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 T(6) 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.