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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

Anomalous

Diffraction

SINBAD diffractometer concept

Nucleus

Synthetic light collecting structureh,k,l

-h,-k,-l

tor Detector

d = 3.5 Å d = 3.5 Å

d = 3.5 Åd = 3.5 Å

sample injector

d = 3.5 Åλ = 5 Å

XFEL beam

Why SINBAD?

Different crystal volumes

New source of error in SFX

Why SINBAD?

Different crystal orientations

Why SINBAD?

Different beam intensities

Why SINBAD?

Different crystal positions

Why SINBAD?

Different structures (non-isomorphism)

Dynamic range

Why SINBAD?

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

ΔIano

Ewald sphere 2

diffracted ra

1Ewald sphere

(h,k,l)

diffracted ra

Osculating Ewald Spheres

(-h,-k,-l)

Nucleus

-h,-k,-l

tor Detector

d = 3.5 Å d = 3.5 Å

d = 3.5 Åd = 3.5 Å

sample injector

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

λ3 LωVcell

Darwin’s Formula

C. G. Darwin (1914)

λ3 LωVcell

Darwin’s Formula

C. G. Darwin (1914)

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

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

Lorentz Factor

Ewald sphere

diffracted ra

Darwin’s Formula

C. G. Darwin (1914)

λ3 LωVcell

Integral under curve

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

“Full” Spot

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

Spot on “Still”

What is "partiality"?

What is “partiality”?

Ewald sphere

diffracted ra

F(h,k,l)

Ewald sphere

diffracted ra

F(h,k,l)

Ewald sphere

diffracted ra

F(h,k,l)

Ewald sphere

diffracted ra

F(h,k,l)

100% !

gg, Ja

ag. Ser.

Ewald sphere

diffracted ra

F(h,k,l)

F(0,0,0)

Partiality is always 100% !

Ewald sphere

diffracted ra

F(h,k,l)

F(0,0,0)

Ewald sphere

diffracted ra

F(h,k,l)

F(0,0,0)

Ewald sphere

diffracted ra

F(h,k,l)

F(0,0,0)

Why SINBAD?

Different crystal orientations

F(h,k,l)

Ewald sphere

spectral dispersion

F(0,0,0)

F(h,k,l)

Ewald sphere

spectral dispersion

F(0,0,0)

Ewald sphere

spectral dispersion

F(0,0,0)

F(h,k,l)

F(0,0,0)

beam divergence

Ewald sphere

diffracted ra

beam divergence

Ewald sphere

F(0,0,0)

diffra

Ewald’s “mosaic” picture

F(0,0,0)

mosaic spread

Ewald sphere

diffracted ra

λ* d*

F(h,k,l)

F(0,0,0)

Ewald sphere

diffracted ra

F(h,k,l)

mosaic spread

F(0,0,0)

mosaic spread

Ewald sphere

diffracted ra

F(h,k,l)

F(0,0,0)

Ewald sphere

diffracted ra

λ* d*

F(h,k,l)

mosaic spread

F(0,0,0)

mosaic spread

Ewald sphere

diffracted ra

λ* d*

F(h,k,l)

F(0,0,0)

mosaic spread

Ewald sphere

F(h,k,l)

F(0,0,0)

mosaic spread

Ewald sphere

diffracted ra

F(h,k,l)

F(0,0,0)

mosaic spread

Ewald sphere

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)

Scattering: line of atomspe

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)

Spot Intensity

Can’t we just rotate the crystal?

100 fs= 90 km/s

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?

Why do we want to rotate the crystal?

The “nanocrystal advantage”

Ispot = k Ncells

Ewald sphererange

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

Scattering: atom by atom

0 0.5 1 1.5 2

h index

0123456789

0 0.5 1 1.5 2

h index

0 0.5 1 1.5 2

h index

0 0.5 1 1.5 2

h index

0 0.5 1 1.5 2

h index

0 0.5 1 1.5 2

h index

0 0.5 1 1.5 2

h index

0 0.5 1 1.5 2

h index

Inter-Bragg spots over-sample unit cell

square

Why SINBAD?

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 1 2 3

F(11,11,4)

F(11,11,5)

Johnson’s ratio

0 1 2 3

F(11,11,4)

F(11,11,5)

Johnson’s ratio

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 (%)

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

tor Detector

d = 3.5 Å d = 3.5 Å

d = 3.5 Åd = 3.5 Å

sample injector

d = 3.5 Åλ = 5 Å

XFEL beam

-h,-k,-l

tor Detector

tor Detectorλ = 5 Å

sample

injector

Si(111)

52.87degSi(111)Si(111)

Si(111)

2 Multilayer mirrorsd=2nm, W/B4C

KB Horiz focusKB vertical focus

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

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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