Transcript IN VIVO X-RAY DIFFRACTION STUDIES OF INDIRECT FLIGHT

Macromolecular Small-Angle
Scattering with Synchrotron
Radiation
Tom Irving
BioCAT, Dept. BCPS and CSRRI
Illinois Institute of Technology
Scope of Lecture
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Why do SAXS?
Physical Principles
Experimental methods
Data interpretation
Advantages of Third Generation
Synchrotrons for SAXS
• References for learning more
What is SAXS?
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Small Angle X-ray Scattering
Scattering proportional to l/Molecular size
Typical x-ray wavelengths ~ 0.1 nm
Typical molecular dimensions 1 -100 nm
Scattering angles are small
0-2o historically.
Now 0-15o range is of increasing experimental
interest
Why SAXS ?
• Atomic level structures from crystallography or
NMR “gold standard” for structural inferences
• Crystallography, by definition, studies static
structures
• Most things crystallize only under rather specific,
artificial conditions
• Kinetics of molecular interactions frequently of
interest
• SAXS can provide useful, although limited,
information on relatively fast time scales
What is SAXS Used for?
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Estimating sizes of particulates
Interactions in fluids
Sizes of micelles etc in emulsions
Size distributions of subcomponents in
materials
• Structure and dynamics of biological
macromolecules
SAXS and Biological Macromolecules
• How well does the crystal structure represents the native
structure in solution?
• Can we get even some structural information from large
proportion of macro-molecules that do not crystallize?
• How can we test hypotheses concerning large scale
structural changes on ligand binding etc. in solution
• SAXS can frequently provide enough information for such
studies
• May even be possible to deduce protein fold solely from
SAXS data
Scattering from Molecules
Molecules are much larger than the
wavelength (~0.1 nm) used => scattered
photons will differ in phase from different
parts of molecule
destructive interference
Observed intensity spherically averaged due to
molecular tumbling
e-
ee- e
ee-
Constructive interference
Intensity in SAXS Experiments:
• Sum over all scatterers (electrons) in molecule to get structure
factor (in units of scattering 1 electron)
F(q) = Si e i q • ri
• Intensity is square (complex conjugate) of structure factor
I(q) = F F* = SjSi e iq • ri,j
• Isotropic, so spherical average (a is rotation angle relative to q)
I(q) =  SjSi e I q • ri,j sina da
• Debye Eq.
<I>(q) = SiSj sin q ri,j/ q ri,j
where q = 4psin q/l
In Scattering Experiments,
Particles are Randomly Oriented
• Intensity is spherically averaged
• Phase information lost
• Low information content fundamental
difficulty with SAXS
• Only a few, but frequently very useful,
structural parameters can be unambiguously
obtained.
Structural Parameters Obtainable
from SAXS
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Molecular weight*
Molecular volume*
Radius of gyration (Rg)
Distance distribution function p( r )
Various derived parameters such as longest
cord from p ( r )
• * requires absolute intensity information
Experimental Geometry
Collimated
X-ray beam
200 cm
Sample
Backstop
“long camera
~1o
in 1 mm capillary
30 cm
Detector
short camera ~ 15o
The data:
Shadow of
lead beam
stop
2-D data needs to be radially integrated
to produce 1-D plots of intensity vs q
Scattering Curves From
Cytochrome C
Red line
= sample
+buffer
Blue =
buffer
only
Black =
difference
I
q nm-1
What does this look like for a
typical protein ?
Since a Fourier
transform, inverse
relationship:
10000
I
Large features at small q
Small features at large q
Globular size
Domain
folds
1000
2o
structure
100
0
2
4
6
8
10
-1
q (nm )
12
14
16
18
What’s Rg?
• Analogous to moment of inertia in
mechanics
• Rg2 = p(r)  r2  dV
p(r)  dV
Rg for representative shapes
• Sphere
Rg2 = 3/5r2
• Hollow sphere (r1 and r2 inner and outer
radii)
Rg2 = 3/5 (r25-r15)/(r23-r13)
• Ellipsoid (semi-axis a, b,c)
Rg2 = (a2+b2+c2)/5
Estimating Molecular Size from SAXS
Data
<I>(q) = SiSj sin q ri,j/ qri,j
Taylor series expansion
= 1 - (qrij )2/6 + (qrij )4/120 ….
