All posts tagged double helix

The Double Helix by James Watson (1968)

The short paper by James Watson and Francis Crick establishing the helical structure of the DNA molecule was published in the science journal, Nature, on April 25, 1953. The blurb of this book describes it as the scientific breakthrough of the 20th century. Quite probably, although it was a busy century – the discovery of antibiotics was quite important, too, not to mention the atom bomb.

James Watson and Francis Crick with their DNA model at the Cavendish Laboratories in 1953

Anyway, what makes this first-person account of the events leading up to the discovery such fun is Watson’s prose style and mentality. He is fearless. He takes no prisoners. He is brutally honest about his own shortcomings and everyone else’s and, in doing so, sheds extraordinarily candid light on how science is actually done. He tells us that foreign conferences where nobody speaks English are often pointless. Many scientists are just plain stupid. Some colleagues are useless, some make vital contributions at just the right moment.

Watson has no hesitation in telling us that, when he arrived in Cambridge in 1951, aged just 23, he was unqualified in almost every way – although he had a degree from the University of Chicago, he had done his best to avoid learning any physics or chemistry, and as a graduate student at Indiana he had also avoided learning any chemistry. In fact the book keeps referring to his astonishing ignorance of almost all the key aspects of the field he was meant to be studying.

The one thing he did have was a determination to solve the problem which had been becoming ever-more prominent in the world of biology, what is a gene? Watson says he was inspired by Erwin Schrödinger’s 1946 book, What Is Life? which pointed out that ‘genes’ were the key component of living cells and that, to understand what life is, we must understand what genes are and how they work. The bacteriologist O.T. Avery had already shown that hereditary traits were passed from one bacterium to another by purified DNA molecules, so this much was common knowledge in the scientific community.

DNA was probably the agent of hereditary traits, but what did it look like and how did it work?

Our hero gets a U.S. government research grant to go to Copenhagen to study with biochemist Herman Kalckar, his PhD supervisor Salvador Luria hoping the Dane would teach him something but… no. Watson’s interest wasn’t sparked, partly because Kalckar was working on the structure of nucleotides, which young Jim didn’t think were immediately relevant to his quest, also because Herman was hard to understand –

At times I stood about nervously while Herman went through the motions of a biochemist, and on several days I even understood what he said. (p.34)

A situation compounded when Herman began to undergo a painful divorce and his mind wandered from his work altogether.

It was a chance encounter at a conference in Naples that motivated Watson to seek out the conducive-sounding environment of Cambridge (despite the reluctance of his funding authorities back in the States to let him go so easily). John Kendrew, the British biochemist and crystallographer, at that point studying the structure of myoglobin, helped smooth his passage to the fens.

Head of the Cavendish Laboratory in Cambridge where Watson now found himself was Sir Lawrence Bragg, Nobel Prize winner and one of the founders of crystallography. The unit collecting X-ray diffraction photographs of haemoglobin was headed up by the Austrian Max Perutz, and included Francis Crick, at this stage (in 1951) 35-years-old and definitely an acquired taste. Indeed the famous opening sentence of the book is:

I have never seen Francis Crick in a modest mood.

followed by the observation that:

he talked louder and faster than anybody else, and when he laughed, his location within the Cavendish was obvious.

So he had found a home of sorts and, in Francis Crick, a motormouth accomplice who was also obsessed by DNA – but there were two problems.

  1. The powers that be didn’t like Crick, who was constantly getting into trouble and nearly got thrown out when he accused the head of the lab, Bragg, of stealing one of his ideas in a research paper.
  2. Most of the work on the crystallography of DNA was being done at King’s College, London, where Maurice Wilkins had patiently been acquiring X-rays of the molecule for nearly ten years.

There was a sub-problem here which was that Wilkins was being forced to work alongside Rosalind Franklin, an expert in X-ray crystallography, who was an independent-minded 31-year-old woman (b.1920) and under the impression that she had been invited in to lead the NA project. The very young Watson and the not-very-securely-based Crick both felt daunted at having to ask to borrow and interpret Wilkins’s material, not least because he himself would have to extract it from the sometimes obstreperous Franklin.

And in fact there was a third big problem, which was that Linus Pauling, probably the world’s leading chemist and based at Cal Tech in the States, was himself becoming interested in the structure of DNA and the possibility that it was the basis of the much-vaunted hereditary material.

Pauling’s twinkling eyes and dramatic flair when making presentations is vividly described (pp.37-8). Along the same lines, Watson later gives a deliberately comical account of how he is scoffed and ignored by the eminent biochemist Erwin Chargaff after making some (typically) elementary mistakes in basic chemical bonding.

