The phase problem
1 / 32

The phase problem in protein crystallography - PowerPoint PPT Presentation

  • Uploaded on

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.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
Download Presentation

PowerPoint Slideshow about ' The phase problem in protein crystallography' - gilles

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

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)

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

Mol B

If we have phases from a similar model... the phases:

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

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.

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)

rotfun (clmn)


hklin (*.mtz)

hklpck0 (*0.hkl)

clmn0 (*0.clmn)


rotfun (cross)

rotfun (generate)

rotfun (clmn)


xyzin1 (*1.pdb)

table1 (*

hklpck1 (*1.hkl)

clmn1 (*1.clmn)

fitfun (rigid)


trafun (CB)

rotfun (cross)





Poor phases yield self-fulfilling prophesies (AMORE)

Amplitudes: Karlé

Phases: Karlé

Amplitudes: Hauptmann

Phases: Hauptmann

Amplitudes: Hauptmann

Phases: Karlé

If Karlé phases Hauptmann, Hauptmann is Karléd!

Can we do holography with crystals? (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.

25 keV

0.5 Å



7 keV

1.8 Å



The MAD periodic table not strictly isomorphous.

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

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.

with absorption:

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)

Metal ions

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