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

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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

Molecular replacement

Mol A: GPGVLIRKPYGARGTWSGGVNDDFFH...

Mol B: GPGIGIRRPWGARGSRSGAINDDFGH...

?

Mol A

Mol B

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

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

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)

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

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!

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

FH2

FP

FPH1

FH1

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.

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

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.

assuming

with absorption:

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.

Can we tell from the anomalous signal?

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

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

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

Thanks to Gleb Bourenkov, MPI Hamburg c/o DESY

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