Taking X-ray diffraction to the limit: Macromolecular structures from femtosecond X-ray pulses and diffraction microscopy of cells with synchrotron radiation

TL;DR: The principle of the oversampling method, which takes advantage of "continuous" diffraction patterns from noncrystalline specimens, is reviewed and the ongoing experiments of imaging nonperiodic objects, such as cells and cellular structures, using coherent and bright X rays produced by third-generation synchrotron sources are discussed.

Abstract: Recent work is extending the methodology of X-ray crystallography to the structure determination of noncrystalline specimens. The phase problem is solved using the oversampling method, which takes advantage of "continuous" diffraction patterns from noncrystalline specimens. Here we review the principle of this newly developed technique and discuss the ongoing experiments of imaging nonperiodic objects, such as cells and cellular structures, using coherent and bright X rays produced by third-generation synchrotron sources. In the longer run, the technique may be applicable to image single biomolecules using anticipated X-ray free electron lasers. Here, computer simulations have so far demonstrated two important steps: (a) by using an extremely intense femtosecond X-ray pulse, a diffraction pattern can be recorded from a macromolecule before radiation damage manifests itself; and (b) the phase information can be retrieved in an ab initio fashion from a set of calculated noisy diffraction patterns of single protein molecules.

Summary

PERSPECTIVE AND OVERVIEW

• X-ray crystallography yields high-resolution 3D images of molecules in the crystalline state, providing essential information in many areas of biology today.
• In comparing diffraction microscopy with crystallographic imaging, the main difference is that the intensity of the diffraction signal is very much weaker in the noncrystalline case.
• Equally important is a second condition, namely that the specimen used in diffraction microscopy be capable of withstanding a greatly intensified X-ray exposure.
• More experience is needed, but indications are that phasing will not be a central problem for these types of experiments See Sec. 2 of the review.
• By 1990 it was established (78, 62) that pattern can be recorded from the general small specimen using synchrotron radiation.

The Principle of the Oversampling Method

• The discovery of X-ray diffraction from crystals by von Laue in 1912 marked the beginning of a new era for visualizing the 3D atomic structures inside crystals.
• When the crystals become small or only have one unit cell (i.e. non-crystalline), the X-ray diffraction intensities are weak and continuous, and the crystallographic phasing methods can be improved upon.
• In 1998, Miao, Sayre & Chapman proposed a different explanation to the oversampling method and concluded that Bates’ criterion is overly restrictive (43).
• When the diffraction pattern is sampled at a spacing finer than the Bragg peak frequency, the number of independent equations increases while the number of unknown variables remains the same.
• Equivalently, oversampling the diffraction pattern corresponds to surrounding the electron density with a no-density region, where the size of the no-density region is proportional to sampling frequency (47).

Iterative Algorithms

• One of the most effective ways is to use iterative algorithms.
• Recently Elser introduced a different algorithm for iterative phase retrieval, which he refers to as the "difference map" approach (15).
• Constraints are enforced on the electron density function.
• The 3D imaging of non-crystalline specimens using the oversampling phasing method has also been demonstrated recently, requiring the recording of a number of 2D diffraction patterns by rotating the specimen about one axis (46, 76).
• The reconstructed bacteria contain dense regions that probably represent the histidine-tagged proteins labeled with manganese and a semi-transparent region that is devoid of proteins.

FROM STORAGE-RING-BASED TO LINAC-BASED X-RAY SOURCES

• The use of synchrotron radiation produced by electron storage rings was recognized and begun to be exploited in the seventies.
• As the sources themselves became much more reliable, and effective instrumentation was developed for taking measurements, there began a strong move toward using synchrotron radiation for x-ray based studies in structural biology (74).
• Limitations on brightness come from the fact that the electron beam size is increased by the natural process of generation of synchrotron radiation.
• While ERLs operating in the x-ray regime remain in the conceptual design stage, a linac-based light source based upon a single pass linac has recently become operational.

OVERCOMING THE RADIATION BARRIER USING FEMTOSECOND X-RAY PULSES

• As described in the previous sections, the ultimate resolution of X-ray diffraction microscopy for biological specimens is limited by radiation damage.
• It is found that although early on in the exposure some Auger electrons and most photoelectrons escape, the Auger electrons start becoming trapped after about <1 to 2 fs.
• One approach, the combination of the oversampling phasing method with femtosecond X-ray pulses, may have the potential to overcome the obstacle (67, 54).
• The oversampled 2D diffraction patterns were assembled to an oversampled 3D diffraction pattern (1603 voxels) with the assumption that the orientation of each molecule (and hence the 2D diffraction pattern) was known.
• Fig. 6B shows the reconstructed electron density map of the active site which is in a good agreement with the same map obtained from the Protein Data Bank (Fig. 6A).

