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BNL_2011.ppt
AcknowledgementsKen Frankel Rick Donahue Howard Padmore Alastair MacDowell
8.3.1 creator: Tom Alber 8.3.1 PRT head: Jamie CateCenter for Structure of Membrane Proteins (PSI)
Membrane Protein Expression Center IICenter 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.
The optimum wavelength for macromolecular crystallography
Higher? or Lower?
dose
Johns, H. & Cunningham, J. (1974). The physics of radiology. Thomas Springfield, Illinois.
~1 cm at 1 MeV fNH
Charged Particle Equilibrium (CPE)
satisfiesCPE
collimator crystal
X-ray
e-
violatesCPE
Assume a spherical crystal…
is there a “problem” with violating CPE?
ICRU report 31 “Average Energy Required to Produce an Ion Pair” (1979)
for air: W ~ 30 eV/ion-pair
yet, final ions are thermalized (<0.1 eV each)
Where does 99% of the energy go?
Answer: non-ionizing excitations
Secondary ionization
e-
Secondary ionization
e-
e-
+
Excitation
e-
Excitation
e-
Excitation e-
Excitation
ionizing interactions
e- +
Violating CPE: two kinds of “dose”?
non-ionizing interactions
ICRU report 36 “Microdosimetry” (1984)
Charged Particle Equilibrium (CPE)
Johns, H. & Cunningham, J. (1974). The physics of radiology. Thomas Springfield, Illinois.
skin not burned
Ionization track
particle transport simulationusing MCNP
collimator crystal
X-ray
Where do photons go?
beamstop
Transmitted (98%)
Protein1A x-rays
Where do photons go?
beamstop
elastic scattering (6%)
Transmitted (98%)
Protein1A x-rays
Elastic scattering
Elastic scattering
Inelastic scattering
e-
+
Where do photons go?
beamstop
elastic scattering (6%)
Transmitted (98%)
Protein1A x-rays
Where do photons go?
beamstop
elastic scattering (6%)
Transmitted (98%)
inelastic scattering (7%)
Protein1A x-rays
Where do photons go?
beamstop
elastic scattering (6%)
Transmitted (98%)
inelastic scattering (7%)
Protein1A x-rays
Re-emitted (99%) Absorbed (~0%)
Photoelectric absorption
Photoelectric absorptione-
+
Where do photons go?
beamstop
elastic scattering (6%)
Transmitted (98%)
inelastic scattering (7%)
Protein1A x-rays
Re-emitted (99%) Absorbed (~0%)
Where do photons go?
beamstop
elastic scattering (6%)
Transmitted (98%)
inelastic scattering (7%) Photoelectric (87%)
Protein1A x-rays
Re-emitted (99%) Absorbed (~0%)
Where do photons go?
beamstop
elastic scattering (6%)
Transmitted (98%)
inelastic scattering (7%) Photoelectric (87%)
Protein1A x-rays
Re-emitted (~0%) Absorbed (99%)Re-emitted (99%) Absorbed (~0%)
Fluorescence
+
Fluorescence
e-
+
Auger emission
+
Auger emission
++
e-
MCNP cuts off at 1 keV
1 MeV 100 GJ/mol Medical radiation therapy
100 keV 10 GJ/mol Medical imaging
10 keV 1 GJ/mol X-ray crystallography
1 keV 100 MJ/mol S and P K-edges
100 eV 10 MJ/mol “water window”
10 eV 1 MJ/mol C≡C bond
1 eV 100 kJ/mol C-C bond, visible light
100 meV 10 kJ/mol hydrogen bond
10 meV 1 kJ/mol heat (~300 K)
bonding affects absorption
Almkvist, et al. (2010)."K-edge XANES analysis of sulfur compounds: an investigation of the relative intensities using internal calibration", J. Sync. Rad. 17, 683-688.
