Transcript Slide 1

Small Angle Neutron Scattering (SANS)
A DANSE Subproject
DANSE Kick-Off meeting
Aug 15-16 Pasadena CA
Paul Butler
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
Anatomy of a SANS instrument
Sizes of interest = “large scale structures” = 1 – 300 nm or more
0.02 < Q ~ 2/d < 6
Q=4 sin / 
Beam
attenutator
3-5<  <20A and 0.1 <  <20
Neutron Guide
2D detector
Velocity
selector
L1
Source
Aperture, A1
sample
Sample
Aperture, A2
L2
20 – 40 k pixels
Sample Scattering
• Contribution to detector counts
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)
aperture
Incident beam
sample
air
cell
Stray neutrons
and Electronic noise
Imeas(i) = Φ t A ε(i) ΔΩ Tc+s[(dΣ/dΩ)s(i) ds + (dΣ/dΩ)c(i) dc] +Ibgd t
Small Angle Neutron Scattering (SANS)
Macromolecular structures: polymers, micelles,complex fluids,
precipitates,porous media, fractal structures
Measure: Scattered Intensity => Macroscopic cross section
= (Scattered intensity(Q) / Incident intensity) T d
 
d 
QS 
d

VS


  3 2

 r exp iQS .r d r
VS
|3-D Fourier Transform of scattering contrast|2
normalized to sample scattering volume
Reciprocity in diffraction:
Fourier features at QS => size d ~ 2/QS
Intensity at smaller QS (angle) => larger structures
Slide Courtesy of William A. Hamilton
Uniqueness of models
SANS Model Independent Concepts
At large q:
S/V = specific surface are
10 % black
90 % white
SANS more detailed analysis
d coh
(Q )  V p  2 P (Q ) S (Q )
d
S(Q) = Structure factor (interactions or correlations)
or Fourier transform of g(r)
1
P(Q) = form factor (shape)
Q
Frequency
Paid Distance Distribution Function PDDF
P(r)
Fourier
transform
r
Dmax
sin( Q  (ri  r j ))
0
Q  (ri  r j )
I (Q)  4Vo  P(ri  r j ) i  j
d (ri  r j )
Shape reconstruction
(ab initio)
So .. SANS DATA Analysis .. Let’s DANSE
At the same time we want:
Analytic form
Modeling
Free form
modeling
Structural
modeling
•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 extend
Graphical interface with full 3D visualization
Preferably with automated guidance and idiot guards
…. Fast (interactive as much as possible)
Choices for Today’s user
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?)
Data taken on NG7 6/7/2000
Fit using Core + shell sphere model\
1/cm
1
0.1
0.01
9
2
3
4
5
6
7
8
9
2
3
Steps to the DANSE
1. Analytical model fits to 2D data sets and model independent fits
1. Include orientation with respect to beam
2. Include instrument resolution
3. Include orientation and resolution corrections
4. Include parametric analysis and simultaneous fitting
5. 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 defaults
3. Include “limit switches”
3. Modeling of arbitrary shapes (including inversion to P(R))
1. 3D model building from simple shapes
2. Coarse grain PDB file
3. Invert real space model to I(Q)
4. MC and MD simulations for complex interacting systems
5. Refinements based on constraints
4. Full instrument simulation with plug in sample for experimental planning
First step
DANSE card
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
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 components
2. Basic applications with sufficient new value to attract large numbers of users
3. 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
THE END
Steps to the DANSE (I)
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
• 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
• Testing files for each components (tested
both C and Python codes) and a simple GUI
application
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()
Class Diagram
Required components
Budget profile SANS
Tennessee Funding Profile
$1,400,000
$1,200,000
$1,000,000
$800,000
$600,000
$400,000
$200,000
$year 1
year 2
year 3
Incremental Funding Profile
year 4
Cumulative
year 5
UML Use Cases for SANS
Simulate
<extend>
Analytic form
Modeling
Structural
modeling
Reduce
User
Analysis
<extend>
Free form
modeling
Staffing plans SANS + QA
SANS:
Project Leader: Paul Butler
Postdoc 1 (Current developer): Jing Zhou
Postdoc 2 : start hiring process during first year to bring on board in year 2
Grad Stud 1: UMBC – eventually working with UT Biochemistry
department and SNS/CSMB
Tennessee FTE by Resource Type
7.00
6.00
5.00
4.00
3.00
2.00
1.00
0.00
year 1
year 2
year 3
year 4
year 5
Postdoc
Tech Writer
Grad Student
Undergrad
Other
Administrative Support
Minority Student
Quality Assurance
UML Activity Diagram (w/o start-stop)
SNS
Laptop
SNS Archive
NeXus
Linux Cluster
gnw(E)
{C1XX’, ...}
reduction
BvK
d/d (Q)
s/M |QU exp(iQr) |2
Compare,
Alter
(C1XX, ..}
g(E)
phononthermo.py
Z, F, S
What we plan to do
II Build Executive level application
Data manager
Parametric series manager
Executive level:
Data manager
Parametric series manager
Data
Reduction
Analytic
forms
Ab initio
modeling
“modeling”
Instrument
simulation
NEW
Packages
Application Specification (from PEP)
Specular Neutron Reflection
Measure: Reflection Coefficient
= Specularly reflected intensity / Incident intensity
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
RQ R

