Site map

This is a map through lecture materials presented at the 2nd Protein Crystallography Intensive Course in March 2006 at the University of Massachusetts Amherst. The lectures were first developed by Karsten Theis during his postdoc with Caroline Kisker at Stony Brook University, and have since been extensively tuned and updated. Kevin Cowtan (York, UK) invented the Fourier duck featured in some of the slides; his color coding of the phases inspired the "color-coded phase calculator", which Karsten Theis developed to help explain diffraction fundamentals (Friedel's law, systematic absences, influence of disorder on intensities at different resolution).

The map is sorted by three categories (you could say it is three-dimensional).

The slides are labeled Fxx, Mxx, and Sxx, refering to figures shown on the Friday and Monday of the course and supplementary material.

Apart from the lecture slides, here are some background reading suggestions and some links to material at other websites:


Real space


Reciprocal space

Crystals (F5-F19, hands-on exercise)

    /THEORY/ periodicity, translational symmetry (F6) 
   /ACTION/ translations in 3 directions (F8)
  /RESULT/ mathematical crystal, unit cell (F6)
    /THEORY/ crystallization requires homogenous sample (F10)
   /ACTION/ check chemical purity, concentration, aggregation (F11-F12)
  /RESULT/ go ahead for crystallization, or back to making sample
    /THEORY/ solubility, nucleation and growth (F13) 
   /ACTION/ vapor diffusion with pure sample (F14-F19)
  /RESULT/ protein crystal (M41)


X-rays (F24)

    /THEORY/ accelerating electrons 
   /ACTION/ electrons and magnets at synchrotron
  /RESULT/ bright "white" X-ray beam

    /THEORY/ bound electrons 
   /ACTION/ electronic transitions in copper anode
  /RESULT/ copper Kalpha radiation (wavelength = 1.54 Angstroems)

Diffraction image (F22, hands-on exercise)

    /THEORY/ reciprocal space, Ewald construction (F39, F41-F42, M15)
   /ACTION/ rotate a crystal between source and detector (F43-F45)
  /RESULT/ series of diffraction images with spots (F46-F47)

Intensities (M2, hand-on exercise)

    /INPUT / diffraction images
   /ACTION/ indexing
  /OUTPUT/ unit cell, crystal orientation
    /INPUT / predicted spots (from indexing), images
   /ACTION/ integration
  /OUTPUT/ intensities I(HKL): observed reflections
    /INPUT / observed reflections 
   /ACTION/ check Laue symmetry, systematic absences (M10, S1, S2)
  /OUTPUT/ space group or set of possible space groups
    /INPUT / Laue symmetry, Friedel's law (M13) 
   /ACTION/ scale images, average symmetry equivalen reflections
  /OUTPUT/ unique reflections with standard deviations
    /INPUT / unique reflections with standard deviations 
   /ACTION/ analysis done while scaling
  /OUTPUT/ resolution, completeness, signal/noise or Rmerge

Scattering and interference (F27-F29, movie)

    /THEORY/ elastic scattering (F25)
   /ACTION/ place sample into X-ray beam (F26)
  /RESULT/ scattered X-rays in all directions
    /THEORY/ interference
   /ACTION/ split beam in Michaelson interferometer (F30)
  /RESULT/ measure distances using light
    /THEORY/ interference, scattering vector (F34)
   /ACTION/ multiple scatterers observed at certain angle (F33-F35)
  /RESULT/ measure position using light with a certain yardstick

Diffraction (F37-F40)

    /THEORY/ diffraction, Laue conditions (F37-F40)
   /ACTION/ mount crystal and place into X-ray beam (hands-on exercise)
  /RESULT/ diffracted X-rays in certain directions, "reflections"
    /THEORY/ protein dynamics
   /ACTION/ static and dynamic disorder (M43-M46)
  /RESULT/ limited resolution of diffraction data (M36-M40)
    /THEORY/ weak crystal contacts
   /ACTION/ crystal imperfections, mosaicity
  /RESULT/ overlapping spots limit resolution for imperfect crystals

Symmetry (M3)

    /INPUT / symmetry of real space (unit cell F6, spacegroup M4-M9)
   /ACTION/ diffraction experiment (M10-M12)
  /OUTPUT/ symmetry of reciprocal space (M13)

Fourier transform (M17-M18, 2D examples M26-M28)

