RELATIONSHIPS
BETWEEN TECHNIQUES
Michael Becker
GM/CA-CAT
Argonne National Laboratory
Argonne, IL
ACA Summer Course at IIT, July 20, 2006
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OUTLINE
1) context
2) radiation and matter
3) X-ray techniques
- 3D
- phasing
- 2D
- dynamics
- future
4) electron techniques
5) neutron techniques
6) other techniques
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PHYSICS
1)
2)
3)
4)
Strong forces
Weak forces
Electromagnetic forces
Gravity
Restrict ourselves to the Interaction of Radiation and Matter
An attempt at a partially unified discussion of physical biochemistry.
(Not discuss other biophysical techniques, such as patch-clamp,
AFM, ultracentrifuge, computational methods, …)
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SOME TYPES OF RADIATION
Energy transmitted in the form of waves or particles
γ-rays
X-rays
UV
Vis
IR
μ-waves
higher energy  lower energy
For particles:
de Broglie wavelength = Planck’s const./momentum [λ = h/p]
For an electron accelerated through 100 Volts,
λ = 1.2 Å, ie. about the size of atoms
For investigating atomic/molecular structure, we use X-rays,
electrons, and neutrons, since they can have wavelengths about
the sizes of atoms
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SOME TYPES OF MATTER:
Atoms
Molecules
Crystals
Particles, Solids, Surfaces, Liquids, Glasses, Gases
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Interaction of Radiation and Matter
- scattering
- elastic (Thomson), inelastic (Compton)
- coherent, incoherent
- absorption
- atoms: can then be emitted as fluorescence,
photoelectrons, Auger electrons
- molecules: can emit fluorescence, phosphorescence,
transfer heat, (stimulated emission)
- refraction (the bending of a wave as it passes from one
medium to another)
- diffraction (bending of waves due to obstructions and small
apertures, as with crystals)
- reflection (radiation bouncing back from one medium to
the original medium, where the wavelength << size of
the object)
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X-rays:
Hard X-ray wavelengths ~ 0.1 Å to 60 Å
Soft X-ray wavelengths ~ 60 Å to 120 Å
Interact weakly, ie. penetrating – therefore, can see inside of a
structure, but most of the beam passes through, unperturbed.
10 x more photons are absorbed than scattered.
X-rays scatter off of valence electrons (~ 1% off of nuclei).
Yield an electron-density map.
Bosons: spin = 1
Can be polarized.
Magnetic effects are very small.
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List of Techniques: Scattering, Diffraction
- 3-D X-ray crystallography
- phasing methods
- 2-D Grazing incidence diffraction
- Low-angle scatter
- Dynamics
- Equilibrium: B factors, diffuse scatter
- Non-equilibrium: Laue method
- Future pulsed experiments
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3D crystallography -- amplitudes
Molecular transform, which is continuous, convoluted with
the reciprocal lattice, yields a 3D lattice
Called reflections because of scattering off
of imaginary planes
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3D crystallography – phases
Compare to imaging via Microscopy & Holography
– see Sayre & Chapman (Acta Cryst. A51, 237-252 (1995)).
Microscopy -- limited by resolution of the zone plate.
Gabor-style (“in line”) holography -- limited by ability of detector
to resolve interference fringes.
Fourier-style holography -- limited by optical perfection of
reflecting or expanding optics.
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Penetration depth of photons in water, from Fig. 5 of
Sayre & Chapman (Acta Cryst. A51, 237-252 (1995))
XC = X-ray crystallography
XM = X-ray microscopy
LM = light microscopy
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In holography, there is a reference beam and an object beam.
In some crystallography phasing methods, the reference beam is
provided by the reference scatterer.
MIR and MR (and anomalous?) methods are equivalent to
Fourier-style holography.
- see Tolin et al., Nature (1966) 209, 603 – 604
Szöke, A., Acta Cryst. (1993) A49, 853 – 866.
They are successful because a reference scatterer is in each unit cell,
insensitive to mosaicity of the crystals.
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Diffraction from 2-D membrane monolayers
- Grazing incidence, ie. below the critical angle
(~ 1 mrad), gives nearly total external reflection.
