Gerald R. Kneller

Harmonicity in slow protein dynamics

The slow dynamics of proteins around its native folded state is usually described by diffusion in a strongly anharmonic potential. In this paper, we try to understand the form and origin of the anharmonicities, with the principal aim of gaining a better understanding of the principal motion types, but also in order to develop more efficient numerical methods for simulating neutron scattering spectra of large proteins. First, we decompose a molecular dynamics (MD) trajectory of 1.5 ns for a C-phycocyanin dimer surrounded by a layer of water into three contributions that we expect to be independent: the global motion of the residues, the rigid-body motion of the sidechains relative to the backbone, and the internal deformations of the sidechains. We show that they are indeed almost independent by verifying the factorization of the incoherent intermediate scattering function. Then, we show that the global residue motions, which include all large-scale backbone motions, can be reproduced by a simple harmonic model which contains two contributions: a short-time vibrational term, described by a standard normal mode calculation in a local minimum, and a long-time diffusive term, described by Brownian motion in an effective harmonic potential. The potential and the friction constants were fitted to the MD data. The major anharmonic contribution to the incoherent intermediate scattering function comes from the rigid-body diffusion of the sidechains. This model can be used to calculate scattering functions for large proteins and for long-time scales very efficiently, and thus provides a useful complement to MD simulations, which are best suited for detailed studies on smaller systems or for shorter time scales.

nMoldyn: A program package for a neutron scattering oriented analysis of molecular dynamics simulations

We present a new implementation of the program nMoldyn, which has been developed for the computation and decomposition of neutron scattering intensities from Molecular Dynamics trajectories (Comp. Phys. Commun 1995, 91, 191–214). The new implementation extends the functionality of the original version, provides a much more convenient user interface (both graphical/interactive and batch), and can be used as a tool set for implementing new analysis modules. This was made possible by the use of a high‐level language, Python, and of modern object‐oriented programming techniques. The quantities that can be calculated by nMoldyn are the mean‐square displacement, the velocity autocorrelation function as well as its Fourier transform (the density of states) and its memory function, the angular velocity autocorrelation function and its Fourier transform, the reorientational correlation function, and several functions specific to neutron scattering: the coherent and incoherent intermediate scattering functions with their Fourier transforms, the memory function of the coherent scattering function, and the elastic incoherent structure factor. The possibility to compute memory function is a new and powerful feature that allows to relate simulation results to theoretical studies.

SUPERPOSITION OF MOLECULAR STRUCTURES USING QUATERNIONS

Abstract An algorithm is developed that finds the optimal orientation of a rigid molecular structure, represented by N reference sites, with respect to the same number of sites in an observed structure. The optimal orientation is found by minimizing the weighted sum of squared deviations of the rotated reference site positions from the observed site positions. The rotation is parametrized by a quaternion whose components, written as a column vector, are shown to be an eigenvector of a characteristic matrix which is defined in terms of the coordinate sets to be superimposed. The presented algorithm is particularly useful with respect to the calculation of orientational correlations of molecular structures.

Transport coefficients of electrolyte solutions from Smart Brownian dynamics simulations

We present results of Brownian dynamics simulations of aqueous 1-1 electrolyte solutions in the 1-molar concentration range. The electrical conductivity and the self-diffusion coefficients obtained from the simulations are compared to experimental data. The interaction potential between the ions is modeled by pairwise repulsive 1/rn soft-core interactions (n=9 or n=12) and Coulomb forces. We take into account hydrodynamic interactions and integrate the stochastic equations of motion with large time steps of about 100 femtoseconds, combined with an acceptance criterion known from the Smart Monte Carlo method. In this way, details of the dynamics of particles in close contact are not considered and the short-ranged repulsive forces act effectively as constraint forces preventing overlap configurations. The lengths of the performed simulations (about 10 nanoseconds) and the number of ions (216) allow to obtain single particle as well as collective transport coefficients with sufficient precision. For this purpose we use Kubo expressions which can be applied on the mesoscopic time scale of Brownian dynamics simulations. It is shown that hydrodynamic interactions must be taken into account to obtain agreement with the experimental data. They lower the electrical conductivity, as expected, but increase the self-diffusion coefficients, confirming a recent finding for colloids.We present results of Brownian dynamics simulations of aqueous 1-1 electrolyte solutions in the 1-molar concentration range. The electrical conductivity and the self-diffusion coefficients obtained from the simulations are compared to experimental data. The interaction potential between the ions is modeled by pairwise repulsive 1/rn soft-core interactions (n=9 or n=12) and Coulomb forces. We take into account hydrodynamic interactions and integrate the stochastic equations of motion with large time steps of about 100 femtoseconds, combined with an acceptance criterion known from the Smart Monte Carlo method. In this way, details of the dynamics of particles in close contact are not considered and the short-ranged repulsive forces act effectively as constraint forces preventing overlap configurations. The lengths of the performed simulations (about 10 nanoseconds) and the number of ions (216) allow to obtain single particle as well as collective transport coefficients with sufficient precision. For this pu...

