Signature of functional enzyme dynamics in quasielastic neutron scattering spectra: The case of phosphoglycerate kinase.

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-analytical resolution-correction of elastic neutron scattering from proteins.

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, E(-(t/τ)) (0 < α < 1), toward the elastic amplitude and that the instrumental resolution function has Gaussian form.

Multiscale relaxation dynamics and diffusion of myelin basic protein in solution studied by quasielastic neutron scattering.

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 DO buffer and a mixture of DO 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) = E(-(t/τ)) (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.

Frequency domain modeling of quasielastic neutron scattering from hydrated protein powders: Application to free and inhibited human acetylcholinesterase.

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.

Asymptotic analysis of quasielastic neutron scattering data from human acetylcholinesterase reveals subtle dynamical changes upon ligand binding.

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.

Memory effects in a random walk description of protein structure ensembles.

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 C-atoms along the protein main chain, and the second is their projections onto the protein axis.

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.

Franck-Condon picture of incoherent neutron scattering.

A spectroscopic interpretation of incoherent neutron scattering experiments is presented which is based on Franck-Condon-type probabilities for scattering-induced transitions between quantum states of the target. The resulting expressions for the scattering functions enable an energy landscape-oriented analysis of neutron scattering spectra as well as a physical interpretation of Van Hove's space-time correlation functions in the quantum regime that accounts for the scattering kinematics. They suggest moreover a combined analysis of quasielastic and elastic scattering that become inseparable for complex systems with slow power-law relaxation.

Communication: A multiscale Bayesian inference approach to analyzing subdiffusion in particle trajectories.

Anomalous diffusion is characterized by its asymptotic behavior for t → ∞. This makes it difficult to detect and describe in particle trajectories from experiments or computer simulations, which are necessarily of finite length. We propose a new approach using Bayesian inference applied directly to the observed trajectories sampled at different time scales.

Asymptotic neutron scattering laws for anomalously diffusing quantum particles.

The paper deals with a model-free approach to the analysis of quasielastic neutron scattering intensities from anomalously diffusing quantum particles. All quantities are inferred from the asymptotic form of their time-dependent mean square displacements which grow ∝t(α), with 0 ≤ α < 2. Confined diffusion (α = 0) is here explicitly included.

Communication: Probing anomalous diffusion in frequency space.

Anomalous diffusion processes are usually detected by analyzing the time-dependent mean square displacement of the diffusing particles. The latter evolves asymptotically as W(t) ∼ 2Dαt(α), where Dα is the fractional diffusion constant and 0 < α < 2. In this article we show that both Dα and α can also be extracted from the low-frequency Fourier spectrum of the corresponding velocity autocorrelation function.

Protein secondary-structure description with a coarse-grained model.

A coarse-grained geometrical model for protein secondary-structure description and analysis is presented which uses only the positions of the C(α) atoms. A space curve connecting these positions by piecewise polynomial interpolation is constructed and the folding of the protein backbone is described by a succession of screw motions linking the Frenet frames at consecutive C(α) positions. Using the ASTRAL subset of the SCOPe database of protein structures, thresholds are derived for the screw parameters of secondary-structure elements and demonstrate that the latter can be reliably assigned on the basis of a C(α) model.

Adaptation of Extremophilic Proteins with Temperature and Pressure: Evidence from Initiation Factor 6.

In this work, we study dynamical properties of an extremophilic protein, Initiation Factor 6 (IF6), produced by the archeabacterium Methanocaldococcus jannascii, which thrives close to deep-sea hydrothermal vents where temperatures reach 80 °C and the pressure is up to 750 bar. Molecular dynamics simulations (MD) and quasi-elastic neutron scattering (QENS) measurements give new insights into the dynamical properties of this protein with respect to its eukaryotic and mesophilic homologue. Results obtained by MD are supported by QENS data and are interpreted within the framework of a fractional Brownian dynamics model for the characterization of protein relaxation dynamics.

