X-ray crystallography stems from a desire to find seemingly invisible internal order. Eighteenth century crystallographer Rene Just Hauy first identified the foundational notion that external symmetry is linked to internal order by illustrating that dog-tooth spar could be described by the packing of little rhombs. However, Johannes Kepler may have preceded Hauy in this quest for order in 1611 when he speculated that the packing of tiny spheres of ice gives rise to snowflakes’ characteristic hexagonal figure. Robert Hooke and Nicolaus Steno followed in the late 17th century with observations that led to Steno’s law, which states that the close-packing of the spheres within a crystal governs the angles of the crystal faces (1).

A close-up of a snowflake illustrates its complex crystalline structure.

A close-up of a snowflake illustrates its complex crystalline structure.

Major developments in X-ray and electron diffraction techniques have taken us from Hooke’s early sketches to complex patterns from which we can derive electron density maps to characterize crystalline materials. Because of these developments, the applications of X-ray crystallography have grown tremendously. In the early 20th century, scientists used X-ray crystallography to explore minerals and basic information about atoms and bonding, but contemporary science dives into more complex structures, including those of proteins. Although X-ray crystallography can be used to determine the structure of any crystal, it is currently the preferred technique for determining protein structure. The technique’s results make up 80 percent of all protein structures and 95 percent of structures with 80 or more amino acids in the Protein Data Bank, and the government now funds contributions to expression libraries (2, 3). Protein structures can reveal how proteins function, and have chemical and biological implications. Research at Dartmouth College reflects the importance of this field. Specifically, professor Jon Kull’s laboratory uses X-ray crystallography to examine protein structure, and unites molecular and cell biology to examine transcription factors of Vibrio cholerae, the cause of cholera in humans. The laboratory’s structural analyses lead to functional insights, and Kull enjoys the work as a “blend of personal interest and professional collaboration” (3). After using structure to determine how these transcription factors function, researchers may revisit the structure to predict possible treatment methods.

Understanding how researchers use invisible X-rays to determine invisible structures requires some background k

nowledge about crystals, diffraction, and computation methods. X-ray crystallography is a multi-step process that requires crystallization of a protein, subsequent diffraction experiments, and finally phase determination and model building.

Crystal Basics

Understanding X-ray crystallography requires a grasp of the key qualities of crystals. Crystals grow as a material’s molecules attempt to reach the lowest free-energy state through uniform packing (4). As they attempt to reach a minimum free-energy state, molecules tend to form symmetric relationships. A crystal may possess rotational symmetry, translational symmetry, or a combination of both. Complete crystal classification requires identification of all of a crystal’s inherent types of symmetry (1). The three spatial directions for translational symmetry give rise to seven crystal systems. Combined with the possible centering combinations for atoms, these crystal systems result in the 14 Bravais lattices. These lattices and motifs, arrangements of atoms that fall on the points of the lattice, are used to describe a crystal’s structure (4). The combination of symmetry and structure gives insight into a crystal’s specific properties.

A crystal’s unit cell is comprised of the fewest numbers of atoms that show the essential structure and symmetry. Each crystal lattice is a three-dimensional stack of unit cells. Although the simplest way to stack atoms is a simple hexagonal structure where the atom centers are placed directly above one another, no elements exist with this structure. Depending on how the atoms fall into the hollows or interstices of other layers, they can result in either hexagonal close-packed or cubic close-packed structure

s. The second layer of atoms slips into the hollows of the layer below, giving rise to close-packed structures. When the third layer of atoms is added, the atoms may slip into either the hollows or interstices of the second layer, ending up directly above the atoms of the first layer or directly above any unoccupied interstices of the first layer. The first case is called hexagonal close-packed structure, and the latter is cubic close-packed (1).

How to Crystallize

For crystallographers, especially those who focus on proteins, the science of recognizing conditions and understanding theory precludes the art of growing the crystals. In solution, crystal growth consists of crystal nucleation, followed by crystal growth. The ideal solution conditions should minimize crystal nucleation while maximizing growth (3). A variety of crystallization techniques and relative saturations provide researchers with flexibility, but these choices come with a cost since the work often relies on trial and error (5).

