X-ray Crystallography

Summary

X-ray crystallography is a technique for determining the three-dimensional arrangement of atoms in a crystalline solid. A beam of X-rays is directed through a crystal, the regular lattice of atoms scatters the beam in particular directions, and the resulting pattern of spots on a photographic plate (or, today, an electronic detector) carries information about how the atoms inside the crystal are spaced and oriented. The relation between the diffraction pattern and the underlying structure was given mathematical form by William Henry Bragg and his son William Lawrence Bragg in the early 1910s, an achievement that earned them the Nobel Prize in physics in 1915. Through the middle decades of the twentieth century the method was extended from inorganic salts to ever more complicated biological materials (proteins, viruses, and finally nucleic acids) and became one of the principal tools by which the structures of biological molecules were determined. The 1953 determination of the DNA double helix is the canonical case. Crystallography did not, by itself, reveal life’s molecules; it had to be combined with chemistry, model building, and theory. But for much of the twentieth century, no other technique could do what it could.

Origin: The Bragg Equation and the Lattice

The technique began with the recognition that a crystal is a regular three-dimensional grid of atoms and that X-rays (having wavelengths comparable to atomic spacings) would diffract from such a grid in calculable ways. In 1915, William Lawrence Bragg, then twenty-five, shared the Nobel Prize in physics with his father William Henry Bragg “for demonstrating the use of X-rays for revealing the structure of crystals.” The relation now called Bragg’s Law, named after the younger Bragg, gave the geometric link between the diffraction angles and the spacing of atomic planes:

Bragg’s Law … builds on the fact that a crystal by its nature suggests an orderly pattern of atoms inside. When X-rays are shone through it, the atoms diffract — that is, scatter in particular directions — and leave spots on a photographic plate. Bragg’s equation relates the positions of the spacing of the atoms and thus to the structure of the molecules that make up the crystal.(Maddox, 2003)

The Bragg result made structural information physically extractable. What it did not do is hand the answer over: a diffraction photograph is not a picture of the crystal but an indirect map of it, and the inverse problem (going from spots back to atomic positions) turns out to be deeply ambiguous. The technical history of crystallography in the twentieth century is largely the history of how that ambiguity was managed.

Development: Cambridge, Bernal, and the Space Groups

After the Braggs, the leading centre of crystallographic theory was Cambridge. In the 1930s J. D. Bernal, working at the Cavendish, refined the nineteenth-century classification of “space groups” (the 230 distinct symmetries into which the seven recognised crystal systems can be organised) and pushed the technique toward larger and more disordered samples.

After Lawrence Bragg, crystallography was developed further at Cambridge in the 1930s by the brilliant and ebullient J. D. Bernal, who refined the nineteenth-century classification of “space groups” — the 230 forms into which the seven recognised crystal systems are organised.(Maddox, 2003)

Bernal’s expansion of the field had practical and intellectual consequences. He trained, among others, Max Perutz and Maurice Wilkins, both of whom would later play central roles in the determination of biological molecular structures. By the late 1930s, Bernal’s laboratory was an entry point for a generation of young scientists (and especially for women, refugees, and others kept out of the older Oxbridge institutions) into work that combined physics, chemistry, and biology in a way that none of the older disciplines did alone.

A representative case is Rosalind Franklin’s undergraduate notebook, written in 1940. Franklin was already attentive to the connection between molecular structure and inheritance. Her notes record the layered geometry of nucleic acid:

She noted the experimentally useful form of nucleic acid, sodium thymonucleate (obtained from calf thymus glands), with its high molecular weight of 800,000 (now known to be much greater) and its bases stacked up at 3.4 Ängstroms along its chains … A sketch in her workbook represents a helical structure. She made a note to herself: “Geometrical basis for inheritance?”(Maddox, 2003)

The question Franklin asked as an undergraduate would be the question her own technique would, twelve years later, decisively help answer.

The Method in Practice

A modern fibre-diffraction experiment of the kind Franklin and Gosling performed at King’s College London involves three intertwined difficulties.

The first is sample preparation. DNA fibres of the kind used by the King’s group depended on a particular preparation of nucleic acid by Rudolf Signer of Berne, distributed at a 1950 conference, that produced fibres of unusually high molecular weight. Reproducing Signer’s preparation was difficult; samples from other sources tended not to crystallise as cleanly. The quality of the diffraction photograph that mattered most for the DNA problem was, in the end, partly a product of the quality of the sample to which Franklin had been given access.

