A hundred years ago – the Hill equation

Posted on May 27, 2010 by Austin

I have been meaning to post this piece for ages, but never seem to find the time to do the necessary re-writes! Since there is now a small lull before I get submerged under the next wave of exam marking, I have finally got round to it. It is adapted from an article I wrote for Physiology News, though I have changed some bits, and added the hyperlinks.

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Teaching students one often finds, as I have said before, that even ten years ago is viewed as “from the ark”. Of course, there was science being done a hundred, or a hundred and fifty years ago, let alone ten. In physiology one can easily find key scientific discoveries that underpin much of the modern subject in the journals of a century and more back, all reported in ways that are quite recognisable to a modern eye.

For a few years now I have been writing a regular article series which takes a look back at papers in the physiology journals exactly one hundred years ago. Here is one such. It deals with one of the earliest works of AV Hill, who we have discussed before over at Stephen Curry’s blog.

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AV Hill, probably photographed in his late 20s or early 30s.

AV Hill (1910)

“The possible effects of the aggregation of the molecules of hæmoglobin on its dissociation curves”

 

 

J Physiol 40 Suppl, iv-vii

First, a bit of background – The Physiological Society is famous, at least in part, for its meetings. And its dinners… In a post back in the Autumn about Charles Darwin and the late Victorian physiologists, I touched on the founding of the Society in 1876. The Physiological Society started as essentially a gentlemens’ dining club, with scientific papers being read before a substantial dinner at a London Club or restaurant.

Almost all the meeting books of the Society survive, so that one can trace the activities of various scientists – both the then-famous, and the later to be so – through the pages. [Links to more (much, much more) history about the Society can be found here ]. The Society also founded a journal – the Journal of Physiology, first published in March 1878. The papers read to the society at the meetings appeared in a special supplementary volume called the Proceedings .

Anyway, enough preamble:

Let me take you to the Proceedings for 1910, and a meeting of the Physiological Society that took place at King’s College London on January 22nd 1910. The meeting marks the first one attended, and first communication to The Society – one of only three papers in total read at the meeting! – of AV Hill (1886-1977), Nobel Laureate, doyen of British biophysicists, and giant of 20th century physiology. And also, of course, the originator of the Hill Equation, and the Hill coefficient, the guise in which non-physiologists are perhaps most likely to encounter him today.

Hill (christened Archibald Vivian, though he disliked both names and was always known as ‘AV’) was just twenty-three at the time on the 1910 meeting. He was working in the Cambridge Physiological Laboratory, having taken his Physiology degree final exams there the previous summer (1909) and his Mathematics finals two years earlier. He had published one single paper, the previous month (Dec 1909) in the Journal of Physiology. He was not yet a member of the Physiological Society (he was not elected until two years later, in 1912) and was introduced for the King’s meeting by his friend the respiratory physiology Joseph Barcroft.

Hill’s main scientific interest through his career, and the one that was to earn him the Nobel prize, was heat production in muscle, and muscle energetics and contraction. However, his earliest work on a number of diverse problems foreshadowed one of his wider contributions, the bringing of mathematics and quantitative thinking to physiology. Hill’s protégé Bernard Katz describes this in his Oxford Dictionary of National Biography entry on Hill:

”[Hill’s] first published papers were concerned mainly with a theoretical and quantitative analysis of experimental results obtained by himself and his senior colleagues in the Cambridge laboratory. They included an analysis of drug action in muscle tissue, of the reaction between oxygen and haemoglobin, and of the effects of electric stimuli on nerves.

Although Hill later regarded this work as being of little importance, it contained the first mathematical formulation of drug kinetics later generally known as the Michaelis-Menten or Langmuir equation. It also introduced the concept of co-operativity in complex chemical reactions, signified by a quantity which was widely referred to as the Hill coefficient.”

David Colquhoun, in an interesting article on the origins of quantitative approaches to drug-receptor interactions, gives a nice account of Hill’s December 1909 paper, which derived the Langmuir adsorption equation some ten years before Langmuir, and the January 1910 communication.

