From the phase problem to structure refinement

Structure factors and electron density. The Fourier transform and its properties. Convolution. The Patterson function. Moduli and phases. The phase problem. Matthews volume. Methods for solving the phase problem for protein crystals.

Phasing the diffraction data through Molecular Replacement. Bulk-solvent correction. Density Modification techniques. Solvent flattening/flipping. Histogram matching. Non-crystallographic symmetry: identification of rotation and translation operators. Density averaging.

Phasing techniques based on isomorphous replacement or anomalous scattering. Data preparation. Determination of the position of the heavy atom or the anomalous scatterer: direct methods and Patterson methods. SIR: Single Isomorphous Replacement. SAD: Single-wavelength Anomalous Diffraction. Resolution of the ambiguity on the phases determined by SIR or SAD. MIR: Multiple Isomorphous Replacement. MAD: Multiple-wavelength Anomalous Diffraction. Electron density maps. Resolution and structural elements.

From phases to electron density. Model building. Refinement in reciprocal space. Observations and parameters. Restraint and constraint. Minimization functions for parameter optimization. Refinement protocol. Side chain conformations. Solvent and ligand modeling. Rfree and Rwork.

Importance of structure validation. Bayesian statistics applied to crystallographic model validation. Global and local parameters. Geometry analysis: bond angles and distances, Ramachandran diagram, repulsive interactions (clashes). Analysis of electron density and correlation parameters for single residues. Validation of the ligand occupancy and geometry.