It is fascinating to read the insights scattered throughout the book about the relative reputations of the different areas of science – physics, biology, biochemistry, crystallography and so on. Typical comments are:

  • ‘the witchcraft-like techniques of the biochemist’, p.63
  • ‘In England, if not everywhere, most botanists and zoologists were a muddled lot.’ p.63

In a typical anecdote, after attending a lecture in London given by Franklin about her work, Watson goes for a Chinese meal in Soho with Maurice Wilkins who is worried that he made a mistake moving into biology, compared to the exciting and well-funded world of physics.

The physics of the time was dominated by the aftershock of the massive wartime atom bomb project, and with ongoing work to develop both the H-bomb and peacetime projects for nuclear power.

During the war Wilkins had helped to develop improved radar screens at Birmingham, then worked on isotope separation at the Manhattan Project at the University of California, Berkeley. Now he was stuck in a dingy lab in King’s College arguing with Franklin almost every day about who should use the best samples of DNA and the X-ray equipment and so on. (Later on, Watson tells us Wilkins’ and Franklin’s relationship deteriorated so badly that he (Watson) was worried about lending the London team the Cambridge team’s wire models in case Franklin strangled Wilkins with them. At one point, when Watson walks in on Franklin conducting an experiment, she becomes so angry at him he is scared she’s going to attack him. Wilkins confirms there have been occasions when he has run away in fear of her assaulting him.)

It’s in this respect – the insights into the way the lives of scientists are as plagued by uncertainty, professional rivalry, and doubts about whether they’re in the right job, or researching the right subject, gnawing envy of more glamorous, better-funded labs and so on – that the book bursts with insight and human interest.

Deoxyribonucleic acid

By about page 50 Watson has painted vivid thumbnail portraits of all the players involved in the story, the state of contemporary scientific knowledge, and the way different groups or individuals (Wilkins, Franklin, Pauling, Crick and various crystallographer associates at the Cavendish) are all throwing around ideas and speculations about the structure of DNA, on bus trips, in their freezing cold digs, or over gooseberry pie at their local pub, the Eagle in Cambridge (p.75).

For the outsider, I think the real revelation is learning how very small the final achievement of Crick and Watson seems. Avery had shown that DNA was the molecule of heredity. Chergaff had shown it contained equal parts of the four bases. Wilkins and Franklin had produced X-ray photos which strongly hinted at the structure and the famous photo 51 from their lab put it almost beyond doubt that DNA had a helix structure. Pauling, in America, had worked out the helical structure of other long proteins and had now began to speculate about DNA (although Watson conveys his and Crick’s immense relief that Pauling’s paper on the subject, published in early 1953, betrayed some surprisingly elementary mistakes in its chemistry.) But the clock was definitely ticking very loudly, rivals were closing in on the answer, and the pages leading up to the breakthrough are genuinely gripping.

In other words, the final deduction of the double helix structure doesn’t come out of the blue; the precise opposite; from Watson’s account it seems like it would have only been a matter of time before one or other of these groups had stumbled across the correct structure.

But it is very exciting when Watson comes into work one day, clears all the clutter from his desk and starts playing around with pretty basic cardboard cutouts of the four molecules which, by now, had become strongly associated with DNA, adenine and guanine, cytosine and thymine.

Suddenly, in a flash, he sees how they assemble the molecules naturally arrange themselves into pairs linked by hydrogen bonds – adenine with thymine and cytosine with guanine.

For a long time they’d been thinking the helix had one strand at the core and that the bases stuck out from it, like quills on a porcupine. Now, in a flash, Watson realises that the the base pairs, which join together so naturally, form a kind of zip, and the bands of sugar-phosphates holding the thing together run along the outside – creating a double helix shape.

The structure of the DNA double helix. The atoms in the structure are colour-coded by element and the detailed structures of two base pairs are shown in the bottom right. (Source: Wikipedia)

Conclusion

I am not qualified to summarise the impact of the discovery of DNA has had on the world. Maybe it would take books to do so adequately. I’ll quote the book’s blurb:

By elucidating the structure of DNA, the molecule underlying all life, Francis Crick and James Watson revolutionised biochemistry. At the time, Watson was only 24. His uncompromisingly honest account of those heady days lifts the lid on the real world of great scientists, with their very human faults and foibles, their petty rivalries and driving ambition. Above all, he captures the extraordinary excitement of their desperate efforts to beat their rivals at King’s College to the solution to one of the great enigmas of the life sciences.

