Practical aspects of SAD/MAD. Judit É Debreczeni

Transcription

1 Practical aspects of SAD/MAD Judit É Debreczeni

2 anomalous scattering Hg sinθ/λ CuKα 0 Å Å Å - Å.5Å 0.83Å f f total (θ, λ) f(θ) + f (λ) + if (λ) f f f total increasing with increasing resolution if diffraction strong enough Anomalous Δ/ for vitamin B: (overall /sigma: 39.0, highest res. shell:.9) Anomalous signal/noise ratios (.0 is random). The first line is based on input sigmas, the second on variances of + and - (if not already averaged): nf A

3 SAD/MAD phasing ± T + f + f f f A + T A cosα ± T A sinα f f f unknowns: T, A and α MAD: overdetermined SAD: approximations. α 90 if + > - 70 if + < -. T / ( ) assuming A << T and f', f"<< f Δ f f " ' A sinα

4 SAD phasing - approximations approximations increased noise in Patterson function importance of E-value selection (example: insulin S-SAD) error caused by approximations ideal A ideal Δ measurement error measured Δ

5 predicting/assessing anomalous signal where is the limit? are our limits theoretical or practical? predicting success estimate from the number and type of anomalous scatterers Δ/ (>.0 in XPREP, or 0.798) CC between independent datasets (>30%) overall / scala, truncate DANO + / - in XDS etc.

6 predicting/assessing anomalous signal CuK α (e - ) Ratio of anomalous differences (%) O P S Zn Cl Ca e U Δ i i n f n f i i " i i anomalous scatterers in a 50-membered polyala the resulting anomalous differences from S are of the order of -% for normal proteins

7 Δ / vs. CC independent measurements error variables: - have a zero mean and the same s.u. - are uncorrelated with each other and with the signal M M S + E S + E the correlation coefficient between two independent measurements: CC Ε( M M D( M ) Ε( M )D( M ) Ε( M ) ) if M and M are equivalent and (equal mean and s.u.) CC Ε( S D( S) ) Ε( S) + D( E )

8 Δ / vs. CC SAD signal (Δ ) follows the distribution: ( ) Δ P Δ exp Σπ Σ measurement errors: normal distribution (zero mean and st. dev.) Σ N j if N anomalous scatterers are randomly distributed in the asymmetric unit. ( A follows an acentric Wilson distribution.) f j CC Σ Σ + + Σ Σ Δ Ε Σ + π π + Σ

9 Δ / vs. CC CC Δ Ε π Δ + Ε π CC can be predicted from Δ / no upper limit for Δ / Δ /.0 when CC 30% (data truncation point) CC CC CC calc CC cins CC otrp CC ttrp CC iod-thau CC rins CC elas Δ / 0.79 when Σ/ 0 (no signal) Δ/ Δ /

10 Δ / vs. / 4 Δ + Δ Ε π π and if Δ<< and + - Gauss error propagation ( ) ( ) Δ Δ Δ Δ Δ Δ Δ Δ Σ π π π Σ + Σ + Δ Ε the anomalous difference is calculated as previously shown that

11 Δ / vs. / Δ Ε + Δ π 4 π all f are measurable given / sufficiently large estimated Δ / required redundancy can be estimated before collecting a complete dataset (/ ~ redundancy) number of HA sites can be estimated (e.g. HA soaks)

12 Δ / vs. / GGPS Se-SAD.45 Δ / Δ / Δ Ε + Δ π 4 π Observed Prediction linear at high / slope: experimental Δ/ (occupancy, B- factor, anisotropy of heavy atoms) / y-intercept: ~0.8 / square root type function if lower /

13 limits? λ0.7å (MoKα) f' 0. f" 0. Δ/0.7% cubic (Zn-free) insulin Mo sealed tube overall redundancy: 3 R int : 5.4%, R sigma :.7% Anomalous Δ/ (for the whole dataset): Anomalous signal/noise ratios (.0 is random). The first line is based on input sigmas, the second on variances of + and - (if not already averaged): nf A

14 why SAD? absorption edge experimentally demanding air absorption (He purged beam path) strong absorption by the crystal, loop,... (scaling) radiation damage limited resolution

15 pseudo-mad λ.54å (CuKα) f' 0.3 f" 0.56 λ0.7å (MoKα) f' 0. f" 0. cubic insulin at two wavelengths Δf'0. dispersive signal sensitive to radiation damage measurement technique might be useful for eg. Cd Xe Correlation between Mo and Cu: Anomalous correlation coefficients (%) against previous datasets nf A

16 initial phases WMPE MapCC SHELXE, heavy atoms included, no density modification Cu-quarter Cu-half Cu-full λ f" redundancy CC CCweak.54Å Å Å insulin S-SAD

17 initial phases WMPE MapCC SHELXE, heavy atoms included, no density modification Mo Anka Cu-quarter WMPE and MapCC do not depend on f λ f" redundancy CC CCweak 0.7Å Å Å insulin S-SAD

18 initial phases substructure initial phases density improvement autotracing what is the signal good enough for? SHELXD/E evolution: viscotoxin A SHELXD: supersulfurs SHELXE: initial phases no interpretable map MR based upon super-s positions SHELXD: DSUL SHELXE: phases good enough for autotracing (arp) after NCS averaging in DM SHELXE: autotracing density modification recycled with autotracing /3 of the molecule traced???? - NCS...?

19 use of anomalous signal SAD/MAD etc equipment testing inverse ourier - anomalous map - confirm biology molecular replacement: -phased molecular replacement - locate molecules with heavy atom sites phased refinement - iffy initial model

20 acknowledgements Göttingen George M. Sheldrick Gábor Bunkóczi many members of the group Delft Leo Straver Anita Coetzee Bram Schierbeek