The second is humidity control. Franklin’s most consequential experimental advance was the systematic control of humidity inside the X-ray camera using salt solutions. By varying the water available to the fibre, she demonstrated for the first time that DNA existed in two distinct forms:

She chose a series of salt solutions through which to bubble hydrogen into the camera at controlled humidities. She first pulled the water out by placing the DNA fibre over a drying agent, then put it back at will by increasing the humidity to a range of different values … There were two forms of DNA. When hydrated, the fibre became longer and thinner. When placed over a drying agent, it changed back. … They called the new, longer, thinner, heavily hydrated DNA, “wet,” or “paracrystalline” or, more simply, the “B” form. The other, shorter, drier alternative … was “dry,” “crystalline” or the “A” form.(Maddox, 2003)

The A and B forms turned out to be different conformations of the same molecule. Recognising that there were two of them (and being able to switch between them at will) was the discovery that made the rest of the work possible.

The third difficulty is mathematical. A diffraction pattern records the intensities of the spots but not their phases, and without phase information the inverse map from spots to atomic positions is underdetermined. The standard tool for working around this in the mid-twentieth century was the Patterson function, named for A. Lindo Patterson, a New Zealander educated at McGill who had developed the method in the 1920s. The Patterson method substitutes intensities (which can be measured) for phases (which cannot), and produces a contour map that shows the distances between heavy atoms even when the atomic positions themselves cannot be read directly. Maddox’s description of the technical demand is worth quoting in full:

“The Patterson” was named after A. Lindo Patterson, a New Zealander educated at McGill University in Montreal, who in the 1920s had developed the method for circumventing the difficult “phase” problem of measuring X-rays’ peaks and troughs. It relies only on the intensities — the blackness — of the spots captured on a photographic plate. A Patterson map, which looks like a contour map, is a complicated overlay of mathematical pictures showing the heavier atoms, such as phosphorus, standing out as peaks … no one had ever attempted “cylindrical sections” — an order of magnitude more difficult, like trying to do a three-dimensional jigsaw puzzle.(Maddox, 2003)

The “cylindrical sections” variant Franklin and Gosling applied to the A form of DNA is the work that supplied, more than any other single contribution, the experimental basis on which the double helix was eventually built.

Crystallography and Biological Molecules

By the late 1940s, X-ray crystallography had moved beyond mineral and small-molecule chemistry into biology. Two events fixed the field’s confidence that biological structures could in principle be solved.

The first was Linus Pauling’s announcement of the alpha helix in proteins in spring 1951. Pauling combined chemical reasoning with X-ray data on simpler peptides to propose a regular helical structure that explained the major X-ray reflections of fibrous proteins. The result devastated William Lawrence Bragg, by then director of the Cavendish, who had been working on the same problem; Bragg later called it “the biggest mistake of my scientific career.” Crick, working on protein at the Cavendish at the time, observed simply: “Helices were in the air.”(Maddox, 2003)

The second was the King’s group’s first public showing of DNA diffraction data, also in 1951. At the Naples conference that May, Wilkins projected an X-ray slide of unprecedented sharpness:

No one had ever shown such a sharp discrete set of reflections from the DNA molecule. There was nothing like it in the literature.(Maddox, 2003)

Watson, in the audience, took from the slide the conviction that DNA had a regular structure that could be solved. The decisive image came a year later. Photograph 51, taken between 1 and 2 May 1952 by Franklin and Gosling, was

the clearest picture ever taken of the B form of DNA, unquestionably a helix.(Maddox, 2003)

Photograph 51 (and the unit-cell measurements that accompanied it) supplied, in 1953, the constraint that made the Watson–Crick model possible. The full institutional and ethical history of how that information was used is treated in Determination of the DNA Double Helix (1953). For the history of the technique itself, the relevant point is that by 1953 X-ray crystallography had crossed a methodological threshold: it could, in principle, deliver atomic-resolution structures of biological macromolecules, even ones (like DNA) that were difficult to crystallise and behaved differently in different humidities.

A Pre-X-ray Precursor: Pasteur’s Crystallography

The strict history of X-ray crystallography begins in 1912–1913 with the work of Max von Laue, the Braggs, and the demonstration of X-ray diffraction. But “crystallography” as a technique for inferring molecular structure is older. The early work of Louis Pasteur on the crystals of tartaric acid in the 1840s and 1850s (separating optical isomers of tartrate by the geometry of the crystals) is now read by historians of science as the start of a chemical and biological line of crystallographic reasoning that long preceded the X-ray apparatus.

The historian Gerald Geison treats Pasteur’s transition from crystallography to fermentation in the late 1850s as a deliberate strategic move:

there is reason to believe that the concerns that lay behind Pasteur’s shift from crystallography to fermentation were almost the opposite of pragmatic or industrial. Here, in fact, we are following Pasteur during the most boldly theoretical phase of his career, where it was not utilitarian goals but rather “preconceived ideas” that were most at play.(Geison, 1995)

Pasteur’s law of hemihedral correlation (the relation between optical activity and the asymmetry of crystal faces) is a pre-X-ray crystallographic claim about the link between molecular structure and biological function. It is not the same technique that Franklin used a century later, but the underlying intuition (that crystals carry information about the molecules that compose them, and that biology can be read in the geometry of the solid) is recognisably the same. Twentieth-century X-ray crystallography is in this sense the technological completion of a research programme Pasteur had already, in chemical and biological terms, formulated.

