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ACA_SINBAD_2013.ppt

AcknowledgementsKen Frankel Alastair MacDowell

John Spence Howard PadmoreLBNL Laboratory Directed Research & Development (LDRD)

ALS 8.3.1 creator: Tom Alber PRT head: Jamie Cate

Center for Structure of Membrane ProteinsMembrane Protein Expression Center II

Center for HIV Accessory and Regulatory Complexes

W. M. Keck FoundationPlexxikon, Inc.

M D Anderson CRCUniversity of California Berkeley

University of California San FranciscoNational Science Foundation

University of California Campus-Laboratory Collaboration GrantHenry Wheeler

The Advanced Light Source is supported by the Director, Office of Science, Office of Basic Energy Sciences, Materials Sciences Division, of the US Department of Energy under contract No. DE-AC02-05CH11231 at Lawrence Berkeley National Laboratory.

Simultaneous

INverse

Beam

Anomalous

Diffraction

SINBAD diffractometer concept

Nucleus

Synthetic light collecting structureh,k,l

-h,-k,-l

Detec

tor Detector

Detec

tor Detector

d = 3.5 Å d = 3.5 Å

d = 3.5 Åd = 3.5 Å

sample injector

Mirr

ors

Mirr

ors

d = 3.5 Åλ = 5 Å

XFEL beam

Why SINBAD?

I+ I-

Different crystal volumes

New source of error in SFX

Why SINBAD?

I+ I-

Different crystal orientations


Why SINBAD?

I+ I-

Different beam intensities


Why SINBAD?

I+ I-

Different crystal positions


Why SINBAD?

I+ I-

Different structures (non-isomorphism)


Dynamic range

Why SINBAD?

I+ I-


Why SINBAD?

I+ I-


Problem:How to get I+ and I-both on Ewald sphereat the same time?

ΔIano

Ewald sphere 2

diffracted ra

y

λ*

λ*

θ

1Ewald sphere

λ*

(h,k,l)

diffracted ra

yλ*

θ

d*

Osculating Ewald Spheres

(-h,-k,-l)

d*


Nucleus


-h,-k,-l

Detec

tor Detector

Detec

tor Detector

d = 3.5 Å d = 3.5 Å

d = 3.5 Åd = 3.5 Å

sample injector

Mirr

ors

Mirr

ors

d = 3.5 Åλ = 5 Å

XFEL beam

Tolerances:

Time: ~10% of 100 fs

Distance: 3 μm

Angle: ~1% of mosaicity~100 μRad

Can’t we just use scaling?

Ispot ≈ |F(hkl)|2

Darwin’s Formula

I(hkl) - photons/spot (fully-recorded)

Ibeam - incident (photons/s/m2 )

re - classical electron radius (2.818x10-15 m)

Vxtal - volume of crystal (in m3)

Vcell - volume of unit cell (in m3)

λ - x-ray wavelength (in meters!)

ω - rotation speed (radians/s)

L - Lorentz factor (speed/speed)

P - polarization factor

(1+cos2(2θ) -Pfac∙cos(2Φ)sin2(2θ))/2

A - attenuation factor

exp(-μxtal∙lpath)

F(hkl) - structure amplitude (electrons)

C. G. Darwin (1914)

P A | F(hkl) |2I(hkl) = Ibeam re2

Vxtal

Vcell

λ3 LωVcell

Darwin’s Formula














C. G. Darwin (1914)


Vxtal

Vcell

λ3 LωVcell

Darwin’s Formula














C. G. Darwin (1914)


Vxtal

Vcell

λ3 LωVcell

Greenhough-Helliwell Formula

ΔΦ - reflecting range (radians)

2η - mosaic spread (radians)


θ - Bragg angle

λ - x-ray wavelength

Δλ - wavelength spread

γHV - horizontal and vertical

beam divergence (radians)

Greenhough & Helliwell (1983)

ΔΦ = L sin2θ (2η + Δλ/λ tanθ)

+ ((L2sin22θ - 1)γH2 + γV

2)1/2

Greenhough-Helliwell Formula

ΔΦ - reflecting range (radians)

2η - mosaic spread (radians)


θ - Bragg angle

λ - x-ray wavelength

Δλ - wavelength spread

γHV - horizontal and vertical

beam divergence (radians)

Greenhough & Helliwell (1983)

ΔΦ = L sin2θ (2η + Δλ/λ tanθ)

+ ((L2sin22θ - 1)γH2 + γV

2)1/2

Lorentz Factor

Ewald sphere

spin

dle

axi

s

diffracted ra

y

Darwin’s Formula














C. G. Darwin (1914)


Vxtal

Vcell

λ3 LωVcell

Integral under curve

-0.1

0.1

0.3

0.5

0.7

0.9

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

inte

nsity

“Full” Spot


-0.1

0.1

0.3

0.5

0.7

0.9

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

inte

nsity

Spot on “Still”

What is "partiality"?