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Grazing Incidence Diffraction
1/
1/
max
- ideally sample by rotating about
the normal to the plane
1/
min
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2-D scatter from monolayers of bacteriorhodpsin
Verclas, S.A.W. et al., J.Mol.Biol., 1999; 387; 837 – 843.
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Low Angle Scatter – solution
- can model structures via an ab initio method of using
dummy residues to model the data
from Svergun, D.I., Petoukhov, M.V., and Koch, M.H.J.
Biophys. J. (2001) 80, 2946 – 2953.
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DYNAMICS
Equilibrium
Non-equilibrium
B factors
Laue crystallography
Diffuse scatter
Rapid Mixing and
Small angle scattering
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B - factors
__
f = f0
2
-B(sin2θ)/λ
e
where B = 8π2u2
___
u2 = mean-square amplitude of atomic vibration
- due to thermal motion, the scattering factor falls off exponentially
more rapidly with resolution than that of a stationary atom.
- experimental data may include contributions from static disorder;
can be distinguised by temperature-dependent experiments (for
example, see Tilton, Jr., R.F., Dewan, J.C., and Petsko, G.A.,
Biochemistry 1992, 31, 2469-2481.)
- anisotropic with high-resolution structures
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DIFFUSE SCATTER
Diffuse scatter from yeast initiator tRNA crystals: (d) = experimental,
(e) = calculated
- from fig. 2 of Kolatkar, A.R., Clarage, J.B., and Phillips, Jr., G.N., Acta
Cryst. (1994) D50, 210 – 218.
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- Diffuse Scatter = the scatter that is not in the Bragg reflections;
every crystal has it. Increases at higher resolution.
- as with B-factors, static disorder can contributes to this,
so caution is required.
- unlike B-facts, disorder modelled on a larger scale than
single atoms.
- can be modelled via analytic methods (global correlation
function) or multicell methods
- compare to calculations of normal modes or of molecular
dynamics
Clarage, J.B. and Phillips, Jr., G.N., pp. 407 – 432, in Methods in Enzymology, vol. 276,
Macromolecular Crystallography, Part A (Ed. C.W. Carter, Jr. and R.M. Sweet),
Academic Press, NY 1997
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Non-equilibrium dynamics
Laue crystallography
Rapid mixing and low-angle scatter
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Some Potential 4th Generation X-Ray Sources
 X-Ray Free Electron Lasers (FELs)
- Linac Coherent Light Source (LCLS) at Stanford
(http://wwwssrl.slac.stanford.edu/lcls)
- X-Ray FEL at DESY in Hamburg
(http://xfel.desy.de)
 Energy Recovery Linacs (ERLs)
- Energy Recovery Linac (ERL) at Cornell
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(http://erl.chess.cornell.edu)
In the context of imaging via microscopy and holography
using soft X-Rays, J.C. Solem (J.Opt.Soc.Am.B 3, 1551-1565
(1986)) calculated that a biological sample can be imaged by a
single pulse, before it is obliterated by the pulse, if the pulse is
sufficiently high in flux and is sufficiently short.
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X-Ray
Detector
Object
DF
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FEL
X-Ray
Detector
Object
DF
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FEL
X-Ray
Detector
Object
DF
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FEL
Single molecule diffraction will be pursued.
Neutze, R., Wouts, R., van der Spoel, D.,
Weckert, E., and Hajdu, J. Potential for
biomolecular imaging with femtosecond
X-ray pulses. Nature, 2000; 406; 752 – 757
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Kinematic Scattering for 2D
I = σ ro2 P |Fhk|2 (N/A) λ2 Lzf
I = 2-D scattering crossection (photons/sec.)
σ = photons/unit area
ro = Thomson scattering length
P = polarization factor
Fhk = Bragg-rod structure factor
N = # of unit cells
A = area of a unit cell
λ = wavelength
Lzf = Lorenz factor
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Calculations:
Monolayer of bacteriorhodopsin trimers
in 10 µm x 10 μm 2-D crystal
Using 1.5-Å X-rays at 400 photons/Å2
(ie., 4x1012 photons in one pulse)
Elastically-scattered photons peak
between 10 and 100 counts in the
3-to-4 Å range.
