By Herbert A. Hauptman (auth.), Suzanne Fortier (eds.)
ISBN-10: 9048149940
ISBN-13: 9789048149940
ISBN-10: 9401590931
ISBN-13: 9789401590938
This ebook of the complaints of the 1997 NATO complicated research Institute (ASI) on Direct tools for fixing Macromolecular buildings was once assembled from the teachers' contributions and represents a finished and in-depth evaluate of crystallographic constitution choice tools for macromolecules. whereas having a spotlight in accordance with the direct equipment, the Institute followed an inclusive and vast standpoint. hence, either direct and experimental phasing suggestions are offered during this e-book, highlighting their complementarities and synergies. As weil, methodologies spanning the whole crystallographic photograph reconstruction method - from low solution envelope definition to excessive solution atomic refinement- are mentioned. the 1st a part of the e-book introduces the array of instruments at the moment utilized in constitution choice, no matter if originating from a mathematical, computational or experimental framework. This part of the publication monitors the diversity and ingenuity of outdated and new phasing ways built to resolve more and more complicated constructions. a number of the contributions concentrate on contemporary advancements and/or implementations that experience given older ways a brand new existence. A working example is the re-implementation of Buerger's superposition process, that is now fixing protein buildings. one other attractive instance is located within the advent to the conventional a number of isomorphous substitute process the place new suggestions, akin to site-directed mutagenesis and using inert gases within the practise of heavy atom derivatives, are defined. both striking are the displays of more recent techniques, which make the most of advances at the experimental entrance (e. g.
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The distribution is maximally noncommittal with respect to alt other matters; it is as uniform ... as it can get without violating the given constraint. " 11. Wh at is the Relevance of all this to Crystallography? All this may seem a long way from the problems of solving crystal structures, but this is not so. There is a very good discussion of how these ideas can be used in a crystallographic context in [2] (pages 8-11) some of which is followed here. Let us look at the formula for the crystallographic structure factor: N F(h,k,l)= If~ exp21ti(hx j + kYj + lZj) (33) ;=1 where there are N atoms in the unit cell with scattering factors h" h,k,l are the Miller indices, and xi' Y;, z; the coordinates of the j-th atom in the cel!.
Due to the dual-space reciprocity, her reduces to her = hx + ky + Qz. (h) is the atomic X-ray scattering factor. The Debye-Waller factor is the Fourier transform of the probability density of atomic displacements from the mean atomic position, 47 S. ), Direct Methodsfor Solving Macromolecular Structures, 47-71. © 1998 Kluwer Academic Publishers. »)], and, at X-ray wavelengths sufficiently far removed from the crystal's resonant electronic absorption edges, the atomic scattering factor is the Fourier transform of the atornic electron density, faCh) = Y[Pa(r - rJ] = Y [1lJ1 a(r - raW].
For a given crystal, however, the positions of the atoms are not fixed relative to any axial system. In space group PI at least one atom has to be fixed relative to the origin of the axial system. [We do not fix anything in the crystal: we onIy specify three parameters XJ,yJ,Zj in order to be able to use an arbitrarily defined axial system to describe the structure. ] Other atoms (in space group PI) then are fixed. Because the entire structure is a physical entity, the interatomic distances are physical quantities, thus the length of an interatomic vector IVijl = Irj - ril is a physical quantity.
Direct Methods for Solving Macromolecular Structures by Herbert A. Hauptman (auth.), Suzanne Fortier (eds.)
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