In biomembranes, lipid mobility exhibits deviations from the classical diffusive behavior of Brownian particles, i.e., “anomalous” diffusion. The question arises as to how this anomalous diffusive behavior varies in gel, ripple, and fluid biomembrane phases. In this study, we perform all-atom molecular dynamics simulations of dimyristoylphosphatidylcholine bilayers in the three different phases and analyze the results using the framework of the generalized Langevin equation. This analysis emphasizes subdiffusive behavior on the relatively short, picosecond to nanosecond timescales, capturing local molecular constraints and transient caging effects during the crossover of atomic dynamics from vibrational to incipient anharmonic motion. The ripple and gel phases are found to exhibit strong transient caging and prolonged memory effects resulting in distinct subdiffusive behavior. The role of hydrogen bonding in lipid confinement is also examined, demonstrating its influence on phase-dependent molecular ordering and on short-time diffusional constraints. These findings demonstrate the generalized Langevin equation framework’s utility in characterizing molecular transport and lipid dynamics, with implications for longer timescale membrane dynamics.

Within the last decades, it was often assumed that in hydrogen-rich disordered samples, such as proteins in solution or hydrated powder form, incoherent neutron scattering from hydrogen nuclei dominated the scattering signal to an extent that allowed all other contributions to be neglected. As incoherent scattering arises solely from self-correlations, it further justified such a choice. Consequently, heavy water was often used as a contrast tool to highlight molecular motions in live samples. Coherent scattering, which implies the scattering from many nuclei and therefore collective processes, is another non-negligible contribution to neutron scattering where cross sections of other nuclei than hydrogen are significant. The recent advent of instrumentation based on polarization of neutron beams and the analysis of their polarization state after scattering for dynamical studies allows us to separate and shed light on the two contributions. In the present study we reveal that, unexpectedly, the isotopic exchange of water in the hydration shell of proteins arises on a much faster timescale than assumed so far. Moreover, the collective and local D-bond network relaxation of hydration water contributes to a high extent to the coherent scattering signal, at odds with usual “static” approaches used to estimate the relative impacts of dynamics in the sample. Hence, hydration water necessarily contaminates nonpolarized standard experiments. The findings are of paramount importance for all neutron scattering experiments where partial or full deuteration is used. Published by the American Physical Society 2024

We present an analysis of high-resolution quasi-elastic neutron scattering spectra of phosphoglycerate kinase which elucidates the influence of the enzymatic activity on the dynamics of the protein. We show that in the active state the inter-domain motions are amplified and the intra-domain asymptotic power-law relaxation ∝t-α is accelerated, with a reduced coefficient α. Employing an energy landscape picture of protein dynamics, this observation can be translated into a widening of the distribution of energy barriers separating conformational substates of the protein.

Quasi-elastic neutron scattering (QENS) from bulk-water at 300 K, measured on the IRIS backscattering neutron spectrometer (ISIS, UK), is interpreted using the jump diffusion model (JDM), a “minimalistic” multi-timescale relaxation model (MRM) and molecular dynamics simulations (MD). In the case of MRM data analysis is performed in the time domain, where the relaxation of the intermediate scattering function is described by a stretched Mittag-Leffler function, E α (−(| t |/ τ ) α ). This function displays an asymptotic power law decay and contains the exponential relaxation function as a special case ( α = 1). To further compare the two approaches, MD simulations of bulk water were performed using the SPCE force field and the resulting MD trajectories analysed using the nMoldyn software. We show that both JDM and MRM accurately describe the diffusion of bulk water observed by QENS at all length scales, and confirm that MD simulations do not fully describe the quantum effects of jump diffusion.

Elastic neutron scattering from proteins reflects the motional amplitudes resulting from their internal collective and single-atom dynamics and is observable if the global diffusion of whole molecules is either blocked or cannot be resolved by the spectrometer under consideration. Due to finite instrumental resolution, the measured elastic scattering amplitude always contains contaminations from quasielastic neutron scattering and some model must be assumed to extract the resolution-corrected counterpart from corresponding experimental spectra. Here, we derive a quasi-analytical method for that purpose, assuming that the intermediate scattering function relaxes with a "stretched" Mittag-Leffler function, Eα(-(t/τ)α) (0 < α < 1), toward the elastic amplitude and that the instrumental resolution function has Gaussian form. The corresponding function can be integrated into a fitting procedure and allows for eliminating the elastic intensity as a fit parameter. We illustrate the method for the analysis of two proteins in solution, the intrinsically disordered Myelin Basic Protein, confirming recently published results [Hassani et al., J. Chem. Phys. 156, 025102 (2022)], and the well-folded globular protein myoglobin. We also briefly discuss the consequences of our findings for the extraction of mean square position fluctuations from elastic scans.

