A log-likelihood-gain intensity target for crystallographic phasing that accounts for experimental error

Abstract

The crystallographic diffraction experiment measures Bragg intensities; crystallographic electron density maps and other crystallographic calculations in phasing require structure factor amplitudes. If data were measured with no errors, the structure factor amplitudes would be trivially proportional to the square roots of the intensities. When the experimental errors are large, and especially when random errors yield negative net intensities, the conversion of intensities and their error estimates to amplitudes and associated error estimates becomes non-trivial. Although this problem has been addressed intermittently in the history of crystallographic phasing, current approaches to accounting for experimental errors in macromolecular crystallography have numerous significant defects. These have been addressed with the formulation of LLGI, a log-likelihood gain function in terms of the Bragg intensities and their associated experimental error estimates. LLGI has the correct asymptotic behaviour for data with large experimental error, appropriately downweighting these reflections without introducing bias. LLGI abrogates the need for conversion of intensity data to amplitudes, usually performed with the French & Wilson method (French, S. & Wilson, K. (1978). Acta Cryst. A35, 517-525), wherever likelihood target functions are required. It has general applicability for a wide variety of algorithms in macromolecular crystallography including scaling, characterising anisotropy and translational non-crystallographic symmetry, detecting outliers, experimental phasing, molecular replacement and refinement. Because it is impossible to reliably recover the original intensity data from amplitudes, it is suggested that crystallographers should always deposit the intensity data in the Protein Data Bank.