A two-dimensional histogram-matching method for protein phase refinement and extension

A new method has been developed for protein phase improvement using the joint distribution of the electron density and its gradient (two-dimensional histogram) as a constraint in a density-modification procedure. Matching the two-dimensional (2D) histogram of a given map to that of an ideal 2D histogram was achieved through alternating applications of one-dimensional (1D) histogram matching on electron density and on density gradient. The 2D histogram-matching method was compared with the 1D density histogram-matching method for phase refinement and extension starting from either medium-resolution or high-resolution data on three different types of phases. These included phase refinement and extension using MIR phases of T₆ insulin and phases with randomly generated errors. The test results demonstrated significant improvement of the phases and the overall map quality using the 2D histogram-matching method compared with the 1D density histogram-matching method in each of the three test cases.