Improving and extending the phases of medium- and low-resolution macromolecular structure factors by density modification

Non-negativity of the electron density function and constancy of the solvent regions were exploited to improve 2633 phases of crystalline yeast tRNA_f^Met (P6₄22, a = 115.3, c = 137.9 Å, z = 12), which had been obtained by multiple isomorphous replacement (MIR) in the resolution zone 14-4.5 Å. Phases were also determined for an additional 912 reflections not previously phased by MIR from the resolution range 100 to 4 Å, the very limits of the diffraction pattern. An iterative procedure was employed in which phases for each cycle were calculated from a density map modified by imposing the above constraints and were combined with the observed amplitudes to produce a new and improved map. Initially phases calculated in each cycle were merged with the original MIR phase probability curve; convergence was achieved in seven cycles. The phases were then released from the MIR analysis by using just the calculated phases until a second convergence was achieved (four cycles). The average difference between the experimental phases and phases calculated from the refined coordinates was reduced from 68° for the original MIR analysis to 43° by the use of these real-space direct methods. Phases determined solely by density modification were as accurate as the original MIR phase set. The map calculated with improved and extended phases was dramatically superior to the MIR map and even approached in quality the map produced with phases calculated from the refined molecular coordinates.