Guinier approximation:
2Rg2/3
-q
e
= 1 – q2Rg2/3 + (q2Rg2 /3 )2/2! …
Equate first two terms
1 - (qrij )2/6 = 1 – q2Rg2 3
Or
ln I/I0 = q2Rg2/3
Guinier Plot
Plot ln I vs. q2
Inner part will be a straight line
Slope proportional to Rg2
– Only valid near q = 0 (i.e. where third term is
insignificant)
– For spherical objects, Gunier approximation holds even
in the third term… so the Guinier region is larger for
more globular proteins
– Usual limit: Rg qmax <1.3
Configuration Changes in
Plasminogen
EACA
Bz
Guinier Fits
1.00E+04
Pg
Rg
PBS
30.6
+EACA
49.1
1.00E+03
blank
+Benzamidine 37.1
eaca
Benz
1.00E+02
0.00E+ 1.00E- 2.00E- 3.00E- 4.00E- 5.00E- 6.00E- 7.00E- 8.00E- 9.00E- 1.00E00
02
02
02
02
02
02
02
02
02
01
Plasminogen data courtesy N. Menhart IIT
Need for Series of
Concentrations
• SAXS intensity equations valid only at infinite
dilution
• Excess density of protein over H2O very low
• Need a non-negligible concentration ( > 1 mg/ml)
to get enough signal.
• In practice use a concentration series from ~ 3 - 30
mg/ml and extrapolate to zero by various means
• Only affects low angle regime
• Can use much higher concentrations for high
angle region (where scattering weak anyway)
Effect of Concentration
Correcting for Concentration
Shape information
•
SAXS patterns have relatively low information
content
• Sources of information loss:
– Spherical averaging
– X-ray phase loss, so can’t invert Fourier
transform
• In general cannot recover full shape, but can
unambiguously compute distribution of distance s
within molecule: i.e. p(r) function
p(r)
• Distribution of distances of atoms
from centroid
• Autocorrelation function of the
electron density
• 1-D: Only distance, not direction
– No phase information
– Can be determined
unambiguously from SAXS
pattern if collected over wide
enough range
– 20:1 ratio qmin :qmax usually
ok
e-
ee-
ee-
Relation of p( r ) to Intensity
I(q) = 4p 0 p( r )sin(qr) dr
D
Relationship of shape to p(r)
• Fourier transform pair
p(r)  I(q)
shape
Can
unambiguously
calculate p( r )
from a given
shape but
converse not
true
Inversion intensity equation not
trivial
• Need to worry about termination effects,
experimental noise and various smearing effects
• Inversion of intensity equation requires use of
various “regularization approaches”
• One popular approach implemented in program
GNOM (Svergun et al. J. Appl. Cryst. 25:495)
Example of p(r ) Analysis
Troponin C structure
• Does p(r) make sense?
Scattering Pattern from Troponin C
I
4
I(q)
10
10
3
10
2
0
2
4
6
8
10
12
14
-1
16
q (nm )
q nm -1
18
Troponin C: Bimodal Distribution
spurious water peak @ 3 A
15 A
0
20
41 A
40
r (A)
60
80
Hypothesis Testing with SAXS
• p (r ) gives an alternative measure of Rg and
also “longest cord”
• Predict Rg and p( r ) from native crystal
structure (tools exist for pdb data) and from
computer generated hypothetical structures
under conditions of interest
• Are the hypothesized structures consistent
with SAXS data?
SAXS Data Alone Cannot Yield
an Unambiguous Structure
• One can combine Rg and P( r ) information with:
Simulations based on other knowledge (i.e. partial
structures by NMR or X-ray)
Or
Whole pattern simulations using various physical
criteria:
– Positive e density,
– finite extent,
– Connectivity
– chemically meaningful density distributions
Reconstruction of Molecular
Envelopes
• Very active area of research
• 3 main approaches:
• Spherical harmonic-based algorithms (Svergun, &
Stuhrmann,1991, Acta Crystallogr. A47, 736),
genetic algorithms (Chacon et al, 1998, Biophys.
J. 74, 2760), simulated annealing
(Svergun,1999Biophys. J. 76, 2879), and “give ‘n
take” algorithms (Walter et al, 2000, J. Appl.
Cryst 33, 350).
• Latter three make use of “Dummy atom approach”
using the Debye formula.
