Protein crystallography

crystallography
- shine x-ray (1.5A = 1x10^-10 wavelength) on crystals (protein + h2o)
- treat reflections as summation waves (constructive interference = intensity)
- Bragg's Law: n(x-ray wavelength) = 2dsin(theta), d=lattice plane separation distance=resolution, theta is the incidence=reflection angle bouncing off the lattice plane, n=integral number of wavelengths in path length (extra distance travelled by beam on the 2nd lattice plane)
- structure factors (F) - wave equations that describe the reflections
- recombine structure factors to get an image of the molecular structure in the unit cell
- fourier transform - transforms reflections (diffraction patterns in reciprocal space) to electron density function in real space (and vice-versa)
- need to measure intensity and position (+ angle of reflection) of dots (miller indices hkl - name of reflections) in diffraction patterns, not errors (sigma)
- large unit crystals (proteins) produce reflections closer together (inverse relationship of theta and d in Bragg's Law)
- For a unit cell edge of 40 Å, and data collected to 2 Å resolution (d spacing)
40/2 = 20 planes = 20 spots along that direction
- For a unit cell edge of 80 Å, you now have 40 spots in the"same space"
so the reflections are twice as close together
- "as cell gets bigger, diffraction info is more + more compressed"
- phase problem - phase information is lost in the experiment, work arounds:
- MAD (multiple anomalous dispersion) - use SeMet, estimate Se atom phase from difference in Friedel mates, need to collect lots of data to find extent of error
- MIR (multiple isomorphous replacement) - soak crystals in heavy atoms (HA) while keeping the protein (P) isomorphic (same form), then we take the difference in structure factors, F(HA+P) - F(HA) = F(P), distance shown in Patterson map
- MR (molecular replacement) - homology, need at least 35% sequence identity, performs rotational and translational operations to match model with unknown
Methods for phase improvement:
- solvent flattening - ignore solvent envelope from e- density and mask it out
- histogram matching
- non-crystallographic symmetry (NCS) averaging