Joe Krahn wrote:
For density modification, it may be possible to converge on a good map if both missing and test reflections use "Fcalc" fill-in values from the previous density-modified transformation. Maybe the people who could not get good results without the test reflections used a DM method that reset missing values to zero on every cycle.
Those suggestions would be supported by results in: Rayment, I. Molecular replacement method at low resolution: optimum strategy and intrinsic limitations as determined by calculations on icosahedral virus models. Acta Crystallogr. A 39, 102–116 (1983). (Perhaps this is the paper B. Shaanan was thinking of?) The authors used what is now called "fill-in" for the missing reflections, and they also tried intentially omitting reflections and using the fillin (Fcalc) values at each cycle. They found when this was done the resulting F's approached the actual unused experimental values with cycles of averaging. If they did not fillin the missing values the averaging suffered, because in effect they were forcing those reflections to zero. Ed PS: NCS averaging can be seen as a numerical method for solving the M.R. equations, i.e. finding a set of phases that is consistent with the observed amplitudes and the known symmetry. NCS averaging with 5% of reflections omitted is finding a set of phases consistent with the known symmetry and observed working reflections *AND* with all of the free refections having amplitude zero (which is probably not the set of phases you want). For example suppose you started with perfect data and perfect phases, and agreement with the NCS operators is very good. Now you make a 2Fo-Fc map with the test set omitted, i.e. replaced by zero. The missing sine waves do not in general obey the NCS, so each omitted one introduces asymmetry in the map-to-be averaged. Averaging then restores the symmetry, but with slightly different density values. Fc for the next round is calculated from the averaged map, and the omitted reflections will in general have non-zero value. If these Fc values are taken for the next round, by fill-in, they may eventually converge to the true values and the map will be correct. If they are rezeroed at each round, the only way for the process to restore symmetry is by modifying the phases of all the other reflections to obtain a symmetrical density wich is different from the correct one obtained with all the reflections.