Crystallography in the Twentieth-Century Reorganisation of Biology

The philosopher of biology Georges Canguilhem treats X-ray crystallography as one of the technologies through which the modern science of life acquired its objects. In Ideology and Rationality in the History of the Life Sciences (1988), he argues that the deciphering of DNA’s structure was not the achievement of a single discipline but the construction of an “interscientific object” requiring a particular conjunction of techniques:

Our present knowledge of the structure and functions of living matter stems from a systematic combination of results from several biological disciplines (such as cytology, microbiology, and biochemistry) with those of formal genetics. But this conjunction of diverse results proved fruitful only to the extent that it required a restructuring of the relations among the disciplines that produced them. … without technologies that would have been inconceivable fifty years ago, such as X-ray diffraction crystallography, electron microscopy, and radioisotope tracing, it would have been impossible to carry out the work that ultimately enabled researchers to show that the conservative and innovative functions of heredity are embodied in the macromolecules of the cell.[cang-ir88-ch05-009]

Canguilhem’s larger claim is epistemological: the DNA crystal itself is not a natural object. It is, in his term, “superreal”, produced by the technical and theoretical labour that constitutes the modern life sciences:

Now consider a crystal of DNA today. It exists not as an artifact but as a “superreal,” nonnatural object, the product of considerable technical and theoretical labor. It is the latest in a long series of new scientific objects invented since the end of the nineteenth century: the cellular extract, the intermediate metabolite, the Drosophila gene, the culture of mutant bacteria, and so on.[cang-ir88-ch05-006]

The historian John Pickstone arrives at a related point from a different direction. In his framework, crystallography belongs to the “age of analysis”, the long nineteenth-century reconfiguration of the sciences around the systematic mobilisation of analytical techniques. The 1953 DNA result is, in Pickstone’s reading, an exemplary case of this analytical mode rather than a triumph of experiment:

The double-helix structure of DNA was revealed, not by experiment as such, but by the systematic mobilisation of a range of analytical techniques — notably organic analysis of the bases and X-ray crystallography of suitable crystals.(Pickstone, John V., 2001)

What both Canguilhem and Pickstone emphasise is that X-ray crystallography is not best understood as a “method” added to biology like a new instrument. It is one of the techniques by which the modern life sciences came to know what they know, and in their absence, what biology means as a discipline would itself be different.

Scholarly Assessment

Crystallography’s place in the history of medicine and biology is now stable. It is treated as the principal twentieth-century technique for determining the structures of biological macromolecules; as the foundation, with NMR and (later) cryo-electron microscopy, of structural biology; and, through the DNA case, as the central tool through which classical genetics was converted into molecular biology. The Bragg equation is taught in undergraduate physics; the Patterson function and the phase problem are taught in graduate biophysics; the human history of the field (Bernal’s Cambridge laboratory, the King’s group’s institutional difficulties, the post-war Cavendish) is the subject of an extensive secondary literature.

For the philosophical and historiographic questions that the encyclopaedia treats elsewhere, X-ray crystallography matters in two further respects. First, it is the canonical example of an analytical, rather than experimental, mid-century technique: the structures it delivers are inferred from the systematic mobilisation of measurement, theory, and chemistry, rather than produced by intervention in the manner of the older experimental physiology. Second, it is the canonical example of an “interscientific object” in Canguilhem’s sense: the molecules it reveals are not facts of nature recovered in pristine form but stable artefacts of a specific technical configuration.

Human Notes

The technique now known as X-ray crystallography sits at an unusual intersection of disciplines. It was created by physicists; refined as a tool of inorganic chemistry; pushed into the biological domain by Bernal, Hodgkin, Perutz, Kendrew, Wilkins, Franklin, and Bragg; and is today most prominent in pharmaceutical drug design, where the structures of target proteins are routinely solved before chemical modification of candidate ligands. Its history is therefore not just a history of biology but a history of how a physical technique becomes biological, and of what is gained, and what is lost, when one discipline’s instruments are taken up by another.

For practitioners and students of the history of medicine, the most important feature of crystallography may be that it is the technique through which biology became, for a time, reducible to physics. Whether one regards that reduction as a triumph (the Watson–Crick view) or as one move among many in a longer reorganisation of the life sciences (the Canguilhem and Pickstone view) is one of the genuine open questions of twentieth-century historiography of biology.

See Also

• Determination of the DNA Double Helix (1953)
• Rosalind Franklin
• Louis Pasteur
• Molecular Biology
• Heredity
• Analytical Science

Footnotes

Editorial Notes

Gaps the encyclopaedia compiler flagged for future evidence work, collected from inline markers in the body and frontmatter.

Scholarly Assessment