Transcript IN VIVO X-RAY DIFFRACTION STUDIES OF INDIRECT FLIGHT

Macromolecular Small-Angle
X-ray Scattering
What is SAXS?
•
•
•
•
•
•
•
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
Why not visible light?
• Diffraction effects limit to ~ l/50 (5)
• i.e. 14 nm visible light vs 1- 2nm RG for
small proteins
• Water absorbs many wavelengths of light
strongly
• 0.2 < l < 160 nm experimentally
inaccessible
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 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) = i e i q • ri
• Intensity is square (complex conjugate) of structure factor
I(q) = F F* = ji e iq • ri,j
• Isotropic, so spherical average ( is rotation angle relative to q)
I(q) =  ji e iq • ri,j sin d
• Debye Eq.
<I>(q) = ij sin q ri,j/ q ri,j
where q = 4sin 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 (or calibrated) 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)/I0 = (1/n2)ij sin q ri,j/ qri,j
I(q)/I0= 1-q2RG2/3+…..
Guinier approximation:
2Rg2/3
-q
e
= 1 – q2Rg2/3 + (q2Rg2 /3 )2/2! …
so
ln I/I0 = -q2Rg2/3 for small enough q
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, Guinier approximation
holds even in the third term… so the Guinier
region is larger for more globular proteins
– Usual limit: Rg qmax <1.3
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
eee-
e-
e-
P( r ) & Intensity related by
Fourier transform pair*

Iq  4 
0
pr 

1
2
sinq.r
p(r)
.dr
q.r
2
 Iq.qr.sinqr.dq
0
* This is a fourier sine transform because of
symmetry (see Glatter & Kratky)
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)
– Rigid body refinement
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
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
Relationship of scattered
intensity distribution to structure
Globular size
10000
I
Domain
folds
1000
2o
structure
100
0
2
4
6
8
10
-1
q (nm )
12
14
16
18
NtrC in BeF
P(r)
GASBOR
Reconstruction
Activated NtrC
De Carlo et al 2006, Genes
and Development, in press
NtrC in various nucleotide states
Courtesy B.T. Nixon
Penn State
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
– BioCAT has special purpose, high sensitivity, low noise
CCD detectors
– Now commercially available from Aviex
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”
• PROBLEM:
LC-SAXS
– Non linear Guinier plots
• Combine size exclusion chromatography with
SAXS
– remove aggregates
– reversibly associating proteins
• facile extrapolation to low concentrations
• Implementation
– Superose-6 1 x 10 cm ; FPLC ; 0.25 ml/min; 2-10mg
bolus injections
Resolution Test
50
• Control mixture:
40
4
– Blue dextran
30
MW > 1 MDa
I0
20
6
2
4
– Cyto c
12 kDa Rg 1.3 nm
2
0
30
40
50
60
70
80
90
fraction number
BD
BSA
Cc
0
100
Rg (nm)
65kDa Rg 3.0 nm
Dimer and higher
oligomers
A280 or
– BSA
Plasminogen
• Sticky protein… curved Guinier plots
• conformational change…DRg 3040 A
Need accurate, reproducible Rgs to see these modest changes
static
0
LC-SAXS
ln I
6
ln I
0.0
-2
4
f38
f42
f46
f50
f54
f58
-0.7
0.0
-4
0.00
0.02
0.1
0.04
0.06
2
2
q (nm )
0.08
0.10
2
0.00
0.02
0.04
0.06
2
2
q (nm )
0.08
0.10
Plasminogen
Reliable data down to 0.3 mg/ml
14
1.2
5
12
1.0
4
0.8
0.6
6
0.4
Rg (nm)
A280 or
8
Rg (nm)
I0
10
3
Rg0 = 32.1 nm
2
4
0.2
2
0.0
1
0
40
50
fraction
60
0
0.0
0.2
0.4
0.6
0.8
[Pg] mg/ml
1.0
1.2
Time resolved studies
Time-resolved
Time-resolvedStopped-flow
Stopped FlowExperiment
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.
Jacob et al.,2004 J Mol Biol338:369-82
Turbulent Continuous-Flow Mixer Design
T-shape mixer has a design adapted from Akiyama et al., 2002.
The mixer dimensions are 200 x 350 x 2000 μm3 .
200 μm
Kapton™
or Mylar
windows
Buffer
Protein
Stainless
steel
plates
Waste
X-ray beam
Capillary mixer by P.Regenfuss et al, Rev.Sci.Instrum. (1985) 56, 283;
Needle mixer by C.K.Chan et al. Proc. Natl. Acad. Sci. USA (1997), 94, 1779;
Mixer by L.Pollack et al. Proc. Natl. Acad. Sci. USA (1999) 96, 10115, with diffusion-based mixing.
T-shape turbulent mixer by S.Akiyama et al. Proc. Natl. Acad. Sci. USA (2002), 99, 1329.
Arrow-shape mixer by O.Bilsel et al. 2005, Rev.Sci.Instrum. 76, 014302.
Courtesy O. Bisel U. Mass
Cytochrome c Folding Probed by TR-SAXS
20 mg/ml solution of cytochrome c unfolded in GdnHCl at 4.5 M concentration was injected
into the mixer at flow rate 2 ml/min and mixed with Tris buffer flowing at 18 ml/min. This
provided 10-fold dilution and final concentration 2 mg/ml of cytochrome c and 0.45 M of
GndHCl. Other parameters: pH 7, 0.2 M imidozole.
Guinear plots


Radius of gyration vs time
Rg exponential decay at t>150 μs is consistent with previous GdnHCl-jump CF-FL and pHjump CF-SAXS results (M.C.Shasty et al. 1998, S.Akiyama et al. 2000).
60 µs time resolution is achieved. The ambiguity of results at t~<150 µs might be attributed to
incomplete mixing.
ACA meeting, 2005
TR-SAXS results on Cytochrome c Folding
Kratky plots
Distance distribution functions
 Collapsed state is globular and significantly more compact (~40%) than the denatured
ensemble.
 Channel scattering and noise are considerably low allowing to reliably measure SAXS signal
at 0.028 < q > 0.34 A-1 at protein concentration of 2 mg/ml.
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