Estimating the influence of finite instrumental resolution on elastic neutron scattering intensities from proteins

Recent experimental and simulation studies show that the fractional Ornstein-Uhlenbeck process describes well the single particle motions in internal protein dynamics. Here the authors use this model to estimate the influence of finite instrumental resolution on elastic neutron scattering intensities from hydrated protein powders. They give, in particular, an estimation of the attenuation factor for the observed atomic position fluctuations, assuming a Gaussian and a triangular resolution function.     

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. Kneller, J. Chem. Phys. 128, 194101 (2008)], one of us showed that virtual internal atomic displacements for small time increments can be derived from Gauss' principle of least constraint, which leads to a rotational superposition problem for the atomic coordinates in two consecutive time frames of the input trajectory. Here, we demonstrate that the accumulation of these displacements in a molecular-fixed frame, which evolves in time according to the virtual rigid-body motions, leads to the desired trajectory for internal motions. The atomic coordinates in the input and output trajectory are related by a roto-translation, which guarantees that the internal energy of the molecule is left invariant. We present a convenient implementation of our method, in which the accumulation of the internal displacements is performed implicitly. Two numerical examples illustrate the difference to the classical approach for removing macromolecular rigid-body motions, which consists of aligning its configurations in the input trajectory with a fixed reference structure.     

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. Using results from a molecular dynamics simulation of lysozyme, we demonstrate that the model fits the position autocorrelation functions of the C(α)-atoms exceptionally well and reveals moreover a strong correlation between the residue's solvent-accessible surface and the fitted model parameters.