100%


50%


50%


90%


15%


1%

What is “partiality”?

Ewald sphere

diffracted ra

yd*

λ*

λ*

F(h,k,l)


Ewald sphere

diffracted ra

yd*

λ*

λ*

F(h,k,l)


Ewald sphere

diffracted ra

yd*

λ*

λ*

F(h,k,l)


Ewald sphere

diffracted ra

yd*

λ*

λ*

F(h,k,l)


100% !


90%


80%


50%


20%

Bra

gg, Ja

mes

& B

osa

nquet

(19

21

). P

hilo

s. M

ag. Ser.

6, 4

1, 3

09

–3

37

.


Ewald sphere

diffracted ra

yd*

λ*

λ*

F(h,k,l)

F(0,0,0)

Partiality is always 100% !


Ewald sphere

diffracted ra

yd*

λ*

λ*

F(h,k,l)

F(0,0,0)



Ewald sphere

diffracted ra

yd*

λ*

λ*

F(h,k,l)

F(0,0,0)



Ewald sphere

diffracted ra

yd*

λ*

λ*

F(h,k,l)

F(0,0,0)


Why SINBAD?

I+ I-

Different crystal orientations


F(h,k,l)

Ewald sphere

spectral dispersion

λ1*

λ2*

F(0,0,0)

100%

~90%

F(h,k,l)

Ewald sphere

spectral dispersion

λ1*

λ2*

F(0,0,0)

100%

~45%

Ewald sphere

spectral dispersion

λ1*

λ2*

F(0,0,0)

F(h,k,l)

100%

0%

F(h,k,l)

F(0,0,0)

beam divergence

Ewald sphere

diffracted ra

yd*

λ*

λ*

beam divergence

Ewald sphere

λ*

λ*

F(0,0,0)

d*

diffra

cted

ray

Ewald’s “mosaic” picture

F(0,0,0)

mosaic spread

Ewald sphere

diffracted ra

y

λ*

λ* d*

d*

F(h,k,l)

F(0,0,0)

Ewald sphere

diffracted ra

y

λ*

λ*

d*

F(h,k,l)

mosaic spread

F(0,0,0)

mosaic spread

Ewald sphere

diffracted ra

yd*

λ*

λ*

F(h,k,l)

F(0,0,0)

Ewald sphere

diffracted ra

y

λ*

λ* d*

F(h,k,l)

mosaic spread

F(0,0,0)

mosaic spread

Ewald sphere

diffracted ra

y

λ*

λ* d*

d*

F(h,k,l)

F(0,0,0)

mosaic spread

Ewald sphere

λ*

d*

F(h,k,l)

F(0,0,0)

mosaic spread

Ewald sphere

diffracted ra

yd*

λ*

λ*

F(h,k,l)

F(0,0,0)

mosaic spread

Ewald sphere

λ*

d*

F(h,k,l)

mosaic spread = 0 º

mosaic spread = 0.1º












Ewald’s “mosaic” picture

What isthis stuff?

Darwin’s original picture

“mosaicity” with visible light

10 atoms 0.1 μm

Scattering: line of atoms

50 atoms 0.5 μm100 atoms 1 μm200 atoms 2 μm300 atoms 3 μm400 atoms 4 μm500 atoms 5 μm1000 atoms 10 μm

position on detector (mm)

inte

nsity

(ph

oton

s/S

R/a

tom

)

Scattering: line of atomspe

ak in

tens

ity (

phot

ons/

SR

)

number of atoms in line

“coherence length”

•depends on detector distance !!!•integrated intensity never changes•peak intensity depends on size

10 atoms 0.1 μm


50 atoms 0.5 μm100 atoms 1 μm200 atoms 2 μm300 atoms 3 μm400 atoms 4 μm500 atoms 5 μm

position on detector (mm)

inte

nsity

(ph

oton

s/S

R/a

tom

)

Spot Intensity

Can’t we just rotate the crystal?