SUMMARY AND OUTLOOK

• X-ray diffraction microscopy, a combination of coherent and bright X-rays with the oversampling phasing method, is a newly developed methodology that makes it possible to escape the “benevolent tyranny” of the crystal in the reconstruction of structure from diffraction data (31).
• Due to the loss of the amplification from a large number of unit cells inside crystals, the major limitation of the application to structural biological seems to be radiation damage.
• By using cryo technologies, radiation damage can be significantly reduced, which makes it possible to image cells and cellular structures using X-ray diffraction microscopy.
• If with the planned femtosecond pulsed Xray lasers, a 2D diffraction pattern can be recorded from a biomolecule before it is destroyed, this technique could open a new horizon of imaging protein molecules without the need of crystallizing them first.

Figure Legends

• Phase retrieval of an oversampled diffraction pattern recorded from a noncrystalline specimen.
• Individual bacteria are seen using transmitted light (A, D) and fluorescence (B, E), where the yellow fluorescence protein is seen throughout most of the bacteria except for one small region in each bacterium that is free of fluorescence .
• An oversampled X-ray diffraction pattern from the E. Coli bacteria. (c) An image reconstructed from (b).
• Also shown is a special type of "sliced" storage ring source, and example of which has recently become operational at the ALS in Berkeley.
• (a) Stereoview of the electron density map of the active site with a Mg(II) of the rubisco molecule (contoured at two sigma) on which the refined atomic model of the rubisco molecule is superimposed.

Full text

UCRL-JRNL-200184
Taking X-ray Diffraction to the Limit:
Macromolecular Structures from
Femtosecond X-ray Pulses and
Diffraction Microscopy of Cells with
Synchrotron Radiation
J. Miao, H. N. Chapman, J. Kirz, D. Sayre, K. O.
Hodgson
October 8, 2003
Annual Review of Biophysics and Biomolecular Structure

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1
TAKING X-RAY DIFFRACTION TO THE LIMIT:
MACROMOLECULAR STRUCTURES FROM FEMTOSECOND X-
RAY PULSES AND DIFFRACTION MICROSCOPY OF CELLS
WITH SYNCHROTRON RADIATION
Jianwei Miao,
1
Henry N. Chapman,
2
Janos Kirz,
3
David Sayre,
3
and Keith O. Hodgson
1,4
1
Stanford Synchrotron Radiation Laboratory, Stanford Linear Accelerator Center,
Stanford University, Stanford, CA 94309-0210;
2
Lawrence Livermore National
Laboratory, 7000 East Avenue, Livermore, California 94550;
3
Department of Physics
and Astronomy, Stony Brook University, Stony Brook, NY 11794;
4
Department of
Chemistry, Stanford University, Stanford, CA 94305;e-mail:
miao@ssrl.slac.stanford.edu; chapman9@llnl.gov; kirz@xray1.physics.sunysb.edu;
sayre@xray1.physics.sunysb.edu; hodgson@ssrl.slac.stanford.edu
Key Words the oversampling phasing method, iterative algorithms, diffraction
microscopy, X-ray free electron lasers, single molecule imaging
Abstract
The methodology of X-ray crystallography has recently been successfully
extended to the structure determination of non-crystalline specimens. The phase problem
was solved by using the oversampling method, which takes advantage of “continuous”
diffraction pattern from non-crystalline specimens. Here we review the principle of this
newly developed technique and discuss the ongoing experiments of imaging non-periodic
objects, like cells and cellular structures using coherent and bright X-rays from the 3
rd
generation synchrotron radiation. In the longer run, the technique may be applied to
image single biomolecules by using the anticipated X-ray free electron lasers. Computer
simulations have so far demonstrated two important steps: (i) by using an extremely
intense femtosecond X-ray pulse, a diffraction pattern can be recorded from a
macromolecule before radiation damage manifests itself, and (ii) the phase information
can be ab initio retrieved from a set of calculated noisy diffraction patterns of single
protein molecules.
CONTENTS
PERSPECTIVE AND OVERVIEW
THE OVERSAMPLING PHASING METHOD AND ITERATIVE
ALGORITHMS
The Principle of the Oversampling Method
Iterative Algorithms
EXPERIMENTS USING SYNCHROTRON RADIATION
FROM STORAGE-RING-BASED TO LINAC-BASED X-RAY SOURCES
OVERCOMING THE RADIATION BARRIER USING FEMTOSECOND X-
RAY PULSES
POTENTIAL OF IMAGING SINGLE PROTEIN MOLECULES
SUMMARY AND OUTLOOK

