title: Sparsity of the normal matrix in the refinement of macromolecules at atomic and subatomic resolution.
abstract: The normal matrix in the least-squares refinement of macromolecules is very sparse when the resolution reaches atomic and subatomic levels. The elements of the normal matrix, related to coordinates, thermal motion and charge-density parameters, have a global tendency to decrease rapidly with the interatomic distance between the atoms concerned. For instance, in the case of the protein crambin at 0.54 A resolution, the elements are reduced by two orders of magnitude for distances above 1.5 A. The neglect a priori of most of the normal-matrix elements according to a distance criterion represents an approximation in the refinement of macromolecules, which is particularly valid at very high resolution. The analytical expressions of the normal-matrix elements, which have been derived for the coordinates and the thermal parameters, show that the degree of matrix sparsity increases with the diffraction resolution and the size of the asymmetric unit.
authors.affiliation: Laboratoire de Cristallographie et de Modélisation des Matériaux Minéraux et Biologiques (LCM3B), CNRS, UHP, Faculté des Sciences, BP 239, 54506 Vandoeuvre-les-Nancy, France. jelsch@lcm3b.uhp-nancy.fr
authors.forename: C
authors.initials: C
authors.lastname: Jelsch
mesh_terms: D000449:Aldehyde Reductase / Q000737:chemistry; D000465:Algorithms; D016880:Anisotropy; D003461:Crystallography; D009243:NAD / Q000737:chemistry; D010940:Plant Proteins / Q000737:chemistry; D011506:Proteins / Q000737:chemistry*; D012604:Scorpion Venoms / Q000737:chemistry; D013696:Temperature; D013816:Thermodynamics
chemical_list: D010940:Plant Proteins; D011506:Proteins; D012604:Scorpion Venoms; D009243:NAD; C024934:crambin protein, Crambe abyssinica; D000449:Aldehyde Reductase