The phase problem in protein crystallography. The phase problem in protein crystallography. Bragg diffraction of X-rays (photon energy about 8 keV, 1.54 Å). Structure factors and electron density are a Fourier pair.
(photon energy about 8 keV, 1.54 Å)
are a Fourier pair
The problem is that the raw data are the squares of the modulus of the Fourier transform.
That´s the famous phase problem.
Molecular replacement the phases:
Mol A: GPGVLIRKPYGARGTWSGGVNDDFFH...
Mol B: GPGIGIRRPWGARGSRSGAINDDFGH...
If we have phases from a similar model... the phases:
...we can combine them with the experimental amplitudes to get a better model.
we can use
Patterson maps can be used to find the phases:
.... the proper orientation (rotation)
.... the proper position (translation)
for the search model.
The density map
The Patterson map
The Patterson map is the Fourier transform of the intensities.
It can be calculated without the phases.
If Karlé phases Hauptmann, Hauptmann is Karléd!
Heavy atom methods (AMORE)
Can we do X-ray holography? (AMORE)
In principle yes, but the limited coherence length requires a local reference scatterer.
For a particular h,k,l (AMORE)
we can collect all knowledge about amplitudes and phases in a diagram
(the so-called Harker diagram)
Absorption is accompanied by dispersion. not strictly isomorphous.
This Kramers-Kronig equation is very general:
Its (almost) only assumption is the existance of a universal maximum speed (c) for signal propagation.
Which elements are useful for MAD data collection? not strictly isomorphous.
The MAD periodic table not strictly isomorphous.
Li Be B C N O F Ne
Na Mg Al Si P S Cl Ar
K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr
Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe
Cs Ba La Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn
Fr Ra Ac Rf Ha
Lanthanides Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu
ActinidesTh Pa U Np Pu Am Cm Bk Cf Es Fm Md No Lr
All phasing can be done on one crystal. not strictly isomorphous.
F1,2 : scattering from b is phase behind
F-1,-2 : scattering from b is phase ahead
In the presence of absorption, Bijvoet pairs are nonequal.
assuming not strictly isomorphous.
Direct methods not strictly isomorphous.
Atomic resolution data
the best approach for small molecules
If atoms can be treated as point-scatterers, then not strictly isomorphous.
if all involved structure factors are strong
100 atoms in the unit cell not strictly isomorphous.
a small protein
The method is blunt for lower resolution or too many atoms.
Three-beam phasing not strictly isomorphous.
very low mosaicity data
an exciting, but not yet practical way
An example from our work not strictly isomorphous.
(solved by a combination of MAD and MR)
Can we tell from the fluorescence scans? not strictly isomorphous.
Normally yes, but not in this case!
Can we tell from the anomalous signal? not strictly isomorphous.
order in the periodic table: Fe, Co, Ni, Cu, Zn
Here´s the maps! not strictly isomorphous.
2fo-fc map, 1.05 Å
anomalous map, 1.05 Å
anomalous map, 1.54 Å
f“ (1.05 Å) = 1.85 0.05 f“ (1.54 Å) = 2.4 0.2
Thanks to my group, particularly S. Odintsov and I. Saba not strictly isomorphous.ła
Thanks to Gleb Bourenkov, MPI Hamburg c/o DESY