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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. - PowerPoint PPT Presentation
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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
The problem is that the raw data are the squares of the modulus of the
Fourier transform.
That´s the famous phase problem.
In protein crystallography, there are several ways to get the phases:
• Molecular replacement
• Heavy atom methods
• Direct methods
• Non-standard methods
Mol A: GPGVLIRKPYGARGTWSGGVNDDFFH...Mol B: GPGIGIRRPWGARGSRSGAINDDFGH...
Mol A Mol B?
Molecular replacement
If we have phases from a similar model...
Amplitudes: Manx
Phases: Manx
Amplitudes: Cat
Phases: Cat
Amplitudes: Cat
we can use
Phases: Manx
...we can combine them with the experimental amplitudes to get a better model.
Patterson maps can be used to find
.... the proper orientation (rotation)
.... the proper position (translation)
for the search model.
The density map The Patterson map
í
iiiilkhlzkyhxifF )](2exp[
,,
j
jjjjlkhlzkyhxifF )](2exp[
,,
ji
jijijijilkhzzlyykxxhiffI
,,,
))]()()((2exp[
The Patterson map is the Fourier transform of the intensities.
It can be calculated without the phases.
The matching procedure requires a search in up to six dimensions
Luckily, the problem can be factorized into
• first, a rotation search
• then, a translation search
Flow chart of a typical molecular replacement procedure (AMORE)
xyzin1 (*1.pdb)
table1 (*1.tab)
hklpck1 (*1.hkl)
clmn1 (*1.clmn)
tabfunrotfun
(generate)rotfun (clmn)
hklin (*.mtz)
hklpck0 (*0.hkl)
clmn0 (*0.clmn)
rotfun (clmn)sortfun
rotfun (cross)}
rotfun (cross)
SOLUTRC
trafun (CB)
SOLUTTF
fitfun (rigid)
SOLUTF
pdbset
solution.pdb
Poor phases yield self-fulfilling prophesies
Amplitudes: Karlé
Phases: Karlé
Amplitudes: Hauptmann
Phases: Hauptmann
Amplitudes: Hauptmann
If Karlé phases Hauptmann, Hauptmann is Karléd!
Phases: Karlé
Heavy atom methods
?
Can we do X-ray holography?
Can we do holography with crystals?
In principle yes, but the limited coherence length requires a local reference scatterer.
For a particular h,k,l
FP
FH1
FH2
FPH1
FPH1
we can collect all knowledge about amplitudes and phases in a diagram
(the so-called Harker diagram)
• Normally, there´s the problem that different crystals are not strictly isomorphous.
• Thus, the best is a reference scatterer that can be switched on and off.
Absorption is accompanied by dispersion.
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?
7 keV
25 keV 0.5 Å
1.8 ÅK
LIII
26-46
64-
H He
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
Actinides Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No Lr
The MAD periodic table
All phasing can be done on one crystal.
F1,2
F-1,-2
ab
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.
dxdydzzyx eF
lzkyhxi
lkh
2
,,,,
dxdydzzyx eF
lzkyhxi
lkh
2
,,,,
zyxzyx ,,,,
FeF lkh
lzkyhxi
lkhdxdydzzyx
,,
2
,,,,
assuming
zyxzyx ,,,, with absorption:
Direct methods
?
Atomic resolution data
the best approach for small molecules
If atoms can be treated as point-scatterers, then
if all involved structure factors are strong
100 atoms in the unit cell
a small protein
The method is blunt for lower resolution or too many atoms.
Three-beam phasing
?
very low mosaicity data
an exciting, but not yet practical way
An example from our work
(solved by a combination of MAD and MR)
Metal ions
Can we tell from the fluorescence scans?
Normally yes, but not in this case!
Co
Zn
FeNi
Cu
Compton
Can we tell from the anomalous signal?
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
Here´s the maps!
Quantitatively:
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. Sabała
Thanks to Gleb Bourenkov, MPI Hamburg c/o DESY
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