Xplor-NIH now incorporates the functionality of the FX-PLOR package of computer programs for macromolecular refinements against X-ray fiber diffraction data (Denny et al., 1997; Wang and Stubbs, 1993). Most features in X-PLOR suitable for crystal structure refinement and structure analysis can be utilized for fiber structure refinement and analysis.
In X-ray fiber diffraction, the Fourier-Bessel structure factor
is defined as:
(15.1) |
(15.2) |
Fiber diffraction intensities are usually measured at small sampling unit along the layer line, where is a constant in reciprocal space. Because the sampling unit is usually small, it is convenient to index the intensity data with reciprocal space index and layer line number . In FX-PLOR, and are stored in H array and L array, respectively. Moreover, because structure factor in fiber diffraction is a multidimensional vector rather than a two-dimensional vector, only amplitude of is stored in the real components of FCALC array and FOBS array.
In order to include X-ray fiber diffraction information in a
molecular dynamics refinement or energy minimization, the
effective energy for fiber diffraction is defined as a function
of the discrepancy between observed and calculated intensities:
(15.3) |
To reduce computational time, look-up tables for , and Bessel function may be set up for structure factor calculation, The size of the Bessel look-up table depends on the following factors: resolution limit of the diffraction data, maximum number of Bessel terms on a layer line (BLMAX) and grid size of the table for Bessel function (TGRID).
The basic symmetry relation of a helical structure is a screw
rotation . In FXPLOR, these symmetry relations can
be utilized in potential energy calculation for non-bonded
interactions between atoms in different subunits. The rotation
matrix of the screw rotation is:
(15.6) |
(15.8) |
(15.9) |