small angle neutron scattering (sans) a danse subproject danse kick-off meeting aug 15-16 pasadena...
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Small Angle Neutron Scattering (SANS)
A DANSE Subproject
DANSE Kick-Off meetingAug 15-16 Pasadena CA Paul Butler
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SANS measures time averaged structure of 1 – 300 nm or more
•Mesoporous structures•Biological structures (membranes, vesicles, proteins in solution)•Polymers•Colloids and surfactants•Magnetic films and nanoparticles•Voids and Precipitates
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Velocity selector
2D detector
sampleL1 L2
Neutron GuideBeam
attenutator
SampleAperture, A2
SourceAperture, A1
Anatomy of a SANS instrument
Sizes of interest = “large scale structures” = 1 – 300 nm or more0.02 < Q ~ 2/d < 6
Q=4 sin / 3-5< <20A and 0.1 < <20
64 cm - 1m
20 – 40 k pixels
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1) Scattering from sample 2) Scattering from other than sample (neutrons still go through sample) 3) Stray neutrons and electronic noise (neutrons don’t go through sample)
Stray neutronsand Electronic noise
Incident beam
aperture
air
sample
cell
• Contribution to detector counts
Sample Scattering
Imeas(i) = Φ t A ε(i) ΔΩ Tc+s[(dΣ/dΩ)s(i) ds + (dΣ/dΩ)c(i) dc] +Ibgd t
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Small Angle Neutron Scattering (SANS)
|3-D Fourier Transform of scattering contrast|2
normalized to sample scattering volume
S
V S
S V
rdrQirQ
d
d S
23.exp
Slide Courtesy of William A. Hamilton
Reciprocity in diffraction:Fourier features at QS => size d ~ 2/QS
Intensity at smaller QS (angle) => larger structures
Measure: Scattered Intensity => Macroscopic cross section = (Scattered intensity(Q) / Incident intensity) T d
Macromolecular structures: polymers, micelles,complex fluids, precipitates,porous media, fractal structures
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Uniqueness of models
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SANS Model Independent Concepts
At large q:
S/V = specific surface are
10 % black90 % white
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SANS more detailed analysis
1
P(Q) = form factor (shape)
Q
S(Q) = Structure factor (interactions or correlations)or Fourier transform of g(r)
)()()( 2 QSQPVQd
dp
coh
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Fourier
transform
P(r)
rF
requ
enc
y
max
0)(
)(
))(sin()(4)(
D
jiji
jijijio rrd
rrQ
rrQrrPVQI
Paid Distance Distribution Function PDDF
Shape reconstruction(ab initio)
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Analytic form Modeling
Structural modeling
Free form modeling
At the same time we want:
•Add constraints•In 2D .. For oriented objects•Optimization with data based on some set of parameters•Non particulate (i.e no P(Q) and S(Q) separation (e.g. Sponge)•G(r) (interactions) – allowing easy input of new ones important•Complicated additions based on specific model (e.g. waters of hydration , exchangeable protons•Conformational or other search•MC and MD ↔ I(Q)•Time resolved (and other parametric studies
AND (of course)Intuitive and easy to use and extendGraphical interface with full 3D visualizationPreferably with automated guidance and idiot guards…. Fast (interactive as much as possible)
So .. SANS DATA Analysis .. Let’s DANSE
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I Get software from somewhere:•IGOR macro package distributed from NIST (latest release last month)•Grasp distributed by ILL (reduction mainly but used for vortex lattices)•ATSAS 2.1 distributed by Dimitri Svergun EMBL (latest release this year)•An eclectic array of routines available from various sources (ISIS maintains a site)II “Do-it yourself” (mostly command line fortran – barrier to doing new stuff)III Minimal Analysis (bigger, smaller, slope of xxx …. fractal?)
0.01
0.1
1
1/cm
9
0.012 3 4 5 6 7 8 9
0.12 3
Data taken on NG7 6/7/2000 Fit using Core + shell sphere model\
Choices for Today’s user
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Steps to the DANSE
1. Analytical model fits to 2D data sets and model independent fits1. Include orientation with respect to beam2. Include instrument resolution3. Include orientation and resolution corrections4. Include parametric analysis and simultaneous fitting5. Include intelligent defaults and intelligent help
2. Ab initio (free form) modeling and P(R)1. include most popular approaches (dummy atom, spherical harmonics, etc)2. Include intelligent help, and defaults3. Include “limit switches”
3. Modeling of arbitrary shapes (including inversion to P(R))1. 3D model building from simple shapes2. Coarse grain PDB file3. Invert real space model to I(Q) 4. MC and MD simulations for complex interacting systems5. Refinements based on constraints
4. Full instrument simulation with plug in sample for experimental planning
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First step
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I NIST and ORNL heavily involved -- Fall meeting planned to determine:• Short term plan for collaboration and distribution of analysis software• How to structure the short term plan to take advantage of DANSE components as soon as they become available• Plan for smooth long term transition to new system
• Some questions: How do we co-ordinate with ATSAS, how to incorporate X-ray, is PDB sufficient or do we need a second “standard”
II Other interested facilities•US
•Los Alamos and IPNS•International SANS instrument scientists interested:
•ILL•ISIS•ANSTO•HANARO
III First contacts with most well known SANS algorithm developers •Svergun•Glatter•Pederson
DANSE card
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When the Music Stops: Beyond DANSE
The goal is NOT software - it is to extract all possible information from the material being studied. Neutron scattering from the user’s point of view is a process in which the sample is placed in the machine and the relevant, meaningful information comes out the other end. Good software enables that process.
