Use of high-order probability laws in phase refinement and extension of protein structures

High-order covariance matrices are used to show that the maximal determinant rule and the regression equation can be applied successfully to the phase refinement and extension of protein structures. With structure factors calculated from the atomic model of insulin, the use of an order-400 covariance matrix leads to the structure phases with an average error ΔΦ of 15°. The method has also been applied to actual data of insulin for phase refinement and for phase extension from 2.8 to 2 Å.