Linear-scaling aspherical crystallographic refinement of proteins: a case study for crambin and rubredoxin

Hirshfeld atom refinement (HAR) provides a more realistic interpretation of crystallographic data than the standard independent atom model (IAM) by using aspherical atomic form factors derived from quantum mechanical (QM) calculations. With this aspherical description, it is possible to obtain improved atomic positions, atomic displacement parameters and correct bond lengths even for hydrogen atoms. Unfortunately, HAR is computationally very demanding for larger molecules. Recently, we suggested how this can be solved by calculating aspherical atomic form factors for small overlapping fragments of the system, the fragHAR approach. Here, we have created a new implementation of fragHAR in Olex2 within the NoSpherA2 interface. We have also solved previous issues with hydrogen bonds by automatically extending the fragments with all hydrogen-bond acceptors. This implementation was successfully tested on three oligopeptides, demonstrating that fragHAR yields indistinguishable results in terms of atomic charge, residual density or R values compared with full HAR. Subsequently, fragHAR was applied to the proteins crambin and rubredoxin, with 843 and 1014 atoms, respectively, showing improved results in terms of e_gross, which decreases from 0.350 with the IAM to 0.318 with fragHAR for crambin, and from 0.195 to 0.176 for rubredoxin, although it turned out to be necessary to keep all bond lengths involving hydrogen atoms constrained for the latter protein. FragHAR shows near-linear scaling and 46-fold speedup for rubredoxin compared with HAR. It also provides a convenient solution to alternative conformations and positional disorder, which cause an exponential increase in the time consumption of the conventional HAR approach. The successful refinement of rubredoxin marks a significant milestone, presenting the first HAR application of a metalloprotein, and further underlines the relevance of fragHAR in protein crystallography.