Improved Fourier coefficients for maps using phases from partial structures with errors

TLDR

Partially refined macromolecular models are incomplete, have large coordinate errors, and bias electron density maps toward the partial structure. The study aims to derive equations that account for errors in partial structures and to estimate the parameter σA from observed and calculated structure factor amplitudes. The authors estimate σA from observed and calculated amplitudes, use its resolution dependence to infer mean coordinate error, and introduce a new non‑centric Fourier coefficient expression to reduce model bias. They show that equations assuming perfect partial structures give inaccurate phase probabilities, and that the newly derived Fourier coefficients yield higher correlation with correct maps than existing methods.

Abstract

Unrefined or partially refined models of macromolecules are generally incomplete and typically have large coordinate errors. It is shown that phase probability equations appropriate for a perfect partial structure lead to inaccurate estimates of phase probabilities in such cases. Therefore, it is necessary to use equations that have been derived allowing for errors in the partial structure. A method is given to estimate the parameter σA in these phase probability expressions from the observed and calculated structure factor amplitudes. From the variation of σA with resolution, one can estimate the mean coordinate error for the model. Electron density maps calculated using partial structure phases are biased towards the partial structure. When there are coordinate errors, a new expression for the non-centric Fourier coefficients [(2m|FN| - D|FcP|) exp(iαcP)] is required to suppress this model bias. Judged by correlation coefficients comparing electron density maps with the correct and the partial structure maps, the Fourier coefficients derived here are superior to others currently in use.