Structures nobody could have guessed

Diffraction hands you intensities and keeps the phases, so a structure is not something you invert a pattern to get. Dorothy Hodgkin solved penicillin against the settled opinion of the most eminent chemists in Britain, then vitamin B₁₂ with 181 atoms and no prior knowledge at all, then insulin after thirty-four years.

1934 – 196918 min

By the end you should be able to

State the phase problem quantitatively, and say why it cannot be brute-forced
Explain how a heavy atom supplies phases the experiment never measured
Describe how the structure of penicillin was settled against expert chemical opinion
Say what changed between penicillin in 1945 and vitamin B₁₂ in 1956

Bragg handed chemistry an instrument, and the instrument came with a hole in it. Every spot is a complex number. The structure factor F has a magnitude and a phase. Get both, transform them, and the electron density appears with the atoms in it. That step is exact and it is not the hard part. The detector records |F|², and nothing else. Intensity is a photon count. It gives you the magnitude squared and it gives you not the faintest indication of the phase. No instrument has ever measured one directly. So the calculation needs two numbers per reflection, the experiment supplies one, and the one that is missing turns out to carry more of the structural information than the one you have. What this meant in practice, through the 1920s and 1930s, is that you could solve a structure only if you already very nearly knew the answer. You proposed an arrangement, calculated what its pattern would be, compared it with the observed intensities, and adjusted. That works for rock salt, where there are two candidates and one is silly. It works for hexamethylbenzene, where the chemistry has narrowed things to a ring. It does not work for a molecule nobody has a proposal for.

Start with the true phases and note that the peaks land on the atoms. Then drag the phase-error slider to the right and watch the amplitude bars, which do not move.

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Amplitudes on top, phases in the middle, and the map they make together at the bottom. The bars are the measurement, complete and unchanged in every setting; the dials are a choice. Every map here is exactly as consistent with the recorded data as every other, which is the whole difficulty in one picture — no further measurement of intensity distinguishes them, because they were all made from the same intensities.

Problem

The size of the easiest case

A centrosymmetric projection of a small molecule yields 100 independent reflections. Every structure factor is real, so each phase is simply a sign — plus or minus. How many distinct combinations of signs are there?

Independent reflections: n = 100
Possible phases per reflection: 2 (+ or −)
Reflections are independent: each sign is free of the others

Dorothy Mary Crowfoot was born in Cairo in 1910, read chemistry at Somerville College, Oxford, and went to Cambridge in 1932 to work with J. D. Bernal. In 1934 the two of them took the first X-ray diffraction photograph of a protein, from a crystal of pepsin — and the reason it worked is worth knowing, because it is a very small piece of technique with an enormous consequence. Everyone before them had mounted crystals dry. Protein crystals are around half water, and drying one destroys the order that makes it a crystal. Bernal and Crowfoot sealed theirs in a thin glass tube along with the liquid it had grown in, and the spots appeared. That photograph is the moment it becomes conceivable that the structure of a protein might one day be known. The same year, aged 24, she was diagnosed with rheumatoid arthritis. It deformed her hands progressively for the rest of her life, and she worked with it for sixty years — the last of them from a wheelchair, still travelling.

This is the same picture with the phases taken from the heavy atom alone. Compare the map with the true atom positions marked below it — then press "Light atoms only" and watch what happens without a rubidium in the cell.

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The heavy-atom method, which is what made all three of the structures below possible. Rubidium carries thirty-six electrons against carbon’s six, so it dominates the structure factor and its phase is close to the true one. You can locate it without phases at all, from a Patterson map. What you get back is the structure plus a ghost of itself reflected through the heavy atom — the known price — and you separate the two by chemistry, then go round again. Without a heavy atom the same procedure collapses onto whichever light atom happens to be largest, and tells you nothing.

