Rigid-body techniques

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. 

An important extension to rigid-body fitting is the so-called directed tweak technique [105]. Directed tweak allows for an RMS fit, simultaneously considering the molecular flexibility. By the use of local coordinates for the handling of rotatable bonds, it is possible to formulate analytical derivatives of the objective function. With a gradient-based local optimizer flexible RMS fits are obtained extremely fast. However, no torsional preferences may be introduced. Therefore, directed tweak may result in energetically unfavorable conformations. 

Usually, the top peaks of the translation search are then submitted to a low resolution quick rigid-body refinement, for which quick algorithms have been devised (Huber and Schneider, 1985 Navaza and Saludjian, 1997).The resolution is usually taken to be 12-4 Angstroms or so if one wants to use the low resolution terms, one should use a solvent effect correction technique (Fokine and Urzhumtsev, 2002). 

Powder diffraction techniques have become increasingly useful as tools for crystal structure determination especially in cases where it is sometimes difficult to get a single crystal of sufficient size and quality for traditional single-crystal studies. The solution of a structure can be considered as a three-step process (i) data collection and indexing, (ii) data preparation and Pawley refinement, and (iii) Monte Carlo simulated annealing and rigid-body Rietveld refinement. 

In the recent years, sophisticated modeling tools have become available, such as the Cerius (8), where various modules aUow the analysis of crystallization, crystal growth, and material form characterization. In brief, this technique uses a simulated annealing and a rigid-body Rietveld refinement procedure, whereby the calculated and measured XRPD patterns are compared if they agree sufficiently, the structure is deemed to be solved. Other modules offered by Cerus include ... 

The basic problem with the fragment assembly method is the use of the least-squares superposition, which means that the proteins are being treated as rigid bodies. This may result in only a small number of equivalent positions being used to pinpoint a large part of the model, and information other than the Ca-positions in known structures is often neglected. Thus, another technique was developed to allow a more flexible representation of protein structure, both for comparison and modelling purposes. 

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