Hill derived the equations that would govern a reversible association between haemoglobin and a ligand, and compared these to the experimental oxygen dissociation curves measured by Barcroft and others. Hill sets out what would subsequently be known as the Hill equation, describing the fraction of the macromolecule saturated by ligand as a function of the ligand concentration. Hill’s equations also took into account possible self-association (multimerization, as we would now say) of haemoglobin. The resulting successive ligand (oxygen) binding events to multiple haemoglobin units give rise to what would eventually become known as the Hill coefficient.

Colquhoun notes that Hill (presciently?) did not attempt to ascribe precise physical meanings to the parameters in his equation:

“My object was rather to see whether an equation of this type can satisfy all the observations, than to base any direct physical meaning on [the parameters]”.

Colquhoun drily adds: “His caveat has often been forgotten since then.”

A.V. Hill – the man and his science

Speaking many years later about how he had come to take up physiology, Hill said:

“A short answer… is, because Walter Morley Fletcher was my tutor at Trinity [College]…During my first year [at Cambridge] I began to lose interest in some of the things [in mathematics] that to me seemed rather remote from reality and hankered after something more practical. I realize now that I was much better fitted to engineering than to mathematics, but physiology proved in the end to be much like engineering, being based on the same ideas of function and design.”

Fletcher persuaded Hill to complete his Mathematics degree before pursuing new directions. As Hill tells us:

“In 1907 I took the Mathematical Tripos [Final year exams], which in those days was an extraordinary business, with fourteen three-hour papers and great public interest as to who would be Senior Wrangler [i.e. achieve the top mark of the year]. It was too much like the Grand National with all its obstacles. I did quite respectably in fact [Hill finished third in the class], but nobody encouraged me to go on with it; which was a very good thing. So I sought Fletcher’s advice again, and decided soon to become a physiologist.”

In the summer of 1910 Hill published the first instalment of his scientific life’s work on muscle energetics (Hill, 1910). This work was to culminate in the Nobel Prize in 1923 – though ‘culminate’ is perhaps the wrong word, given that Hill continued to publish papers on muscle energetics until the early 1960s (the last ones in J Physiol., in 1961 and 1962, with his final PhD student Roger Woledge).

Though Hill is often associated with University College London, the institution where he spent all his later career (after 1923), the Nobel Committee honoured him for his muscle work carried out in Cambridge (1909-19) and Manchester (1920-23). During the Manchester years Hill, who had been a keen athlete, developed a parallel interest in human exercise physiology, and is credited with originating the idea of ‘oxygen debt’.

Hill married into the Keynes academic dynasty (his wife Margaret was the sister of the economist John Maynard Keynes, and aunt to Professor Richard Keynes). Among Hill’s four children, his son David or ‘DK’ Hill (1915-2002) followed in his father’s footsteps to become a muscle physiologist, Professor and FRS. Nicholas Humphrey, Hill’s grandson, has written a touching memoir of helping his grandfather with his experiments as a child in the early 1960s in a chapter of the book Curious Minds: How a Child Becomes a Scientist.

Outside the laboratory

AV Hill was an early example of a scientist who engaged in many spheres beyond the laboratory, and it would take a decent-sized book to do justice to even a selection of his activities. He worked in wartime ‘operational’ research in both World Wars, and was an independent MP for Cambridge University during the Second War. He served The Physiological Society and Royal Society in many capacities, and was an early populariser of science, giving the 1926 Royal Institution Christmas Lectures. Perhaps the ‘extracurricular’ activity for which he is most remembered is his leading role in the 1930s in the Academic Assistance Council which helped Jewish academics flee from the Nazis.

Hill had used his Thomas Huxley Memorial lecture in November 1933 to denounce the Nazi persecution of the Jewish people, especially of scientists who had been forced out of Germany. This triggered an extended argument, in the pages of Nature in early 1934, with the German physics Nobelist Johannes Stark who had become an enthusiastic Nazi. Stark insisted that Jews were not being persecuted, only people guilty of “high treason” against the Nazi state. Hill’s response was withering:

“With Prof. Stark’s political anti-Semitism I need not deal… it appears absurd. It is a fact, in spite of what he says, that many Jews or part-Jews have been dismissed from their posts in universities … No doubt in Germany, after this reply, my works in the Journal of Physiology and elsewhere will be burned.”

