What Mad Pursuit (7 page)

There is also a well-known limitation on rotation axes. Wallpaper can have a twofold rotation axis—it looks exactly the same if it is rotated by 180 degrees—or a threefold, fourfold, or sixfold one. All other rotational axes are impossible, including a fivefold one. This restriction is true for any extended pattern with two-dimensional symmetry, known as a plane group, and thus also for three-dimensional extended symmetry, or a space group. Of course a
single
object can have fivefold symmetry. The regular dodecahedron and icosahedron, which have fivefold rotational axes, were known to the Greeks, but what is allowed for a point group (which has no dimensions) is impossible for a plane group (of two dimensions) or a space group (of three dimensions). Moslem art, which for religious reasons is forbidden to depict people or animals (since the Prophet was very hostile to paganism), is often for this reason very geometrical in design. One can sometimes see the artist flirting with local fivefold symmetry without ever attaining it on a repeating basis. As it turns out, the protein shells of many small “spherical” viruses (such as the polio virus) usually have fivefold symmetry, but that is another story.

The theory of the X-ray diffraction of crystals is straightforward, so much so that most modern physicists find it rather dull. Although it is necessary to be able to handle the algebraic details, I soon found I could see the answer to many of these mathematical problems by a combination of imagery and logic, without first having to slog through the mathematics.

Some years later, when Jim Watson joined us at the Cavendish, I used some of these visual methods, based on the deeper mathematics, to teach him the outlines of X-ray diffraction. I even considered writing a small didactic monograph on it, to be entitled “Fourier Transforms for Bird Watchers” (Jim had become a biologist because of an early interest in bird-watching), but there were too many other distractions and I never wrote it.

At that time there was no easily available textbook along these lines. The existing texts usually used a step-by-step method, based largely on Bragg’s law and the historical development of the subject. To someone like myself this only made it more difficult and certainly more tedious, since an elementary method often arouses deeper questions in the learner and these worries can impede one’s progress in learning. It is often better, at least for the brighter pupils, to go straight to the advanced treatment and try to get over the more powerful formalism while at the same time attempting to provide some insight into what is going on. In my case there was no alternative but to teach X-ray diffraction to myself. This was useful as I acquired a fairly thorough and intimate knowledge of it. Moreover, because Perutz was studying the shrinkage stages of a crystal made of large molecules, I learned how to deal with diffraction from a
single
molecule, and only then arranged them in a regular crystal lattice, rather than following the more conventional path of starting off with them in a lattice. This proved valuable to me later.

Armed with this new knowledge, I reread Perutz’s papers and spent some time thinking about how the problem of protein structure was to be solved. Perutz had tentatively suggested that the shape of the molecule was somewhat like an old-fashioned lady’s hatbox, and he had put such a diagram into his first paper. (Incidentally, diagrams of models are often difficult to draw satisfactorily, since, unless care is taken, they usually convey more than one intends.) For various reasons I thought that the hatbox was implausible, and I tried to find evidence for other possible shapes. Remember that the relevant X-ray data could not by itself tell us the shape, but that any proposed shape could be used to calculate the X-ray data. The shape influences only the few X-ray reflections that correspond to the coarse structure of the crystal. Their strength depends on the contrast between the high electron density of the protein and the lower electron density of the “water” (actually a salt solution) in between the molecules. Even if such a low-resolution picture of the electron density were available, it would not immediately give the shape of a single molecule, since at various places the protein molecules are in close contact. Where one molecule finished and the next began could not be seen. Fortunately Perutz had studied a set of similar packings—the several shrinkage stages—and by assuming that protein molecules are relatively rigid and merely packed together a little differently in the different stages, the range of possible shapes could be restricted.

I made some progress with the main problem but eventually became stuck. Meanwhile Bragg had independently thought about it. Whereas I had gotten bogged down, he made rapid progress. He boldly assumed that one could approximate the shape by an ellipsoid—a particularly simple type of distorted sphere. Then he looked at what little was known of the crystals of hemoglobin of other species of animal, on the assumption that all types of hemoglobin molecules were likely to have about the same shape. Moreover, he was not disturbed if the data did not
exactly
fit his model, since it was unlikely that the molecule was
exactly
an ellipsoid. In other words he made bold, simplifying assumptions; looked at as wide a range of data as possible; and was critical but not pernickety, as I had been, about the fit between his model and experimental facts. He arrived at a shape that we now know is not a bad approximation to the molecule’s real shape, and he and Perutz published a paper on it. The result was not of first-class importance, if only because the method was indirect and needed confirmation by more direct methods, but it was a revelation to me as to how to do scientific research and, more important, how
not
to do it.

As I learned more about the main problem, I began to worry about how it might be solved. As I have said, the X-ray data contained just half the necessary information, though it was known that some of what was available was probably redundant. Was there any systematic way to use the available data? It turned out there was. Some years earlier a crystallographer, Lindo Patterson, had shown that experimental data could be used to construct a special density map, now called a Patterson. [All the amplitudes of the Fourier components are squared and all the phases are put to zero.]

What did this density map mean? Patterson showed that it represented all the possible
interpeak
distances in the real electron density map, all superimposed, so that if the real density map frequently had high density a distance of 10 Å apart in a certain direction, then there would be a peak at 10 Å from the origin in the appropriate direction in the Patterson map. (One Ångstrom unit is equal to one ten-billionth of a meter.) In mathematical terms, this would be a three-dimensional map of the autocorrelation function of the electron density. For a unit cell with very few atoms in it, and using high-resolution X-ray data, one could sometimes unscramble this map of all the possible interatomic distances and obtain the real map of the atomic arrangements. Alas, for protein there were far too many atoms and the resolution was too poor, so that doing this was quite hopeless. Nevertheless, strong features in the Patterson could hint at broad features in the atomic arrangements, and indeed Perutz had predicted that the protein was folded to give rods of electron density, lying in a particular direction, because he saw rods of high density in that direction in the Patterson. As it turned out the latter rods were not really as high as he had imagined (he had at that time only the relative intensity of his X-ray spots, not their absolute value) so the folding was not quite as simple as he had conjectured.

