On the suitability of using the diagonal Gaussian approximation in the calculation of the magnitude-based likelihood functionстатья
Статья опубликована в высокорейтинговом журнале
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Дата последнего поиска статьи во внешних источниках: 17 июня 2021 г.
Аннотация:Statistical likelihood maximization is currently one of the main tools incomputational procedures in biological crystallography. In these procedures, thelikelihood function is calculated, as a rule, within the framework of a diagonalGaussian approximation (DGA) of the joint probability distribution of the realand imaginary parts of a set of structure factors. This approximation assumespairwise uncorrelated values of various structure-factor components. In thispaper, exact formulas are derived for pairwise correlations of structure factors,and conditions under which these correlations can be considered to be negligibleare discussed. It is shown that in the case where the probability distribution ofthe atomic coordinates is related to the region of the molecule or its domains,the correlation of the structure factors of reflections s and w is determinedmostly by the magnitudes of the Fourier transform of the probabilitydistribution calculated at the points 2s, 2w, s w and s + w. However, in thecase where the probability distribution describes small corrections to thecoordinates of the existing preliminary atomic model, the correlation isdetermined by the values of the structure factors of the preliminary model thatcorrespond to the 2s, 2w, s w and s + w reflections rather than by the Fouriertransform of the probability distribution. Test cases demonstrate that thepractice of using the DGA for calculation of the likelihood when based on setscontaining neighbouring reflections may be unjustified in some crystallographicapplications, especially in single-particle studies.