Programming new geometry restraints: parallelity of atomic groups

Improvements in structural biology methods, in particular crystallography and cryo-electron microscopy, have created an increased demand for the refinement of atomic models against low-resolution experimental data. One way to compensate for the lack of high-resolution experimental data is to use a priori information about model geometry that can be utilized in refinement in the form of stereochemical restraints or constraints. Here, the definition and calculation of the restraints that can be imposed on planar atomic groups, in particular the angle between such groups, are described. Detailed derivations of the restraint targets and their gradients are provided so that they can be readily implemented in other contexts. Practical implementations of the restraints, and of associated data structures, in the Computational Crystallography Toolbox (cctbx) are presented.