Configuration Changes in
Plasminogen
EACA
Bz
Guinier Fits
1.00E+04
Pg
Rg
PBS
30.6
+EACA
49.1
1.00E+03
blank
+Benzamidine 37.1
eaca
Benz
1.00E+02
0.00E+ 1.00E- 2.00E- 3.00E- 4.00E- 5.00E- 6.00E- 7.00E- 8.00E- 9.00E- 1.00E00
02
02
02
02
02
02
02
02
02
01
Plasminogen data courtesy N. Menhart IIT
Pg Complete Scattering curves
unliganded
Bz
EACA
I
10000
1000
100
0
2
4
6
8
10
q (nm)
-1
12
14
16
18
20
Shape Reconstruction using
SAXS3D *:
+EACA
+BNZ
2Å
2Å
* D. Walther et. al., UCSF
Technical Requirements for
SAXS
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Monodispersed sample (usually)
Very stable, very well collimated beam
Very mechanically stable apparatus
Methods to assess and control radiation damage and
radiation induced aggregation (flow techniques)
• Ability to accurately measure and correct for variations in
incident and transmitted beam intensity
• High dynamic range, high sensitivity and low noise
detector
Detectors For SAXS
• 1-D or 2 D position sensitive gas proportional
counters
– Pros: High dynamic range, zero read noise
– Cons: limited count rate capability typically 105 - 106
cps, 1-D detectors very inefficient high q range
• 2D CCD detectors
– Pros: integrating detectors - no intrinsic count rate limit,
2-D so can efficiently collect high q data
– Cons: Significant read noise, finite dynamic range
– Most commercial detectors designed for
crystallography too high read noise
SAXS at Third Generation
Synchrotron Sources
The Advanced Photon Source
The APS is Optimized for
Producing Undulator Radiation
Why is APS Undulator Radiation
Good for Biological Studies?
• Wide energy range available for
spectroscopy
• High flux for time resolved applications
• Very low beam divergence for high quality
diffraction/scattering patterns
• Can focus to very small beams to examine
small samples or regions within samples
BioCAT
What is BioCAT?
A NIH Supported Research Center
• A NIH-supported research center for the study of partially
ordered and disordered biological materials
• Supported techniques are X-ray Spectroscopy (XAS and
high resolution), powder diffraction, fiber diffraction, and
SAXS
• Comprises an undulator based beamline, (18-ID)
associated laboratory and computational facilities.
• Available to all scientists on basis of peer-reviewed
beamtime proposals
The BioCAT Sector at the APS
SAXS Instrument on the BioCAT
18ID - Undulator Beamline
Working beam size
and divergence:
Scattering
145 x 40 µm
0.19 x 0.16 µrad chamber
250 - 5000 mm
Beam
Stop
Slow
Sample and Fast Alflow
Shutters filters
cell
Guard
Slits
Beam
Monitor
Mirror,
vertically
focusing
Collimator
Slits
CCD
68 m
63 m
56 m
Monochromator:
Si (111) or (400),
flat
Undulator
18ID
Si (111) or (400), Source size
(FWHM) and
horizontally
divergence:
focusing
597 x 28 µm
16 x 3 µrad
52.6 m
0m
BioCAT PERFORMANCE FOR
SAXS
• 3 m camera can access a range of q from ~0.04 to 1.3 nm-1
•
0.3 m camera accesses range of q from ~0.8
to 20.0 nm-1
• 55 x 88 mm high sensitivity CCD detector can detect
single photons
• Useful SAXS patterns can be collected from 5 mg./ml
cytochrome c in 300 ms => can do time resolved
experiments on ms time scales or less
Why Do You Need a Third
Generation Source for SAXS?
• Time resolved protein folding studies using
SAXS
=> The “Protein Folding Problem”
• High throughout molecular envelope
determinations using SAXS
=> “Structural genomics”
Time-resolve Stopped Flow Experiment
Time-resolved Stopped-flow Experiment
Radius of gyration (Rg) obtained from
Guinier analysis as a function of
denaturant concentration. Black squares
denote equilibrium data and red circles
indicate values obtained ~1 msec after
initiation of refo lding at differen t GdmC l
concentrations.
For further reading…..
• A Guinier “X-ray Diffraction in Crsytals,
Imperfect Crystals and Amorphous Bodies”
Freeman, 1963
• C. Cantor and P. Schimmel “Biophysical
Chemistry part II: Techniques for the study of
Biological Strcutre and Function” Freeman, 1980
• O. Glatter and O. Kratky “Small-angle X-ray
Scattering” Academic Press 1982
• See Dmitri Svergun’s web site at
http://www.emblhamburg.de/Externalinfo/Research/Sax