Communication: A scaling approach to anomalous diffusion.

The paper presents a rigorous derivation of the velocity autocorrelation function for an anomalously diffusing slow solute particle in a bath of fast solvent molecules. The result is obtained within the framework of the generalized Langevin equation and uses only scaling arguments and identities which are based on asymptotic analysis. It agrees with the velocity autocorrelation function of an anomalously diffusing Rayleigh particle whose dynamics is described by a fractional Ornstein-Uhlenbeck process in velocity space.

Motional heterogeneity in human acetylcholinesterase revealed by a non-Gaussian model for elastic incoherent neutron scattering.

We study the dynamical transition of human acetylcholinesterase by analyzing elastic neutron scattering data with a simulation gauged analytical model that goes beyond the standard Gaussian approximation for the elastic incoherent structure factor [G. R. Kneller and K.

Model-free simulation approach to molecular diffusion tensors.

In the present work, we propose a simple model-free approach for the computation of molecular diffusion tensors from molecular dynamics trajectories. The method uses a rigid body trajectory of the molecule under consideration, which is constructed a posteriori by an accumulation of quaternion-based superposition fits of consecutive conformations. From the rigid body trajectory, we compute the translational and angular velocities of the molecule and by integration of the latter also the corresponding angular trajectory.

A comparison of reduced coordinate sets for describing protein structure.

In all-atom molecular simulation studies of proteins, each atom in the protein is represented by a point mass and interactions are defined in terms of the atomic positions. In recent years, various simplified approaches have been proposed. These approaches aim to improve computational efficiency and to provide a better physical insight.

ScrewFit: combining localization and description of protein secondary structure.

A new application of the ScrewFit algorithm [Kneller & Calligari (2006), Acta Cryst. D62, 302-311] is presented which adds the detection of protein secondary-structure elements to their detailed geometrical description in terms of a curve with intrinsic torsion. The extension is based on confidence and persistence criteria for the ScrewFit parameters which are established by analyzing the structural fluctuations of standard motifs in the SCOP fold classes.

nMoldyn 3: using task farming for a parallel spectroscopy-oriented analysis of molecular dynamics simulations.

We present a new version of the program package nMoldyn, which has been originally developed for a neutron-scattering oriented analysis of molecular dynamics simulations of macromolecular systems (Kneller et al., Comput. Phys.

Communication: a minimal model for the diffusion-relaxation backbone dynamics of proteins.

We present a model for the local diffusion-relaxation dynamics of the C(α)-atoms in proteins describing both the diffusive short-time dynamics and the asymptotic long-time relaxation of the position autocorrelation functions. The relaxation rate spectra of the latter are represented by shifted gamma distributions, where the standard gamma distribution describes anomalous slow relaxation in macromolecular systems of infinite size and the shift accounts for a smallest local relaxation rate in macromolecules of finite size. The resulting autocorrelation functions are analytic for any time t ≥ 0.

Communication: consistent picture of lateral subdiffusion in lipid bilayers: molecular dynamics simulation and exact results.

This communication presents a molecular dynamics simulation study of a bilayer consisting of 128 dioleoyl-sn-glycero-3-phosphocholine molecules, which focusses on the center-of-mass diffusion of the lipid molecules parallel to the membrane plane. The analysis of the simulation results is performed within the framework of the generalized Langevin equation and leads to a consistent picture of subdiffusion. The mean square displacement of the lipid molecules evolves as ∝ t(α), with α between 0.

Least constraint approach to the extraction of internal motions from molecular dynamics trajectories of flexible macromolecules.

We propose a rigorous method for removing rigid-body motions from a given molecular dynamics trajectory of a flexible macromolecule. The method becomes exact in the limit of an infinitesimally small sampling step for the input trajectory. In a recent paper [G.

From NMR relaxation to fractional Brownian dynamics in proteins: results from a virtual experiment.

In a recent simulation study [J. Chem. Phys.