The most common method of crystal growth, the hanging drop method, uses the principle of vapor diffusion. A drop of protein solution is added to a drop of precipitant solution above a well of the same precipitant solution. As water diffuses from the drop to the precipitant solution, a crystal can nucleate and grow in a slow, controlled manner under optimal conditions (3). Batch crystallization, the oldest method, simplifies this process by merely leaving crystal to grow from a supersaturated solution. Other techniques include liquid-liquid diffusion and dialysis. For liquid-liquid diffusion, protein and precipitant solutions are layered within a small-bore capillary. As the layers gradually diffuse, crystallization is induced. In dialysis, changing conditions allow for crystal formation, but a semi-permeable membrane is used to separate the layers (5).  Because of gravity’s effect on nucleation, different variations of these methods have been explored on space shuttles (6). Finally, the techniques of macro- and micro-seeding involve placing initial crystals into solutions of various proteins concentrations, with the hope that the smaller crystals will grow into larger ones. Currently, experimentation de-termines the desired concentrations. The problem, as professor Jon Kull notes, is that “there are no rules, so you don’t know how your protein of interest will crystallize” (3).

The crystals grow in characteristic patterns, with plane faces that will eventually diffract the X-rays. Their angles reflect their chemical composition and limit the directions in which they may diffract the X-rays. The unique growth patterns of different crystals are what ultimately allow for structural determination.

X-ray Diffraction

To view an object, the light striking that object must be at least half of the said object’s wavelength. X-rays are thus chosen for structural determination, because their wavelengths are small enough to permit the viewing of molecules. Unfortunately, X-rays cannot be focused with traditional lenses. Instead, researchers rely on computers to act as the lens by interpreting diffraction patterns.

Contemporary techniques for X-ray diffraction are built upon ideas developed in the early 20th century by German physicist Max von Laue. Laue’s X-ray diffractions relied on three components: the crystallized sample, an X-ray source, and a place to collect the radiation (7). Tremendous improvements in crystal rotation methods and X-ray source quality have allowed for better diffraction patterns. Capturing the true identity of a crystal demands that all corresponding lattice points are brought to the correct diffraction position. Rotating cameras with devices to remove background scatter have been developed in response to this requirement. With regard to X-ray sources, the synchrotron, a large-scale particle accelerator, has emerged as the source of choice for high-intensity, beam-like X-rays that can yield high-resolution diffraction patterns in short amounts of time (3, 8). Indeed, modern synchrotrons are so efficient that the limiting factor has become the act of mounting of the crystal, instead of the actual diffraction, which can now be viewed in real-time on a computer. The numerous high quality images produced from the synchrotron source can each be a megabyte in size, so “backup can become an issue” (3).

Successful X-ray crystallography also relies on detectors that can accurately collect diffraction patterns. The classic technique involves high-quality photographic film. More recently, photographic film has been replaced by faster and cheaper alternatives, and single-proton counters once valued for accuracy are no longer used in protein crystallography because of time constraints. Instead, image plates are the prime choice for detection. Featuring a thin layer of inorganic storage phosphor on a flat-base, these plates have a broad collection range and are sensitive to shorter wavelengths. These characteristics allow for the plates to be erased with white light, which eliminates the need for absorption correction. The lone disadvantage of image plates is that the images begin to fade when stored (4).

Once struck by an X-ray, the electrons of atoms within a crystal scatter the rays, which then constructively interfere with each other in specific patterns according to Bragg’s law. The repeated unit cell of the crystal amplifies the diffraction pattern, which is then converted into an electron density map via Fourier transformation. This valuable map allows for the predictions of atom locations and the construction of a structural model (5).

Data Interpretation and Model Building: the Phase Problem

After obtaining a successful diffraction pattern, proper analysis ideally leads to model building. However, analysis introduces its own set of complications: namely, the phase problem. Light detectors used in X-ray crystallography only measure intensity, but the combination of known intensity and phase allow for mathematical Fourier synthesis. This loss of the phase information constitutes what X-ray crystallographers refer to as the phase problem (7). To overcome these limitations, crystallographers may use different techniques such as multiwave anomalous diffraction (MAD), the Patterson method, molecular replacement, multiple isomorphous replacement (MIR), and/or direct methods.