We show that time autocorrelation functions exhibiting an asymptotic power law decay similar to t(-rho)/Gamma(1 - rho) take the form of a "stretched" Mittag-Leffler function, E rho(-(t/tau)rho), if the associated memory function attains its asymptotic form on a time scale which is much shorter than the characteristic time scale of the asymptotic regime itself. The range for the exponent is here restricted to if 0 < rho < 1 and we show that the time scale separation can be enforced by downscaling the amplitude of the memory function. Reasoning along the same lines, we demonstrate that the velocity autocorrelation function of an anomalously diffusing particle behaves as E2-alpha(-(t/tau(D))(2-alpha)) if the associated memory function attains its asymptotic form on time scales much shorter than the diffusion time scale, tau(D). The exponent a defines here the asymptotic form of its mean square displacement, <(x(t) - x(0))(2)> similar to t(alpha), and 0 < alpha < 2.

The main characteristic of liquid water is the formation of dynamic hydrogen bond networks that occur over a broad range of time scales from tens of femtoseconds to picoseconds and are responsible for water's unique properties. However, in many important processes water does not exist in its bulk form, but in confined nanometer scale environments. The investigation of this confined water dynamics is challenging since the intermediate strength of the hydrogen bonds makes it possible to alter the structure and dynamics of this constrained water. Even if no single experimental technique can give a full picture of such intricate dynamics, it is well established that quasielastic neutron scattering (QENS) is a powerful tool to study the modification of hydrogen bonds in confinement in various materials. This is possible because neutrons tell us where the atoms are and what they are doing, can detect hydrogen, are penetrative and non-destructive. Furthermore, QENS is the only spectroscopic technique that provides information on the dynamics and atomic-motion amplitudes over a predetermined length scale. However scientific value of these data is hardly exploited and never to its full potential. This perspective highlights how new developments on instrumentation and data analysis will lead to appreciable progress in our understanding of the dynamics of complex systems, ranging from biological organisms to cloud formation.

We report an analysis of high-resolution quasielastic neutron scattering spectra from Myelin Basic Protein (MBP) in solution, comparing the spectra at three different temperatures (283, 303, and 323 K) for a pure D2O buffer and a mixture of D2O buffer with 30% of deuterated trifluoroethanol (TFE). Accompanying experiments with dynamic light scattering and Circular Dichroism (CD) spectroscopy have been performed to obtain, respectively, the global diffusion constant and the secondary structure content of the molecule for both buffers as a function of temperature. Modeling the decay of the neutron intermediate scattering function by the Mittag-Leffler relaxation function, ϕ(t) = Eα(-(t/τ)α) (0 < α < 1), we find that trifluoroethanol slows down the relaxation dynamics of the protein at 283 K and leads to a broader relaxation rate spectrum. This effect vanishes with increasing temperature, and at 323 K, its relaxation dynamics is identical in both solvents. These results are coherent with the data from dynamic light scattering, which show that the hydrodynamic radius of MBP in TFE-enriched solutions does not depend on temperature and is only slightly smaller compared to the pure D2O buffer, except for 283 K, where it is much reduced. In accordance with these observations, the CD spectra reveal that TFE induces essentially a partial transition from β-strands to α-helices, but only a weak increase in the total secondary structure content, leaving about 50% of the protein unfolded. The results show that MBP is for all temperatures and in both buffers an intrinsically disordered protein and that TFE essentially induces a reduction in its hydrodynamic radius and its relaxation dynamics at low temperatures.

