A robust bulk-solvent correction and anisotropic scaling procedure

Abstract

A reliable method for the determination of bulk-solvent model parameters and an overall anisotropic scale factor is of increasing importance as structure determination becomes more automated. Current protocols require the manual inspection of refinement results in order to detect errors in the calculation of these parameters. Here, a robust method for determining bulk-solvent and anisotropic scaling parameters in macromolecular refinement is described. The implementation of a maximum-likelihood target function for determining the same parameters is also discussed. The formulas and corresponding derivatives of the likelihood function with respect to the solvent parameters and the components of anisotropic scale matrix are presented. These algorithms are implemented in the CCTBX bulk-solvent correction and scaling module.

Figure 1

Algorithm for calculation of flat bulk-solvent model parameters k _sol and B _sol and the anisotropic scale matrix B _cart as implemented in CCTBX.

Figure 2

Flat bulk-solvent model parameters k _sol and B _sol determined for 21 test models (see text for details of the models) using the least-squares (LS) or maximum-likelihood (ML) target functions.

Figure 3

Flat bulk-solvent model parameters k _sol and B _sol for 35 structures selected from the PDB (PDB codes 1ci3, 1gzk, 1jh7, 1jj1, 1jvx, 1jzb, 1ev8, 1evf, 1k33, 1ijk, 1izr, 1kk7, 1kzn, 1lee,1 lfv, 1dzj, 1m5u, 1m8s, 1nfg, 1oz4, 3gwx, 1ev5, 1evg, 1f3u, 1g1b, 1p9h, 1r30, 1tve, 1hw3, 1hw4, 1ijb, 1izp, 1izq, 1ktk, 2gwx). Blue diamonds and red squares correspond to the bulk-solvent parameters calculated in CCTBX using least-squares (LS) and maximum-likelihood (ML) target functions, respectively. Black triangles represent the bulk-solvent parameters reported in the PDB file under keywords ‘KSOL’ and ‘BSOL’.

Figure 4

R factor (a) and ML function (b) (ML is normalized by the number of reflections in bins) calculated in resolution bins (for the structure with PDB code 1jj1): no scaling and bulk-solvent correction (black), parameters k _sol and B _sol and scale matrix B _cart taken from the PDB file (blue), scaling and bulk-solvent correction parameters calculated using CCTBX with the least-squares (a) and maximum-likelihood target (b).

Figure 5

R factor as a function of resolution (in Å) for the structures with PDB code 1jj1 (a) and 1lee (b). Bulk-solvent correction and anisotropic scaling performed with CNS1.0 (green), CNS1.1 (blue) and CCTBX (red).