MCNP model
particle transport simulationusing MCNP
collimator crystal
X-ray
dose reduction with 1 Å radiation
00.10.20.30.40.50.60.70.80.9
1
0.01 0.1 1 10 100 1000
Crystal diameter (µm)
Dos
e ca
ptur
e fr
actio
n
fNH
←???→
1 keV e- pathlength
100 μm crystal vs energy
00.10.20.30.40.50.60.70.80.9
1
1000 10000 100000 1000000
Photon Energy
Dos
e ca
ptur
e fr
actio
n
1 keV 10 keV 100 keV 1 MeV
fNH
dose reduction vs energy
00.10.20.30.40.50.60.70.80.9
1
1000 10000 100000 1000000
100 um20 um5 um1 um
Photon Energy
Dos
e ca
ptur
e fr
actio
n
1 keV 10 keV 100 keV 1 MeV
2 variablesD
ose
capt
ure
frac
tion
Critical escape diameter
02468
101214161820
0 10000 20000 30000 40000 50000
half
Photon Energy (eV)
Cry
stal
dia
met
er (µ
m)
Critical escape diameter
02468
101214161820
0 10000 20000 30000 40000 50000
half90%
Photon Energy (eV)
Cry
stal
dia
met
er (µ
m)
Critical escape diameter
0.1
1
10
100
1000
10000
1000 10000 100000 1000000 10000000
half90%
Photon Energy
Cry
stal
dia
met
er (µ
m)
1 keV 10 keV 100 keV 1 MeV 10 MeV
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 - absorption factor
exp(-μxtal∙lpath)
F(hkl) - structure amplitude (electrons)
P A | F(hkl) |2I(hkl) = Ibeam re2
Vxtal
Vcell
λ3 LωVcell
Darwin, C. G. (1914)."The theory of X-ray reflexion. Part I", Philos. Mag. 27, 315-333.
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 - absorption factor
exp(-μxtal∙lpath)
F(hkl) - structure amplitude (electrons)
P A | F(hkl) |2I(hkl) = Ibeam re2
Vxtal
Vcell
λ3 LωVcell
Darwin, C. G. (1914)."The theory of X-ray reflexion. Part I", Philos. Mag. 27, 315-333.
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 - absorption factor
exp(-μxtal∙lpath)
F(hkl) - structure amplitude (electrons)
P A | F(hkl) |2I(hkl) = Ibeam re2
Vxtal
Vcell
λ3 LωVcell
Darwin, C. G. (1914)."The theory of X-ray reflexion. Part I", Philos. Mag. 27, 315-333.
Dose Formula
dose - absorbed energy (Gy)
Ibeam - incident (photons/s/μm2 )
texp - exposure time (s)
λ - x-ray wavelength (in Å)
dose ≈ Ibeam ·texp λ2
2000
Dose Formula
Dmax - maximum dose (Gy)
Ibeam - incident (photons/s/μm2 )
tdataset - accumulated exposure time (s)
λ - x-ray wavelength (in Å)
Dmax ≈ Ibeam ·tdatasetλ2
2000
Dose Formula
Dmax - maximum dose (Gy)
Ibeam - incident (photons/s/μm2 )
tdataset - accumulated exposure time (s)
R - radius of crystal
Ten - transmission of a sphere ~ exp(-μen·2R)
- density of crystal
Eph - photon energy
qe - electron charge
Dmax = Ibeam ·tdataset
3qeEph
4R(1-Ten)
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 - absorption factor
exp(-μxtal∙lpath)
F(hkl) - structure amplitude (electrons)
P A | F(hkl) |2I(hkl) = Ibeam re2
Vxtal
Vcell
λ3 LωVcell
Darwin, C. G. (1914)."The theory of X-ray reflexion. Part I", Philos. Mag. 27, 315-333.
Darwin’s Formula
Dmax - maximum dose (kGy)
tdataset - accumulated exposure (s)
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 - absorption factor
exp(-μxtal∙lpath)
F(hkl) - structure amplitude (electrons)
P A | F(hkl) |2I(hkl) = re2
Vxtal
Vcell
2 λ LωVcell
Dmax
tdataset
Darwin, C. G. (1914)."The theory of X-ray reflexion. Part I", Philos. Mag. 27, 315-333.
Darwin’s Formula
Dmax - maximum dose (kGy)
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!)
2π - rotation range (radians)
L - Lorentz factor (speed/speed)
P - polarization factor
(1+cos2(2θ) -Pfac∙cos(2Φ)sin2(2θ))/2
A - absorption factor
exp(-μxtal∙lpath)
F(hkl) - structure amplitude (electrons)
P A | F(hkl) |2I(hkl) = re2
Vxtal
Vcell
2 λ L2πVcell
Dmax
Darwin, C. G. (1914)."The theory of X-ray reflexion. Part I", Philos. Mag. 27, 315-333.
Holton & Frankel (2010) Acta D 66 393-408.
Holton & Frankel (2010) Acta D 66 393-408.