This calculation of the Patterson of his crystals of horse hemoglobin was a difficult and laborious piece of work, since in those days the methods, both for collecting X-ray data and for calculating Fourier Transforms, were, by modern standards, primitive in the extreme. Many crystals had to be mounted (since each would only take a certain dose of X rays before deteriorating); many X-ray photos had to be taken, cross-calibrated, measured by eye, and systematic corrections made. The calculations were not done on what we would now call a computer (that came later) but using an IBM punched card machine. They took an assistant three months and were very laborious. Then all the numbers obtained had to be plotted and contours drawn, till eventually one ended up with a stack of transparent sheets, each having a section of the Patterson density shown on them as contours. As I recall, the negative contours (the average correlation was taken as zero) were omitted and only the positive ones plotted.

I received another lesson when Perutz described his results to a small group of X-ray crystallographers from different parts of Britain assembled in the Cavendish. After his presentation, Bernal rose to comment on it. I regarded Bernal as a genius. For some reason I had acquired the idea that all geniuses behaved badly. I was therefore surprised to hear him praise Perutz in the most genial way for his courage in undertaking such a difficult and, at that time, unprecedented task and for his thoroughness and persistence in carrying it through. Only then did Bernal venture to express, in the nicest possible way, some reservations he had about the Patterson method and this example of it in particular. I learned that if you have something critical to say about a piece of scientific work, it is better to say it firmly but nicely and to preface it with praise of any good aspects of it. I only wish I had always stuck to this useful rule. Unfortunately I have sometimes been carried away by my impatience and expressed myself too briskly and in too devastating a manner.

It was at such a seminar that I gave my first crystallographic talk. Although I was over thirty it was only the second research seminar I had ever given, the first having been about moving magnetic particles in cytoplasm. I made the usual beginner’s mistake of trying to get too much into the allotted twenty minutes and was disconcerted to see, after I was about halfway through, that Bernal was fidgeting and only half paying attention. Only later did I learn that he was worrying about where his slides were for the talk he was to give following mine.

All this was of little consequence compared to the subject of my talk, which, broadly speaking, was that they were all wasting their time and that, according to my analysis, almost all the methods they were pursuing had no chance of success. I went through each method in turn, including the Patterson, and tried to demonstrate that all but one was quite hopeless. The exception was the so-called method of isomorphous replacement, which I had calculated had some prospect of success, provided it could be done chemically.

As I mentioned earlier, X-ray diffraction data normally gives us only half the information we need to reconstruct the three-dimensional picture of the electron density of a crystal. We need this three-dimensional picture to help us locate the many thousands of atoms in the crystal. Is there any means of obtaining the missing part of the data? It turns out there is. Suppose a very heavy atom, such as mercury, can be added to the crystal at the same spot on every one of the protein molecules it contains. Suppose this addition does not disturb the packing together of the protein molecules but only displaces an odd water molecule or two. We can then obtain two different X-ray patterns: one without the mercury there, and one with it. By studying the
differences
between the two patterns we can, with luck, locate where the mercury atoms lie in the crystal [strictly, in the unit cell]. Having found these positions, we can obtain some of the missing information by seeing, for each X-ray spot, whether the mercury has made that spot weaker or stronger.

This is the so-called method of isomorphous replacement. “Replacement,” because we have replaced a light atom or molecule, such as water, with a heavy atom, such as mercury, which diffracts the X rays more strongly. “Isomorphous,” because the two protein crystals—one with the mercury and one without—should have the same form [for the unit cell]. In a loose way, we can think of the added heavy atom as representing a locatable marker to help us find our way among all the other atoms there. It turns out that we usually need at least two
different
isomorphous replacements to allow us to retrieve most of the missing information, and preferably three or more.

This well-known method had already been used successfully to help solve the structure of small molecules. There had previously been one or two halfhearted attempts to use it on proteins, but these had failed, probably because the chemistry used was too crude. Nor was I helped by my title. I had told John Kendrew the sort of thing I intended to say and asked him what I should call it. “Why not,” he said, “call it ‘What Mad Pursuit’!” (a quotation from Keats’ “Ode on a Grecian Urn”)—which I did.

Bragg was furious. Here was this newcomer telling experienced X-ray crystallographers, including Bragg himself, who had founded the subject and been in the forefront of it for almost forty years, that what they were doing was most unlikely to lead to any useful result. The fact that I clearly understood the theory of the subject and indeed was apt to be unduly loquacious about it did not help. A little later I was sitting behind Bragg, just before the start of a lecture, and voicing to my neighbor my usual criticism of the subject in a rather derisive manner. Bragg turned around to speak to me over his shoulder. “Crick,” he said, “you’re rocking the boat.”

There was some justification for his annoyance. A group of people engaged in a difficult and somewhat uncertain undertaking are not helped by persistent negative criticism from one of their number. It destroys the mood of confidence necessary to carry through such a hazardous enterprise to a successful conclusion. But equally it is useless to persist in a course of action that is bound to fail, especially if an alternative method exists. As it has turned out, I was completely correct in all my criticisms with one exception. I underestimated the usefulness of studying simple, repeating, artificial peptides (distantly related to proteins), which before long was to give some useful information, but I was quite correct in predicting that only the isomorphous replacement method could give us the detailed structure of a protein.