The correspondence famously ended with Hill commenting, with characteristic dry wit, that since his previous letter he had received many donations to help the AAC’s cause – but he felt he could not really take the credit, as the donors’ generosity surely owed something to Stark’s (racist-ideological) arguments. Bernard Katz, himself a Jewish refugee from the Nazis, sought Hill out partly because of the correspondence (see e.g. here, and would later write that the letters:

“Gave me the first glimpse of A.V. Hill’s personality…[which] I found… so attractive that I made every effort to go and work with him”.

Katz also quoted a favourite saying of Hill’s:

“Laughter is the best detergent of nonsense”.

The definitive scientific biographical source on Hill is Bernard Katz’s monumental (78 page!) Royal Society Biographical Memoir; for a shorter introduction Katz’s DNB entry is a useful starting point.

References

Colquhoun D (2006). Trends Pharmacol Sci 27, 149-157.

Hill AV (1909). J Physiol 39, 361-373.

Hill AV (1910). J Physiol 40, 389-403.

Hill AV (1969). J Physiol 204, 1-13.

Katz B (1978). Biogr Mem Fellows R Soc 24, 71-149.

Posted in History, Physiology | Tagged | 2 Comments

Funding the elite is not the real problem

Posted on May 6, 2010 by Austin

I have a guest blog over at the Times Online today (May 6th):

A response to Sir Paul Nurse: it’s not only the elite who are feeling the strain

Note: May 17th – I’ve now posted the whole thing here (with minor updates) in case it got rather lost amid the Election Day fever. And in the hope it will encourage a few more readers, and particular commenters

Sir Paul Nurse’s remarks about science funding, widely reported a couple of weeks ago just after the announcement that he was likely to become the next President of the Royal Society, ruffled a few feathers amid the rank and file of UK science. Nurse was describing his view that a scheme for “no strings” funding of a small number of elite scientists, modelled on the Howard Hughes Medical Institute in the US, would be a good idea.

Several critiques of Nurse’s remarks have appeared in the science blogosphere (e.g. by Bob O’Hara at Nature Network, or here, or by Sylvia McClain here). Some have pointed out that elite scientists are actually already likely to be among the best-funded in the country. Others, in similar vein, have noted that a variety of schemes offering longer-term, and sometimes renewable, research funding already exist (see, for instance, the Wellcome Trust’s switch to “Investigator Awards” for staff in established posts). In many comments is an undercurrent that any funding for such schemes would necessarily reduce the “response mode funding pool” – the pot of money which funds most scientific research in the UK, and which scientists compete for by writing grant applications for specific projects, usually of 3 years duration.

However, the misgivings evoked by Nurse’s remarks also reflect, I think, a deeper underlying worry among UK scientists. This is that his thoughts are directed at something which most of us think is a side issue. In the minds of most scientists in UK universities that I know, the key problem facing UK science is the unsustainability of a system where almost all scientists are required to spend more and more time filling in grant application forms, and less and less time doing science.

I have been working in UK science for a quarter of a century, give or take. Over that period the fraction of scientists’ time that goes on chasing funding – writing research grants – has increased inexorably. The other thing that has changed is the ability to do research in universities if you do not have a sizeable research grant; this has vastly decreased to the point of being close to none. Funding that comes directly through Universities nowadays underpins academics’ salaries and some infrastructure only, with little or nothing to meet the direct costs of doing research.

This second change also goes some way to explaining the first change, since without a research grant these days a scientist in many disciplines is basically dead in the water. They will have no lab technician to support their work – nowadays technicians only come with successful grants. They will also be less likely to have a PhD student; many departments prefer to send students to labs with grants, on the unsurprising grounds that without any grant funds the lab will struggle to support the cost of the student’s experimental work. Other PhD students are funded off -you guessed it -grants.

