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

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 σ_A in these phase probability expressions from the observed and calculated structure factor amplitudes. From the variation of σ_A 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|F_N| - D|F^c_P|) exp(iα^c_P)] 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.