Phases you did not measure, from an atom you did not need to place

The trick has two halves, and both of them are needed. A Patterson map needs no phases. Transform the intensities rather than the structure factors and you do not get the structure — you get a map of every interatomic vector in the cell, each weighted by the product of the two atoms’ scattering powers. With one atom far heavier than the rest, the heavy–heavy vectors tower over everything else, and its position falls out. Patterson published this in 1934, the same year as the pepsin photograph. A heavy atom dominates the phase. If one atom contributes most of F, then arg F is close to what that atom alone would give — and you can calculate that, because you now know where it is. Put the measured amplitudes together with those approximate phases and you get a map that is wrong but usefully wrong: the light atoms show up in it, faintly, alongside a mirror ghost of the structure through the heavy atom. Decide by chemistry which set is real, add those atoms, recompute the phases with them included, and repeat. Each cycle sharpens. This is why so much of the crystallography of that era consists of persuading a substance to form a salt with the largest available cation. It was not chemistry for its own sake. It was phasing.

The experiment

The X-ray structure of penicillin

Dorothy Crowfoot Hodgkin and Barbara Low, Oxford; in parallel with Charles Bunn and A. Turner-Jones at ICI · Begun 1942; structure settled 1945; published 1949, the work having been secret · The Department of Mineralogy and Crystallography, Oxford — a basement

The question: Penicillin was saving lives and nobody knew what it was. Two structures had been proposed for it: a β-lactam, with a strained four-membered nitrogen-containing ring fused to a five-membered thiazolidine, and a tricyclic oxazolone–thiazolidine arrangement using only ordinary five-membered rings. Which is it?
The apparatus: Crystalline salts of benzylpenicillin — sodium, potassium and rubidium — grown so that the same molecule could be examined in three different lattices. Rubidium, with 36 electrons against the 23 non-hydrogen atoms of the penicillin itself, is the heavy atom. Two-dimensional Fourier projections computed by hand and on Hollerith punched-card machines, at a time when a single map was weeks of arithmetic.

Theory predicted

On the chemical evidence and on the judgement of the senior structural chemists involved — Robert Robinson foremost among them — the oxazolone structure. Four-membered rings are strained, rare, and were widely regarded as too unstable to be sitting at the centre of a usable drug.

They measured

The β-lactam. A four-membered ring containing nitrogen, fused to the thiazolidine, exactly as Chain had proposed and as the chemists had rejected.

How sure could they be? The argument rests on the three salts agreeing. The same molecular geometry emerging from three different crystal lattices is very hard to explain as an artefact of any one of them — and the rubidium salt supplied phases the other two could not.

Why it mattered

A measurement settled a structural question against the considered opinion of the most eminent chemists in Britain, and it settled it in a way anyone could check by growing the same crystals. That is worth stating plainly because it is the entire claim this site makes. It also mattered enormously in practice: the β-lactam ring is the part of penicillin that does the work, and knowing it was there is what made it possible to strip the rest away and rebuild.

It is easy to tell this as a story about a stubborn establishment and a lone woman who was right. That is not quite what happened, and the real version is more interesting. Robert Robinson was Waynflete Professor of Chemistry at Oxford and would win the 1947 Nobel Prize in Chemistry. He was, by a wide margin, one of the best structural chemists alive, and his intuition about what molecules are like had been right for thirty years. He thought the β-lactam was wrong. His reasoning was good. Four-membered rings are strained. They are rare in nature. They are unstable — which is exactly the objection: a molecule you can put in a bottle and inject into people should not have one at its centre. Against that, the oxazolone structure uses only comfortable five-membered rings and accounts for most of the chemical behaviour. Ernst Chain, who had proposed the β-lactam, was a biochemist arguing about structure with organic chemists, in a subject where they had the authority. What resolved it was not a better argument. Robinson could not have been talked out of his position and should not have been. What resolved it is that Hodgkin grew three salts, computed the maps, and the four-membered ring was in all three of them. The instability the chemists objected to is real. It is also the mechanism: the ring is strained enough to open when it meets the enzyme a bacterium uses to cross-link its cell wall, and it destroys the enzyme in the process. Robinson’s objection was correct chemistry pointing at the wrong conclusion, which is a much more common failure than being simply mistaken.