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 0.5 and 0.6, and the fractional diffusion coefficient is close to the experimental value for a similar system obtained by fluorescence correlation spectroscopy. We show that the long-time tails of the lateral velocity autocorrelation function and the associated memory function agree well with exact results which have been recently derived by asymptotic analysis [G. Kneller, J. Chem. Phys. 134, 224106 (2011)]. In this context, we define characteristic time scales for these two quantities.

Fractional Brownian dynamics in proteins.

Correlation functions describing relaxation processes in proteins and other complex molecular systems are known to exhibit a nonexponential decay. The simulation study presented here shows that fractional Brownian dynamics is a good model for the internal dynamics of a lysozyme molecule in solution. We show that both the dynamic structure factor and the associated memory function fit well the corresponding analytical functions calculated from the model. The numerical analysis is based on autoregressive modeling of time series.

nMOLDYN: A program package for a neutron scattering oriented analysis of Molecular Dynamics simulations

nMOLDYN is a modular program package for the analysis of Molecular Dynamics simulations. It is especially designed for the computation and decomposition of neutron scattering spectra. The structure and dynamics of the simulated systems can be characterized in terms of various space and time correlation functions. To analyze the dynamics of complex systems, rigid-body motions of arbitrarily chosen molecular subunits can be studied. All modules use a common input data structure for the MD trajectory files which facilitates an efficient calculation of time correlation functions by Fast Fourier Transform algorithms.

A simplified force field for describing vibrational protein dynamics over the whole frequency range

The empirical force fields used for protein simulations contain short-ranged terms (chemical bond structure, steric effects, van der Waals interactions) and long-ranged electrostatic contributions. It is well known that both components are important for determining the structure of a protein. We show that the dynamics around a stable equilibrium state can be described by a much simpler midrange force field made up of the chemical bond structure terms plus unspecific harmonic terms with a distance-dependent force constant. A normal mode analysis of such a model can reproduce the experimental density of states as well as a conventional molecular dynamics simulation using a standard force field with long-range electrostatic terms. This finding is consistent with a recent observation that effective Coulomb interactions are short ranged for systems with a sufficiently homogeneous charge distribution.

Quasielastic neutron scattering and relaxation processes in proteins: analytical and simulation-based models

The present article gives an overview of analytical and simulation approaches to describe the relaxation dynamics of proteins. Particularly emphasised are recent developments of theoretical models, such as fractional Brownian dynamics. The latter connects dynamical events seen on the pico- to nanosecond time scale, accessible to quasielastic neutron scattering, and functional dynamics of proteins on much longer time scales.

Methyl group dynamics in the crystalline alanine dipeptide: A combined computer simulation and inelastic neutron scattering analysis

The dynamics of the methyl groups in the crystalline alanine dipeptide is examined over a wide range of temperatures using elastic and inelastic neutron scattering experiments and molecular dynamics (MD) simulations of the full crystal. Neutron scattering spectra are calculated from the simulations and directly compared to the experimental profiles. The N‐ter and C‐ter methyl groups in the molecule have low rotational barriers, i.e., ≲1 kcal/mol. They undergo rotations that are activated on time scales faster than ≊1 ns at temperatures as low as 50–100 K and are on the picosecond time scale at 150 and 300 K. At 300 K the rotational motion becomes strongly diffusive in the simulation. In contrast, the side‐chain methyls possess a significant intramolecular intrinsic torsional barrier, ≊3 kcal/mol. As a result, their dynamics consists of librations and rare jumps between wells. The simulations are further analyzed to characterize in detail the motions giving rise to the calculated scattering. Using a quaternion‐based method the simulated methyl dynamics is decomposed into rigid‐body rotational and translational components. The decomposed motions and their contributions to the calculated neutron profiles are examined.