Communication: Probing anomalous diffusion in frequency space

Physica B: Condensed Matter, 1993

Neutron high-resolution spectroscopic studies of biomolecular dynamics have been pursued actively in the last decade due to the recognised role of the microscopic dynamics in determining the functional properties of many biomolecular assemblies. As a result of instrumental advances and progress in molecular dynamics simulations it is nowadays possible to describe quantitatively the complex low-frequency motions exhibited by biologically active systems. Some selected examples referring to different biopolymers and biological membranes will be illustrated.

The Journal of Physical Chemistry B, 1997

Translational diffusion of molecules in one-dimensional channel systems has been measured by quasi-elastic neutron scattering. The scattering function for a single-file diffusion model has been derived in order to differentiate this transport model from normal 1D diffusion. In the AlPO 4 -5 structure, ordinary 1D diffusion is observed for methane and ethane, whatever the loading, which indicates that the molecules are able to pass each other. The diffusion coefficients for both molecules are on the order of 10 -9 m 2 s -1 . On the other hand, a quite different regime is obtained by varying cyclopropane concentration in the same structure. At low loading, normal 1D diffusion is observed because the molecules can be considered as isolated, but at higher concentration cyclopropane is found to follow single-file diffusion. However, the mobility is too small to be determined. In the less open channel system of ZSM-48, ordinary 1D diffusion is found for small methane concentration, the diffusion coefficient being 2.5 × 10 -9 m 2 s -1 , at 155 K. At medium loading, single-file diffusion is observed with a mobility factor of 2 × 10 -12 m 2 s -1/2 . This is the first time that this technique has provided experimental evidence of single-file diffusion in zeolites.

Physica B: Condensed Matter, 1992

Neutron high-resolution spectroscopic studies of biomolecular dynamics have been pursued actively in the last decade due to the recognised role of the microscopic dynamics in determining the functional properties of many biomolecular assemblies. As a result of instrumental advances and progress in molecular dynamics simulations it is nowadays possible to describe quantitatively the complex low-frequency motions exhibited by biologically active systems. Some selected examples referring to different biopolymers and biological membranes will be illustrated.

ISRN Biophysics, 2013

Diffusion is the fundamental mechanism for lipids and other molecules to move in a membrane. It is an important process to consider in modelling the formation of membrane structures, such as rafts. Lipid diffusion is mainly studied by two different techniques: incoherent neutron scattering and fluorescence microscopy. Both techniques access distinctly different length scales. While neutron scattering measures diffusion over about 3 lipid diameters, microscopic techniques access motions of lipids over micrometer distances. The diffusion constants which are determined by these two methods often differ by about an order of magnitude, with the neutrons usually seeing a faster lipid diffusion. Different theories are used to describe lipid diffusion in the two experiments. In order to close the “gap” between these two techniques, we propose to study lipid diffusion at mesoscopic length scales using a neutron spin-echo (NSE) spectrometer. We have conducted an experiment in highly oriented,...

New Journal of Physics

The emerging diffusive dynamics in many complex systems show a characteristic crossover behaviour from anomalous to normal diffusion which is otherwise fitted by two independent power-laws. A prominent example for a subdiffusive-diffusive crossover are viscoelastic systems such as lipid bilayer membranes, while superdiffusive-diffusive crossovers occur in systems of actively moving biological cells. We here consider the general dynamics of a stochastic particle driven by so-called tempered fractional Gaussian noise, that is noise with Gaussian amplitude and power-law correlations, which are cut off at some mesoscopic time scale. Concretely we consider such noise with built-in exponential or power-law tempering, driving an overdamped Langevin equation (fractional Brownian motion) and fractional Langevin equation motion. We derive explicit expressions for the mean squared displacement and correlation functions, including different shapes of the crossover behaviour depending on the concrete tempering, and discuss the physical meaning of the tempering. In the case of power-law tempering we also find a crossover behaviour from faster to slower superdiffusion and slower to faster subdiffusion. As a direct application of our model we demonstrate that the obtained dynamics quantitatively describes the subdiffusion-diffusion and subdiffusion-subdiffusion crossover in lipid bilayer systems. We also show that a model of tempered fractional Brownian motion recently proposed by Sabzikar and Meerschaert leads to physically very different behaviour with a seemingly paradoxical ballistic long time scaling.

EPJ Web of Conferences, 2015

For decades, quasi-elastic neutron scattering has been the prime tool for studying molecular diffusion in membranes over relevant nanometer distances. These experiments are essential to our current understanding of molecular dynamics of lipids, proteins and membrane-active molecules. Recently, we presented experimental evidence from X-ray diffraction and quasi-elastic neutron scattering demonstrating that ethanol enhances the permeability of membranes. At the QENS 2014/WINS 2014 conference we presented a novel technique to measure diffusion across membranes employing 2-dimensional quasielastic neutron scattering. We present results from our preliminary analysis of an experiment on the cold neutron multi-chopper spectrometer LET at ISIS, where we studied the self-diffusion of water molecules along lipid membranes and have the possibility of studying the diffusion in membranes. By preparing highly oriented membrane stacks and aligning them horizontally in the spectrometer, our aim is to distinguish between lateral and transmembrane diffusion. Diffusion may also be measured at different locations in the membranes, such as the water layer and the hydrocarbon membrane core. With a complete analysis of the data, 2-dimensional mapping will enable us to determine diffusion channels of water and ethanol molecules to quantitatively determine nanoscale membrane permeability.

