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PioneeringScience andTechnology

RELATIONSHIPS BETWEEN TECHNIQUES

Michael Becker

GM/CA-CATArgonne National Laboratory

Argonne, IL

ACA Summer Course at IIT, July 20, 2006


OUTLINE

1) context2) radiation and matter3) X-ray techniques

- 3D- phasing - 2D- dynamics- future

4) electron techniques5) neutron techniques6) other techniques


PHYSICS

1) Strong forces2) Weak forces3) Electromagnetic forces4) 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, …)


SOME TYPES OF RADIATION

Energy transmitted in the form of waves or particles

higher energy lower energy

For particles:

de Broglie wavelength = Planck’s const./momentum [_ = h/p]

For an electron accelerated through 100 Volts, _ = 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 aboutthe sizes of atoms

_-rays X-rays UV Vis IR _-waves


SOME TYPES OF MATTER:

Atoms

Molecules

Crystals

Particles, Solids, Surfaces, Liquids, Glasses, Gases


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 ofthe object)


X-rays:

Hard X-ray wavelengths ~ 0.1 Å to 60 ÅSoft 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.


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


3D crystallography -- amplitudes

Molecular transform, which is continuous, convoluted with the reciprocal lattice, yields a 3D lattice

Called reflections because of scattering offof imaginary planes


3D crystallography – phases

Microscopy -- limited by resolution of the zone plate.

Gabor-style (“in line”) holography -- limited by ability of detectorto resolve interference fringes.

Fourier-style holography -- limited by optical perfection ofreflecting or expanding optics.

Compare to imaging via Microscopy & Holography – see Sayre & Chapman (Acta Cryst. A51, 237-252 (1995)).


Penetration depth of photons in water, from Fig. 5 of Sayre & Chapman (Acta Cryst. A51, 237-252 (1995))

XC = X-ray crystallographyXM = X-ray microscopyLM = light microscopy


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.


Diffraction from 2-D membrane monolayers

- Grazing incidence, ie. below the critical angle(~ 1 mrad), gives nearly total external reflection.


Grazing Incidence Diffraction

1/λ

1/λmax

1/λmin

- ideally sample by rotating aboutthe normal to the plane


2-D scatter from monolayers of bacteriorhodpsin

Verclas, S.A.W. et al., J.Mol.Biol., 1999; 387; 837 – 843.


Low Angle Scatter – solution

- can model structures via an ab initio method of usingdummy residues to model the data

from Svergun, D.I., Petoukhov, M.V., and Koch, M.H.J.Biophys. J. (2001) 80, 2946 – 2953.


DYNAMICS

Equilibrium Non-equilibrium

B factors Laue crystallography

Diffuse scatter Rapid Mixing andSmall angle scattering


B - factors __

f = f0e-B(sin2_)/_2 where B = 8!2u2

___

u2 = mean-square amplitude of atomic vibration

- due to thermal motion, the scattering factor falls off exponentiallymore rapidly with resolution than that of a stationary atom.

- experimental data may include contributions from static disorder;can be distinguised by temperature-dependent experiments (forexample, see Tilton, Jr., R.F., Dewan, J.C., and Petsko, G.A.,Biochemistry 1992, 31, 2469-2481.)

- anisotropic with high-resolution structures


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., ActaCryst. (1994) D50, 210 – 218.


- 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 thansingle atoms.

- can be modelled via analytic methods (global correlationfunction) 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


Non-equilibrium dynamics

Laue crystallography

Rapid mixing and low-angle scatter


Some Potential 4th Generation X-Ray Sources

X-Ray Free Electron Lasers (FELs) - Linac Coherent Light Source (LCLS) at Stanford

(http://www-ssrl.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 (http://erl.chess.cornell.edu)


In the context of imaging via microscopy and holographyusing soft X-Rays, J.C. Solem (J.Opt.Soc.Am.B 3, 1551-1565(1986)) calculated that a biological sample can be imaged by asingle pulse, before it is obliterated by the pulse, if the pulse issufficiently high in flux and is sufficiently short.


DF FEL

ObjectX-RayDetector


Single molecule diffraction will be pursued.

Neutze, R., Wouts, R., van der Spoel, D.,Weckert, E., and Hajdu, J. Potential forbiomolecular imaging with femtosecondX-ray pulses. Nature, 2000; 406; 752 – 757


Kinematic Scattering for 2D

I = _ ro2 P |Fhk|2 (N/A) _2 Lzf

I = 2-D scattering crossection (photons/sec.)_ = photons/unit area ro = Thomson scattering length

P = polarization factor Fhk = Bragg-rod structure factorN = # of unit cells A = area of a unit cell_ = wavelength Lzf = Lorenz factor


Becker, M., Weckert, E. On the Possibility ofDetermining Structures of Membrane Proteins inTwo-Dimensional Crystals using X-ray Free ElectronLasers. (2004) in “Conformational Proteomics ofMacromolecular Architecture” (Eds. R.H. Cheng,L. Hammar), World Scientific, Singapore, pp. 133-147.

Using 1.5-Å X-rays at 400 photons/Å2 (ie., 4x1012 photons in one pulse)

Calculations:

Monolayer of bacteriorhodopsin trimersin 10 µm x 10 _m 2-D crystal

Elastically-scattered photons peak between 10 and 100 counts in the 3-to-4 Å range.

Not taking into account disorderand background scatter.


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 = _

Interact strongly – need thin samples

Get a Coulomb potential map

Charge effects.


With electron crystallography of 2D crystals,get phases via microscopy, and amplitudesvia diffraction.

(Other techniques include staining, STEM, pulsedelectrons …)


1/λ

Electrons


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.


A lattice line, and tilts through lattice lines for a photosynthetic light-harvesting protein, from Wang, D.N. and Kühlbrandt, W., Biophys.J. (1992) 61, 287 – 297.


Using the electron microscope, many single particlescan be averaged to yield low-resolution structures ofviruses and ribosomes.


Averaged rhinovirus particles in 3 different states, and X-ray protein structurefitted to Coulomb potential map, from Xing, L., Casasnovas, J.M., and Cheng, R.H., J.Virol. (2003) 77, 6101 – 6107.


The X-ray and EM maps are usually implicitlyassumed to be the same, due to experimentaluncertainties. But they are actually different,and if experimental errors can be reduced,they could be combined to provide electrostaticinformation, of functional importance.


The Poisson Equation

σ2Φ = - 4πρ/ε

where Φ = the Coulomb Potential

ρ = Electron Density

ε = the Dielectric Constant


Rearranging, and considering position explicitly:

ε (x,y,z) = - 4πρ (x,y,z) σ2Φ (x,y,z)

where ρ(x,y,z) is an electron-density map from X-Ray experiments, and Φ(x,y,z) is a Coulomb-potential map from EM.


A plan to use lasers to align molecules in ice droplets for electronbeam diffraction, from Spence, J.C.H. et al., Acta Cryst. (2005) A61, 237 – 245.

a) electrostatic potential mapfor pthalocyanine

b) simulated oversamplingdiffraction pattern

c) sum of diffraction patterns ifalignment distributed over 5°


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.


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


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)).


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

…


Hopefully this lecture provides a useful overview of the types of techniques that exist, and some insights that might be helpfulin learning more about these techniques and those that haven’tbeen mentioned, or yet discovered.

Thank you for your attention, and thank the scientists on whose shoulders we stand …

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