Biomedical subjects

G R Kneller

Publications and source records attributed to G R Kneller.

7 recordsLinked to original sources

PubMed2006

Hamiltonian formalism for semiflexible molecules in Cartesian coordinates.

The article gives a concise description of Hamiltonian dynamics and thermal averages of semiflexible molecules in Cartesian coordinates. Using the concept of constrained inverse matrices introduced by Bott and Duffin [Trans. Am. Math. Soc. 74, 99 (1953)] explicit expressions are derived for the constrained Hamiltonian, the corresponding equations of motion, and the momentum partition function. In this context Fixman-type corrections of constrained configurational averages are derived for different forms of the constraints. It is shown that the use of mass-weighted coordinates leads to a nonbiased sampling of constrained configurational averages in Cartesian coordinates. The formalism allows moreover to define and to calculate effective masses arising in thermal velocity averages of atoms in semiflexible molecules. These effective masses are identical to the corresponding Sachs-Teller recoil masses, which are here generalized to the case of only partially rigid molecules.

Journal Article↗

PubMed2005

Comment on "Using quaternions to calculate RMSD" [J. Comp. Chem. 25, 1849 (2004)].

Coutsias et al. have recently published a method to find the optimal rotational superposition of two molecular structures, which is based on a representation of rotations by quaternions (J. Comp. Chem. 25(15), 1849 (2004)). The method, which has been suggested by other authors before, is compared to the one by Kabsch, where the elements of the rotation matrix are directly used as variables of the optimization problem. The statement that the two methods are equivalent is misleading in the sense that the Kabsch method may yield an improper optimal rotation, which must be explicitly checked for, whereas the quaternion method does not mix proper and improper rotations. Nevertheless, both types of solutions can be considered by solving the same eigenvector problem. The relation between the two types of solutions is briefly discussed and bounds for the eigenvalues are given.

Algorithms↗

PubMed2004

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.

Journal Article↗

PubMed2004

Scaling of the memory function and Brownian motion.

It has been recently shown that the velocity autocorrelation function of a tracer particle immersed in a simple liquid scales approximately with the inverse of its mass. With increasing mass the amplitude is systematically reduced and the velocity autocorrelation function tends to a slowly decaying exponential, which is characteristic for Brownian motion. We give here an analytical proof for this behavior and comment on the usual explanation for Brownian dynamics which is based on the assumption that the memory function is proportional to a Dirac distribution. We also derive conditions for Brownian dynamics of a tracer particle which are entirely based on properties of its memory function.

Journal Article↗

PubMed2003

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.

Journal Article↗

PubMed1994

Liquid-like side-chain dynamics in myoglobin.

At temperatures above approximately 200 K the motions of atoms in globular proteins contain a non-vibrational component that gives rise to characteristic elastic and quasi-elastic neutron scattering profiles. There is evidence that the non-vibrational dynamics is required for protein function. Here we show by analysing a molecular dynamics simulation of myoglobin that the neutron scattering results from liquid-like rigid-body motion of the protein side-chains.

Computer Simulation↗

PubMed1993

Picosecond timescale rigid-helix and side-chain motions in deoxymyoglobin.

The contribution of rigid-body motions to the atomic trajectories in a 100 ps molecular dynamics simulation of deoxymyoglobin is examined. Two types of rigid-body motions are considered: one in which the helices are rigid units and one in which the side-chains are rigid units. Using a quaternion-based algorithm, fits of the rigid reference structures are made to each time frame of the simulation to derive trajectories of the rigid-body motions. The fitted trajectories are analysed in terms of atomic position fluctuations, mean-square displacements as a function of time, velocity autocorrelation functions and densities of states. The results are compared with the corresponding quantities calculated from the full trajectory. The relative contribution of the rigid helix motions to the helix atom dynamics depends on which quantity is examined and on which subset of atoms is chosen; rigid-helix motions contribute 86% of the rms helix backbone atomic position fluctuations, but 30% of the helix atom (backbone and side-chain) mean square displacements and only 1.1% of total kinetic energy. Only very low-frequency motions contribute to the rigid-helix dynamics; the rigid-body analysis allows characteristic rigid-helix vibrations to be identified and described. Treating the side-chains as rigid bodies is found to be an excellent approximation to both their diffusive and vibrational mean-square displacements: 96% of side-chain atom mean-square displacements originate from rigid side-chain motions. However, the errors in the side-chain atomic positional fits are not always small. An analysis is made of factors contributing to the positional error for different types of side-chain.

Computer Simulation↗