Using a minimal model approach for interpreting the intermediate scattering function, F(Q t), to analyze quasi-elastic neutron scattering (QENS) data from interlayer water as a function of temperature in the 2D-layered clay minerals montmorillonite (Mt) and hectorite (Ht) a clear difference in behavior was observed. This was related to the polarization effect induced on the water molecules by both the exchangeable cation and surface charge within the interlayer. Although crucial for improving the wide range of industrial applications of clays as well as for explaining water uptake and retention by clays such information is neither obtained straightforwardly by other experimental methods nor fully accounted by molecular dynamics simulations. Furthermore, analysis of the evolution of the fitted parameters as a function of temperature shows that hydrogen atoms have a relaxation with a smaller average motional amplitude for Mt. Physically this can be explained as stronger hydrogen-bonding by water at the interlayer surfaces in Mt. These results allow for a novel and realistic description of these nanomaterials at the atomic scale, which is crucial for improving functional properties. These findings also prove that this new approach to modeling QENS captures subtle changes hidden in the spectra.

The Mittag-Leffler (ML) relaxation function, E(-t(alpha)) (0 < alpha <= 1), describes multiscale relaxation processes with a broad range of relaxation rates, where alpha = 1 corresponds to exponential relaxation. For 0 < alpha < 1 it decays asymptotically similar to t(alpha) and is thus asymptotically self-similar, i.e. form invariant under a scale transform t -> mu t. In the language of asymptotic analysis, such functions are referred to as regularly varying. Based on this observation we derive a refined, 'weakly self-similar' asymptotic form by applying a theorem due to J Karamata. Reasoning along the same lines, we derive also a corresponding weakly self-similar form for the time derivatives of the ML relaxation function in the short time limit. In both cases the respective asymptotic power law forms are approached by slowly varying functions in the sense of asymptotic analysis and we show that the range of validity of the respective approximations increases strongly with the decrease of alpha.

Doster (1) criticizes a number of points in ref. 2, where a Franck–Condon-type spectroscopic formulation of incoherent neutron scattering is presented. My responses are given below. First, the Franck–Condon formulation of incoherent neutron scattering does not contradict standard scattering theory, and it is even based on it. It merely starts from a nonstandard form of the intermediate scattering function, which is (probably) due to Wick (3), instead from the usual form that appears in the well-known paper by Van Hove (4). As long as the Van Hove form is considered in the quantum regime, both forms are completely equivalent. The two textbook models are presented to … [↵][1]1Email: gerald.kneller{at}cnrs.fr. [1]: #xref-corresp-1-1

This article reports on a frequency domain analysis of quasielastic neutron scattering spectra from free and Huperzine-A-inhibited human acetylcholinesterase, extending a recent time domain analysis of the same experimental data [M. Saouessi et al., J. Chem. Phys. 150, 161104 (2019)]. An important technical point here is the construction of a semianalytical model for the resolution-broadened dynamic structure factor that can be fitted to the experimental spectra. We find comparable parameters as in our previous study and demonstrate that our model is sensitive to subpercent changes in the experimental data, which are caused by reversible binding of the inhibitor Huperzine A.

In this paper, we show that ensembles of well-structured and unstructured proteins can be distinguished by borrowing concepts from non-equilibrium statistical mechanics. For this purpose, we represent proteins by two different polymer models and interpret the resulting polymer configurations as random walks of a diffusing particle in space. The first model is the trace of the Cα-atoms along the protein main chain, and the second is their projections onto the protein axis. The resulting trajectories are subsequently analyzed using the theory of the generalized Langevin equation. Velocities are replaced by displacements relating consecutive points on the discrete protein axes and equilibrium ensemble averages by averages over appropriate protein structure ensembles. The resulting displacement autocorrelation functions resemble those of the velocity autocorrelation functions of simple liquids and display a minimum, which can be related to the lengths of secondary structure elements. This minimum is clearly more pronounced for well-structured proteins than for unstructured ones, and the corresponding memory function displays a slower decay, indicating a stronger “folding memory.”

In this paper, we show that subtle changes in the internal dynamics of human acetylcholinesterase upon ligand binding can be extracted from quasielastic neutron scattering data by employing a nonexponential relaxation model for the intermediate scattering function. The relaxation is here described by a stretched Mittag-Leffler function, which exhibits slow power law decay for long times. Our analysis reveals that binding of a Huperzine A ligand increases the atomic motional amplitudes of the enzyme and slightly slows down its internal diffusive motions. This result is interpreted within an energy landscape picture for the motion of the hydrogen atoms.