EINS) and molecular dynamics (MD) simulations. As the variations were expected to be very small, three different hydration levels and timescales (instrumental resolutions) were measured. In addition, we used two models to extract the mean square displacements (MSDs) from the EINS data, one taking into account the motional heterogeneity of the MSD. At a timescale of several nanoseconds, small differences in the amplitudes between the calcium enriched and depleted alpha-lactalbumin are visible, whereas at lower timescales no changes can be concluded within the statistics. The results are compared to MD simulations at 280 and 300 K by extracting the MSDs of the trajectories in two separate ways: first by direct calculation, and second by a virtual neutron experiment using the same models as for the experimental data. We show that the simulated data give qualitatively similar results as the experimental data but quantitatively there are differences. Furthermore, the distribution of the MSDs in the simulations suggests that the inclusion of heterogeneity is reasonable for alpha-lactalbumin, but a bi-or trimodal approach may be sufficient.

Analysis of elastic incoherent neutron scattering data beyond the Gaussian approximation

This work addresses the use of the Gaussian approximation as a common tool to extract atomic motions in proteins from elastic incoherent neutron scattering and whether improvements in data analysis and additional information can be obtained when going beyond that. We measured alpha-lactalbumin with different levels of hydration on three neutron backscattering spectrometers, to be able to resolve a wide temporal and spatial range for dynamics. We demonstrate that the Gaussian approximation gives qualitatively similar results to models that include heterogeneity, if one respects a certain procedure to treat the intercept of the elastic intensities with the momentum transfer axis. However, the inclusion of motional heterogeneity provides better fits to the data. Our analysis suggests an approach of limited heterogeneity, where including only two kinds of motions appears sufficient to obtain more quantitative results for the mean square displacement. Finally, we note that traditional backscattering spectrometers pose a limit on the lowest accessible momentum transfer. We therefore suggest that complementary information about the spatial evolution of the elastic intensity close to zero momentum transfer can be obtained using other neutron methods, in particular, neutron spin-echo together with polarization analysis.

Neutron scattering in the biological sciences: progress and prospects

The scattering of neutrons can be used to provide information on the structure and dynamics of biological systems on multiple length and time scales. Pursuant to a National Science Foundation-funded workshop in February 2018, recent developments in this field are reviewed here, as well as future prospects that can be expected given recent advances in sources, instrumentation and computational power and methods. Crystallography, solution scattering, dynamics, membranes, labeling and imaging are examined. For the extraction of maximum information, the incorporation of judicious specific deuterium labeling, the integration of several types of experiment, and interpretation using high-performance computer simulation models are often found to be particularly powerful.

Determination of Dynamical Heterogeneity from Dynamic Neutron Scattering of Proteins

Motional displacements of hydrogen (H) in proteins can be measured using incoherent neutron-scattering methods. These displacements can also be calculated numerically using data from molecular dynamics simulations. An enormous amount of data on the average mean-square motional displacement (MSD) of H as a function of protein temperature, hydration, and other conditions has been collected. H resides in a wide spectrum of sites in a protein. Some H are tightly bound to molecular chains, and the H motion is dictated by that of the chain. Other H are quite independent. As a result, there is a distribution of motions and MSDs of H within a protein that is denoted dynamical heterogeneity. The goal of this paper is to incorporate a distribution of MSDs into models of the H incoherent intermediate scattering function, I(Q,t), that is calculated and observed. The aim is to contribute information on the distribution as well as on the average MSD from comparison of the models with simulations and experiment. For example, we find that simulations of I(Q,t) in lysozyme are well reproduced if the distribution of MSDs is bimodal with two broad peaks rather than a single broad peak.

Dynamic Neutron Scattering by Biological Systems

Dynamic neutron scattering directly probes motions in biological systems on femtosecond to microsecond timescales. When combined with molecular dynamics simulation and normal mode analysis, detailed descriptions of the forms and frequencies of motions can be derived. We examine vibrations in proteins, the temperature dependence of protein motions, and concepts describing the rich variety of motions detectable using neutrons in biological systems at physiological temperatures. New techniques for deriving information on collective motions using coherent scattering are also reviewed.

Critical structural fluctuations of proteins upon thermal unfolding challenge the Lindemann criterion

Internal subnanosecond timescale motions are key for the function of proteins, and are coupled to the surrounding solvent environment. These fast fluctuations guide protein conformational changes, yet their role for protein stability, and for unfolding, remains elusive. Here, in analogy with the Lindemann criterion for the melting of solids, we demonstrate a common scaling of structural fluctuations of lysozyme protein embedded in different environments as the thermal unfolding transition is approached. By combining elastic incoherent neutron scattering and advanced molecular simulations, we show that, although different solvents modify the protein melting temperature, a unique dynamical regime is attained in proximity of thermal unfolding in all solvents that we tested. This solvation shell-independent dynamical regime arises from an equivalent sampling of the energy landscape at the respective melting temperatures. Thus, we propose that a threshold for the conformational entropy provided by structural fluctuations of proteins exists, beyond which thermal unfolding is triggered.

