View
218
Download
2
Category
Preview:
Citation preview
Use of anomalous signal in phasing
Zbigniew Dauter
Title
ACA Summer SchoolIn Macromolecular Crystallography
Chicago, July 2006
Scattering
Normal (elastic) scattering changes with not with
Anomalous (resonant) scattering not dependent on , changes with
Equation
Structure factor equation
for normal scattering
Fh = j fj exp(2ih.r) = |Fh|exp(i)
for anomalous scattering
f = fo + f’ + if”
f” is proportional to absorption and fluorescence f’ and f” related by Kramer-Kronig transformation
f’(E) = 2/ ___________ dE’
E’.f”(E’)
(E2 – E’2)
fSe
Black – ideal f” curve by CROSSEC (for isolated atom)
Blue – experimental f” curve with white line (affected by environment)
fHg
Excitation spectrum of Hg(calculated theoretically)
f1a
Structure factor – vector sum of contributions of individual atoms
Fh = j fj exp(2ih.rj) = |Fhkl|exp(i)
B factors (ADP’s) omitted for simplicity
f1b
Fh = j fj exp(2ih.rj) + j fj exp(2ih.rj) P H
f1c
Fh = j fj exp(2ih.rj) + j (fj +fj+ifj)exp(2ih.rj) N A o / //
i.exp(i) =
= i.[cos() + i.sin()]
= i.cos() - sin()
= i.sin(+90o) + cos(+90o)
= exp[i(+90o)]
f1d
FT = FN + FA + FA + iFA
/ //
FA is perpendicular to FA
if all anomalous scatterers are of the same kind
//
f1e
FT = FN + FA + FA + iFA
/ //
// imaginary term iFA
breaks Friedel’s law
|FT| = |FT|
T = - T
+ -
+ -
/
/
f1f
F represented by its
complex conjugate *F
-
-
f1g
more realistic proportions
Bijvoet ratio <F>/<F> ~ 3 – 6% for Se
for S can be 0.6% (B.C. Wang)
<F>/<F> = (2.NA/NT)1/2
. f”/6.7
sad2
sad2a Glucose isomerase: 1 Mn in 388 aa
sad2b
Fanom is available from experiment
Fanom = 2 FA” sin(T – A)
FA” = FA . f”/fo
therefore FA ~ Fanom if Fanom is large
and Fanom can be used to locateanomalous scatterers instead of FA
- using Patterson synthesis - using direct methods
Sav3 anom. Patt.
Subtilisin in P212121 , = 1.54 ÅHarker sections of anomalous diffr. Patterson
Three calcium sites (f”Ca = 0.70)
sad1
Single-wavelength anomalous diffraction
SAD phase ambiguity
sad3
with experimental errors
sad4
sad5 Idea of B.C.Wang (1985)
SAD maps
SAD Fourier maps
proper wrong overlap
solvent flattening
sad6
Partial structure (Sim) contribution
sad6a
Ferredoxin – 2 Fe4S4 in 55 aa
sad7
mad1
Crambin
First SAD result – crambin Hendrickson & Teeter, 1981
6 S among 46 amino acids=1.54 Å, f”(S)=0.56, <F>/<F>=1.4%
7 SeMAD
Rice, Earnest & Brünger (2000) re-solved 7 SeMAD structures with SAD and recommended collecting first complete peak data set, and then other MAD wavelengths data, as a sort of insurance policy
1.5-wavelength approach (2002) collecting peak data and rapid phasing, if successful, postponement of next (now it may be < 1-wavelength)
Blow
David Blow, Methods Enzymol. 374, 3-22 (2003)“How Bijvoet made the difference ?” (written probably in 2001) . . .
The future of SAD
It seems likely, however, thatthe various improvements toanalyze MAD data more correctlyare fading into insignificance.The MAD technique is losingground to SAD. . . .
PDB statistics
SAD/(SAD+MAD) structures deposited in PDB
2001 2002 2003 2004 2005
11% 22% 32% 45% 55%
Proteinase K
Proteinase K 279 amino acids, 1 Ca + 10 S f”(S) = 0.23e, f”(Ca) = 0.35e
Beamline SER-CAT 22-ID
Unit-cell parameters (Å) a=67.55, c=106.88
Space group P43212
Wavelength (Å) 0.98
Distance (mm) 150
Number of images 660
Oscillation (°)/exposure time (s) 0.5 / 2
Transmission 10%
Resolution (Å) 50-1.27 (1.32-1.27)
Number of unique reflections 63537
Completeness (%) 96.4 (92.7)
Overall I/σI 106.1 (31.5)
Redundancy 27.1 (26.3)
Rmerge (%) 3.3 (13.0)
Prot. K SHELXD
Anomalous difference Fourier
Rank Position Height
1 Ca 1.0000
2 Cys73 0.5105
3 Met111 0.4967
4 Met225 0.4571
5 Met55 0.4560
6 Cys178 0.4417
7 Met238 0.4341
8 Cys123 0.3938
9 Cys249 0.3862
10 Met154 0.3861
11 Cys34 0.3696
12 0.1400
Results of SHELXD
Prot. K SHELXE
Experimental map after SHELXE
Mean phase error 27.5o
Prot. K redundancy
Effect of data redundancy
0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.650.00
0.02
0.04
0.06
0.08
0.10
0.12
<F
>/<F
>
1/d2
045 060 090 120 150 180 210 240 270 300 330
Dataset
Label
Peak Height (σ) Number of sites
SHELXD Ca <10S> SO42-
045 25.77 10.48 5.47 -
060 29.07 11.68 6.22 -
090 35.71 13.95 6.23 -
120 39.51 15.59 6.54 3
150 43.59 17.20 6.96 8
180 46.81 18.64 7.30 11
210 48.93 19.27 7.44 11
240 52.17 20.51 7.62 11
270 54.56 21.24 7.87 11
300 56.37 21.79 7.80 11
330 58.13 22.29 8.19 11
Indicators
Indicators of anomalous signal
- Bijvoet amplitude or intensity ratio
- Ranom
- 2 difference if Friedels merged
- list of outliers
- measurability
- anomalous signal to noise ratio
- correlation between data sets
- relation between signal in acentrics and centrics
GI Bijvoet ratio
<F± >/<F> = (2 NA/NP)1/2 . (fA” /6.7)
Ranom = (F+ - F-) / (F+ + F-)/2
Four data sets from glucose isomerase
1 Mn in 375 a.a.
Bijvoet ratio and Ranom
Chi2 and Rmerge
Merging 2 difference
crystal soaked in Ta6Br12 cluster compound
blue – 2
red - Rmerge
when Friedels independent
orange – 2
green - Rmerge
when Friedels equivalent
Outliers
List of outliers
If redundancy if high enough, clearly shows anomalous differences
Signal to noise
Signal to noise ratio (F±)/(F)
for proteinase K
requires proper estimation of ’s (which is not trivial)
signal is meaningful, if this ratio is > 1.3
Correlation Correlation between data sets
corr (F1±, F2
±)
F1 and F2 may be at different MAD or merged partial SAD data If higher than 25 - 30% - meaningful
(advocated by George Sheldrickfor SHELXD resolution cutoff)
No indicator
No indicator is fully satisfactory
these indicators of anomalous signal
do not tell if the signal is sufficient
for structure solution
e.g. difficulties with Cu-thionein (Vito Calderone)
8 Cu in ~53 a.a. (12 Cys), P4332
eventually solved from
extremely redundant data
Conclusion
only one satisfactory indicator of anomalous signal exists:
successful structure solution
nowadays the structure can be solved in few minutes, when the crystal is still at the beam line
Recommended