Where:IDL - average damage-limited intensity (photons/hkl) at a given resolution105 - converting R from μm to m, re from m to Å, ρ from g/cm3 to kg/m3 and MGy to Gyre - classical electron radius (2.818 x 10-15 m/electron)h - Planck’s constant (6.626 x 10-34 J∙s)c - speed of light (299792458 m/s)fdecayed - fractional progress toward completely faded spots at end of data setρ - density of crystal (~1.2 g/cm3)R - radius of the spherical crystal (μm)λ - X-ray wavelength (Å)fNH - the Nave & Hill (2005) dose capture fraction (1 for large crystals)nASU - number of proteins in the asymmetric unitMr - molecular weight of the protein (Daltons or g/mol)VM - Matthews’s coefficient (~2.4 Å3/Dalton)H - Howells’s criterion (10 MGy/Å)θ - Bragg anglea
2 - number-averaged squared structure factor per protein atom (electron2)Ma - number-averaged atomic weight of a protein atom (~7.1 Daltons)B - average (Wilson) temperature factor (Å2)μ - attenuation coefficient of sphere material (m-1)μen - mass energy-absorption coefficient of sphere material (m -1)
Self-calibrated damage limit
22
sphere2
4425 sin2expsin
4cos301
)2(Tsin2ln
5.0f
f109
2 BM
f
θθ
,R,μT θ ,μ,R λH
VMnλρR
hcrI
a
a
ensphereMrASUNH
decayedeDL
Holton & Frankel (2010) Acta D 66 393-408.
minimum required crystal size
1
1.5
2
2.5
3
3.5
4
4.5
5
1 10 100 1000
photon energy (keV)
crys
tal d
iam
eter
(mic
rons
)
2 A perfect lysozyme
wavelength dependencecr
ysta
l dia
met
er (μ
m)
Å
Minimum size for complete data set
fNH = 1
Where:IDL - average damage-limited intensity (photons/hkl) at a given resolution105 - converting R from μm to m, re from m to Å, ρ from g/cm3 to kg/m3 and MGy to Gyre - classical electron radius (2.818 x 10-15 m/electron)h - Planck’s constant (6.626 x 10-34 J∙s)c - speed of light (299792458 m/s)fdecayed - fractional progress toward completely faded spots at end of data setρ - density of crystal (~1.2 g/cm3)R - radius of the spherical crystal (μm)λ - X-ray wavelength (Å)fNH - the Nave & Hill (2005) dose capture fraction (1 for large crystals)nASU - number of proteins in the asymmetric unitMr - molecular weight of the protein (Daltons or g/mol)VM - Matthews’s coefficient (~2.4 Å3/Dalton)H - Howells’s criterion (10 MGy/Å)θ - Bragg anglea
2 - number-averaged squared structure factor per protein atom (electron2)Ma - number-averaged atomic weight of a protein atom (~7.1 Daltons)B - average (Wilson) temperature factor (Å2)μ - attenuation coefficient of sphere material (m-1)μen - mass energy-absorption coefficient of sphere material (m -1)
Self-calibrated damage limit
22
sphere2
4425 sin2expsin
4cos301
)2(Tsin2ln
5.0f
f109
2 BM
f
θθ
,R,μT θ ,μ,R λH
VMnλρR
hcrI
a
a
ensphereMrASUNH
decayedeDL
Holton & Frankel (2010) Acta D 66 393-408.
minimum required crystal size
0
0.5
1
1.5
2
2.5
3
1 10 100 1000 10000
photon energy (keV)
crys
tal d
iam
eter
(mic
rons
)
2 A perfect lysozyme
Lysozyme with MCNPNave-Hill effect
wavelength dependencecr
ysta
l dia
met
er (μ
m)
Å
Minimum size for complete data set
minimum required crystal size
0.1
0.3
0.5
0.7
0.9
1.1
1.3
1.5
1.7
0 5 10 15 20 25 30 35 40 45 50
photon energy (keV)
crys
tal d
iam
eter
(mic
rons
)
2 A perfect lysozyme
Lysozyme with MCNP Nave-Hill effect
wavelength dependencecr
ysta
l dia
met
er (μ
m)
Å
Minimum size for complete data set
minimum required crystal size
0.1
0.3
0.5
0.7
0.9
1.1
1.3
1.5
1.7
0 5 10 15 20 25 30 35 40 45 50
photon energy (keV)
crys
tal d
iam
eter
(mic
rons
)
3.5 A perfect xtal 100 kDa protein
2 A perfect lysozyme
Lysozyme with MCNP Nave-Hill effect
wavelength dependencecr
ysta
l dia
met
er (μ
m)
Å
Å
Minimum size for complete data set
0.1
1
10
100
100.0 1000.0 10000.0 100000.0 1000000.0 10000000.0
molecular mass
crys
tal d
iam
eter
(um
)
no escape
MCNP
molecular weight
crys
tal d
iam
eter
(μm
)
100 Da 1 kDa 10 kDa 100 kDa 1 MDa 10 MDa
Minimum size for complete data set
1 ÅX-rays
2 Åspots
B = 24
50% solvent
Prediction:
Exploiting Nave-Hill effect will require multi-crystal datasets
Other reasons for high energy
room temperature
Zero-parallax microscope
pinhole
mirror
microscope
High energy compresses pattern
2 Å data
2 Å data
Example Room-temperature Data
• lysozyme
• 50 μm beam
• 37 Gy/s (0.775 Å)
• 30s exposures at 20C
• 90° of data, 97% complete
• I/ = 1.5 at 1.9 Å
• Rmerge 18% (overall) 5% (low)
• ΔB same as 20 min at 100K
B factor-2
-4
-6
scale vs batch
2
1
0
high energy myth: less background
elastic background/spot intensity ratio is wavelength-independent!
photon energy (eV)
norm
aliz
ed fi
gure
of m
erit
obliquityeffect
high energy myth: less background
elastic background/spot intensity ratio is wavelength-independent!
