Anomalous dispersion

Transcription

1 Selenomethionine MAD Selenomethionine is the amino acid methionine with the Sulfur replaced by a Selenium. Selenium is a heavy atom that also has the propery of "anomalous scatter" at some wavelengths, and not at others. Proteins grown in smet will incorporate teh Se atoms. These crystals can be solved by Multiwavelength Anomalous Dispersion (MAD). 3 data sets are collected on a single crystal (sometimes at the same time!) F λ1 PH, F λ2+ PH, F λ2+ PH

2 Anomalous dispersion Heavy atom phase shift of anomalous scatter free electrons β F r bound electrons F i Inner electrons scatter with a phase shift relative to the phase of the free electrons. An anomalous scatter at the Origin scatters with phase β. imaginary part of anomalous scatter real part of anomalous scatter

3 Reminder: Friedel's Law F(h k l) F(-h -k -l) F + (h k l) α α F - (h k l) Friedel mates have same amplitude, opposite sign.

4 Anomalous dispersion violates Friedel's Law F(h k l) F(-h -k -l) F + (h k l) α+β α+β F - (h k l) + and - contributions for just a heavy atom with anomalous scattering.

5 MAD experiment Protein is grown in smet (or another anomalous scatterer ispresent, such as Iron). Three data seta are collected on 1 crystal at multiple (usually 2) wavelengths. λ 1 is a wavelength where Se does not absorb, normal diffraction. λ 2 is a wavelength where Se does absorb, anomalous F is added. F - λ 1 (h k l) F + λ 1 (h k l) F - λ 2 (h k l) F + λ 2 (h k l) Friedel mates (same amplitude, merged) collected non-anomalous wavelength. Friedel mates (different, not merged) collected anomalous dispersion wavelength.

6 Friedel mates with anomalous have different amplitudes F - λ 1 (h k l) F - λ 2 (h k l) F + λ 2 (h k l) F + λ 1 (h k l)

7 MAD phasing using vector math F - λ 2 (h k l)* = Fλ 1 (h k l) + F - (h k l) F - λ 2 (h k l) e -iα 2- = Fλ 1 (h k l) e iα 1 + F - (h k l)e i(α h-β h ) F - λ 2 (h k l) cos(α2-) = Fλ 1 (h k l) cos(α 1 ) + F - (h k l) cos(αh-βh) - F - λ 2 (h k l) sin(α2-) = Fλ 1 (h k l) sin(α 1 ) + F - (h k l) sin(αh-βh) F + λ 2 (h k l) = Fλ 1 (h k l) + F + (h k l) F + λ 2 (h k l) e iα 2+ = Fλ 1 (h k l) e iα 1 + F + (h k l)e i(α h+β h ) F - λ 2 (h k l) cos(α2+) = Fλ 1 (h k l) cos(α 1 ) + F - (h k l) cos(αh+βh) F - λ 2 (h k l) sin(α2+) = Fλ 1 (h k l) sin(α 1 ) + F - (h k l) sin(αh+βh) Four equations in three unknowns: α 1, α 2 -, α 2 +

8 Phase probability distribution Radii are F p and k*f ph Width are σ p and k*σ ph The red area are the places in Argand space where both F P and F PH -F H can be

9 Most probable versus best phase The most probable phase is not necessarily the best for computing the first e-density map. Shaded regions are possible F p and F ph solutions. weighted average, best phase

10 Figure of merit Figure of merit m is a measure of how good the phases are. C is the center of mass of a ring of phase probabilities (probability is the mass ). Assume the radius of the ring is 1. If the probabilities are sharply distributed, m 1. If they are distributed widely, m is smaller. F best (hkl) = F(hkl)*m*e -iα best

11 Heavy atom phasing methods SIR = single isomorphous replacement, without anomalous. Fourier transform uses: Figure-of-merit weighted amplitudes, alpha-best phases and centric reflections. MIR = multiple isomorphous replacement, without anomalous. Same Fourier terms, but Figure-of-merit is generally better than for SIR.

12 Heavy atom phasing methods SAD = single wavelength anomalous dispersion. Phases from F+ and F- from one crystal. Fourier transform uses: Figure-of-merit weighted amplitudes, alpha-best phases and centric reflections. MAD = multi-wavelength anomalous dispersion. Phases from three datasets from one crystal at 2 wavelengths (or more). F+, F- at anomalous wavelength, and F at nonanomalous wavelength.

13 R-factor: How good is the model? Calculate F calc s based on the model. Compute R-factor R = " h F obs ( h)! F calc ( h) " h F obs ( h) Depending on the space group, an R-factor of ~55% would be attainable by scaled random data. The R-factor must be < ~50%. Note: It is possible to get a high R-factor for a correct model. What kind of mistake would do this?

14 What can you do if the phases are not good enough? 1. Collect more heavy atom derivative data 2. Try density modification techniques. initial phases Density modification : Fo s and (new) phases Map Modified map Fc s and new phases

15 Low-resolution At 4-6Å resolution, alpha helices look like sausages.

16 Medium resolution ~3Å data is good enough to se the backbone with space inbetween.

17 Holes in rings are a good thing Seeing a hole in a tyrosine or phenylalanine ring is universally accepted as proof of good phases. You need at least 2Å data.

18 Great map: holes in rings

19 Superior map: Atomicity Rarely is the data this good. 2 holes in Trp. All atoms separated.

20 Only small molecule structures are this good Atoms are separated down to several contours. Proteins are never this well-ordered. But this is what the density really looks like.

21 FÉTHIÈRE et al, Protein Science (1996), 5: Two inhibitor peptides bound to thrombin. The inhibitors were omited from the F c calculation. (stereo images)

22 The final model Other data commonly reported: total unique reflections, completeness, free R-factor

23 From crystal to data Indexed film Internal scaling Intensity, I p (hkl) = F 2 I is relative Bigger crystal, higher I Better crystal, higher I Longer exposure, higher I More intense Xrays, higher I native data: F p Because there is no absolute scale: F p and F ph are on different scales

24 From data to Patterson map native data: F p heavy atom data: F ph Find the best scale factor, w Calculate F diff = w* F ph F p Calculate difference Patterson

25 From data to phases native data: F p heavy atom data: F ph Calculate difference Patterson Find heavy atom peaks on Harker sections Solve for heavy atom positions using symmetry Calculate heavy atom vectors Estimate phases

26 From data to model Collect native data: F p Collect heavy atom data: F ph Estimate phases Calculate ρ Is the map traceable? yes no density modification? Trace the map Refine