Cracking the Phase Problem


For Max Perutz, proving that X-rays could reveal the structures of complex, biologically important proteins would require a large dose of inspiration followed by an even larger amount of perspiration.

It must have been one of the most embarrassing moments in Max Perutz’s life. Perutz had just presented his proposed structure for haemoglobin at a meeting of the leading UK protein researchers in the Cavendish Laboratory in Cambridge in July 1951. The next speaker was a relatively new research student of Perutz’s called Francis Crick, giving his first talk to an audience of this calibre. Crick, who at the suggestion of his fellow Cavendish researcher John Kendrew titled his talk ‘What mad pursuit’, proceeded to tell the assembled audience in no uncertain terms why his supervisor’s model couldn’t possibly be correct. Adding insult to injury, Crick explained why X-ray crystallographers were wasting their time with a method that had no chance of success.

Sir Lawrence Bragg, head of the Cavendish, was furious. How dare a newcomer to the field tell himself – one of the founders of X-ray crystallography – and colleagues who had been at the forefront of their field for decades that their research was unlikely to produce any positive results. Bragg threatened to throw Crick out, but Perutz was more sanguine about Crick’s stinging criticism. Perutz knew he finally had to tackle the perplexing problem that he had tried to circumvent for almost 15 years.

In 1937 Perutz began the ambitious project of using X-ray diffraction to uncover the biological function of haemoglobin, the protein in red blood cells responsible for transporting oxygen. No protein structure had been solved using X-ray crystallography, and at the time researchers questioned whether this method, which had been so successful in identifying the structure of simple compounds, could ever be useful in identifying the structures of more complex compounds like proteins.

It wasn’t that Perutz found it difficult to get X-ray diffraction images of the more complex haemoglobin crystals, quite the opposite.  Perutz’s photographs were almost picture perfect, with characteristic regular arrays of sharp spots indicating a regular, repeating pattern of crystals. Perutz would proudly show the photos to any willing – and often unwilling – bystander. Even the doyenne of X-ray crystallography, Dorothy Hodgkin, said they were the most beautiful protein X-ray photographs yet seen.

However, when any bystander asked what the photographs actually meant, Perutz would change the subject. Perutz’s, and indeed all his colleagues’, problem was how to translate the patterns on the X-ray photographs into the three-dimensional arrangement of the atoms in the crystal, because of a complicated mathematical issue known as the phase problem.

Problem Phase

As X-rays pass through crystals, they constantly deflect off atoms and interact with each other, which results in the characteristic pattern of scattered, but regularly spaced, spots referred to as the X-ray diffraction pattern. Bragg and his father, William Henry Bragg, were the first to show that these diffraction patterns could reveal the structure of compounds, but as researchers began to use the Bragg’s X-ray crystallography method to identify increasingly complex structures, they soon discovered its limits.

For instance, each spot on a diffraction pattern provides information only about the intensity of the X-ray waves that have been deflected off the atoms in the crystal into the path of that spot. Ideally researchers also needed to know which particular point in the undulating cycle of movement from one wave peak to the next – known as the phase of the wave – these X-ray waves are at when they hit the film and form each spot in the diffraction pattern. In the case of simple molecules containing only tens of atoms the diffraction pattern and wave intensity information was sufficient to identify a structure, with the help of a formula devised by the French mathematician Joseph Fourier in the 19th century, which breaks down complex waveforms into their constituent waves. Although it was a painstaking task, researchers in the early years of crystallography could almost always rely on this Fourier synthesis formula, together with a healthy dose of trial-and-error and informed intuition, to hit upon the right structure of these compounds.

However, larger molecules with thousands of atoms, like haemoglobin, posed a much greater problem. The number of reflections and interactions that occur within crystals of this size is so complex that to translate X-ray patterns into molecular structures requires more than just knowledge about the intensity of waves. To have any chance of deducing the structure researchers needed to find a way of knowing what phase the X-ray waves are at when they form each spot in the diffraction pattern. This information could be calculated by knowing the phase angle, the distance between a point on a wave and a specified reference point. However, this information couldn’t be directly obtained from the Fourier synthesis, or indeed any other method. Researchers called the case of this missing information ‘the phase problem’, and at the time solving this was the ultimate goal for anyone interested in trying to determine protein structures from X-ray crystallography.

Without this missing phase information, researchers turned to another method that tried to get around the problem. Lindo Patterson devised a variation of this Fourier synthesis in the 1930s, which creates a contour map that can be used to define the distances between atoms in a crystal, through knowing only the position and intensity data in an X-ray photograph. The upside of these Patterson maps was that you didn’t need to know the phases of the reflections, but the downside was that creating a Patterson map was a hugely time-consuming task even for simple compounds, involving hundreds of calculations for each spot in a diffraction pattern. Added to that, Patterson maps were not necessarily guaranteed to be successful with more complex compounds.

