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Title
ACA Summer School
In Macromolecular Crystallography
Chicago, July 2006
Use of anomalous
signal in phasing
Zbigniew Dauter
Scattering
Normal (elastic) scattering
changes with q , not with l
Anomalous (resonant) scattering
not dependent on q , changes with l
Equation
Structure factor equation
for normal scattering
Fh = Sj fj exp(2pih.r) = |Fh|exp(ij)
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/p
E’.f”(E’)
___________
(E2
–
E’2)
dE’
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 = Sj fj exp(2pih.rj) = |Fhkl|exp(ij)
B factors (ADP’s)
omitted for
simplicity
f1b
P
H
Fh = Sj fj exp(2pih.rj) + Sj fj exp(2pih.rj)
f1c
N
A
o
Fh = Sj fj exp(2pih.rj) + Sj (fj +fj+ifj)exp(2pih.rj)
/
//
i.exp(ij) =
= i.[cos(j) + i.sin(j)]
= i.cos(j) - sin(j)
= i.sin(j+90o) + cos(j+90o)
= exp[i(j +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
|F+T| =
/ |FT|
jT+ =
/ - jT
f1f
-
F represented by its
complex conjugate
*F-
f1g
more realistic proportions
Bijvoet ratio
<D F>/<F> ~ 3 – 6% for Se
for S can be 0.6% (B.C. Wang)
<D F>/<F> = (2.NA/NT)1/2 . f”/6.7
sad2
sad2a
Glucose isomerase: 1 Mn in 388 aa
sad2b
DFanom is available from experiment
DFanom = 2 FA” sin(jT – jA)
FA” = FA . f”/fo
therefore
FA ~ DFanom if DFanom is large
and DFanom can be used to locate
anomalous scatterers instead of FA
- using Patterson synthesis
- using direct methods
Sav3 anom. Patt.
Subtilisin in P212121 , l = 1.54 Å
Harker 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 Fourier maps
SAD maps
proper
wrong
solvent
flattening
overlap
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
l=1.54 Å, f”(S)=0.56, <DF>/<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 l
(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, that
the various improvements to
analyze MAD data more correctly
are fading into insignificance.
The MAD technique is losing
ground to SAD.
. . .
PDB statistics
SAD/(SAD+MAD)
structures deposited in PDB
11%
22%
32%
45%
2001
2002
2003
2004
55%
2005
Proteinase K
279 amino acids, 1 Ca + 10 S
f”(S) = 0.23e, f”(Ca) = 0.35e
Proteinase K
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)
Anomalous difference
Fourier
Results of SHELXD
Prot. K SHELXD
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
Prot. K SHELXE
Experimental map after SHELXE
Mean phase error 27.5o
Prot. K
redundancy
Effect of data redundancy
0.12
0.10
<DF>/<F>
0.08
0.06
045
060
090
120
150
180
210
240
270
300
330
0.04
0.02
0.00
0.25
0.30
0.35
0.40
0.45
1/d
2
0.50
0.55
0.60
0.65
Peak Height (σ)
Number of
sites
SHELXD
Dataset
Label
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
- c2 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
Bijvoet ratio and Ranom
<DF± >/<F> = (2 NA/NP)1/2 . (fA” /6.7)
Ranom = S (F+ - F-) / S (F+ + F-)/2
Four data
sets from
glucose
isomerase
1 Mn in
375 a.a.
Chi2 and Rmerge
Merging c2 difference
crystal soaked in Ta6Br12 cluster compound
blue – c2
red - Rmerge
when Friedels
independent
orange – c2
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 (DF±)/s(F)
for proteinase K
requires proper
estimation of s’s
(which is not trivial)
signal is meaningful,
if this ratio is > 1.3
Correlation
Correlation between data sets
corr (DF1±, DF2±)
F1 and F2 may be
at different MAD l
or merged partial
SAD data
If higher than
25 - 30%
- meaningful
(advocated by
George Sheldrick
for 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