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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.

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slide1
The phase problem

in protein crystallography

slide2
The phase problem

in protein crystallography

slide3
Bragg diffraction of X-rays

(photon energy about 8 keV, 1.54 Å)

slide5
The problem is that the raw data are the squares of the modulus of the Fourier transform.

That´s the famous phase problem.

slide6
In protein crystallography, there are several ways to get the phases:
  • Molecular replacement
  • Heavy atom methods
  • Direct methods
  • Non-standard methods
slide7
Molecular replacement

Mol A: GPGVLIRKPYGARGTWSGGVNDDFFH...

Mol B: GPGIGIRRPWGARGSRSGAINDDFGH...

?

Mol A

Mol B

slide8
If we have phases from a similar model...

Amplitudes: Manx

Phases: Manx

Amplitudes: Cat

Phases: Cat

Phases: Manx

Amplitudes: Cat

...we can combine them with the experimental amplitudes to get a better model.

we can use

slide9
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

slide10
The Patterson map is the Fourier transform of the intensities.

It can be calculated without the phases.

slide11
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
slide12
Flow chart of a typical molecular replacement procedure (AMORE)

rotfun (clmn)

sortfun

hklin (*.mtz)

hklpck0 (*0.hkl)

clmn0 (*0.clmn)

}

rotfun (cross)

rotfun (generate)

rotfun (clmn)

tabfun

xyzin1 (*1.pdb)

table1 (*1.tab)

hklpck1 (*1.hkl)

clmn1 (*1.clmn)

fitfun (rigid)

pdbset

trafun (CB)

rotfun (cross)

SOLUTF

SOLUTTF

solution.pdb

SOLUTRC

slide13
Poor phases yield self-fulfilling prophesies

Amplitudes: Karlé

Phases: Karlé

Amplitudes: Hauptmann

Phases: Hauptmann

Amplitudes: Hauptmann

Phases: Karlé

If Karlé phases Hauptmann, Hauptmann is Karléd!

slide16
Can we do holography with crystals?

In principle yes, but the limited coherence length requires a local reference scatterer.

slide17
For a particular h,k,l

FH2

FP

FPH1

FH1

FPH1

we can collect all knowledge about amplitudes and phases in a diagram

(the so-called Harker diagram)

slide18
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.
slide19
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.

slide20
Which elements are useful for MAD data collection?

25 keV

0.5 Å

LIII

64-

7 keV

1.8 Å

K

26-46

slide21
The MAD periodic table

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

ActinidesTh Pa U Np Pu Am Cm Bk Cf Es Fm Md No Lr

slide22
All phasing can be done on one crystal.

F1,2

a

b

F-1,-2

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.

slide23
assuming

with absorption:

slide24
Direct methods

?

Atomic resolution data

the best approach for small molecules

slide25
If atoms can be treated as point-scatterers, then

if all involved structure factors are strong

slide26
100 atoms in the unit cell

a small protein

The method is blunt for lower resolution or too many atoms.

slide27
Three-beam phasing

?

very low mosaicity data

an exciting, but not yet practical way

slide28
An example from our work

(solved by a combination of MAD and MR)

Metal ions

slide29
Can we tell from the fluorescence scans?

Compton

Zn

Cu

Fe

Ni

Co

Normally yes, but not in this case!

slide30
Can we tell from the anomalous signal?

order in the periodic table: Fe, Co, Ni, Cu, Zn

slide31
Here´s the maps!

2fo-fc map, 1.05 Å

anomalous map, 1.05 Å

anomalous map, 1.54 Å

Quantitatively:

f“ (1.05 Å) = 1.85  0.05 f“ (1.54 Å) = 2.4  0.2

slide32
Thanks to my group, particularly S. Odintsov and I. Sabała

Thanks to Gleb Bourenkov, MPI Hamburg c/o DESY

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