The DANSE project is not the end but the beginning. It cannot deliver everything. Rather it must meet two objectives:
1. Provide baseline software that includes:1. A library of well documented and tested re-usable components2. Basic applications with sufficient new value to attract large numbers of users3. A new vision of ease of use as a means of fully utilizing the heavy invetsments
in hardware
• For success must do 3 things:• Must provide everything that is commonly doable with today’s packages• Must provide new functionality not commonly available with today’s packages• Must provide an easy framework for extension and contribution by the community
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THE END
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Steps to the DANSE (I)
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An application for protein conformational study by SANS
• Have been told the need of such program more than a year ago
• Two study cases:– domain hinge movement of yeast guanylate kinase
from unligated to GMP binded– The inconsistence between the crystal structure and
SANS data of a protein
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• Protein motions– http://molmovdb.mbb.yale.edu/molmovdb/
• SANS is a unique technique for domain orientations, conformational changes and/or flexibility under near physiological conditions
• Software for shape determination (including sophiscated method to retrieve complexed shape using sphere harmonics and debye formula) from SANS data– Over-interpretation? Fact: extract 3D data from 1D data
• Major mechanisms of motions are “hinge” and “shear”
• By directly starting from high-resolution structures and moving the subunit (hinge or shear) with subunits’ structure restrained, we can reduce the ambiguity and study the conformational changes– Expanding PDB data bank with atomic-resolution structures – Available software to link high-resolution structures to SANS data
• There is no such tool that allows users easily manipulate protein’s conformation through interactive way and link the conformations to SANS data at run-time
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• Testing files for each components (tested both C and Python codes) and a simple GUI application
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Working Progress• Package SANSsimulation
– Available components (for sphere and hollow sphere only):• analmodelpy: new_analmodel(), calculateIQ()
• pointsmodelpy:new_loresmodel(), fillpoints(), distdistribution(), calculateIQ
• geoshapespy: new_sphere(), new_hollowsphere()
• iqpy: new_iq(), outputIQ()
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Class Diagram
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Required components
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Budget profile SANS
Tennessee Funding Profile
$-
$200,000
$400,000
$600,000
$800,000
$1,000,000
$1,200,000
$1,400,000
year 1 year 2 year 3 year 4 year 5
Incremental Funding Profile Cumulative
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UML Use Cases for SANS
<exten
d>
Analytic form Modeling
User
Analysis
Simulate
ReduceStructural modeling
<extend>
Free form modeling
<extend>
<ext
end>
<extend>
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Staffing plans SANS + QASANS:Project Leader: Paul ButlerPostdoc 1 (Current developer): Jing ZhouPostdoc 2 : start hiring process during first year to bring on board in year 2Grad Stud 1: UMBC – eventually working with UT Biochemistry department and SNS/CSMB
Tennessee FTE by Resource Type
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
year 1 year 2 year 3 year 4 year 5
Postdoc Tech Writer Grad Student Undergrad
Other Administrative Support Minority Student Quality Assurance
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UML Activity Diagram (w/o start-stop)
NeXus
reduction B v K
{C1XX’, ...}
/M |QUexp(iQr) |2
Compare, Alter (C1XX, ..}
g(E)
phononthermo.py
Z, F, S
Laptop Linux Cluster
SNS Archive
SNS
gnw(E)
d/d (Q)
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What we plan to do
II Build Executive level application
