1 Phasing the Diffraction Pattern 1. Direct Methods – random assignment of phases based on known phase relationship. Requires very high resolution. 2. Multiple Isomorphous Replacement (MIR) – phase assignment based on addition of heavy atoms (e.g. Hg) to the crystal, and measuring the change in diffraction. 3. Multiple Wavelength Anomalous Dispersion (MAD) – phase assignment based on anomalous diffraction of X-ray absorbing atoms (e.g. Se, S, Hg, Xe, etc.) where the X-ray wavelength is varied to near the absorption edge. 4. Molecular replacement – phase assignment based on taking a related protein with known structure and determining its orientation in the unknown unit cell. Typical Anomalous Scatterers • Hg (80 e‑): reacts well with Cys. Generally soaked in.!• Pt (78 e‑): reacts with nucleophiles (Met, His, others).!• Xe (54 e‑): inert gas that fills pockets in proteins.!• Br (35 e‑): nonspecific ionic interactions.!• Se (34 e‑): recombinant proteins can be produced with ! SeMet.!2 Isomorphous Replacement: Fhkl1 ≠ Fhkl2 If αH can be determined, αP and αPH can be estimated Difference Fourier ρxyz = 1/V∑h (FPH- FP) cos [2π(hx+ky+lz) + αh] ! - (FPH- FP) sin [2π(hx+ky+lz) + αh]!What would this map look like?3 Multiple Wavelength Anomalous Dispersion (MAD): Fhkl ≠ F-h-k-l f(λ) = fo – δf’(λ) + if’’(λ) Note: FPH+ ≠ FPH- Patterson Function – Map of Atom Vectors Puvw = 1/V∑h (FPH- FP)2 cos [2π(hu+kv+lw)] !Note: phase = 0, F24 Patterson Function – Map of Atom Vectors For Triclinic case (P1), place atom at 0,0,0!For higher symmetry, Harker sections highlight symmetry!Patterson Map5 Phase Circles Vector FH known from Patterson Phase Circles Amplitude for FP known, phase unknown6 Phase Circles Amplitude FP estimate: FPH - FH Phase Circles FP = FPH - FH Possible phase angles for FP7 Phase Relationships Phase Relationships8 Phase Probability Assessing MIR/MAD maps 1. The map should have interpretable features, e.g. helices and sheets. 2. Phasing statistics should have more signal than noise: |FH| > lack of closure error, xαp FOM > 0.5 3. Correct hand is evident. E = [Σh |FH| / xαp] /
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