The science is interesting, but has been overtaken and superseded generations ago. It’s the characters and the atmosphere of the time (the dingy English rooms with no heating, the appalling English food), the dramatic reality of scientific competition, and then the genuinely exciting pages leading up to the breakthrough which makes Watson’s book such a readable classic.

Rosalind Franklin

I marked all the places in the text where a feminist might explode with anger. Both Watson, but even more Crick, assume pretty young girls are made for their entertainment. They are referred to throughout as ‘popsies’ and Crick in particular, although married, betrays an endless interest in the pretty little secretaries and au pairs which adorn Cambridge parties.

It is through this patronising and sexist prism that the pair judged the efforts of Franklin who was, reasonably enough, a hard-working scientist not at all interested in her appearance or inclined to conform to gender stereotypes of the day. She felt marginalised and bullied at the King’s College lab, and irritated by the ignorance and superficiality of most of Watson and Crick’s ideas, untainted as they were by any genuine understanding of the difficult art of X-ray crystallography – an ignorance which Watson, to his credit, openly admits.

Eventually, Franklin found working with Wilkins so intolerable that she left to take up a position at Birkbeck College and then, tragically, discovered she had incurable cancer, although she worked right up to her death in April 1958.

Franklin has become a feminist heroine, a classic example of a woman struggling to make it in a man’s world, patronised by everyone around her. But if you forget her gender and just think of her as the scientist called Franklin, it is still a story of misunderstandings and poisonous professional relations such as I’ve encountered in numerous workplaces. Watson and Crick’s patronising tone must have exacerbated the situation, but the fundamental problem was that she was given clear written instructions that she would be in charge of the X-ray crystallography at King’s College but then discovered that Wilkins thought he had full control of the project. This was a management screw-up more than anything else.

It does seem unfair that she wasn’t cited in the Nobel Prize which was awarded to Crick, Watson and Wilkins in 1962, but then she had died in 1958, and the Swedish Academy had a simple rule of not awarding the prize to dead people.

Still, it’s not like her name has disappeared from the annals of history. Quite the reverse:

Impressive list, don’t you think?

And anyone who hasn’t read the book might be easily persuaded that she was an unjustly victimised, patronised and ignored figure. But just to set the record straight, Watson chooses to end the entire book not with swank about his and Crick’s later careers, but with a tribute to Franklin’s character and scientific achievement.

In 1958, Rosalind Franklin died at the early age of thirty-seven. Since my initial impressions of her, both scientific and personal (as recorded in the early pages of this book), were often wrong, I want to say something here about her achievements. The X-ray work she did at King’s is increasingly regarded as superb. The sorting out of the A and B forms [of DNA], by itself, would have made her reputation; even better was her 1952 demonstration, using Patterson superposition methods, that the phosphate groups must be on the outside of the DNA molecule. Later, when she moved to Bernal’s lab, she took up work on tobacco mosaic virus and quickly extended our qualitative ideas about helical construction into a precise quantitative picture, definitely establishing the essential helical parameters and locating the ribonucleic chain halfway out from the central axis.

Because I was then teaching in the States, I did not see her as often as did Francis, to whom she frequently came for advice or when she had done something very pretty, to be sure he agreed with her reasoning. By then all traces of our early bickering were forgotten, and we both came to appreciate greatly her personal honesty and generosity, realising years too late the struggles that the intelligent woman faces to be accepted by a scientific world which often regards women as mere diversions from serious thinking. Rosalind’s exemplary courage and integrity were apparent to all when, knowing she was mortally ill, she did not complain but continued working on a high level until a few weeks before her death. (p.175)

That is a fine, generous and moving tribute, don’t you think? And as candid and honest as the rest of the book in admitting his and Crick’s complete misreading of her situation and character.

In a literal sense the entire book leads up to this final page [these are the last words of the book] and this book became a surprise bestseller and the standard source to begin understanding the events surrounding the discovery. So it’s hard to claim that her achievement was ‘suppressed’ or ‘ignored’ when this is the climax of the best-selling account of the story.

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1 Comment
by Simon on April 15, 2019  •  Permalink
Posted in Biology, Books, Chemistry, Science
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Posted by Simon on April 15, 2019

https://astrofella.wordpress.com/2019/04/15/the-double-helix-james-watson/

Nature’s Numbers by Ian Stewart (1995)

Ian Stewart is a mathematician and prolific author, having written over 40 books on all aspects of maths, as well as publishing several guides to the maths used in Terry Pratchett’s Discworld books, writing half a dozen textbooks for students, and co-authoring a couple of science fiction novels.