However: inelastic and fluorescence are less, as is absorption
Other reasons for high energy
room temperature
high pressure?
Room temperature damage rates
0
0.5
1
1.5
2
2.5
0.0001 0.001 0.01 0.1 1 10
Southworth-Davies (lyso)Barker (native)Barker (additives)Blake & Phillips (1962)lysozyme (unpublished)
dose rate (kGy/s)
dose
at h
alf i
nten
sity
(MG
y)
Room temperature damage rates
0
0.5
1
1.5
2
2.5
0.0001 0.001 0.01 0.1 1 10
powdered lysozymeSouthworth-Davies (lyso)Cheresov (lipid)Barker (native)Barker (additives)Blake & Phillips (1962)lysozyme (unpublished)
dose rate (kGy/s)
dose
at h
alf i
nten
sity
(MG
y)
Room temperature damagehas a size dependence?
Radiation Damage “scale factor”
F2 alone
cannot
explain
change
in overall
scale!
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 - absorption 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
“scale factor” implies that damaging motions are larger than unit cell
Room temperature damagehas a size dependence?
high pressure will hold it together?
suggests micro-fracture mechanism of spot fading
Radiation Damage prediction
3
exposureps2
kdamage
data
large displacements cannot be faster than the speed of sound
Timescales of radiation damage
Garret et. al. (2005) Chem. Rev. 105, 355-389
Two types of reactions
Garret et. al. (2005) Chem. Rev. 105, 355-389
nonhomogeneous
homogeneous
Timescales of radiation damage
Garret et. al. (2005) Chem. Rev. 105, 355-389
LCLS
ALSbunch
Room temperature damage rates
0
0.5
1
1.5
2
2.5
0.0001 0.001 0.01 0.1 1 10
powdered lysozymeSouthworth-Davies (lyso)Barker (native)Barker (additives)Blake & Phillips (1962)lysozyme (unpublished)
dose rate (kGy/s)
dose
at h
alf i
nten
sity
(MG
y)
Room temperature damage rates
0.01
0.1
1
10
100
1000
0.0001 0.1 100 100000 1E+08 1E+11 1E+14 1E+17 1E+20
powdered lysozymeSouthworth-Davies (lyso)Cheresov (lipid)Barker (native)Barker (additives)Blake & Phillips (1962)lysozyme (unpublished)Chapman (2011)
dose rate (kGy/s)
dose
at h
alf i
nten
sity
(MG
y)
Nozzle ground to provide large X-ray diffraction angle
Droplets freeze at 106 o/sec.in vacuumto vitreousice if cryoprotectantadded.
Hand-grinding to micron gives large take-off anglefor X-rays ! D. DePonte
X-rays
5 microns
Flow rate 12 microliters per minute.
An environmental SEM image of operating protein-beam injector for LCLS.
What about very low energy?
sample shadow on detector
Cu
sample shadow on detector
X-ray of cryo stream
low-energy X-rays
Cu
λ=2d sinθ
2.5 Å data with 5 Å X-rays
International Tables for Crystallography, Vol. C, 2nd ed., chapter 6.3
Detecto
r Detector
Detecto
r Detector
d = 2.5 Å d = 2.5 Å
d = 2.5 Åd = 2.5 Å
sam
ple
inje
ctor
Mirr
ors
Mirr
ors
λ = 5 Åd = 2.5 Å
h,k,l
-h,-k,-l
CollidingBeamAnomalousMeasurement
0 20 40 60 80 100
Anomalous differences are resilient to non-isomorphism
Riso (%)
1.0
0.8
0.6
0.4
0.2
0
Cor
rela
tion
Coe
ffici
ent o
f ΔF a
no
100 x 100 lysozyme PDBs
The optimum wavelength for macromolecular crystallography
Maximize data/damage → 15-50 keV
Turn the crank → 12.68 keV
Native element phasing → 2-2.5 keV
the future: multi-crystal data sets
PowerPoint File available:
http://bl831.als.lbl.gov/~jamesh/powerpoint/
BNL_2011.ppt
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