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The method of joint probability distribution functions has been applied to molecular replacement techniques. The rotational search is performed by rotating the reciprocal lattice of the protein with respect to the calculated transform of the model structure; the translation search is performed by fast Fourier transform. Several cases of prior information are studied, both for the rotation and for the translation step: e.g. the conditional probability density for the rotation or the translation of a monomer is found both for ab initio and when the rotation and/or the translation values of other monomers are given. The new approach has been implemented in the program REMO09, which is part of the package for global phasing IL MILIONE [Burla, Caliandro, Camalli, Cascarano, De Caro, Giacovazzo, Polidori, Siliqi & Spagna (2007). J. Appl. Cryst. 40, 609-613]. A large set of test structures has been used for checking the efficiency of the new algorithms, which proved to be significantly robust in finding the correct solutions and in discriminating them from noise. An important design concept is the high degree of automatism: REMO09 is often capable of providing a reliable model of the target structure without any user intervention.

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