4 

2
4
R
Q
d z 
z dz expiQR z dz
2
|1-D FT of depth derivative of scattering contrast|2 / QR4
Similar to SANS but ...
This is only an approximation valid at large QR
of an Optical transform - refraction happens
At lower QR, R reaches its maximum R=1 i.e. total reflection
Slide Courtesy of William A. Hamilton
Specular Reflectivity vs. Scattering length density profiles
T

sld step  
a
Thin film
QR=2/T
Critical edge
R=1 for QR<QC
QC=4()1/2
Fresnel reflectivity
Slide Courtesy of William A. Hamilton
Thin film
Interference fringes
Fourier features (as per SANS)
Multilayer
QR=2/a
Bragg peak
Sizes of interest = “large scale structures” = 1 – 300 nm or more
0.02 < Q ~ 2/d < 6
Cold source spectrum 
3-5<  <20A
 small θ … how
1.00E+13
neutrons/cm^2/A/ster/sec
Q=4 sin / 
Cold Source Brightness
1.00E+12
1.00E+11
1.00E+10
1.00E+09
0
5
10
Approaches to small θ:
Wavelength (A)
• Small detector resolution/Small slit (sample?) size
• Large collimation distance
Intensity  balance sample size with instrument length
15
20
Sizes of interest = “large scale structures” = 1 – 300 nm or more
kS
QS
SANS Approach
ki
S1
S1
≈
2θ
2 S2
Δθ
3m – 16m
1m – 15m
SSD
≈
SDD
Optimized for ~ ½ - ¾ inch diameter sample
Sizes of interest = “large scale structures” = 1 – 300 nm or more
NR Approach
Point by point scan
QR
ki
kR
Ls
?
? = Ls sinθ
? ~ 1mm for low Q
θ
Sizes of interest = “large scale structures” = 1 – 300 nm or more
Ultra Small Angle Approach – when SANS isn’t small enough
QS
kS
ki
105
I Pe ak = 60,000 s -1
104
10
3
10
2
empty
Ewald + Bgd
latex
101
100
Point by point scan - again
IBGD = 0.025 s -1
10-1
10-2
0 10
0
4 10
-4
8 10
-4
-1

q (Å )

