use of anomalous signal in phasing zbigniew dauter title aca summer school in macromolecular...
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Use of anomalous signal in phasing
Zbigniew Dauter
Title
ACA Summer SchoolIn Macromolecular Crystallography
Chicago, July 2006
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Scattering
Normal (elastic) scattering changes with not with
Anomalous (resonant) scattering not dependent on , changes with
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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)
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fSe
Black – ideal f” curve by CROSSEC (for isolated atom)
Blue – experimental f” curve with white line (affected by environment)
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fHg
Excitation spectrum of Hg(calculated theoretically)
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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
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f1b
Fh = j fj exp(2ih.rj) + j fj exp(2ih.rj) P H
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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)]
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f1d
FT = FN + FA + FA + iFA
/ //
FA is perpendicular to FA
if all anomalous scatterers are of the same kind
//
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f1e
FT = FN + FA + FA + iFA
/ //
// imaginary term iFA
breaks Friedel’s law
|FT| = |FT|
T = - T
+ -
+ -
/
/
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f1f
F represented by its
complex conjugate *F
-
-
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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
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sad2
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sad2a Glucose isomerase: 1 Mn in 388 aa
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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
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Sav3 anom. Patt.
Subtilisin in P212121 , = 1.54 ÅHarker sections of anomalous diffr. Patterson
Three calcium sites (f”Ca = 0.70)
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sad1
Single-wavelength anomalous diffraction
SAD phase ambiguity
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sad3
with experimental errors
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sad4
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sad5 Idea of B.C.Wang (1985)
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SAD maps
SAD Fourier maps
proper wrong overlap
solvent flattening
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sad6
Partial structure (Sim) contribution
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sad6a
Ferredoxin – 2 Fe4S4 in 55 aa
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sad7
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mad1
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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%
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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)
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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. . . .
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PDB statistics
SAD/(SAD+MAD) structures deposited in PDB
2001 2002 2003 2004 2005
11% 22% 32% 45% 55%
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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)
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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
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Prot. K SHELXE
Experimental map after SHELXE
Mean phase error 27.5o
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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
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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
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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
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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
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Outliers
List of outliers
If redundancy if high enough, clearly shows anomalous differences
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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
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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)
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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
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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