Physical Review E, 2009

We use a long, all-atom molecular dynamics (MD) simulation combined with theoretical modeling to investigate the dynamics of selected lipid atoms and lipid molecules in a hydrated diyristoylphosphatidylcholine (DMPC) lipid bilayer. From the analysis of a 0.1 µs MD trajectory we find that the time evolution of the mean square displacement, [δr(t)] 2 , of lipid atoms and molecules exhibits three well separated dynamical regions: (i) ballistic, with [δr(t)] 2 ∼ t 2 for t < ∼ 10 fs; (ii) subdiffusive, with [δr(t)] 2 ∼ t β with β < 1, for 10 ps < ∼ t < ∼ 10 ns; and (iii) Fickian diffusion, with [δr(t)] 2 ∼ t for t > ∼ 30 ns. We propose a memory function approach for calculating [δr(t)] 2 over the entire time range extending from the ballistic to the Fickian diffusion regimes. The results are in very good agreement with the ones from the MD simulations. We also examine the implications of the presence of the subdiffusive dynamics of lipids on the self-intermediate scattering function and the incoherent dynamics structure factor measured in neutron scattering experiments.

Journal of Physics: Condensed Matter, 2011

Quasielastic neutron scattering is a powerful tool for the study of non-periodic motions in condensed matter as a detailed line shape analysis can give information about the geometry and rate of the scatterers' displacements. Unfortunately, there are also a number of artifacts which can masquerade as signatures of motions and can therefore lead to erroneous results. Their influence on the evaluation of the motions of the phospholipid dimyristoylphosphatidylcholine (DMPC) is discussed. On a 60 ps time scale, the long-range motion of the molecules has a flowlike character with similar velocities above and below the main phase transition. It is proposed that the concepts of dynamical heterogeneities and "floppy modes" developed in glass physics provide a framework to explain the observed behaviour.

Spectroscopy, 2010

In the present contribution we present a new procedure for the Mean Square Displacement (MSD) determination from Elastic Incoherent Neutron Scattering (EINS) where the connection between the Self-Distribution Function (SDF) and the measured EINS intensity profile is highlighted. We show how the SDF procedure allows both the total and the partial MSD evaluation, through the total and the partial SDFs. The procedure is applied on EINS data collected, by the IN13 backscattering spectrometer (ILL, Grenoble), on aqueous mixtures of sucrose and trehalose.

The self-diffusion of myoglobin in concentrated solutions was investigated up to volume fractions of 0.4 by neutron back-scattering spectroscopy. The quasi-elastic spectrum can be decomposed into two Lorentz curves: (1) a narrow line, where the width increases with Q, which is assigned to translational diffusion, and (2) a broad Q-independent line, reflecting proteininternal motions. The apparent diffusion coefficient decreases with increasing concentration and wave-vector, suggesting that protein diffusion deviates at high Q (1.75 Å -1 ) from its long-time Brownian limit. Jump diffusion, sample heterogeneity and time-dependent diffusion are discussed as possible explanations.

The Journal of Chemical Physics, 2011

For the first time, the diffusion phase diagram in highly confined colloidal systems, predicted by Continuous Time Random Walk (CTRW), is experimentally obtained. Temporal and spatial fractional exponents, α and µ, introduced within the framework of CTRW, are simultaneously measured by Pulse Field Gradient Nuclear Magnetic Resonance technique in samples of microbeads dispersed in water. We find that α depends on the disorder degree of the system. Conversely, µ depends on both bead sizes and magnetic susceptibility differences within samples. Our findings fully match the CTRW predictions.

Molecular Simulation, 1993

IEEE Communications Letters, 2015

We consider anomalous diffusion to model a molecular communication channel. To account for general and practical molecular propagation, we use the fractional diffusion equation and derive the distribution of first passage time in terms of Fox's H-function. We then analyze the bit error rate for timing and amplitude binary modulation schemes in anomalous diffusion.

Springer Proceedings in Physics, 2019

The determination of the self-diffusion coefficient \( D_{\text{s}} \) is one of well known applications of the quasi-elastic incoherent neutron scattering. Here we will show that the half-width of the neutron peak considered as a function of wave vector can be used for the determination of (1) the residence time \( \tau_{0} \) for water molecules and (2) the very important ratio \( D_{\text{c}} /D_\text{s} \) where \( D_{\text{c}} \) is the collective part of the self-diffusion coefficient, caused by its drift in the field of thermal hydrodynamic fluctuations. The applicability region for the simplest diffusion approximation is discussed in details. The influence of the rotational motion of water molecules on spectra of the intermediate scattering function (ISF) is studied. A new type of the high-frequency asymptote for the ISF-spectra is predicted.

The Journal of Chemical Physics, 2022

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 &lt; α &lt; 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 coher...