Phase problem sorts out all the problem which occurs after the x-ray crystallization data. In this way, we have to find out maximum values of phases and amplitude both to give the better picture of electron density map and later it is verified and validated upto maximum refined 3-D structure.

2. PHASE
PROBLEM
SWARAJ PRASAD
M.Phil BIOINFORMATICS
?

3. Why Do We Need the Phase?
Structure Factor
Fourier transform
InverseFouriertransform
Electron D
In order to reconstruct the molecular image (electron density)
from its diffraction pattern both the intensity and phase, which
can assume any value from 0 to 2 , of each of the thousands of
measured reflections must be known.

4. WHAT IS PHASE PROBLEM?
• From x-ray diffraction, we have obtained two parameters
• A. Amplitudes
• B. Phases
• In almost most of the cases amplitudes are retrieved but
retrieving of phases is a bit difficult issue.
• In small molecule crystallography basic assumptions on
atomicity and amplitudes can give rise to phase
extraction.
• But, it is not possible in macromolecular crystallography.
• From that we need a different system which include,
MIR, MR, SAD,MAD, AS, etc.

7. Methods to solve phase problem
Molecular Isomprphous Replacement Method
A. Single Isomorphous Replacement Method
Anomalous Scattering Method
A. Single wavelength anomalous diffraction
method(SAD)
B. Multiple wavelength anomalous diffraction
method(MAD)

8. Single Isomorphous Replacement Method
The contribution of the added heavy atom to the
structure-factor amplitudes and phases is best
illustrated on an Argand diagram.
The amplitudes of a reflection are measured for the
native crystal, |fp|, and for the derivative crystal,
|fph|.
The isomorphous difference, |fh| ’ |fph| |fp|, can
be used as an estimate of the heavy atom.
Structure-factor amplitude to determine the heavy
atom’s positions using patterson or direct methods.

9. Argand diagram for SIR. |FP| is the
amplitude of a reflection for the native
crystal and |FPH| is that for the derivative
crystal.

10. Anomalous Dispersion Methods
All elements display an anomalous dispersion (AD) effect in X-ray diffraction .
For elements such as e.g. C,N,O, etc., AD effects are negligible.
For heavier elements, especially when the X-ray wavelength approaches an atomic
absorption edge of the element, these AD effects can be very large.
The scattering power of an atom exhibiting AD effects is:
fAD = fn + f' + i f”
fnis the normal scattering power of the atom in absence of AD effects
f' arises from the AD effect and is a real factor (+/- signed) added to fn
f" is an imaginary term which also arises from the AD effect
f" is always positive and 90 ahead of (fn + f') in phase angle
The values of f' and f" are highly dependent on the wave-length of the X-
radiation.
In the absence AD effects, Ihkl = I-h-k-l (Firedel’s Law).
With AD effects, Ihkl ≠ I-h-k-l (Friedel’s Law breaks down).

11. Breakdown of Friedel’s Law
(Fhkl Left) Fn represents the total scattering
by "normal" atoms without AD effects, f’
represents the sum of the normal and real AD
scattering values (fn + f'), f" is the
imaginary AD component and appears 90° (at a
right angle) ahead of the f’ vector and the
total scattering is the vector F+++.
(F-h-k-l Right) F-n is the inverse of Fn (at -
f’
f’

12. Multiple Wavelength Anomalous Diffraction
method
Isomorphous replacement has several problems:
Nonisomorphism between crystals (unit-cell changes, reorientation
of the protein.
Conformational changes, changes in salt and solvent ions.
Problems in locating all the heavy atoms.
Problems in refining heavy-atom positions, occupancies.
Thermal parameters and errors in intensity measurements.
Data are collected from a single crystal at several wavelengths,
typically three, in order to maximize the absorption and dispersive
effects.
Wavelengths are chosen at the absorption (f’’) peak (λ1), at the point
of inflection on the absorption curve (λ 2), where the dispersive term
f ‘ has its minimum, and at a remote wavelength (λ 3 and/or λ 4) to
maximize the dispersive difference to λ 2.

14. This Multiwavelength Anomalous Diffraction
method often gives very strong phase
information and is the source of many new
structures.

15. SINGLE WAVELENGTH ANOMALOUS DIFFRACTION
SAD can simply utilize the intrinsic anomalous scatterers
present in the macromolecule, such as the S atoms of
cysteine and methionine or bound ions.
The challenge is in maximizing and measuring the very
small signal, since the Bijvoet ratio can be as low as 1%
when the typical merging R factor is several times this
value.
The trick lies in making multiple measurements of
reflections at an appropriate wavelength in order to
achieve a high multiplicity that will give statistically
accurate measurements of the anomalous difference.
The data should also be as complete as possible

18. 2.1 A ° electron-density map for the S-SAD example before and after density modification
using SHELXE

19. A SHELXE-derived 2.1 A ° resolution electron-density map phased from
a Hg-SAD data set with superimposed polyalanine trace produced by
SHELXE. The view is down the crystallographic threefold axis.

20. PHASE IMPROVEMENT

22. (a) 2.6 A ° MIR electron density. (b) Electron density after solvent flattening and
histogram matching in DM. The solvent envelope determined by DM is shown in green.