Rigid body fitting

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. 

Figure 4. Comparison of astacin and the catalytic domain of coUagenase. Stereo ribbon diagram [54] of the structure of astacin (green) and the catalytic domain of coUagenase (orange) superimposed using a rigid body fit of the catalytic hehces. The catalytic zinc atom (cyan) and the zinc ligands (blue) are marked. The overall similarity in the open beta sandwich region, N-terminal to the active site helix is apparent.

Ferro D R and J Hermans 1977. A Different Best Rigid-body Molecular Fit Routine. Acta Crystallographica A33 345-347. 

Figure 3 Calculated X-ray diffuse scattering patterns from (a) a full molecular dynamics trajectory of orthorhombic hen egg white lysozyme and (b) a trajectory obtained by fitting to the full trajectory rigid-body side chains and segments of the backbone. A full description is given in Ref. 13.

The pressure dependence of wavenumbers has been investigated theoretically by LD methods on the basis of a Buckingham 6-exp potential. In the studies of Pawley and Mika [140] and Dows [111] the molecules were treated as rigid bodies in order to obtain the external modes as a function of pressure. Kurittu also studied the external and internal modes [141] using his deformable molecule model [116]. The force constants of the intramolecular potential (modified UBFF) were obtained by fitting to the experimental wavenumbers. The results of these studies are in qualitative agreement with the experimental findings. 

If the correspondences of at least three reference points are available for two rigid-body objects, RMS fitting minimizes the sum of the squared distances of... 

Each refined orientation of the probe received a correlation coefficient that shows how well it fits the Patterson map of ALBP. The orientation receiving the highest correlation coefficient was taken as the best orientation of the probe, and then used to refine the position of the probe in the ALBP unit cell. The orientation and position of the model obtained from the molecular replacement search was so good that refinement of the model as a rigid body produced only slight improvement in R. The authors attribute this to the effectiveness of the Patterson correlation refinement of model orientation, stage two of the search. 

Rigid-Body Motions and Least-Squares Fitting... 

The general numerical approach employs rigid body motions and least-squares fitting. Given two sets of points xt,i = 1,2,..., N and yui= 1,2,..., N (here xt and yt are vectors specifying atomic coordinates), find the best rigid motion of the points y h) such that the sum of the squares of the deviations E xt — Yt 2 is a minimum. 

Similar conclusions can be drawn when one uses models describing the anisotropic motion of rigid bodies good cmwe fitting may be obtained fortuitously, but, in contrast with the case of the BY on HH expressions, this fitting does not lead to stable and significant parameters. 

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