A three-dimensional model built from stacked transparent sheets, each carrying a contour map of electron density, with a schematic diagram of the penicillin structure beside it. — Not a drawing of a molecule — a stack of contour maps. Each sheet carries the electron density in one plane through the crystal, and the atoms are the places where the contours close in on themselves. This is what a structure determination physically was before computers drew them: sheets of glass or perspex, one section per sheet, stacked up so you could look through the molecule. The work behind it is Hodgkin’s and Barbara Low’s at Oxford with Charles Bunn and A. Turner-Jones at ICI.

What the four-membered ring was worth

Establishing a structure can look like scholarship — a fact filed away, correct and inert. This one paid for itself within about a decade, and it is worth following the chain. Knowing the ring is there tells you what the molecule does. The β-lactam is strained, so it is reactive, and what it reacts with is the transpeptidase enzyme a bacterium uses to cross-link its cell wall. The ring opens, attaches itself to the enzyme permanently, and the bacterium can no longer build a wall. It is destroyed in the act of working, which is why penicillin is a suicide inhibitor rather than a poison. Knowing which part matters tells you which part you can change. In 1957–59 a team at Beecham isolated 6-aminopenicillanic acid — penicillin with the side chain removed and the ring intact — which meant new side chains could be attached at will. Methicillin followed in 1959 and ampicillin in 1961. The entire family of semi-synthetic penicillins comes out of that one move, and the move only makes sense if you know where the business end of the molecule is. And it explains the allergy. Penicillin allergy is a reaction to the opened β-lactam ring binding to your own proteins, which is why it generalises across the whole family and why it has nothing to do with the mould. A structure is not an ornament. It is the thing that tells you what to do next.

The experiment

The structure of vitamin B₁₂

Dorothy Hodgkin, with John White, Jenny Pickworth Glusker, Kenneth Trueblood and others · 1948 – 1956 · Oxford, with the computing done on the SWAC at UCLA

The question: Pernicious anaemia had been treatable with raw liver since 1926 and nobody knew what the active substance was. B₁₂ was crystallised in 1948. What is it? Chemical degradation had failed: the fragments could not be reassembled into anything consistent.
The apparatus: Crystals of the vitamin and of a hexacarboxylic acid derived from it. The molecule supplies its own heavy atom — a cobalt sitting at the centre — which is why B₁₂ was solvable at all. Thousands of reflections, and Fourier syntheses far beyond hand computation: the calculations were run on the SWAC, one of the earliest stored-program electronic computers, by Kenneth Trueblood in Los Angeles, with data and results crossing the Atlantic by post.

Theory predicted

Nothing specific. This is the point — there was no candidate structure to test. Chemistry had produced fragments and no way to put them together, and the molecule was far larger than anything previously solved from scratch.

They measured

A corrin ring — related to the porphyrin of haem but with one bridging carbon missing — with cobalt at its centre, a nucleotide loop tucked underneath, and 181 atoms in all, 93 of them heavier than hydrogen. Including a cobalt–carbon bond, the first ever found in a biological molecule.

How sure could they be? The corrin ring is not a porphyrin, and the difference is a single missing carbon in one bridge. Nothing in the chemical evidence had suggested it, and no chemist proposed it. It came out of the maps.

Why it mattered

This is the demonstration that crystallography can determine a structure with no prior structural knowledge whatever — that it is a method of discovery and not merely of confirmation. Lawrence Bragg, who had solved rock salt with two positions to choose between, said solving B₁₂ was as difficult as breaking an enemy cipher. It also converted the technique into something the whole of biochemistry would come to depend on.

And then insulin, which she began in 1935 and finished in 1969. Thirty-four years. Fifty-one amino acids in two chains, several hundred non-hydrogen atoms, no convenient heavy atom of its own, and crystals with a great deal of water in them. She obtained her first insulin diffraction photographs as a young researcher, put the problem down when it proved impossible, and picked it up again repeatedly across four decades while solving penicillin and B₁₂ in between. She was awarded the Nobel Prize in Chemistry in 1964 — for penicillin and B₁₂. Insulin was still unsolved. It came out five years after the prize. It is worth pausing on what that means about the shape of a scientific life. The public record is three structures and a medal. The actual work is thirty-four years of a problem that would not yield, carried alongside everything else, with no guarantee at any point that it ever would.

