Geometric Constraints for the Phase Problem in X-Ray Crystallography

X-ray crystallography is one of the main methods to establish the three-dimensional structure of biological macromolecules. In an X-ray experiment, one can measure only the magnitudes of the complex Fourier coefficients of the electron density distribution under study, but not their phases. The problem of recovering the lost phases is called the phase problem. Building on earlier work by Lunin/Urzhumtsev/Bockmayr, we extend their constraint-based approach to the phase problem by adding further 0-1 linear programming constraints. These constraints describe geometric properties of proteins and increase the quality of the solutions. The approach has been implemented using SCIP and CPLEX, first computational results are presented here.