Executive level:Data managerParametric series manager
Reduction Analyticforms
Ab initiomodeling
“modeling”Instrumentsimulation
NEWPackages
Data
Data managerParametric series manager
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Application Specification (from PEP)
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Specular Neutron Reflection
|1-D FT of depth derivative of scattering contrast|2 / QR4
2
4
2
exp4
z
RR
R dzziQdz
zd
QQR
Slide Courtesy of William A. Hamilton
At lower QR, R reaches its maximum R=1 i.e. total reflection
Similar to SANS but ...This is only an approximation valid at large QR
of an Optical transform - refraction happens
Layered structures or correlations relative to a flat interface:Polymeric, semiconductor and metallic films and multilayers, adsorbed
surface structures and complex fluid correlations at solid or free surfaces
Measure: Reflection Coefficient = Specularly reflected intensity / Incident intensity
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Specular Reflectivity vs. Scattering length density profiles
Critical edgeR=1 for QR<QC
QC=4()1/2
T
Bragg peak
a
QR=2/aQR=2/T
sld step Thin film Multilayer
Fourier features (as per SANS)Fresnel reflectivity
Slide Courtesy of William A. Hamilton
Thin filmInterference
fringes
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small θ … how
Sizes of interest = “large scale structures” = 1 – 300 nm or more0.02 < Q ~ 2/d < 6
Q=4 sin /
Cold source spectrum 3-5< <20A
Intensity balance sample size with instrument length
Cold Source Brightness
1.00E+09
1.00E+10
1.00E+11
1.00E+12
1.00E+13
0 5 10 15 20
Wavelength (A)n
eu
tro
ns
/cm
^2
/A/s
ter/
se
cApproaches to small θ:• Small detector resolution/Small slit (sample?) size• Large collimation distance
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Δθ
Sizes of interest = “large scale structures” = 1 – 300 nm or more
SANS Approach QS
ki
kS
SSD SDD≈
S1 ≈ 2 S2
Optimized for ~ ½ - ¾ inch diameter sample
2 θ
S1
3m – 16m 1m – 15m
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Sizes of interest = “large scale structures” = 1 – 300 nm or more
NR Approach
θ?
? = Ls sinθ
QR kRkiPoint by point scan
? ~ 1mm for low Q
Ls
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10-2
10-1
100
101
102
103
104
105
0 100 4 10 -4 8 10-4 1.2 10-3
emptyEwald + Bgdlatex
q (Å-1)
IBGD
= 0.025 s-1
IPeak
= 60,000 s-1
Sizes of interest = “large scale structures” = 1 – 300 nm or more
QS
ki
kS
Ultra Small Angle Approach – when SANS isn’t small enough
Point by point scan - again
Fundamental Rule: intensity OR resolution… but not both
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Imeas = Φ A ε t R +Ibgd t
Rocking Curve
i fixed, 2f varying
Specular Scan
2f = 2I
f = i
i 2f
Background Scan
f ≠ I
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When measuring a gold layer on a Silicon substrate for example, many reflectometers can go to Q > 0.4 Å-1 and reflectivities of nearly 10-8. However most films measured at the solid solution interface only get to 10-5 and a Qmax of ~ 0.25Å-1 Why might this be and what might be done about it. (hint: think of sources of background)
SANS is a transmission mode measurement, so with an infinitely thick sample the transmission will be zero and thus no scattering can be measured. If the sample is infinitely thin, there is nothing to scatter from…. So what thickness is best? (hint: look at the Imeas equation)
For a strong scatterer, a large fraction of the beam is coherently scattered. This is good for signal but how might it be a problem? (hint: think of the scattering from the back or downstream side of the sample)
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Given the SANS pattern on the right, how can know what Q to associate with each pixel? (hint use geometry and the definition for Q)
NR and SANS measure structures in the direction of Q. Given the NR Q is in the z direction, can NR be used to measure the average diameter of the spherically symmetric object floating randomly below the interface?
USANS gets to very small angle. However SANS is a long instrument in order to reach small angles. Why not make the instrument longer?(Hint: particle or wave?)
