Rigid-body approach

Various approaches have been used to model metal-cyclopentadienyl fragments. In some of the reported studies a rigid-body approach was used for die ligand1222, 225,228,231] might be reasonable for most metal-cyclopentadienyl com-... 

In addition to overall conformational changes, one or a few individual residues might show particularly large conformational changes and this could markedly affect the viability of the rigid-body approach. The control cut-offs for the movement of an individual residue are 3.0 A for a Ca and 5.6 A for side-chain displacements. Examination of the complexes showed that all large movements of exposed residues that were not in the interface can be explained by either their close proximity to the interface or by structural disorder. For a few of the systems, there are movements of individual or a set of residues in the interface that are above the control cut-offs. These shifts are intimately involved in the complex formation. Thus there are several complexes with substantial conformational change for one or a few residues whilst still there is overall a limited structural perturbation. 

Rigid-body approaches are used for measuring the root-mean-sqnare deviation (RMSD) or average distance between two protein structures after superposition of... 

Rotation matrices may be viewed as an alternative to particles. This approach is based directly on the orientational Lagrangian (1). Viewing the elements of the rotation matrix as the coordinates of the body, we directly enforce the constraint Q Q = E. Introducing the canonical momenta P in the usual manner, there results a constrained Hamiltonian formulation which is again treatable by SHAKE/RATTLE [25, 27, 20]. For a single rigid body we arrive at equations for the orientation of the form[25, 27]... 

These difficulties have led to a revival of work on internal coordinate approaches, and to date several such techniques have been reported based on methods of rigid-body dynamics [8,19,34-37] and the Lagrange-Hamilton formalism [38-42]. These methods often have little in common in their analytical formulations, but they all may be reasonably referred to as internal coordinate molecular dynamics (ICMD) to underline their main distinction from conventional MD They all consider molecular motion in the space of generalized internal coordinates rather than in the usual Cartesian coordinate space. Their main goal is to compute long-duration macromolecular trajectories with acceptable accuracy but at a lower cost than Cartesian coordinate MD with bond length constraints. This task mrned out to be more complicated than it seemed initially. 

The simplest theory of impact, known as stereomechanics, deals with the impact between rigid bodies using the impulse-momentum law. This approach yields a quick estimation of the velocity after collision and the corresponding kinetic energy loss. However, it does not yield transient stresses, collisional forces, impact duration, or collisional deformation of the colliding objects. Because of its simplicity, the stereomechanical impact theory has been extensively used in the treatment of collisional contributions in the particle momentum equations and in the particle velocity boundary conditions in connection with the computation of gas-solid flows. 

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