Stewart writes in a marvellously clear style but, more importantly, he is interesting: he sees the world in an interesting way, in a mathematical way, and manages to convey the wonder and strangeness and powerful insights which seeing the world in terms of patterns and shapes, numbers and maths, gives you.

He wants to help us see the world as a mathematician sees it, full of clues and information which can lead us to deeper and deeper appreciation of the patterns and harmonies all around us. It makes for a wonderfully illuminating read.

1. The Natural Order

Thus Stewart begins the book by describing just some of nature’s multitude of patterns: the regular movements of the stars in the night sky; the sixfold symmetry of snowflakes; the stripes of tigers and zebras; the recurring patterns of sand dunes; rainbows; the spiral of a snail’s shell; why nearly all flowers have petals arranged in one of the following numbers 5, 8, 13, 21, 34, 55, 89; the regular patterns or ‘rhythms’ made by animals scuttling, walking, flying and swimming.

2. What Mathematics is For

Mathematics is brilliant at helping us to solve puzzles. It is a more or less systematic way of digging out the rules and structures that lie behind some observed pattern or regularity, and then using those rules and structures to explain what’s going on. (p.16)

Having gotten our attention, Stewart trots through the history of major mathematical discoveries including Kepler discovering that the planets move not in circles but in ellipses; the discovery that the nature of acceleration is ‘not a fundamental quality, but a rate of change’, then Newton and Leibniz inventing calculus to help us work outcomplex rates of change, and so on.

Two of the main things that maths are for are 1. providing the tools which let scientists understand what nature is doing 2. providing new theoretical questions for mathematicians to explore further. These are handy rules of thumb for distinguishing between, respectively, applied and pure mathematics.

Stewart mentions one of the oddities, paradoxes or thought-provoking things that crops up in many science books, which is the eerie way that good mathematics, mathematics well done, whatever its source and no matter how abstract its origin, eventually turns out to be useful, to be applicable to the real world, to explain some aspect of nature.

Many philosophers have wondered why. Is there a deep congruence between the human mind and the structure of the universe? Did God make the universe mathematically and implant an understanding of maths in us? Is the universe made of maths?

Stewart’s answer is simple and elegant: he thinks that nature exploits every pattern that there is, which is why we keep discovering patterns everywhere. We humans express these patterns in numbers, but nature doesn’t use numbers as such – she uses the patterns and shapes and possibilities which the numbers express or define.

Mendel noticing the numerical relationships with which characteristics of peas are expressed when they are crossbred. The double helix structure of DNA. Computer simulations of the evolution of the eye from an initial mutation creating a patch of skin cells sensitive to light, published by Daniel Nilsson and Susanne Pelger in 1994. Pattern appears wherever we look.

Resonance = the relationship between periodically moving bodies in which their cycles lock together so that they take up the same relative positions at regular intervals. The cycle time is the period of the system. The individual bodies have different periods. The moon’s rotational period is the same as its revolution around the earth, so there is a 1:1 resonance of its orbital and rotational periods.

Mathematics doesn’t just analyse, it can predict, predict how all kinds of systems will work, from the aerodynamics which keep planes flying, to the amount of fertiliser required to increase crop yield, to the complicated calculations which keep communications satellites in orbit round the earth and therefore sustain our internet and mobile phone networks.

Time lags The gap between a new mathematical idea being developed and its practical implementation can be a century or more: it was 17th century interest in the mathematics of vibrating violin strings which led, three hundred years later, to the invention of radio, radar and TV.

3. What Mathematics is About

The word ‘number’ does not have any immutable, God-given meaning. (p.42)

Numbers are the most prominent part of mathematics and everyone is taught arithmetic at school, but numbers are just one type of object that mathematics is interested in.

Stewart outlines the invention of whole numbers, and then of fractions. Some time in the Dark Ages the invention of 0. The invention of negative numbers, then of square roots. Irrational numbers. ‘Real’ numbers.

Whole numbers 1, 2, 3… are known as the natural numbers. If you include negative whole numbers, the series is known as integers. Positive and negative numbers taken together are known as rational numbers. Then there are real numbers and complex numbers. Five systems in total.

But maths is also about operations such as addition, subtraction, multiplication and division. And functions, also known as transformations, rules for transforming one mathematical object into another. Many of these processes can be thought of as things which help to create data structures.

Maths is like a landscape in which similar proofs and theories cluster together to create peaks and troughs.

4. The Constants of Change

Newton’s basic insight was that changes in nature can be described by mathematical processes. Stewart explains how detailed consideration of what happens to a cannonball fired out of a cannon helps us towards Newton’s fundamental law, that force = mass x acceleration.