Not taking into account disorder
and background scatter.
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Becker, M., Weckert, E. On the Possibility of
Determining Structures of Membrane Proteins in
Two-Dimensional Crystals using X-ray Free Electron
Lasers. (2004) in “Conformational Proteomics of
Macromolecular Architecture” (Eds. R.H. Cheng,
L. Hammar), World Scientific, Singapore, pp. 133-147.
Electrons:
Electrons scatter off of atoms, ie. they are charged and
interact via Coulomb forces of an atom’s nucleus and
its electrons
Fermion: spin = ½
Interact strongly – need thin samples
Get a Coulomb potential map
Charge effects.
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With electron crystallography of 2D crystals,
get phases via microscopy, and amplitudes
via diffraction.
(Other techniques include staining, STEM, pulsed
electrons …)
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Electrons
1/
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Averaged bacteriorhodopsin trimers from noisy data, and
electron diffraction, from Subramaniam, S., Hirai, T., and Henderson, R.
Phil.Trans.R.Soc.Lond. A (2002) 360, 859 – 874.
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A lattice line, and tilts through lattice lines for a photosynthetic lightharvesting protein, from Wang, D.N. and Kühlbrandt, W., Biophys.J.
(1992) 61, 287 – 297.
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Using the electron microscope, many single particles
can be averaged to yield low-resolution structures of
viruses and ribosomes.
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Averaged rhinovirus particles in 3 different states, and X-ray protein structure
fitted to Coulomb potential map, from Xing, L., Casasnovas, J.M., and Cheng, R.H.,
J.Virol. (2003) 77, 6101 – 6107.
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The X-ray and EM maps are usually implicitly
assumed to be the same, due to experimental
uncertainties. But they are actually different,
and if experimental errors can be reduced,
they could be combined to provide electrostatic
information, of functional importance.
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The Poisson Equation
2 = - 4/
where  = the Coulomb Potential
 = Electron Density
 = the Dielectric Constant
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Rearranging, and considering position
explicitly:
 (x,y,z) = - 4 (x,y,z)
2 (x,y,z)
where (x,y,z) is an electron-density map
from X-Ray experiments, and (x,y,z)
is a Coulomb-potential map from EM.
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A plan to use lasers to align molecules in ice droplets for electron
beam diffraction, from Spence, J.C.H. et al., Acta Cryst. (2005) A61, 237 – 245.
a) electrostatic potential map
for pthalocyanine
b) simulated oversampling
diffraction pattern
c) sum of diffraction patterns if
alignment distributed over 5°
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Neutrons:
Scatter off of nuclei via strong nuclear forces.
Fermions: spin = 1/2; uncharged
Interact weakly, and sources are weak; large samples
are needed for long collection times.
Sensitive to protons.
Membrane and small angle scattering.
Inelastic neutron scattering provides vibrational information.
Can scatter due to magnetic fields as well.
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NEUTRON SOURCES
Nuclear reactors, such as the high-flux reactof at ILL in Grenoble
Spallation Neutron Sources, such as at Oak Ridge National Laboratory
- pulsed neutrons generated via a proton beam impinging
on a mercury target
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X-rays vs. Electrons vs. Neutrons
When there is absorption, can get damage!
R. Henderson’s calculations comparing the merits of X-Rays,
electrons, and neutrons for imaging at atomic resolution
(Quart.Rev.Biophys. 28, 171-193 (1995)).
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Other Techniques
Other scattering:
- Raman (inelastic, due to vibrations)
- visible Rayleigh (elastic, tells particle size and
dynamics)
Absorption and related techniques:
EXAFS (measure fluorescence in an excitation spectrum)
UV, vis, IR (electronic, vibrations)
- absorption (CD, linear, time-resolved)
- fluorescence (anisotropy, time-resolved, freq. domain,
FTIR, microscopy), phosphorescence (luminescence)
Magnetic: NMR, EPR
…
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Hopefully this lecture provides a useful overview of the types of
techniques that exist, and some insights that might be helpful
in learning more about these techniques and those that haven’t
been mentioned, or yet discovered.
Thank you for your attention, and thank the scientists on whose
shoulders we stand …
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