SIR2000, a program for the automatic ab initio crystal structure solution of proteins.

A new phasing procedure is described working both in direct and in reciprocal space. The procedure has been implemented into the program SIR2000, the heir to SIR99, and it is able routinely to solve ab initio crystal structures of proteins without any use of prior information and any user intervention. The moduli and the flow diagram of SIR2000 are also described and its efficiency tested on several protein diffraction data sets. Success has been attained for crystal structures with up to almost 2000 non-hydrogen atoms in the asymmetric unit and resolution higher than 1.2 A. The phasing process is analysed to provide a better insight into the role of the various steps of the procedure.

The probability distribution function of structure factors with non-integral indices. III. The joint probability distribution in the P1; case.

The joint probability distribution function method has been developed in P1; for reflections with rational indices. The positional atomic parameters are considered to be the primitive random variables, uniformly distributed in the interval (0, 1), while the reflection indices are kept fixed. Owing to the rationality of the indices, distributions like P(F(p1), F(p2)) are found to be useful for phasing purposes, where p1 and p2 are any pair of vectorial indices. A variety of conditional distributions like P(|F(p1)| | |F(p2)|), P(|F(p1)| |F(p2)), P(varphi(p1)| |F(p1)|, F(p2)) are derived, which are able to estimate the modulus and phase of F(p1) given the modulus and/or phase of F(p2). The method has been generalized to handle the joint probability distribution of any set of structure factors, i.e. the distributions P(F(1), F(2),ellipsis, F(n+1)), P(|F(1)| |F(2),ellipsis, F(n+1)) and P(varphi(1)| |F|(1), F(2),ellipsis, F(n+1)) have been obtained. Some practical tests prove the efficiency of the method.

SIR99, a program for the automatic solution of small and large crystal structures.

The moduli and flow diagram of the program SIR99 are described. New phasing algorithms are proposed working both in direct and in reciprocal space. Their cooperative work is able to solve the structures of both small and large molecules. In particular, small proteins can be solved ab initio without any use of prior information and any user intervention. The efficiency of the various algorithms employed by SIR99 has been tested, and the role of the tangent formula clarified. The user is also provided with some practical information concerning the computer power needed.

The ab initio crystal structure solution of proteins by direct methods. II. The procedure and its first applications.

A direct phasing method is described that is potentially able to solve ab initio protein structures. The method uses the information contained in diffraction data of the native structure and of one isomorphous derivative. The various steps of the procedure are analysed in order to estimate their robustness against experimental errors in measurements and lack of isomorphism. Experimental tests involve four typical protein structures and show that crystal structure solution is attained in a rather straightforward way.