Phase problem

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.

1. PHASE PROBLEM SWARAJ PRASAD M.Phil BIOINFORMATICS ?

2. Why Do We Need the Phase? Structure Factor Fourier transform Inverse Fourier transform Electron Density 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.

3. 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.

4. 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)

5. 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.

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

7. 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: f AD = f n +  f' + i  f ” f n is 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 f n  f" is an imaginary term which also arises from the AD effect  f" is always positive and 90° ahead of (f n +  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, I hkl = I -h-k-l ( Firedel’s Law). With AD effects, I hkl ≠ I -h-k-l ( Friedel’s Law breaks down).

8. Breakdown of Friedel’s Law ( F hkl Left) F n represents the total scattering by "normal" atoms without AD effects, f’ represents the sum of the normal and real AD scattering values (f n +  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 F n (at -  hkl ) and f’ is the inverse of f’ , the  f" vector is once again 90° ahead of f’ . The resultant vector, F --- in this case, is obviously shorter than the F +++ vector. f’ f’

9. 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 ( λ 1), 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.

10. This M ultiwavelength A nomalous D iffraction method often gives very strong phase information and is the source of many new structures.

11. 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

12. 2.1 A ° electron-density map for the S-SAD example before and after density modification using SHELXE

13. 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.

14. PHASE IMPROVEMENT

15. (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.