Oxford housewife wins Nobel

That was the Daily Mail’s headline in October 1964. Other papers led with the prize money and the fact that she had three children. She remains the only British woman to have won a Nobel Prize in any of the sciences, sixty years on. She was appointed to the Order of Merit in 1965, the second woman ever, after Florence Nightingale. A detail that is usually told as a curiosity and is worth more than that: she taught chemistry at Somerville to an undergraduate named Margaret Roberts, who supervised a fourth-year project on an antibiotic and later became Prime Minister. Thatcher kept a portrait of Hodgkin at Downing Street. Hodgkin, a lifelong campaigner for nuclear disarmament and for scientific contact across the Iron Curtain, disagreed with almost everything her former student did in office, and the two of them corresponded politely about it for years. The reason to include any of this is not colour. It is that the popular record of a scientist is assembled by people who are not interested in the science, and the version that survives is usually about something else — the arthritis, the children, the headline. What she actually did was work out where the atoms are in molecules nobody could otherwise have known.

You might think

The computers solved these structures — vitamin B₁₂ came out of one of the first electronic machines.

Actually

The SWAC did the Fourier syntheses, and without it B₁₂ would have taken decades rather than years. But a Fourier synthesis is arithmetic, and arithmetic was never the obstacle: the obstacle was that the phases going into it were not measured and had to be supplied. Every phase the machine used came from a decision somebody made — locate the cobalt in a Patterson map, assume its phases, read the resulting map, judge by chemistry which peaks are real atoms and which are the mirror ghost, add them, recompute. The machine could not do any of that and was never asked to. It is a fair description of B₁₂ to say that a computer did in weeks what a person could not do in a lifetime, and a false one to say that a computer solved it. The same distinction is worth carrying into any modern claim of the same shape.

I was captured for life by chemistry and by crystals.
Dorothy Crowfoot HodgkinFrom the autobiographical note she wrote for the Nobel Foundation in 1964, describing being given a book on crystals at sixteen.

1934Bernal and Crowfoot photograph a wet pepsin crystal: the first diffraction pattern from a protein.
1934Patterson publishes the map that gives interatomic vectors from intensities alone — no phases needed.
1934She is diagnosed with rheumatoid arthritis, aged 24.
1935First X-ray photographs of insulin crystals. The structure will take another 34 years.
1942Work on penicillin begins, in wartime secrecy.
1945The β-lactam ring, against the settled opinion of the chemists. Publication waits until 1949.
1948Vitamin B₁₂ is crystallised. Nobody has any idea what it is.
1956B₁₂ solved: 181 atoms, a corrin ring, and a cobalt–carbon bond nobody expected.
1957Beecham isolate 6-APA and begin building semi-synthetic penicillins on Hodgkin’s ring.
1964Nobel Prize in Chemistry. "Oxford housewife wins Nobel."
1969Insulin, at last — five years after the prize she was given for the other two.

Where this leaves us

What Hodgkin established is that a molecule nobody could have guessed can be pinned down beyond argument, from spots on a plate, given a heavy atom and enough patience. Not proposed. Determined. And it worked. The structures of the twentieth century — the double helix, haemoglobin, the ribosome, every drug target anyone has ever designed against — come out of this technique and the methods that grew from it. But look again at what one of those structures actually is. It is an average. Every molecule in the crystal contributes to every spot, so what comes out of the transform is the mean electron density over all of them — of order 10¹⁶ copies in a grain you could lose on a fingertip — each held in the position and orientation the lattice imposes. If some part of the molecule is floppy, it does not appear blurred; it appears absent, because it averages away. No one in this lesson ever looked at a molecule. They looked at what 10¹⁶ of them have in common. Which raises the obvious question, and it took another forty years to answer. What would it take to look at just one?