    /INPUT / Structure factors (magnitudes and phases)
   /ACTION/ Fourier synthesis (1D-example: M20-M25)
  /OUTPUT/ Electron density
    /INPUT / Electron density
   /ACTION/ Fourier analysis (1D-example: M19)
  /OUTPUT/ Structure factors (magnitudes and phases)

Electron density maps (M51, S12)

    /INPUT / observed magnitudes |Fo|(hkl), MIR or MAD phases 
   /ACTION/ Fourier transform
  /OUTPUT/ MIR or MAD electron density
    /INPUT / observed magnitudes |Fo|(hkl), Fc calculated from model 
   /ACTION/ Fourier transform of |Fo|-|Fc|, phic (S8, S9, S10, S11)
  /OUTPUT/ difference density
    /INPUT / observed magnitudes |Fo|(hkl), Fc calculated from model 
   /ACTION/ Fourier transform of 2|Fo|-|Fc|, phic
  /OUTPUT/ 2Fo-Fc density (M32)

    /INPUT / low resolution data, model phases 
   /ACTION/ Fourier transform
  /OUTPUT/ density with large model bias (M39-M40)   

    /INPUT / low quality phases, high resolution, non-cryst. symmetry
   /ACTION/ density modification: symmetry, solvent regions (S7)
  /OUTPUT/ density with less model bias

Atomic model (hands-on exercise)

    /INPUT / electron density 
   /ACTION/ manual building at graphic station (M53-M54)
  /OUTPUT/ atomic model (F1, M52)


Structure factor magnitudes

    /THEORY/ |F|(hkl) proportional to square root of I(hkl) 
   /ACTION/ take square roots of I, deal with negative I
  /RESULT/ observed structure factor magnitudes |Fo|(hkl)
    /THEORY/ diffraction from atoms at random positions 
   /ACTION/ compare theory to observed data
  /RESULT/ overall B-factor, test for twinning, solvent content (M47-M50)

Obtaining phases to solve the structure (M16, M29)

    /THEORY/ structure factors define structure 
   /ACTION/ estimate phases somehow (M30-M35)
  /RESULT/ electron density and atomic model (M51)

    /THEORY/ isomorphous replacement (MIR) or anomalous diffraction (MAD) 
   /ACTION/ make derivative or SeMet-variant, solve heavy atom structure
  /RESULT/ positions of heavy atoms, their contribution Fh 
    /THEORY/ linearity of Fourier transform: Fph = Fh + Fp 
   /ACTION/ compare calculated Fh and measured |Fp| and |Fph| (S3, S4)
  /RESULT/ approximate phases phi(hkl) for measured magnitudes (S5, S6)
    /THEORY/ small diff. in structure: small diff. in phases
   /ACTION/ Fourier transform of model to obtain phases (M32-33)
  /RESULT/ model phases that are similar to phases of crystal


Refinement (M42, S14, S13, S15)

    /INPUT / electron density, old model (S16) 
   /ACTION/ manual rebuilding at graphic station
  /OUTPUT/ new model (large changes, geometry somewhat broken)
    /INPUT / observed magnitudes |Fo|(hkl), ideal geometry, old model
   /ACTION/ optimize atomic positions against ideal geometry and R-factor
  /OUTPUT/ new model (small changes), new R-factor and free R-factor

    /INPUT / observed magnitudes |Fo|(hkl), ideal geometry, old model 
   /ACTION/ molecular dynamics restrained by diffraction data
  /OUTPUT/ new model, new R-factor and free R-factor

Model quality (M55-56)

    /THEORY/ structures are lowest energy, Fo=Fc
   /ACTION/ check model vs. ideal structures, B-factors, density
  /OUTPUT/ level of confidence for entire structure and parts of it


    /THEORY/ evolution 
   /ACTION/ correlate sequence conservation with structure
  /RESULT/ regions of possible functional importance
    /THEORY/ chemical properties of amino acids 
   /ACTION/ calculate charge distribution, hydrophobicity, accessibility
  /RESULT/ possible binding regions
    /THEORY/ functional models 
   /ACTION/ engineer protein based on structure and test mutant
  /RESULT/ support for model, or new model

    /INPUT / biochemical, genetic, structural data 
   /ACTION/ think
  /OUTPUT/ new ideas


-Karsten Theis, Mar 2006; for comments, please email