2
PERSPECTIVE AND OVERVIEW
X-ray crystallography yields high-resolution 3D images of molecules in the
crystalline state, providing essential information in many areas of biology today.
However, in important areas of molecular biology and throughout cell biology, structures
of key biological interest exist which cannot currently be crystallized and are hence not
accessible by conventional crystallography. An effort has therefore been underway for
some years to extend the diffraction methodology employed in X-ray crystallography to
the general small non-crystalline specimen, which we refer to as “X-ray diffraction
microscopy”. This approach, based primarily on the emergence of more powerful
synchrotron X-ray sources, and on the presence of more favorable circumstances for
dealing with the phase problem, is now looking promising, and is the subject of this
review.
By "general small specimen" is meant a finite non-periodic isolated object of less
than a few microns in size. This definition includes e.g. a single biomolecule, a cluster of
biomolecules, an organelle, or a complete small cell. (Larger and non-isolated objects
may also be possibilities for future study.) The objects covered closely resemble the
objects covered by optical and electron microscopy. But, X-ray diffraction microscopy
offers imaging resolution that is much higher than in the optical microscope and allows
specimen thickness much higher than in the electron microscope.
In comparing diffraction microscopy with crystallographic imaging, the main
difference is that the intensity of the diffraction signal is very much weaker in the non-
crystalline case. This is due to the absence of the very large signal amplification which
occurs at the Bragg peaks in the crystal case; that amplification can be of the order of N
2
,
where N is the number of unit cells in the crystal. This lowering of signal explains why
the development of new X-ray sources is important for diffraction microscopy -- we are
asking for the loss of Bragg-peak amplification to be made up for by the increase in
source brightness. Fortunately, new sources of synchrotron radiation do appear to be
capable of living up to that request. Equally important is a second condition, namely that
the specimen used in diffraction microscopy be capable of withstanding a greatly
intensified X-ray exposure. As will be seen, this, at least in the field of biological
specimens, set the resolution limit of the technique.
The absence of Bragg-peak amplification also has an advantage: the observed
diffraction pattern does not lose the information, which exists between the Bragg peaks.
The favorable consequence of this is that the phase problem, difficult for the crystal
specimen, becomes simpler for diffraction microscopy. More experience is needed, but
indications are that phasing will not be a central problem for these types of experiments
See Sec. 2 of the review.
Returning to the problem of the specimen withstanding of increased radiation
exposure, there are two basic situations to be considered. In one, there is no crystal, but
there exists a large supply of exact copies of the structure of interest, while in the other,
exact copies do not exist. The first case is exemplified by a protein molecule, and is the
more favorable in terms of the high-resolution quality of 3D imaging that can be
envisioned; the second case is exemplified by a whole biological cell. In the first case the
strategy can be to use a femtosecond flash X-ray source which will capture diffraction

3
data before the damage has had time to become evident, and expend many copies of the
structure in the collecting of the full 3D dataset. In the second case, the strategy must be
to employ measures, e.g. cryoprotection, to extend the lifetime of the specimen as much
as possible during the 3D data collection in a high-brightness synchrotron X-ray beam.
Detailed simulations indicate are that in the first scenario near atomic resolution imaging
will be possible at least for relatively large macromolecules, while for the second
scenario 10nm (or large-molecular) resolution may be possible. More detailed discussion
of the second case will be found in Sec. 3, and of the first case in Secs. 4, 5, and 6.
Historically, work on the subject had its inception in the early 1980s at the Stony
Brook physics department and the Brookhaven synchrotron (61). By 1990 it was
established (78, 62) that pattern can be recorded from the general small specimen using
synchrotron radiation. In 1995 an approximate treatment was given (63) of the
relationship between dose and resolution, and by 1998 it was established (62, 64, 43) that
with the gaining of information lying between Bragg peaks the phase problem is much
reduced in difficulty. Finally, in 1999, Miao et al. (44) successfully demonstrated the
complete procedure of pattern recording, phasing, and imaging, on a 2D man-made
radiation-resistant specimen. Following this, other groups began to take up the subject
(see references in later sections), and with this considerable research strength in the field
has been brought into existence.
THE OVERSAMPLING PHASING METHOD AND ITERATIVE ALGORITHMS
The Principle of the Oversampling Method
The discovery of X-ray diffraction from crystals by von Laue in 1912 marked the
beginning of a new era for visualizing the 3D atomic structures inside crystals. Indeed,
after almost a century’s development, X-ray crystallography has developed to a point that
it can determine almost any structures, as long as good quality crystals are obtained. This
remarkable achievement can be partially attributed to the development of powerful
crystallographic phasing methods such as the direct methods (20), isomorphous
replacement (21), molecular replacement (1), multiple wavelength anomalous dispersion
(57, 28), and others (77). However, when the crystals become small or only have one unit
cell (i.e. non-crystalline), the X-ray diffraction intensities are weak and continuous, and
the crystallographic phasing methods can be improved upon. It turns out that, when the
diffraction pattern is continuous, the phase information is much easier to recover by
sampling the diffraction pattern at a spacing finer than the Bragg peak frequency (i.e.
oversampling). It was first suggested by Sayre in 1952 that having the intensities between
as well as at the Bragg peaks may provide the phase information (60). Bates proposed an
explanation to the oversampling method in 1982 (2). Based on the argument that the
autocorrelation function of any sort of object is twice the size of object itself in each
dimension, Bates concluded that the phase information can only be recovered by
sampling the intensities twice finer in each dimension than the Bragg peak frequency. In
1996, Millane further relieved Bates’ criterion in three and higher dimensions (52).
In 1998, Miao, Sayre & Chapman proposed a different explanation to the
oversampling method and concluded that Bates’ criterion is overly restrictive (43). If