The role of momentum transfer during incoherent neutron scattering is explained by the energy landscape model

We recently introduced a model of incoherent quasielastic neutron scattering (QENS) that treats the neutrons as wave packets of finite length and the protein as a random walker in the free energy landscape. We call the model ELM for "energy landscape model." In ELM, the interaction of the wave packet with a proton in a protein provides the dynamic information. During the scattering event, the momentum [Formula: see text] is transferred by the wave packet to the struck proton and its moiety, exerting the force [Formula: see text] The resultant energy [Formula: see text] is stored elastically and returned to the neutron as it exits. The energy is given by [Formula: see text], where [Formula: see text] is the ambient temperature and [Formula: see text] ([Formula: see text] 91 K Å) is a new elastobaric coefficient. Experiments yield the scattering intensity (dynamic structure factor) [Formula: see text] as a function of [Formula: see text] and [Formula: see text] To test our model, we use published data on proteins where only thermal vibrations are active. ELM competes with the currently accepted theory, here called the spatial motion model (SMM), which explains [Formula: see text] by motions in real space. ELM is superior to SMM: It can explain the experimental angular and temperature dependence, whereas SMM cannot do so.

The fluctuating ribosome: thermal molecular dynamics characterized by neutron scattering

Conformational changes associated with ribosome function have been identified by X-ray crystallography and cryo-electron microscopy. These methods, however, inform poorly on timescales. Neutron scattering is well adapted for direct measurements of thermal molecular dynamics, the ‘lubricant’ for the conformational fluctuations required for biological activity. The method was applied to compare water dynamics and conformational fluctuations in the 30 S and 50 S ribosomal subunits from Haloarcula marismortui, under high salt, stable conditions. Similar free and hydration water diffusion parameters are found for both subunits. With respect to the 50 S subunit, the 30 S is characterized by a softer force constant and larger mean square displacements (MSD), which would facilitate conformational adjustments required for messenger and transfer RNA binding. It has been shown previously that systems from mesophiles and extremophiles are adapted to have similar MSD under their respective physiological conditions. This suggests that the results presented are not specific to halophiles in high salt but a general property of ribosome dynamics under corresponding, active conditions. The current study opens new perspectives for neutron scattering characterization of component functional molecular dynamics within the ribosome.

Bile Acid Recognition by NAPE-PLD

The membrane-associated enzyme NAPE-PLD (N-acyl phosphatidylethanolamine specific-phospholipase D) generates the endogenous cannabinoid arachidonylethanolamide and other lipid signaling amides, including oleoylethanolamide and palmitoylethanolamide. These bioactive molecules play important roles in several physiological pathways including stress and pain response, appetite, and lifespan. Recently, we reported the crystal structure of human NAPE-PLD and discovered specific binding sites for the bile acid deoxycholic acid. In this study, we demonstrate that in the presence of this secondary bile acid, the stiffness of the protein measured by elastic neutron scattering increases, and NAPE-PLD is ∼7 times faster to catalyze the hydrolysis of the more unsaturated substrate N-arachidonyl-phosphatidylethanolamine, compared with N-palmitoyl-phosphatidylethanolamine. Chenodeoxycholic acid and glyco- or tauro-dihydroxy conjugates can also bind to NAPE-PLD and drive its activation. The only natural monohydroxy bile acid, lithocholic acid, shows an affinity of ∼20 μM and acts instead as a reversible inhibitor (IC₅₀ ≈ 68 μM). Overall, these findings provide important insights into the allosteric regulation of the enzyme mediated by bile acid cofactors and reveal that NAPE-PLD responds primarily to the number and position of their hydroxyl groups.

Quasielastic neutron scattering in biology: Theory and applications

Neutrons scatter quasielastically from stochastic, diffusive processes, such as overdamped vibrations, localized diffusion and transitions between energy minima. In biological systems, such as proteins and membranes, these relaxation processes are of considerable physical interest. We review here recent methodological advances and applications of quasielastic neutron scattering (QENS) in biology, concentrating on the role of molecular dynamics simulation in generating data with which neutron profiles can be unambiguously interpreted. We examine the use of massively-parallel computers in calculating scattering functions, and the application of Markov state modeling. The decomposition of MD-derived neutron dynamic susceptibilities is described, and the use of this in combination with NMR spectroscopy. We discuss dynamics at very long times, including approximations to the infinite time mean-square displacement and nonequilibrium aspects of single-protein dynamics. Finally, we examine how neutron scattering and MD can be combined to provide information on lipid nanodomains. This article is part of a Special Issue entitled "Science for Life" Guest Editor: Dr. Austen Angell, Dr. Salvatore Magazù and Dr. Federica Migliardo.

Anomalous and anisotropic nanoscale diffusion of hydration water molecules in fluid lipid membranes

We have studied nanoscale diffusion of membrane hydration water in fluid-phase lipid bilayers made of 1,2-dimyristoyl-3-phosphocholine (DMPC) using incoherent quasi-elastic neutron scattering. Dynamics were fit directly in the energy domain using the Fourier transform of a stretched exponential. By using large, 2-dimensional detectors, lateral motions of water molecules and motions perpendicular to the membranes could be studied simultaneously, resulting in 2-dimensional maps of relaxation time, τ, and stretching exponent, β. We present experimental evidence for anomalous (sub-diffusive) and anisotropic diffusion of membrane hydration water molecules over nanometer distances. By combining molecular dynamics and Brownian dynamics simulations, the potential microscopic origins for the anomaly and anisotropy of hydration water were investigated. Bulk water was found to show intrinsic sub-diffusive motion at time scales of several picoseconds, likely related to caging effects. In membrane hydration water, however, the anisotropy of confinement and local dynamical environments leads to an anisotropy of relaxation times and stretched exponents, indicative of anomalous dynamics.