Fundamental Rule: intensity OR resolution
… but not both
1.2 10
-3
i
Rocking Curve
i fixed, 2f varying
Imeas = Φ A ε t R +Ibgd t
2f
Specular Scan
2f = 2I
f = i
Background Scan
f ≠ I
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)
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?)
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?
ki
QR
D
kR
Beam
attenutator
Neutron Guide
2D detector
Velocity
selector
L1
Source
Aperture, A1
sample
L2
Sample
Aperture, A2
Neutron Scattering 102:
SANS and NR
Paul Butler
Pre-requisites:
•Fundamentals of neutron scattering 100
•Neutron diffraction 101
•Nobel Prize in physics
Grade based on attendance and participation
SANS and NR assume elastic scattering
SANS and NR measures interference patterns from
structures in the direction of Q
f = i = R
ki
i
QR
f
Neutron Reflectometry (NR)
Reflection mode
QS
ki
incident beam
wavevector |ki|=2/
kR
kR = ki+QR
2 R
QR =4 sinR / 
Perpendicular to surface
2s
kS
kS = ki+Qs
Qs=|Qs|=4 sins / 
scattered beam
wavevector |kS|=2/
Small Angle Neutron Scattering (SANS)
Transmission mode
Sample Scattering
• Contribution to detector counts
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)
aperture
Incident beam
sample
air
cell
Stray neutrons
and Electronic noise
• We need MORE measurements
Summary
•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:
SANS
Imeas(i) = Φ t A ε(i) ΔΩ Tc+s[(dΣ/dΩ)s(i) ds + (dΣ/dΩ)c(i) dc] +Ibgd t
d coh
(Q )  V p  2 P (Q ) S (Q )
d
NR
Imeas = Φ A ε t R +Ibgd t
A VISION
Rg = 31Å
MA
2
0.01
8
6
wm 0.5 mg/ml (Rg=35±1Å)
wm 0.5(Rg=31Å)
mg/ml (Rg=35±1Å)
model
I(Q) cm
-1
4
2
0.001
8
6
NC
4
CA
2
0.0001
3
4
5
6 7 8 9
0.01
2
3
4
5
6 7 8 9
0.1
2
3
-1
Q (Å )
image
constraints
High resolution structure
Protein Data Bank
When life is easy
Data taken on NG7 6/7/2000
Fit using Core + shell sphere model\
1/cm
1
0.1
0.01
9
2
3
4
5
6
0.01
7
8
9
2
0.1
1/Å
smear_parameters_css smear_coef_css W_sigma
scale
0.01
0
core radius (A)
43.8081
0.130794
shell thickness (A)
18.2979
0.190327
Core SLD (A-2)
6.15162e-06 1.80823e-05
Shell SLD (A-2)
3.14889e-06 1.80825e-05
Solvent SLD (A-2)
6.26021e-06 1.80778e-05
bkg (cm-1)
0.00627994 0.00012066
3
When life is easy
Data taken on NG7 6/7/2000
Fit using Core + shell sphere model\
1/cm
1
0.1
0.01
9
2
3
4
5
6
0.01
7
8
9
2
0.1
1/Å
smear_parameters_css smear_coef_css W_sigma
scale
0.01
0
core radius (A)
43.8081
0.130794
shell thickness (A)
18.2979
0.190327
Core SLD (A-2)
6.15162e-06 1.80823e-05
Shell SLD (A-2)
3.14889e-06 1.80825e-05
Solvent SLD (A-2)
6.26021e-06 1.80778e-05
bkg (cm-1)
0.00627994 0.00012066
3

L3
“c”
L
R
=0.400.08 s
R = C
exp[-EF/kBT] 
EF = 6.7kBT
(170 meV)
PRL 2004
Beyond the Sponge to Lamellar TransitionA Lamellar Collapse:
(when life starts to get really hard)
z
x
Structural analysis of
a 4% Lamellar at
1500 s-1
Simultaneous fits
SLD,bgd,membrane
thickness fixed
Model: polydisperse aligned prolate ellipsoidal shells (vesicles)
Qx semi-major axis ~ 520Å along flow direction
Qz semi-minor axis ~ 225Å
SANS: a plan
Project Leader: Paul Butler
Advisors: Sean Langridge, Dean Myles
Postdoc 1: (Current developer): Jing Zhou
Start hiring process in middle of first year to bring on board in year 2
Grad Students: UMBC and UT
Work with ORNL’s CSMB and SANS team
Work with NIST SANS team and Structural bio group
Plans for international steering committee
PostDoc and other developer FTE by year
Total Funding Profile
7.00
$1,400
6.00
$1,200
$1,000
5.00
$800
4.00
$600
3.00
$400
2.00
$200
1.00
$year 1
year 2
year 3
year 4
year 5
0.00
year 1
Incremental Funding Profile
Cumulative
year 2
year 3
year 4
year 5
When life starts to get hard
Clay polymer gels under shear
Clay polymer gels at rest
How does one really calculate a theoretical Intensity
Frequency
P(r)
Fourier
I(Q)
transform
r
Dmax
sin( Q  (ri  r j ))
0
Q  (ri  r j )
I (Q)  4Vo  P(ri  r j ) i  j
d (ri  r j )
User-interactive GUI application
• Link the conformational changes to SANS data
– Example
– showing the I(Q) for the corresponding conformation in Runtime
• 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
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
UML Use Cases for SANS
Simulate
Plan
Experiment
Analytic form
Modeling
Structural
modeling
Reduce
User
Analysis
<extend>
Free form
modeling