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## PowerPoint Slideshow about ' Molecular Biophysics Solving the phase problem' - brock

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Solving the phase problem

Röntgenkristallstruktur eines Proteins

Electron density equation

The electron density equation

Electron density equation

F(hkl) = cellr(xyz)exp (2pi{hx+ ky+lz}) d3r

r(xyz)= ShklF(hkl) exp (-2pi{hx+ ky+lz})

But we can only measure the intensity

I(hkl) = F(hkl) . F*(hkl) = |F(hkl)|2

We have lost the phase information: this is the fundamental problem in X-ray crystallography –

The PHASE PROBLEM

Patterson map

Direct space

Density

and

position

Patterson

map

Fourier

transformation

Fourier

transformation

Amplitudes

and

phases

Intensities

Reciprocal space

Patterson map symmetry

Patterson map with symmetry

Harker vectors

u, v, w

2x, 1/2, 2z

P21

x, y, z

-x, y+1/2, -z

The crystallographic phase problem can be solved via:

Single isomorphous replacement (SIR)

Multiple isomorphous replacement (MIR)

Single isomorphous replacement with anomalous scattering (SIRAS)

Multiple wavelength anomalous dispersion (MAD)

Molecular replacement (MR)

Difference Fourier methods

Derivative data

Once we have an heavy atom structure rH(r), we can use this to calculate FH(S). In turn, this allows us to calculate phases for FP and FPH for each reflection.

Derivative data

Once we have an heavy atom structure rH(r), we can use this to calculate FH(S). In turn, this allows us to calculate phases for FP and FPH for each reflection.

Derivative data

Once we have an heavy atom structure rH(r), we can use this to calculate FH(S). In turn, this allows us to calculate phases for FP and FPH for each reflection.

Harker diagramOnce we have an heavy atom structure rH(r), we can use this to calculate FH(S). In turn, this allows us to calculate phases for FP and FPH for each reflection.

Harker construction for

single isomorphous replacement (SIR)

The phase probability distribution shows that SIR results in a phase ambiguity

mir

We can use a second derivative to resolve the phase ambiguity

Harker construction for

multiple isomorphous replacement (MIR)

m=

Wave anom

Anomalous scattering involves resonance effects

Anomalous scattering data can also be used to solve the phase ambiguity

Note that the anomalous differences are very small; thus very accurate data are necessary

Phase solution

The crystallographic phase problem can be solved via:

Single isomorphous replacement (SIR)

Multiple isomorphous replacement (MIR)

Single isomorphous replacement with anomalous scattering (SIRAS)

Multiple wavelength anomalous dispersion (MAD)

Molecular replacement (MR)

Difference Fourier methods

Röntgenkristallstruktur eines Proteins

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