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A method of dual-space molecular-replacement model completion has been proposed which involves the programs ARP/wARPREFMACOASIS and DMOASIS is used in reciprocal space for phase refinement based on models built by ARP/wARP. For this purpose, the direct-method probability formula of breaking SAD/SIR phase ambiguities has been redefined. During the phase refinement, \varphi_{\bf h}'' in the expression φh = \varphi_{\bf h}'' \pm |\Delta \varphi_{\bf h}| is redefined as a reference phase calculated from a randomly selected 5% of the atoms in the current structure model, while |Δφh| is defined as the absolute difference between the phase of the current model and \varphi_{\bf h}''. The probability formula P+(Δφh) = ½ + ½ tanh {sin |Δφh| × [∑hmhmh − hκh,h sin(Φ′3 + Δφh′best + Δφh − h′best) + χ sin δh]} is then used to derive the sign of Δφh. In this way the `0–2π' phase problem is reduced to a `plus or minus' sign problem. The redefinition implies that during the refinement phases close to the true values will probably be kept unchanged, while those distant from the true values will probably undergo a large shift. This is the desired property of phase refinement. The procedure has been tested using protein diffraction data without SAD/SIR signals. The results show that dual-space MR-model completion making use of OASIS is much more efficient than that without.

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