Retrieving low- and medium-resolution structural features of macromolecules directly from the diffraction intensities - a real-space approach to the X-ray phase problem

A simple mathematical algorithm is proposed to generate electron-density functions whose Fourier amplitudes match the diffraction intensities. The function is by construction everywhere positive. Using appropriate averaging procedures, the high-density regions of such functions could yield important structural information about macromolecular crystals. Trial calculations on protein crystals show that the protein envelope plus other structural motifs such as barrels and secondary structures could be recognized in the density maps. As such, the algorithm could provide a basis for new phasing methods or supplement existing phasing methods.