In football and in science, relegation is too often a one-way street

Having the 3 or 4 year research grant run out in British science nowadays is akin to getting relegated from the Premier League in football; you have one, perhaps two years to get back on track before the “parachute payment” – the papers derived from the last grant – run out. After that the climb back up again will become incredibly difficult. So the reality is that people in this setting will do no science whatsoever while they desperately scramble for funding.

This would not matter so much if the chance of success in the grant system was something people could live with. But the current overall grant application success rate is around 20%, or one in five. And for most labs the “effective” rate will be considerably less than that. This is because grants at the top end of the pile (from “elite 50” labs, or people with a super-hot project or a recent super-hot paper) will have a much higher change of funding. So it is widely believed that the success rate for ordinary mortals – which means most of the professional scientists working in UK universities – is well below the one in five figure.

And with most people viewing deep cuts in public spending as inevitable, no scientist believes the success rate – or the total number of projects funded – is going to rise. Every single one I have talked to expects it to fall. In other words, the days of “a one in ten chance” of being funded, if they are not already with us, are in sight.

This is not, I should make clear, to say that competition for grant funding is a bad thing. Some sifting of research proposals in competition is clearly necessary – it is a key part of ensuring that poorly-thought-out ideas are sifted out, and that the available money is spent wisely. However, “some competition is good” does not equate to “more competition is necessarily always better“. If one goes down that road, one eventually reaches a point where all time is devoted to the act of competing and no time to anything else.

“Get funded or die trying”

And here lies the problem. The current “get funded or die trying” grant chase, with its dismal success rate, devours the time and energy of academic scientists. It is particularly harsh on those in their first five years a university job. This is the stage directly after you have spent the best part of a dozen years learning to be a first-rate professional scientist. At which point, people have to stop being scientists, and have to become deal-makers, paper pushers, and indefatigable salesmen. One of the starkest accounts of this is given by the Cambridge academic Peter Lawrence, who subtitled his October 2009 article in the journal PLoS Biology

“The granting system turns young scientists into bureaucrats and then betrays them”

Another analogy might be spending ten to fifteen years training a consultant surgeon, and then making sure he or she spends almost all their time, not operating, but instead writing proposals to get someone to give them the money to pay an assistant surgeon do their operating for them.

The relentless competition, and the morale-sapping and attrition of those who are unsuccessful, also means a decreased “diversity” of the UK research base. Unfashionable research areas, or experimental techniques, gradually disappear as those in them fail to get funded. If it is possible to keep going in a minimal way without a big grant, such labs can keep slowly ticking over and the skills and ideas they have developed do not die out. But if the labs need a grant to survive at all, they go under. And if the fashion later changes – then you have to set up special new initiatives to re-train scientists in the lost skills, since the older scientists who used to teach people these things are now retired or not doing research any more. If this scenario seems far-fetched, it has already happened in the UK for “in vivo” skills – that is, the skills to do experiments on anaesthetized animals – and probably for other things too.

The only way to increase the present unsustainable grant success rate, it seems to me, is to decrease the number of applications relative to the amount of available funding. Some universities have already decided how they are going to address this – by trying to retire or make redundant the staff without research grants.

Of course, this strategy means that the typically large amount of teaching and university paperwork done by these people will then fall increasingly on the staff that do have the research grants. It is not a scenario that is set to make anyone happy. I also doubt it will raise the grant success rate, or the rate of scientific discovery.

There is an alternative. It is to look to a time before the grant chase became mandatory. When I started working in British universities, people still carried out, and published, high-quality research funded on a modest budget via the University itself. They also trained graduate students. More ambitious or upwardly-mobile people also applied for external research grants, as now.

The major objections to this old system, largely retrospective, were seen to be unaccountability and that it fostered, and indeed funded, complacency. However, is the present system, with its funding of (at best) one in five, and probably more like one in ten, research proposals, an improvement? Not as far as I can see.

