August, 19

• 9.00-10.30 Fundamentals :
  • – field of crystallography
  • – basic goal of structural crystallography
  • – crystals; direct space; fractional coordinates;
  • – crystallographic symmetries
  • – crystallographic space groups
  • – diffraction by crystals; structure factors; phase problem
• 11.00-12.30 Fundamentals of Fourier transformation
  • – Fourier transformation of a periodic function
  • – three-dimensional Fourier transformation
  • – Fourier transformation of a grid function
  • – Fourier transformation and a convolution
  • – Fourier coefficients and the origin shift
• 14.00-15.30 Models of crystals:
  • – Atomic structure
  • – Ionic crystals
  • – Symmetry and phase transitions
  • – Molecular crystals; macromolecules
  • – Proteins, nucleic acids, viruses, macromolecular complexes
  • – secondary and spatial structure
  • – model of independent isotropic atoms
  • – fixed-bond models for chain molecules
  • – anisotropic atoms
  • – multipolar modelling
  • – crystallographic solvent molecules and bulk solvent
  • – other models
  • – different levels of a crystal description
• 16.00-17.30 Problem of structure determination :
  • – phase problem
  • – direct methods
  • – intermediate density calculation
  • – density analysis and interpretation
  • – model refinement
  • – history and milestones

August, 20

• 9.00-10.30 Patterson methods
  • – Patterson function and its properties
  • – Patterson function and the atomic structure
  • – resolution of the Patterson function
  • – superposition methods
• 11.00-12.30 Fundamentals of probabilities , statistics and linked tools
  • – Central Limit Theorem
  • – Bayesian approach
  • – likelihood approach
  • – least-squares method
  • – von Mises distribution; modified Bessel functions
• 14.00-15.30 Direct methods
  • – distribution of structure factors
  • – sigma-2 formula
  • – tangent-formula
  • – MULTAN approach
• 16.00-17.30 Molecular Replacement :
  • – use of a particular information : approximate model
  • – 6D-search
  • – rotation function
  • – translation function
  • – rigid-body refinement

August, 21

• 9.00-10.30 Experimental methods (MIR, SIR, MAD)
  • – experiment in modified conditions
  • – SIR method
  • – Hendrickson-Lattman phase distribution
  • – MIR method
  • – MAD method
• 11.00-12.30 Optimisation techniques :
  • – different classes of optimisation techniques
  • – optimisation without derivatives
  • – gradient methods
  • – second-order optimisation methods
  • – numeric realisation of optimisation techniques
  • – random search methods; Metropolis algorithm
  • – optimisation of several criteria simultaneously
  • – optimisation with constraints
  • – methods of Binary Integer Programming
• 14.00-15.30 Atomic model refinement :
  • – the problems of the refinement
  • – Fast Differentiation algorithm
  • – fast calculation of structure factors
  • – crystallographic criteria and their derivatives
  • – scheme of a refinement program
  • – model quality
• 16.00-17.30 Model building :
  • – main difficulties
  • – main information
  • – basic ideas : connectivity, libraries
  • – automated model building

August, 22

• 9.00-10.30 Density improvement
  • – main principles of density improvement
  • – iterative algorithms
  • – density modification
  • – solvent flattening
  • – histogram matching
  • – atomicity
• 11.00-12.30 Direct phasing from low resolution
  • – phasing and extra general information
  • – different approaches to phasing; direct and reciprocal space
  • – generalised models
  • – multiples minima and the search of the solution
  • – cluster analysis and general scheme of the direct phasing
  • – direct phasing with histograms
  • – connectivity features of Fourier maps and direct phasing
  • – binary integer programming and direct phasing
• 14.00-15.30 Currently existing methodological problems
  • – data analysis, space group determination; twinning
  • – difficult cases of molecular replacement; search with multiple models or with a very small partial model;
  • – phase improvement: decreasing limits on starting phase error and resolution
  • – modelling at subatomic resolution
  • – modelling at low and at intermediate resolution
  • – refinement: large objects, high resolution; large number of data and parameters;
  • – folding; model building by homology; structure prediction
  • – direct phasing from low resolution; determination of the secondary structure elements
  • – structure analysis; docking