1 μm

1°

100 fs= 90 km/s

9 nm

17.26 km/s (90 km/s)2

0.5 μm= 1.5 x 1015 G = 0.5 nN

Can’t we just rotate the crystal?

NO

Why do we want to rotate the crystal?

The “nanocrystal advantage”

Ispot = k Ncells

Ewald sphererange

2

Fraunhofer Formula

Ipixel - photons/pixel/s



hkl - index of pixel (a·(up+us)/λ)

a - orientation (recip. cell vectors)

up,us - unit vector pointing at pixel,source


N - number of cells (each direction)

Ω - solid angle of pixel (steradian)



A - attenuation factor exp(-μxtal∙lpath)


Circa 1820s

see: Kirian et al. (2010)

P A | F(hkl) |2sin(πN·hkl)

sin(π·hkl)Ipixel = Ibeam re

2 Ω2

Scattering: atom by atom

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 0.5 1 1.5 2

one

two

h index

inte

nsity


0123456789

10

0 0.5 1 1.5 2

one

two

three

h index

inte

nsity


0

2

4

6

8

10

12

14

16

18

0 0.5 1 1.5 2

two

three

four

h index

inte

nsity


0

5

10

15

20

25

30

0 0.5 1 1.5 2

three

four

five

h index

inte

nsity


0

5

10

15

20

25

30

35

40

0 0.5 1 1.5 2

four

five

six

h index

inte

nsity


0

10

20

30

40

50

60

0 0.5 1 1.5 2

five

six

seven

h index

inte

nsity


0

10

20

30

40

50

60

70

0 0.5 1 1.5 2

six

seven

eight

h index

inte

nsity


0

10

20

30

40

50

60

70

80

90

0 0.5 1 1.5 2

seven

eight

nine

h index

inte

nsity

Inter-Bragg spots over-sample unit cell

square

round

Why SINBAD?

I+ I-

Different structures (non-isomorphism)


Dear James

The story of the two forms of lysozyme crystals goes back to about 1964 when it was found that the diffraction patterns from different crystals could be placed in one of two classes depending on their intensities. This discovery was a big set back at the time and I can remember a lecture title being changed from the 'The structure of lysozyme' to 'The structure of lysozyme two steps forward and one step back'. Thereafter the crystals were screened based on intensities of the (11,11,l) rows to distinguish them (e.g. 11,11,4 > 11,11,5 in one form and vice versa in another). Data were collected only for those that fulfilled the Type II criteria. (These reflections were easy to measure on the linear diffractometer because crystals were mounted to rotate about the diagonal axis). As I recall both Type I and Type II could be found in the same crystallisation batch . Although sometimes the external morphology allowed recognition this was not infallible.

The structure was based on Type II crystals. Later a graduate student Helen Handoll examined Type I. The work, which was in the early days and before refinement programmes, seemed to suggest that the differences lay in the arrangement of water or chloride molecules (Lysozyme was crystallised from NaCl). But the work was never written up. Keith Wilson at one stage was following this up as lysozyme was being used to test data collection strategies but I do not know the outcome.

An account of this is given in International Table Volume F (Rossmann and Arnold edited 2001) p760.

Tony North was much involved in sorting this out and if you wanted more info he would be the person to contact. I hope this is helpful. Do let me know if you need more.

Best wishes

Louise

Non-isomorphism in lysozyme

0

100

200

300

400

500

600

700

800

900

0 1 2 3

F(11,11,4)

F(11,11,5)

Johnson’s ratio

Str

uct

ure

fac

tor

(e- )


0

100

200

300

400

500

600

700

800

900

0 1 2 3

F(11,11,4)

F(11,11,5)

Johnson’s ratio

Str

uct

ure

fac

tor

(e- )


RH 84.2% vs 71.9% Riso = 44.5%RMSD = 0.18 Å


Dear James

The story of the two forms of lysozyme crystals goes back to about 1964 when it was found that the diffraction patterns from different crystals could be placed in one of two classes depending on their intensities. This discovery was a big set back at the time and I can remember a lecture title being changed from the 'The structure of lysozyme' to 'The structure of lysozyme two steps forward and one step back'. Thereafter the crystals were screened based on intensities of the (11,11,l) rows to distinguish them (e.g. 11,11,4 > 11,11,5 in one form and vice versa in another). Data were collected only for those that fulfilled the Type II criteria. (These reflections were easy to measure on the linear diffractometer because crystals were mounted to rotate about the diagonal axis). As I recall both Type I and Type II could be found in the same crystallisation batch . Although sometimes the external morphology allowed recognition this was not infallible.