So what to do?

Here is a vaguely radical proposal. I would suggest that ALL academic post-holders in UK science departments that are rated above a certain research attainment threshold should receive a minimal level of baseline research funding – say £5,000 to £15,000 per year. This would be “seed-corn” research funding to enable people to do stuff, whether “bridging” a research assistant’s salary for a month or two, subsidising a PhD student’s work, replacing equipment, funding their own experiments – whatever. I have lost count of the academic scientists I know who tell me that they are stymied because the grant has run out and they don’t have the money, or personnel, to wrap up the experimental work and publish it until they get another grant. A scheme of this kind would directly address this problem.

If this seems far-fetched, consider the current hidden cost of the response-mode system with its one-in-five to one-in-ten success rates. Writing grants takes time. A lot of time, And time means salary costs. A recent study by two Canadian academics concludes that the cost of the grant system, and the time spent penning fruitless applications, exceeds the cost of simply giving every qualifying University scientist in Canada £20,000.

I am not even suggesting baseline funding at this level – just some seeding money which would “lubricate” the system, and potentially reduce the number of desperate applications overloading the response mode grant system. One could also imagine various refinements to a baseline funding system like this – “banding” the direct support depending on past productivity would be one obvious idea.

Of course this sort of scheme would necessarily take some money out of the “response mode” pool. But at least this way it would be spread more widely, and into places where it would likely have more effect than a system which currently tends, by its nature, to reward those with the most funding by giving them even more of it. Most scientists do not believe, I suggest, that key advances arise predictably from the “top 50”, or even one hundred, labs. And few would believe that giving a sixth large grant to a lab which already has five achieves more than giving five small grants to labs with none, or second grants to labs with one. Indeed, one of the UK’s traditional science strengths has been precisely doing good science with small amounts of funding. Smaller labs do good science. They also still train most of the country’s PhDs. They are just as necessary to the “health” of the UK scientific enterprise as are the elite. And they are under threat.

Anyway, Sir Paul Nurse’s remarks suggest that he worries about the effect of having to pitch repeatedly for money, and be tied to targets, on the UK’s scientific elite. But the problem is far wider that that. I hope that, if he becomes Royal Society president, he will be looking to lobby for more than just the Manchester Uniteds and Chelseas of the system. UK science needs its mid-table, Championship, and League One and Two sides as well.

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Quantum homeopathic flapdoodle

Posted on April 20, 2010 by Austin

I had wanted to post something for World Homeopathy Awareness Week (WHAW), which ended a few days ago.

However, I have been hampered by the fact that, whenever I think about writing anything more about homeopathy, I tend to find myself losing conciousness. Or the will to live.

This partly reflects just how many words – undoubtedly running into tens of thousands – I have expended on homeopathy in other places – right back to around four years ago when I started commenting on Ben Goldacre’s Bad Science blog.

And, of course, my fellow-bloggers Stephen Curry and Richard Grant have already signposted WHAW here at NN. Not to mention Kausik Datta, who is partway through a multi-post broadside.

But I would still like to do my little bit to mark the occasion.

And also – the comments on Stephen’s blogpost reminded me that there always remain hard-core enthusiasts for Alternative Medicine Realities, people whom nothing could ever “un-convince”.

And, of course, there also remain people in science who can always use a small reminder of just how far from their world a fair number of the Alternative Medicine Reality people are.

So I thought I would give you a small literature comprehension exercise.—————————————————————————————————————————-

Unreality Detection 101

You are provided with the URLs of two freely accessible online papers concerning quantum mechanical descriptions of homeopathy.

Paper A – Is a Unified Theory of Homeopathy and Conventional Medicine Possible?

Paper B – Towards a Quantum Mechanical Interpretation of Homeopathy

One of the two is a spoof.

One of them is not.

