scholarly journals Isomorphous replacement: effects of errors on the phase probability distribution

Author(s):  
T. C. Terwilliger ◽  
D. Eisenberg

Crystals of hen egg-white lysozyme, grown at pH 4.7 (Alderton & Fevold 1946), are tetragonal with a = b = 79.1 Å, c = 37.9 Å, space group P 4 3 2 1 2 (Palmer, Ballantyre & Galvin 1948; Blake, Fenn, North, Phillips & Poljak 1962). Each of the eight asymmetric units in the cell comprises a single lysozyme molecule, molecular weight about 14 600, together with 1 M sodium chloride solution which constitutes some 33.5% of the weight of the crystal (Steinrauf 1959). The structure of these crystals has been determined by X-ray analysis by the method of multiple isomorphous replacement developed in the studies of haemoglobin (Green, Ingram & Perutz 1954; Blow 1958; Perutz, Rossmann, Cullis, Muirhead, Will & North 1960) and myoglobin (Kendrew, Dickerson, Strandberg, Hart, Davies, Phillips & Shore 1960). Anomalous scattering data were used in conjunction with the isomorphous replacement intensity differences (North 1965) to form a joint probability distribution for the phase of each reflexion. The position of the centroid of each probability distribution gave a phase angle and weighting factor for each reflexion from which the electron density map with minimum r.m.s. error was calculated (Blow & Crick 1959). A large number of different heavy atom derivatives were studied (Poljak 1963; Blake, Koenig, Mair, North, Phillips & Sarma 1965) and three proved satisfactory for calculating an electron density map at 2 Å resolution. They contained respectively ortho -mercuri hydroxytoluene para -sulphonic acid, UO 2 F 5 3- and an ion derived from UO 2 (NO 3 ) 2 , probably UO 2 (OH) n (n-2)-


2001 ◽  
Vol 15 (25) ◽  
pp. 1155-1169
Author(s):  
HONG-YI FAN ◽  
XIAN-TING LIANG ◽  
ZHI-HU SUN

A phase state presentation |ξ= reiθ> for a two-mode light field is constructed in the context of quantum optics. This phase space formalism is directly connected to phase-related operators. The generalized quasi-probability distribution function Q(ξ) and measurable phase probability distribution function P(θ) are constructed and are useful to obtain information about phase properties of light fields.


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