Next: Optimal superposition. Up: Rigid-Body Trajectory Previous: Rigid-Body Trajectory Contents

####
Theory and implementation

To analyze the dynamics of complex molecular systems it is often desirable to consider the overall motion of molecules or molecular subunits. We will call this motion rigid-body motion in the following. Rigid-body motions are fully determined by the dynamics of the centroid, which may be the center-of-mass, and the dynamics of the angular coordinates describing the orientation of the rigid body. The angular coordinates are the appropriate variables to compute angular correlation functions of molecular systems in space and time. In most cases, however, these variables are not directly available from MD simulations since MD algorithms typically work in cartesian coordinates. Molecules are either treated as flexible, or, if they are treated as rigid, constraints are taken into account in the framework of cartesian coordinates [54]. In nMOLDYN, Rigid-Body Trajectory (RBT) can be defined from a MD trajectory by fitting rigid reference structures, defining a (sub)molecule, to the corresponding structure in each time frame of the trajectory. Here `fit' means the optimal superposition of the structures in a least-squares sense. We will describe now how rigid body motions, i.e. global translations and rotations of molecules or subunits of complex molecules, can be extracted from a MD trajectory. A more detailed presentation is given in [55]. We define an optimal rigid-body trajectory in the following way: for each time frame of the trajectory the atomic positions of a rigid reference structure, defined by the three cartesian components of its centroid (e.g. the center of mass) and three angles, are as close as possible to the atomic positions of the corresponding structure in the MD configuration. Here `as close as possible' means as close as possible in a least-squares sense.

Subsections

- Optimal superposition.
- Quaternions and rotations.
- Solution of the minimization problem.

Next: Optimal superposition. Up: Rigid-Body Trajectory Previous: Rigid-Body Trajectory Contents