After reading briefly through as much of the papers as you find necessary, answer the following questions:

1. A scientist or scientists with a PhD wrote
A   paper A
B   paper B
C   both paper A and paper B

2. The spoof paper
A   depends which universe you are in
B   is paper A
C   is paper B

3. The likelihood that a homeopath can tell which paper is the spoof is
A   high
B   low
C   homeopathically dilute

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In case you were wondering, question three is set because homeopaths posting pro-homeopathy links on Twitter have linked approvingly to both of the above papers as:

“Evidence that homeopathy works by quantum mechanics”

Following which, any comment seems superfluous.

Though here’s one. Finally, whenever I think about homeopathy, the following line always floats back into my mind:

“Only two things are infinite…..

…the universe and human folly.”

“And I’m not sure about the universe.”

(Attributed to Albert Einstein)

Posted in Annoyances, Humour, Medicine, Pseudoscience | Tagged | 5 Comments

Pioneer of muscle contraction

Posted on March 24, 2010 by Austin

My own small contribution to Ada Lovelace Day…

Students tend to think that discoveries underpinning what they get taught in first year lectures were made long, long ago, by ancient scientists long-dead.

Of course, this is not true in “young” disciplines. Some of the founders of molecular biology are still with us, for instance. And though now fairly old, they are not all much older than me than I am older than my students (if you see what I mean).

The “long-dead discoverers” is also not necessarily true in what one might think of as older (“more mature”?) disciplines like physiology/biophysics.
edited 54 Nature AUs.jpg
Here is a picture I show to first and second year undergraduate students when I teach them muscle contraction. It is culled from the cover of Nature a few years ago (2004), and appeared as part of a celebration of the 50th anniversary of the sliding filament theory of muscle contraction, published in two back-to-back papers in Nature in 1954. You can find more on this here.

Among the things I tell the students is that three of the people in the picture are still alive, these being, from left to right, Rolf Niedergerke, Sir Andrew Huxley, and Hugh Huxley.

The only one not around is Jean Hanson, at the bottom right. Hanson, born in 1919 in Derbyshire and a graduate of Bedford College London, worked at the MRC Biophysics Unit at King’s College, founded after WW2 by the physicist John Randall. She became Professor of Biology at the University of London in 1966, was elected FRS in 1967 and ultimately succeeded Randall as head of the unit in 1970. Tragically, she died in 1973 after contracting meningitis. She was only 54.

The sliding filament theory is a landmark in biology, hence the Nature 50th Anniversary coverage (including a perspective by a certain Maxine Clark, which is here if you are a Nature subscriber).

As with many things that reach the textbooks, it is perhaps not remembered so much now that, like any new theory, the sliding filament hypothesis, and the implied co-ordinated macromolecular motion, took a while to get accepted. Here is one account featuring Hanson:
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“When Jean Hanson spoke at the Symposia of the Society for Experimental Biology held at Leeds in September 1954, William Astbury and other physicists were all negative about the concept of the directional movement of filaments. Even in the early 1960s when a symposium of biomacromolecules was held in Pittsburgh, PA, most physical chemists including Paul Flory (1910-1985; Nobel Prize for Chemistry, 1974) strongly objected to the directionality of the filament movement. The writer still remembers Jean Hanson shouting: “I know I cannot explain the mechanism yet, but the sliding is a fact.”“

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Coming back to the picture of the four sliding filament pioneers: Jean Hanson was also my father’s PhD supervisor. So I get to tell the students that I have actually met all four of the people in the picture. My father always says he owed a great deal to Jean Hanson’s teaching and friendship. I don’t know if it was her influence, but a lot of the people who worked in my father’s laboratory and who he helped train over the years were female, including his first ever postdoc, Ada Yonath, and his first PhD student after he became Professor at the Open University, Julia Goodfellow.

Sadly, Jean Hanson’s early death, and the (slightly surprising) fact that no Nobel Prize has ever been awarded for the sliding filament theory, means that she is less well known that other women biophysics pioneers of the early post-war era, such as Rosalind Franklin (who of course also died tragically young) and Dorothy Hodgkin. However, you can read more about Hanson’s life and work on a section of the King’s College London archives website here.

Posted in History, Uncategorized | Tagged | 11 Comments