STRUCTURAL STUDIES on SINGLE PARTICLES and BIOMOLECULES

1
Crystallography without Crystals and the
Potential of Imaging Single Molecules
John Miao Stanford Synchrotron Radiation
Laboratory Stanford Linear Accelerator
Center   
2
The Phase Problem
Detector
Coherent Beam
Atoms
The trivial phases
3
Regular Sampling Sampling at the Bragg-peak
Frequency
of unknown variables of independent equations
1D 2N N
2D 2N2 N2
3D 2N3 N3
of unknown variables of independent equations
1D N N/2
2D N2 N2/2
3D N3 N3/2
4
Oversampling Sampling at Twice of the Bragg-peak
Frequency
of unknown variables of independent equations
1D 2N 2N
2D 2N2 4N2
3D 2N3 8N3
of unknown variables of independent equations
1D N N
2D N2 2N2
3D N3 4N3
Miao, Sayre Chapman, J. Opt. Soc. Am. A 15,
1662 (1998). Miao Sayre, Acta Cryst. A 56, 596
(2000).
5
The Oversampling Method
Eq. (2) ?
? gt 2 the phase information exists inside the
diffraction intensity!
6
Multiple Solutions
1D Case (? 2N multiple solutions)
2D 3D Case (No multiple solutions)
Mathematically, 2D and 3D polynomials usually can
not be factorized.
Bruck Sodin, Opt. Commun. 30, 304 (1979).
7
Coherence Requirements of the Oversampling Method
Oversampling vs. spatial coherence
sample size

Oversampling vs. temporal coherence

desired resolution
Miao et al., Phys. Rev. Lett. 89, 088303 (2002).
8
An Iterative Algorithm
(I)
with ? gt 5
(II)
0
(III)
FFT-1(
)

(IV)
(V)
)
FFT(
(VI)
Adopt
from
(VII)
Fienup, Appl. Opt. 21, 2758 (1982). Miao et al.,
Phys. Rev. B 67, 174104 (2003).
9
The First Experiment of Crystallography without
Crystals
(a) A SEM image
(b) An oversampled diffraction pattern
(in a logarithmic scale) from (a).
(c) An image reconstructed from (b).
(d) The convergence of the reconstruction.
Miao, Charalambous, Kirz, Sayre, Nature 400, 342
(1999).
10
Phase Retrieval as a Function of the oversampling
ratio (?)

? 5 (180 x 180 pixels)
? 4 (160 x 160 pixels)
? 2.6 (130 x 130 pixels)
? 1.9 (110 x 110 pixels)
Miao et al., PRB, in press.
11
Imaging Buried Nanostructures
(a) A SEM image of a double-layered sample made
of Ni (2.7 x 2.5 x 1 ?m3)
(b) A coherent diffraction pattern from (a)
(the resolution at the edge is 8 nm)
(c) An image reconstructed from (b)
Miao et al., Phys. Rev. Lett. 89, 088303 (2002).
12
3D Imaging of Nanostructures
The reconstructed top pattern
The reconstructed bottom pattern
An iso-surface rendering of the reconstructed 3D
structure
13
Determining the Absolute Electron Density of
Disordered Materials at Sub-10 nm Resolution
(a) A coherent diffraction pattern from a porous
silica particle
(b) The reconstructed absolute electron density
(c) The absolute electron density distribution
within a 100 x 100 nm2 area
Miao et al., Phys. Rev. B, in press.
14
Imaging E. Coli Bacteria
(a) Light and fluorescence microscopy images
of E. Coli labeled with manganese oxide
(b) A Coherent X-ray diffraction pattern
from E. Coli
Miao et al., Proc. Natl. Acad. Sci. USA 100, 110
(2003).
(c) An image reconstructed from (b).
15
3D Electron Diffraction Microscopy
Electron gun
Aperture
Lens
Sample
Detector
16
Computer Simulation of Imaging a 3D Nanocrystal
(Al12Si12O488) with coherent electron
diffraction
Si
Al
O
(b) One of the 29 diffraction patterns (the
0? projection), SNR 3
(a) A section (0.5 Å thick) viewed along 100
at z 0
(c) The reconstructed section (0.5 Å thick) of
the nanocrystal viewed along 100 at z 0
Miao et al., Phys. Rev. Lett. 89, 155502 (2002).
17
The Linac Coherent Light Source (LCLS)
18
Peak and Time Averaged Brightness of the LCLS and
Other Facilities Operating or Under Construction
TESLA
TESLA
19
A Potential Set-up for Imaging Single
Biomolecules Using X-FELs
X-ray Lens
Molecular Spraying Gun
X-FEL Pulses
CCD
20
Two Major Challenges
Radiation Damage

• Solemn Baldwin, Science 218, 229 (1982).
  
• Neutze et al., Nature 400, 752 (2000).
• When an X-ray pulse is short enough ( lt 50
  fs), a 2D diffraction pattern could
• be recorded from a molecule before it is
  destroyed.

Orientation Determination
Use the methods developed in cryo-EM to determine
the molecular orientation based on many 2D
diffraction patterns. Crowther, Phil. Trans.
Roy. Soc. Lond. B. 261, 221 (1971). Use laser
fields to physically align each molecule.
Larsen et al., Phys. Rev. Lett. 85, 2470 (2000).
21
An Oversampled 3D Diffraction Pattern Calculated
from 3 x 105 Rubisco Protein Molecules

• One section of the oversampled 3D
• diffraction pattern with Poisson noise

(b) Top view of (a)
22
The Reconstructed Electron Density from the
Oversampled Diffraction Pattern
The 3D electron density map of a rubisco molecule
The active site of the molecule
The reconstructed 3D electron density map
The reconstructed active site
Miao, Hodgson Sayre, Proc. Natl. Acad. Sci. USA
98, 6641 (2001).
23
Summary

• Proposed a theoretical explanation to the
  oversampling method.
• Carried out the first experiment of
  crystallography without crystals.
• Opened a door to atomic resolution 3D X-ray
  diffraction microscopy.
• Proposed 3D electron diffraction microscopy
  for achieving sub-atomic resolution.
• Future application with the LCLS imaging
  non-crystalline materials
• nanocrystals, and large biomoleucles.

24
Acknowledgements

• B. Johnson, D. Durkin, K. O. Hodgson, SSRL
• J. Kirz, D. Sayre, SUNY at Stony Brook
• R. Blankenbecler, SLAC
• D. Donoho, Stanford University
• C. Larabell, UC San Francisco LBL
• M. LeGros, E. Anderson, M. A. OKeefe, LBL
• B. Lai, APS
• T. Ishikawa, Y. Nishino, Y. Kohmura,
  RIKEN/SPring-8
• J. Amonette, PNL
• O. Terasaki, Tohoku University

25
Schematic Layout of the Experimental Instrument
25.4 mm
12.7 mm
743 mm
Pinhole
Sample
X-rays
Corner
Beamstop
Photodiode
CCD
26
Experimental Demonstration of Electron
Diffraction Microscopy
Left The reconstructed DWNT image Right A
structure model of the DWNT.
The recorded diffraction pattern from a DWNT.
Zuo et al., Science 300, 1419 (2003).