QR
kRki
D
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Velocity selector
2D detector
sampleL1 L2
Neutron GuideBeam
attenutator
SampleAperture, A2
SourceAperture, A1
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•Fundamentals of neutron scattering 100•Neutron diffraction 101•Nobel Prize in physics
Neutron Scattering 102:SANS and NR
Pre-requisites:
Grade based on attendance and participation
Paul Butler
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SANS and NR measures interference patterns from structures in the direction of Q
SANS and NR assume elastic scattering
QR kRki
2R
i f
QS
ki
kS
incident beamwavevector |ki|=2/ scattered beam
wavevector |kS|=2/
2s
Neutron Reflectometry (NR) Reflection mode
Small Angle Neutron Scattering (SANS) Transmission mode
f = i = R
kR = ki+QR
QR =4 sinR / Perpendicular to surface
kS = ki+Qs
Qs=|Qs|=4 sins /
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1) Scattering from sample 2) Scattering from other than sample (neutrons still go through sample) 3) Stray neutrons and electronic noise (neutrons don’t go through sample)
• We need MORE measurements
Stray neutronsand Electronic noise
Incident beam
aperture
air
sample
cell
• Contribution to detector counts
Sample Scattering
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•SANS and NR measure structures in the direction of Q only•SANS and NR assume elastic scattering•SANS is a transmission technique that measures the average structures in the volume probed•NR is a reflection technique that measures the z (depth) density profile of structures strongly correlated to the reflection interface
Thinking aids:SANSImeas(i) = Φ t A ε(i) ΔΩ Tc+s[(dΣ/dΩ)s(i) ds + (dΣ/dΩ)c(i) dc] +Ibgd t
NRImeas = Φ A ε t R +Ibgd t
Summary
)()()( 2 QSQPVQd
dp
coh
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MA
CANC
Rg = 31Å
0.0001
2
4
68
0.001
2
4
68
0.01
2
I(Q
) cm
-1
3 4 5 6 7 8 90.01
2 3 4 5 6 7 8 90.1
2 3
Q (Å-1
)
wm 0.5 mg/ml (Rg=35±1Å) model (Rg=31Å)
0.0001
2
4
68
0.001
2
4
68
0.01
2
I(Q
) cm
-1
3 4 5 6 7 8 90.01
2 3 4 5 6 7 8 90.1
2 3
Q (Å-1
)
wm 0.5 mg/ml (Rg=35±1Å)
image
A VISION
constraintsHigh resolution structure
Protein Data Bank
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smear_parameters_css smear_coef_css W_sigmascale 0.01 0
core radius (A) 43.8081 0.130794shell thickness (A) 18.2979 0.190327
Core SLD (A-2) 6.15162e-06 1.80823e-05Shell SLD (A-2) 3.14889e-06 1.80825e-05
Solvent SLD (A-2) 6.26021e-06 1.80778e-05bkg (cm-1) 0.00627994 0.00012066
0.01
0.1
1
1/cm
9
0.012 3 4 5 6 7 8 9
0.12 3
1/Å
Data taken on NG7 6/7/2000 Fit using Core + shell sphere model\
When life is easy
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When life is easy
smear_parameters_css smear_coef_css W_sigmascale 0.01 0
core radius (A) 43.8081 0.130794shell thickness (A) 18.2979 0.190327
Core SLD (A-2) 6.15162e-06 1.80823e-05Shell SLD (A-2) 3.14889e-06 1.80825e-05
Solvent SLD (A-2) 6.26021e-06 1.80778e-05bkg (cm-1) 0.00627994 0.00012066
0.01
0.1
1
1/cm
9
0.012 3 4 5 6 7 8 9
0.12 3
1/Å
Data taken on NG7 6/7/2000 Fit using Core + shell sphere model\
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R = C exp[-EF/kBT]
EF = 6.7kBT (170 meV)PRL 2004
“c”L
L3
R
=0.400.08 s
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Beyond the Sponge to Lamellar Transition-A Lamellar Collapse:
(when life starts to get really hard)
Simultaneous fitsSLD,bgd,membrane
thickness fixed
x
z
Model: polydisperse aligned prolate ellipsoidal shells (vesicles) Qx semi-major axis ~ 520Å along flow directionQz semi-minor axis ~ 225Å
Structural analysis of a 4% Lamellar at
1500 s-1
Something is sti
ll
missing
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SANS: a planProject Leader: Paul ButlerAdvisors: Sean Langridge, Dean MylesPostdoc 1: (Current developer): Jing ZhouStart hiring process in middle of first year to bring on board in year 2Grad Students: UMBC and UTWork with ORNL’s CSMB and SANS teamWork with NIST SANS team and Structural bio groupPlans for international steering committee
PostDoc and other developer FTE by year
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
year 1 year 2 year 3 year 4 year 5
Total Funding Profile
$-
$200
$400
$600
$800
$1,000
$1,200
$1,400
year 1 year 2 year 3 year 4 year 5
Incremental Funding Profile Cumulative
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Clay polymer gels at rest
When life starts to get hard
Clay polymer gels under shear
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I(Q)
P(r)
Fourier
transform
r
Fre
quen
cy
How does one really calculate a theoretical Intensity
max
0)(
)(
))(sin()(4)(
D
jiji
jijijio rrd
rrQ
rrQrrPVQI
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User-interactive GUI application
• Link the conformational changes to SANS data– Example– showing the I(Q) for the corresponding conformation in Run-
time
• Mouse click to move selected subunit – VMD provide shear movement but no hinge movement
• Plan: start with the existing codes which uses VTK to load PDB files into 3D graphics and move models around– Other requirements: program CRYSON or XTAL2SAS and a
2D plotter
• Immediate usage at NIST• Future distribution for broad users
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Motivation: Structural studies of protein and nucleic acid complexes in solution
CRP protein (yellow ribbon) and the DNA (blue spheres)Krueger et al., Biochemistry, 47(7), 1958-1968, 2003
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UML Use Cases for SANS
<extend>
Analytic form Modeling
User
Analysis
PlanExperiment
ReduceStructural modeling
<extend>
Free form modeling
<extend>
<exten
d>
<extend>
Simulate
<include>