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Molecular Biophysics Solving the phase problem PowerPoint PPT Presentation


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Molecular Biophysics Solving the phase problem. Der Weg zur Röntgenkristallstruktur eines Proteins. Electron density equation. The electron density equation. Electron density equation. F ( h k l ) =  cell r ( x y z ) exp (2 p i { hx + ky + lz }) d 3 r.

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Molecular Biophysics Solving the phase problem

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Molecular biophysics solving the phase problem

Molecular Biophysics

Solving the phase problem


Molecular biophysics solving the phase problem

Der Weg zur

Röntgenkristallstruktur eines Proteins


Electron density equation

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


Molecular biophysics solving the phase problem

The phase problem


Molecular biophysics solving the phase problem

The phase problem


Molecular biophysics solving the phase problem

Influence of intensities

Influence of phases

The phases are more important than the amplitudes!!!!


Wave 1

Wave 1


Wave deri

Wave deri


Patterson map

Patterson map

Direct space

Density

and

position

Patterson

map

Fourier

transformation

Fourier

transformation

Amplitudes

and

phases

Intensities

Reciprocal space


Patterson map symmetry

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


Molecular biophysics solving the phase problem

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

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 data1

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 data2

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 diagram

Harker diagram

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 construction for

single isomorphous replacement (SIR)

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


Molecular biophysics solving the phase problem

mir

We can use a second derivative to resolve the phase ambiguity

Harker construction for

multiple isomorphous replacement (MIR)


Molecular biophysics solving the phase problem

02p

m=


Wave 11

Wave 1


Wave deri1

Wave deri


Wave anom

Wave anom

Anomalous scattering involves resonance effects


Molecular biophysics solving the phase problem

Anomalous scattering leads to a breakdown of Friedel‘s law


Molecular biophysics solving the phase problem

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

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


Molecular biophysics solving the phase problem

Der Weg zur

Röntgenkristallstruktur eines Proteins


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