Model parameters, such as coordinates and ADPs, are not refined simultaneously but at separate steps (see §2.2 for details). phenix.refine uses the following refinement target function for restrained refinement of individual coordinates, A similar function is used in restrained ADP refinement, Here, Texp is the crystallographic term that relates the experimental data to the model structure factors. It can be a least-squares target (LS; for example, as defined in Afonine et al., 2005a ▶ ), an amplitude-based maximum-likelihood target (ML; for example, as defined in Afonine et al., 2005a ▶ ) or a phased maximum-likelihood target (MLHL; Pannu et al., 1998 ▶ ). For refinement of coordinates, Texp can also be defined in real space (see below).
Txyz_restraints and Tadp_restraints are restraint terms that introduce a priori knowledge, thus helping to compensate for the insufficient amount of experimental data owing to finite resolution or incompleteness of the data set typically observed in macromolecular crystallography. Note that the restraint terms are not used in certain situations, for example rigid-body coordinate refinement, TLS refinement, occupancy refinement, f′/f′′ refinement or if the data-to-parameter ratio is extremely high. In these cases the total refinement target is reduced to Texp.
The weights wxcscale, wxc and wc (or wxuscale, wxu and wu, correspondingly) are used to balance the relative contributions of experimental and restraints terms. The automatic weight-estimation procedure is implemented as described in Brünger et al. (1989 ▶ ) and Adams et al. (1997 ▶ ) with some variations and is used by default to calculate wxc and wxu. The long-term experience of using a similar scheme in CNS and PHENIX indicates that it is typically robust and provides a good estimate of weights in most cases, especially at medium to high resolution. In cases where this procedure fails to produce optimal weights, a more time-intensive automatic weight-optimization procedure may be used, as originally described by Brünger (1992 ▶ ) and further adopted by Afonine et al. (2011 ▶ ), in which an array of wxcscale or wxuscale values is systematically tested in order to find the value that minimizes Rfree while keeping the overall model geometry deviations from ideality within a predefined range. The weight wc (or wu, correspondingly) is used to scale the restraints contribution, mostly duplicating the function of wxcscale (or wxuscale), while allowing an important unique option of excluding the restraints if necessary (for example, at subatomic resolution). Setting wc = 0 (or wu = 0) reduces the total refinement target to Texp.
In maximum-likelihood (ML)-based refinement (Pannu & Read, 1996 ▶ ; Bricogne & Irwin, 1996 ▶ ; Murshudov et al., 1997 ▶ ; Adams et al., 1997 ▶ ; Pannu et al., 1998 ▶ ) the calculation of the ML target (Lunin & Urzhumtsev, 1984 ▶ ; Read, 1986 ▶ , 1990 ▶ ; Lunin & Skovoroda, 1995 ▶ ) requires an estimation of model error parameters, which depend on the current atomic parameters and bulk-solvent model and scales. Since the atomic parameters and the bulk-solvent model are updated during refinement, the ML error model has to be updated correspondingly, as described in Lunin & Skovoroda (1995 ▶ ), Urzhumtsev et al. (1996 ▶ ) and Afonine et al. (2005a ▶ ).
Txyz_restraints and Tadp_restraints are restraint terms that introduce a priori knowledge, thus helping to compensate for the insufficient amount of experimental data owing to finite resolution or incompleteness of the data set typically observed in macromolecular crystallography. Note that the restraint terms are not used in certain situations, for example rigid-body coordinate refinement, TLS refinement, occupancy refinement, f′/f′′ refinement or if the data-to-parameter ratio is extremely high. In these cases the total refinement target is reduced to Texp.
The weights wxcscale, wxc and wc (or wxuscale, wxu and wu, correspondingly) are used to balance the relative contributions of experimental and restraints terms. The automatic weight-estimation procedure is implemented as described in Brünger et al. (1989 ▶ ) and Adams et al. (1997 ▶ ) with some variations and is used by default to calculate wxc and wxu. The long-term experience of using a similar scheme in CNS and PHENIX indicates that it is typically robust and provides a good estimate of weights in most cases, especially at medium to high resolution. In cases where this procedure fails to produce optimal weights, a more time-intensive automatic weight-optimization procedure may be used, as originally described by Brünger (1992 ▶ ) and further adopted by Afonine et al. (2011 ▶ ), in which an array of wxcscale or wxuscale values is systematically tested in order to find the value that minimizes Rfree while keeping the overall model geometry deviations from ideality within a predefined range. The weight wc (or wu, correspondingly) is used to scale the restraints contribution, mostly duplicating the function of wxcscale (or wxuscale), while allowing an important unique option of excluding the restraints if necessary (for example, at subatomic resolution). Setting wc = 0 (or wu = 0) reduces the total refinement target to Texp.
In maximum-likelihood (ML)-based refinement (Pannu & Read, 1996 ▶ ; Bricogne & Irwin, 1996 ▶ ; Murshudov et al., 1997 ▶ ; Adams et al., 1997 ▶ ; Pannu et al., 1998 ▶ ) the calculation of the ML target (Lunin & Urzhumtsev, 1984 ▶ ; Read, 1986 ▶ , 1990 ▶ ; Lunin & Skovoroda, 1995 ▶ ) requires an estimation of model error parameters, which depend on the current atomic parameters and bulk-solvent model and scales. Since the atomic parameters and the bulk-solvent model are updated during refinement, the ML error model has to be updated correspondingly, as described in Lunin & Skovoroda (1995 ▶ ), Urzhumtsev et al. (1996 ▶ ) and Afonine et al. (2005a ▶ ).
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