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Molecular Biophysics Solving the phase problem

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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  1. Molecular Biophysics Solving the phase problem

  2. Der Weg zur Röntgenkristallstruktur eines Proteins

  3. 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

  4. The phase problem

  5. The phase problem

  6. Influence of intensities Influence of phases The phases are more important than the amplitudes!!!!

  7. Wave 1

  8. Wave deri

  9. Patterson map Direct space Density and position Patterson map Fourier transformation Fourier transformation Amplitudes and phases Intensities Reciprocal space

  10. 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

  11. 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

  12. 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.

  13. 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.

  14. 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.

  15. 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

  16. mir We can use a second derivative to resolve the phase ambiguity Harker construction for multiple isomorphous replacement (MIR)

  17. 02p m=

  18. Wave 1

  19. Wave deri

  20. Wave anom Anomalous scattering involves resonance effects

  21. Anomalous scattering leads to a breakdown of Friedel‘s law

  22. 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

  23. 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

  24. Der Weg zur Röntgenkristallstruktur eines Proteins

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