Computational Caveat

It has been noted (Welsh et al., 2000) that fiber electron density calculations contain an artifact:

"The observed equatorial data for the higher order Bessel functions (i.e. not J0) includes both complex conjugates, and to calculate electron density it is necessary to correct for this effect, as pointed out by Symmons et al. (1995). The reason for this correction can be illustrated by a simple thought experiment. Imagine a non-integral helix with (say) not quite nine units per turn. For sufficiently well resolved layer-lines, J9 contributions will be observed off the equator in both the upper and lower halves of the fibre-diffraction pattern and only one of these would be included in any calculation. Now imagine that the helix changes slightly to precisely nine units per turn; both J9 contributions merge on the equator, but still only one of them should be used in any calculation. The refinement program FX-PLOR does not take account of this effect and both complex conjugates of higher order Bessel function terms are calculated on the equator, so we left our observed data uncorrected for this effect in refinement calculations. This means that higher resolution equatorial data enter the refinement at double weight, but since the lowest order non-zero Bessel function on the equator of Pf1H is J27, in practice the error introduced into our refinement is negligible. To calculate electron-density distributions, we used the program DIFF (Nave et al., 1981), which does deal correctly with the complex conjugates on the equator."

Xplor-NIH 2023-11-10