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