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It is the electron density that gives rise to the 3D structure

The intensity of the diffraction spots are known, however we do not know the phase of the wave, whrequired to calculate the electron density in the unit cell (phase problem).

(xyz)= h k l F(hkl)exp[-2T i(hx + ky + lz)]REQUIRED?

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= electron densityx, y, z = point where density has to be calculated|F| = magnitude of structure factor |F| = square root of intensityh, k, l = indices of diffraction spots

Obtaining Phase Information:For small molecules this can be done directly using a Patterson map or direct methodsThis cannot be done for proteins

Isomorphous replacement methodDepends on two crystals having the same structure, but differing by a few heavy metal atomsCrystals are soaked in heavy atom solutions such as HgCl2, the heavy atoms will bind to the same specificplaces on each protein. Hg interacts well wit cysteine.Although there are only a few heavy atoms (HA), each has a large number of electrons and they conappreciably to the scattering.The diffraction intensities from the derivatised crystal will differ slightly to those from the native cr

It is important to know the positions of the heavy atoms and the differences in intensities between tdiffraction patterns of the two structures.It is then possible to determine approximates phases (E ), which can be used to calculate an initial electrondensity ( ).

Not used so often anymore.

Multi-wavelength Anomalous Diffraction (MAD)

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Similar to MIRMAD relies on the fact that some Has have an absorption edge (wavelength needed to knock an eleof the atom) close to the wavelengths used in X-ray crystallography (0.7-2.0 ).Close to the absorption edge, small changes inP give rise to significant changes in the phase of the scatterwave. This is known as anomalous dispersion.

The method requires access to a synchrotron with a tuneable radiation source, so the wavelength ofused can be changed.

Friedels Law is only approximately correct, and the relationship it describes can be changed depenthe wavelength used for detection. Differences can be generated by using HAs, which can be maximusing different wavelengths.HA such as selenium cause anomalous scattering of X-rays

Selenomethionine SubstitutionMethionine synthesis auxotroph is used to generate a protein where the sulphur of Met is replaced bselenium. The anomalous difference effect in MAD is then used for phase determination.

Molecular ReplacementIf a closely related structure is known, or a previous model in a different crystal form is available, thmolecule can be located in the unit cell and phases determined from the model.

A similar protein of known structure is used to find structural homology with the protein of interestYou can then search within the crystal lattice to find a position that would allow it to be located.Electron density maps can be calculated for a known model.

One the position is know the phases can be calculated, along with the electron density maps.

Building the Structure: Once phase information has been determined, an electron density map can be calculatedAtoms are placed in the centres of peaks, leading to a model of the structureThe model is improved by computer software (before computers were done in 3D by hand)Several cycles of model building and refinement are required to obtain the best possible model

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ResolutionVery important in crystal structure determination

High (better than 2.0 )o Easy to interpreto Almost atomico Holes in aromatic groupso Ordered water molecules

Medium (2.5 - 3.5 )o Sidechains become visible

Low (below 4.5 )o Overall shape of molecule

Map are calculated using the final, refined phasesInitial ,maps have large phase errors and are far worse

RefinementModel improvement - manual model building is not sufficient to build a completely accurate modelRefinement aims to adjust the atomic model so that it gives a better fir to the observed data

Minimizing the differences between observed intensities, and the intensities calculated from the momodifying the model.Stereochemical restraints are applied model must have regular bond lengths and angles like all othproteins do.Computational process that is more objective than model buildingSuccessful structure determination requires several inter-leaved rounds of model building and refineR factor is a measure of the quality of the structure

Observations / parameters ratio is important, and is often a problem in protein crystallography as thmany parameter that have to be refined at one timeThis problem is solved using stereochemical information

The positions of atoms need to be well defined in 3D as well as the B -factor (a measure of how dynflexible a part of the structure is).Stereochemical Restraints

4 Map

2 Map

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5% of data is not used in the refinement process, it is used to calculate the Free R value only, an independent

way of checking is a model is correct or not.

Ramachandran Plot

Because of steric clashes, only certain combinations of torsion angles are allowed

The plot can be used to plot the allowed combinations in the y,f plane

Planar peptide bond has and angles

Allowed regions are in yellow

Favoured regions are in red

Certain structural motifs will predominate indifferent regions of the Ramachandran plot.

The model can be run through a

Ramachandran plot program to see if there

are any disallowed regions.

We expect to find 90+% of residues to fall intothe red regions.