Without an alternative method available, Perutz had no choice but to create a Patterson map of haemoglobin crystals, which he said was “one of the worst and most tedious jobs that have ever been done in my subject.” So for the fruits of his considerable labours to have been so brutally torn apart by his research student Crick must have been soul-destroying. Presumably Perutz’s lack of reaction reflected his suspicions deep down that the method was flawed. As he later said, “I pushed this thought aside, because I could not face the stark truth that the years of tedious labour, the many nights of interrupted sleep and the appalling strain of measuring the intensities of thousands of little black spots by eye had brought me no nearer the solution of the structure of haemoglobin.”

However, during the course of Crick’s diatribe, he did concede that one method might successfully deduce the structures of proteins. It was a technique invented by J.M. Robertson at Glasgow University for small organic molecules, known as the isomorphous replacement method. Robertson’s method introduced an atom into the crystal that was much heavier than the others, without changing the shape of the molecule. The heavy atom contained many more electrons and therefore scattered X-rays differently. The two diffraction patterns of the molecule with and without the heavy atom essentially show the same pattern of spots, but crucially there are some significant differences in intensity, which allow researchers to pinpoint the positions of the heavy atoms, and from this provided the missing reference point from which the phase of the reflected X-rays can be calculated.

No one was fully confident that the isomorphous replacement method would work in big proteins. With thousands of atoms in the haemoglobin molecule, how much effect could a single heavy atom really have? In 1953 Perutz received a paper that brought him closer to the answer. Austin Riggs from Harvard University was working on the blood disorder sickle cell anaemia, and he had discovered that introducing mercury atoms into haemoglobin did not affect its oxygen-carrying capacity. In other words the addition of mercury hadn’t changed the structure of haemoglobin.

This was the breakthrough that Perutz needed. He successfully attached two molecules of mercury to a single haemoglobin molecule by soaking haemoglobin crystals in mercury solutions, and took X-ray pictures of crystals from both haemoglobin and its mercury derivative. When Perutz developed these pictures in the summer of 1953, he could hardly contain himself. There were subtle differences in the diffraction patterns from the two haemoglobin crystals that would allow Perutz to derive the position of the mercury atoms, and from that the phases of one set of reflections in haemoglobin.

“I raced up three floors to Bragg’s office and asked him to come down to the darkroom,” Perutz later recalled. “As we looked at the two pictures, we realised that the phase problem which had baffled us for the past 16 years was at last solved.” Within one year, Perutz thought at the time, the haemoglobin structure would be solved.

Slow Success

In fact, it took six years for Perutz to come up with the first low-resolution structure of haemoglobin. As always the devil lies in the details, of which Perutz found many. Several heavy atom derivatives were needed to determine the phase angles, not to mention the difficulties in calculating calculations and constructing the coordinates oflocating all the atoms of haemoglobin.

John Kendrew, who had worked closely with Perutz for years, used the adaptations of the isomorphous replacement method to determine the structure of a smaller related protein, myoglobin, which carries oxygen to muscles. Myoglobin, at around 2,600 atoms, might be four times smaller than haemoglobin, yet Kendrew had to examine 110 crystals and measure the intensities of around 250,000 X-ray reflections to solve its structure.

For being the first to successfully identify the structures of complex proteins, Max Perutz and John Kendrew were rewarded with the Nobel Prize for Chemistry in 1962. Perhaps fate ensured that Perutz and Kendrew were joined by a very familiar face who received the Nobel Prize in Physiology or Medicine that year. As well as Maurice Wilkins and James Watson, the third Laureate receiving the Prize for his work on the structure of DNA was the daring and outspoken student who had fuelled Perutz’s desire to solve the phase problem, Francis Crick.


Blow, David. Outline of crystallography for biologists, Oxford University Press, 2002.

Brown, Andrew. J. D. Bernal. The Sage of Science (Oxford University Press, 2005).

Eisenberg, D. Max Perutz’s achievements: How did he do it? Protein Science 3, 1625–1628 (1994).

Ferry, Georgina. Max Perutz and the secret of life. Chatto & Windus, London, 2007.

Perutz, Max. X-ray analysis of haemoglobin. Nobel lecture, December 11, 1962.

Petsko, G. A. The father of us all. Genome Biology 3, comment 1004.1–1004.2 (2002).

Rhodes, D. Climbing mountains. A profile of Max Perutz 1914–2002: a life in science. EMBO Reports 3, 393–395 (2002).

Rossmann, M. G. The beginnings of structural biology. Protein Science 3, 1731–1733 (1994).

Tanford, Charles & Reynolds, Jacqueline. Nature’s robots. A History of Proteins. Oxford University Press, 2001.

Taylor, G. The phase problem. Acta Crystallographica D59, 1881–1890 (2003).

By Joachim Pietzsch, for

To cite this section
MLA style: Cracking the Phase Problem. Nobel Media AB 2018. Fri. 21 Sep 2018. <>

Back to top Back To Top Takes users back to the top of the page

Explore prizes and laureates

Look for popular awards and laureates in different fields, and discover the history of the Nobel Prize.