The structure was based on Type II crystals. Later a graduate student Helen Handoll examined Type I. The work, which was in the early days and before refinement programmes, seemed to suggest that the differences lay in the arrangement of water or chloride molecules (Lysozyme was crystallised from NaCl). But the work was never written up. Keith Wilson at one stage was following this up as lysozyme was being used to test data collection strategies but I do not know the outcome.

An account of this is given in International Table Volume F (Rossmann and Arnold edited 2001) p760.

Tony North was much involved in sorting this out and if you wanted more info he would be the person to contact. I hope this is helpful. Do let me know if you need more.

Best wishes

Louise


Non-isomorphism = dehydration?

= 1 nL

100 μm

Anomalous difference is resilient to non-isomorphism

Nucleus

Synthetic light collecting structure

0 20 40 60 80 100

Riso (%)

1.0

0.8

0.6

0.4

0.2

Co

rrel

atio

n C

oef

fici

ent

of

ΔF

ano 100 x 100

lysozyme PDBs

Why SINBAD?

New sources of error in SFX:

1.Partiality

2.Dynamic range

3.Jitter

4.Non-isomorphism

?


Nucleus


-h,-k,-l

Detec

tor Detector

Detec

tor Detector

d = 3.5 Å d = 3.5 Å

d = 3.5 Åd = 3.5 Å

sample injector

Mirr

ors

Mirr

ors

d = 3.5 Åλ = 5 Å

XFEL beam

h,k,l

-h,-k,-l

Detec

tor Detector

Detec

tor Detectorλ = 5 Å

sample

injector

Si(111)

52.87degSi(111)Si(111)

Si(111)

Si(111)

Si(111)

2 Multilayer mirrorsd=2nm, W/B4C

KB Horiz focusKB vertical focus

~ 1m

How to reflect x-rays at 90° ?

λ = 2 d sinθSilicon: absorbs ~50%/bounce

Diamond:Unit cell too small

Platinum:Too soft = high mosaic

Iridium: high hardnessCsI: just miss edge

d = 0.7 λ

Want:Large structure factorLow absorbance

Most promising:

Summaryhttp://bl831.als.lbl.gov/~jamesh/powerpoint/ACA_SINBAD_2013.ppt

• SFX introduces new sources of error

• Software solutions are tractable, but hard

• SINBAD could solve them “in hardware”

• Non-isomorphism can be controlled?

• Mono xtal has applications for seeding

Muybridge’s galloping horse (1878)

Muybridge’s multi-camera

Hot questions: 21st centuryhow do molecules work?

Beernink, Endrizzi, Alber & Schachman (1999). PNAS USA 96, 5388-5393.

a “crystal” of horses

realistic “crystal” of horses

average structure: galloping horse

not enough signal

brighter light

even brighter

very bright light

average structure: galloping horse

Horse: real and reciprocal

Supporting a model with data

Molecular Dynamics Simulation

1aho Scorpion toxin

0.96 Å resolution64 residuesSolvent: H20 + acetate

Cerutti et al. (2010).J. Phys. Chem. B 114, 12811-12824.

using realcrystal’s lattice

30 conformers from 24,000

Electron density from 24,000 conformers

Regular model with real data!

Molecular Dynamics vs Observation

Fobs

1aho.cif 1aho.pdb

Fsim FcalcFcalc

Rcryst= 0.137 Rcryst= 0.116Rvault = 0.69

refined_vs_Fsim.pdb

LSQ rmsd = 0.43Å

rmsd = 1.05 Å

1aho 64-residue scorpion toxin in water to 1.0 Å resolution

Rvault = 0.48 to 4 Å

Riso =


RMSD1.05 Å


RMSD0.45 Åaligned

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