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.
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(photon energy about 8 keV, 1.54 Å)
are a Fourier pair
That´s the famous phase problem.
Mol A: GPGVLIRKPYGARGTWSGGVNDDFFH...
Mol B: GPGIGIRRPWGARGSRSGAINDDFGH...
...we can combine them with the experimental amplitudes to get a better model.
we can use
.... the proper orientation (rotation)
.... the proper position (translation)
for the search model.
The density map
The Patterson map
It can be calculated without the phases.
If Karlé phases Hauptmann, Hauptmann is Karléd!
In principle yes, but the limited coherence length requires a local reference scatterer.
we can collect all knowledge about amplitudes and phases in a diagram
(the so-called Harker diagram)
This Kramers-Kronig equation is very general:
Its (almost) only assumption is the existance of a universal maximum speed (c) for signal propagation.
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
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.
Atomic resolution data
the best approach for small molecules
if all involved structure factors are strong
a small protein
The method is blunt for lower resolution or too many atoms.
very low mosaicity data
an exciting, but not yet practical way
(solved by a combination of MAD and MR)
Normally yes, but not in this case!
order in the periodic table: Fe, Co, Ni, Cu, Zn
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 Gleb Bourenkov, MPI Hamburg c/o DESY