The Hamburg Outstation of the European Molecular Biology Laboratory determined this DNA complex structure through protein crystallography.

The Hamburg Outstation of the European Molecular Biology Laboratory determined this DNA complex structure through protein crystallography.

MAD is possible only when the diffraction is obtained with a synchrotron. The crystallographer scans the X-ray beyond the crystal’s absorption edge three times to controllably alter scattering. Solving for “the substructure of the anonymously diffracted atoms” gives the crystallographer initial phases (9). Crystallographers can also use a Patterson map, a Fourier transform of the diffraction intensities, to analyze vectors between atoms. Although the Patterson method yields success with smaller molecules, when applied to larger molecules, it becomes overly complex. However, portions of the Patterson method are found throughout other methods such as the molecular replacement method. If a crystallographer knows the structure for a molecule closely related to the molecule of interest, he or she may use these known structures to decipher the rotational and translational properties of the molecule using Patterson maps of intermolecular and intramolecular forces.

MIR, also known as the heavy atom or heavy protein method, involves using electron-dense molecules to induce changes in the scatter intensity. The differences in intensity, when analyzed with a Patterson map, reveal the locations of the heavy atoms to give help crystallographers deduce phase angles. Direct methods operate on known phase relationships and are used most commonly for smaller molecules (10). At Dartmouth, Professor Jon Kull’s laboratory group primarily uses the MIR and molecular replacement methods to combat the phase problem (3).

After determining intensity with initial X-ray diffraction and solving for the phase, Fourier transformations lead to electron density maps. The maps allow crystallographers to construct models. Furthermore, these models may be used for phase refinement or may be continuously refined. Once finalized, structures are often added to protein data banks or applied to help solve problems related to protein interactions.

Conclusion

In short, research in X-ray crystallography echoes the structure-function relationships on which chemistry relies. Its expansion of applications and improved technology over the last century mark it as an established yet flexible technique. The artistic crystallographer must optimize conditions through altered parameters to allow for a useful crystal structure, yet the complex process introduces more choice in collection of the diffraction pattern and final phase-determining experiments. X-ray crystallography’s flexible nature makes it a worthy contender for deciphering molecule and protein structure.

References

1. C. Hammond, Basics of Crystallography and Diffraction (Oxford University Press, New York, 2001).
2. M. Weiss, X-ray Crystallography in 5401 Seconds (2001).  Available at http://www.embl-hamburg.de/~msweiss/teach/ (04 May 2009).
3. J. Kull, personal interview, 26 May 2009.
4. J. Drenth, Principles of Protein X-ray Crystallography (Springer Science+Business Media, New York, 2007).
5. R. Hanson, X-ray Crystallography. Available at http://www.stolaf.edu/people/hansonr/mo/X-ray.html#difract (30 Sept 2009).
6. NASA, Last Round of DCAM Specimens Set for Launch (1998).  Available at http://spacescience.spaceref.com/newhome/headlines/pdf/DCAM.pdf (29 Sept 2009).
7. P. Ewald, Fifty Years of X-ray Diffraction (1962, 1999).  Available at http://www.iucr.org/publ/50yearsofxraydiffraction (14 May 2009).
8. M. Ladd, R. Palmer, Structure Determination by X-ray Crystallography (2003).  Available at http://books.google.com/books?id=vNJrAe36BBMC&lpg=PP1&ots=QwgPBPEIE2&dq=Marcus%20Frederick%20Charles%20Ladd%2C%20Rex%20Alfred%20Palmer&pg=PR4#v=onepage&q=synchroton&f=false (20 May 2009).
9. S. Ealick, Current Opinion in Chemical Biology 4, 495-499 (2003).
10. R. Read, The Phase Problem: Introduction to Phasing Methods (2009). Available at http://www-structmed.cimr.cam.ac.uk/Course/Basic_phasing/Phasing.html (29 Sept 2009).