the phase problem in protein crystallography
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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 PresentationTRANSCRIPT
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The phase problem
in protein crystallography
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The phase problem
in protein crystallography
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Bragg diffraction of X-rays
(photon energy about 8 keV, 1.54 Å)
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Structure factors and electron density
are a Fourier pair
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The problem is that the raw data are the squares of the modulus of the
Fourier transform.
That´s the famous phase problem.
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In protein crystallography, there are several ways to get the phases:
• Molecular replacement
• Heavy atom methods
• Direct methods
• Non-standard methods
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Mol A: GPGVLIRKPYGARGTWSGGVNDDFFH...Mol B: GPGIGIRRPWGARGSRSGAINDDFGH...
Mol A Mol B?
Molecular replacement
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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.
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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
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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.
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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
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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
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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
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Heavy atom methods
?
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Can we do X-ray holography?
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Can we do holography with crystals?
In principle yes, but the limited coherence length requires a local reference scatterer.
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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)
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• 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.
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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.
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Which elements are useful for MAD data collection?
7 keV
25 keV 0.5 Å
1.8 ÅK
LIII
26-46
64-
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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
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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.
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dxdydzzyx eF
lzkyhxi
lkh
2
,,,,
dxdydzzyx eF
lzkyhxi
lkh
2
,,,,
zyxzyx ,,,,
FeF lkh
lzkyhxi
lkhdxdydzzyx
,,
2
,,,,
assuming
zyxzyx ,,,, with absorption:
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Direct methods
?
Atomic resolution data
the best approach for small molecules
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If atoms can be treated as point-scatterers, then
if all involved structure factors are strong
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100 atoms in the unit cell
a small protein
The method is blunt for lower resolution or too many atoms.
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Three-beam phasing
?
very low mosaicity data
an exciting, but not yet practical way
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An example from our work
(solved by a combination of MAD and MR)
Metal ions
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Can we tell from the fluorescence scans?
Normally yes, but not in this case!
Co
Zn
FeNi
Cu
Compton
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Can we tell from the anomalous signal?
order in the periodic table: Fe, Co, Ni, Cu, Zn
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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
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Thanks to my group, particularly S. Odintsov and I. Sabała
Thanks to Gleb Bourenkov, MPI Hamburg c/o DESY