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Patterson and molecular replacement techniques, and the use of noncrystallographic symmetry in phasing
Tong, L., Rossmann, M. G. and Arnold, E.  International Tables for Crystallography (2010). Vol. B, ch. 2.3, pp. 244-281 [ doi:10.1107/97809553602060000765 ]
... been used extensively in conjunction with the isomorphous replacement method (Rossmann, 1960; Blow, 1958) or anomalous dispersion (Rossmann, 1961a) to determine the position of heavy-atom substitution. Pattersons ... the crystallographic asymmetric unit in the same or different crystals (Rossmann & Blow, 1962). Finally, the orientation and placement of ...

Introduction
Rossmann, M. G. and Arnold, E.  International Tables for Crystallography (2012). Vol. F, Section 13.4.1, p. 352 [ doi:10.1107/97809553602060000842 ]
Introduction 13.4.1. Introduction Electron-density averaging for phasing crystal structures has become a widespread and nearly routine technique. High noncrystallographic symmetry (NCS) permits the solution of structures using relatively poor and even ab initio phasing starts, while lower NCS electron-density averaging can significantly improve initial phases obtained by techniques such ...

Noncrystallographic symmetry averaging of electron density for molecular-replacement phase refinement and extension
Rossmann, M. G. and Arnold, E.  International Tables for Crystallography (2012). Vol. F, ch. 13.4, pp. 352-363 [ doi:10.1107/97809553602060000842 ]
... axes in the plane of the paper (design by Audrey Rossmann). [Reprinted with permission from Rossmann (1972). Copyright (1972) Gordon & Breach.] A product of superimposed ... point symmetry of the noncrystallographic operation. [Reprinted with permission from Rossmann (1990).] There must be space between the confining ...

Programs
Rossmann, M. G. and Arnold, E.  International Tables for Crystallography (2012). Vol. F, Section 13.4.14, p. 361 [ doi:10.1107/97809553602060000842 ]
... are well suited to cases with high NCS include ENVelope (Rossmann et al., 1992) and GAP (Jonathan Grimes and David Stuart ... 28, Albuquerque, New Mexico, Vol. 21, p. 51. Cornea-Hasegan, M. A., Zhang, Z., Lynch, R. E., Marinescu, D. C., Hadfield, A., Muckelbauer, J. K., Munshi, S., Tong, L. & Rossmann, M. G. (1995). Phase refinement and extension by ...

Recent salient examples in low-symmetry cases: multidomain averaging and systematic applications of multiple-crystal-form averaging
Rossmann, M. G. and Arnold, E.  International Tables for Crystallography (2012). Vol. F, Section 13.4.13, pp. 360-361 [ doi:10.1107/97809553602060000842 ]
... such as salt and polyethylene glycol. References Bragg, L. & Perutz, M. F. (1952). The structure of haemoglobin. Proc. R. Soc. ... P. L., Clark, P., Smith, R. H. Jr, Kroeger Smith, M. B., Michejda, C. J., Hughes, S. H. & Arnold, E. (1996 ... Janssen, P. A. J., Smith, R. H. Jr, Kroeger Koepke, M., Michejda, C. J., Hughes, S. H. & Arnold, E. (1995) ...

Ab initio phasing starts
Rossmann, M. G. and Arnold, E.  International Tables for Crystallography (2012). Vol. F, Section 13.4.12, p. 360 [ doi:10.1107/97809553602060000842 ]
... done either by using an R-factor search (Tsao, Chapman & Rossmann, 1992) or by using low-angle X-ray scattering data ... value. Such a limited initial start was first explored by Rossmann & Blow (1963). Figure 13.4.12.1 | | Structure amplitudes of the type ... Willingmann, Ilag, Krishnaswamy et al., 1992; McKenna, Xia, Willingmann, Ilag & Rossmann, 1992; Tsao, Chapman & Rossmann, 1992; Tsao, Chapman, Wu et ...

Convergence
Rossmann, M. G. and Arnold, E.  International Tables for Crystallography (2012). Vol. F, Section 13.4.11, pp. 359-360 [ doi:10.1107/97809553602060000842 ]
... used (Sim, 1959; Rayment, 1983; Arnold et al., 1987; Arnold & Rossmann, 1988). As mentioned above, the rate of convergence can ... in the final phasing has been shown to be (Arnold & Rossmann, 1986) proportional to where N is the NCS redundancy, f ... content and diffraction-data quality and completeness. References Arnold, E. & Rossmann, M. G. (1986). Effect of errors, redundancy, and ...

Phase extension and refinement of the NCS parameters
Rossmann, M. G. and Arnold, E.  International Tables for Crystallography (2012). Vol. F, Section 13.4.10, p. 359 [ doi:10.1107/97809553602060000842 ]
... constantly improved and updated to match the improved resolution. Arnold & Rossmann (1986, 1988) discussed phase error as a function of error ... C., Abdel-Meguid, S. S., Johnson, J. E., Leslie, A. G. W., Rayment, I., Rossmann, M. G., Suck, D. & Tsukihara, T. (1980). Structure ...

Combining different crystal forms
Rossmann, M. G. and Arnold, E.  International Tables for Crystallography (2012). Vol. F, Section 13.4.9, p. 358 [ doi:10.1107/97809553602060000842 ]
... the cycle can be repeated. References Bjorkman, P. J., Saper, M. A., Samraoui, B., Bennett, W. S., Strominger, J. L. & Wiley ... Acta Cryst. A32, 125-132. Varghese, J. N., Laver, W. G. & Colman, P. M. (1983). Structure of the influenza virus glycoprotein antigen ...

Interpolation
Rossmann, M. G. and Arnold, E.  International Tables for Crystallography (2012). Vol. F, Section 13.4.8, p. 358 [ doi:10.1107/97809553602060000842 ]
... grid interval is less than 1/2.5 of the resolution (Rossmann et al., 1992). Other interpolation schemes have also been ... tensor product of three one-dimensional linear interpolants). Let G be the position at which the density is to be ... 13.4.8.1 | | Interpolation box for finding the approximate electron density at G([Delta]x, [Delta]y, [Delta]z), given the eight ...

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