Newton invented calculus to help work out solutions to moving bodies. Its two basic operations – integration and differentiation – mean that, given one element – force, mass or acceleration – you can work out the other two. Differentiation is the technique for finding rates of change; integration is the technique for ‘undoing’ the effect of differentiation in order to isolate out the initial variables.

Calculating rates of change is a crucial aspect of maths, engineering, cosmology and many other areas of science.

5. From Violins to Videos

He gives a fascinating historical recap of how initial investigations into the way a violin string vibrates gave rise to formulae and equations which turned out to be useful in mapping electricity and magnetism, which turned out to be aspects of the same fundamental force, electromagnetism. It was understanding this which underpinned the invention of radio, radar, TV etc and Stewart’s account describes the contributions made by Michael Faraday, James Clerk Maxwell, Heinrich Hertz and Guglielmo Marconi.

Stewart makes the point that mathematical theory tends to start with the simple and immediate and grow ever-more complicated. This is because of a basic approach common in lots of mathematics which is that, you have to start somewhere.

6. Broken Symmetry

A symmetry of an object or system is any transformation that leaves it invariant. (p.87)

There are many types of symmetry. The most important ones are reflections, rotations and translations.

7. The Rhythm of Life

The nature of oscillation and Hopf bifurcation (if a simplified system wobbles, then so must the complex system it is derived from) leads into a discussion of how animals – specifically animals with legs – move, which turns out to be by staggered or syncopated oscillations, oscillations of muscles triggered by neural circuits in the brain.

This is a subject Stewart has written about elsewhere and is something of an expert on. Thus he tells us that the seven types of quadrupedal gait are: the trot, pace, bound, walk, rotary gallop, transverse gallop, and canter.

8. Do Dice Play God?

This chapter covers Stewart’s take on chaos theory.

Chaotic behaviour obeys deterministic laws, but is so irregular that to the untrained eye it looks pretty much random. Chaos is not complicated, patternless behaviour; it is much more subtle. Chaos is apparently complicated, apparently patternless behaviour that actually has a simple, deterministic explanation. (p.130)

19th century scientists thought that, if you knew the starting conditions, and then the rules governing any system, you could completely predict the outcomes. In the 1970s and 80s it became increasingly clear that this was wrong. It is impossible because you can never define the starting conditions with complete certainty.

Thus all real world behaviours are subject to ‘sensitivity to initial conditions’. From minuscule divergences at the starting point, cataclysmic differences may eventually emerge in mature systems.

Stewart goes on to explain the concept of ‘phase space’ developed by Henri Poincaré: this is an imaginary mathematical space that represents all possible motions in a given dynamic system. The phase space is the 3-D place in which you plot the behaviour in order to create the phase portrait. Instead of having to define a formula and worrying about identifying every number of the behaviour, the general shape can be determined.

Much use of phase portraits has shown that dynamic systems tend to have set shapes which emerge and which systems move towards. These are called attractors.

9. Drops, Dynamics and Daisies

The book ends by drawing some philosophical conclusions.

Chaos theory has all sorts of implications but the one Stewart closes on is this: the world is not chaotic; if anything, it is boringly predictable. And at the level of basic physics and maths, the laws which seem to underpin it are also schematic and simple. And yet, what we are only really beginning to appreciate is how complicated things are in the middle.

It is as if nature can only get from simple laws (like Newton’s incredibly simple law of thermodynamics) to fairly simple outcomes (the orbit of the planets) via almost incomprehensibly complex processes.

To end, Stewart gives us three examples of the way apparently ‘simple’ phenomena in nature derive from stupefying complexity:

  • what exactly happens when a drop of water falls off a tap
  • computer modelling of the growth of fox and rabbit populations
  • why petals on flowers are arranged in numbers derived from the Fibonacci sequence

In all three cases the underlying principles seem to be resolvable into easily stated laws and functions – and in our everyday lives we see water dropping off taps or flowerheads all the time – and yet the intermediate steps between simple mathematical principles and real world embodiment turn out to be mind-bogglingly complex.

Coda: Morphomatics

Stewart ends the book with an epilogue speculating, hoping and wishing for a new kind of mathematics which incorporates chaos theory and the other elements he’s discussed – a theory and study of form, which takes everything we already know about mathematics and seeks to work out how the almost incomprehensible complexity we are discovering in nature gives rise to all the ‘simple’ patterns which we see around us. He calls it morphomatics.

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2 Comments
by Simon on March 31, 2019  •  Permalink
Posted in Books, Mathematics
Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , ,

Posted by Simon on March 31, 2019

https://astrofella.wordpress.com/2019/03/31/natures-numbers-ian-stewart/

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