Fiber Structure Refinement

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:

where

(15.6) |

The sign in formula (15.7) is determined by the handedness of the helix. A right handed helix has a positive value while left-handed helix has a negative value. Other symmetry relations can be derived from (15.4) and (15.5):

(15.8) |

(15.9) |

- Setting up Fiber Structure Parameters and Diffraction Information: The Fiber_refin Statement
- Example: setting up structure parameters and fiber diffraction data of a helical virus structure
- Example of fiber diffraction file
- Computation of Electron Density Maps of a helical structure

- Symmetric Linkage