{"id":126,"date":"2010-05-27T22:30:24","date_gmt":"2010-05-27T22:30:24","guid":{"rendered":"http:\/\/occamstypewriter.org\/notranting\/2010\/05\/27\/a_hundred_years_ago_-_the_hill_equation\/"},"modified":"2012-10-22T13:24:09","modified_gmt":"2012-10-22T13:24:09","slug":"a_hundred_years_ago_-_the_hill_equation","status":"publish","type":"post","link":"https:\/\/occamstypewriter.org\/notranting\/2010\/05\/27\/a_hundred_years_ago_-_the_hill_equation\/","title":{"rendered":"A hundred years ago – the Hill equation"},"content":{"rendered":"

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,<\/a> though I have changed some bits, and added the hyperlinks.<\/span><\/p>\n

\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014—–<\/p>\n

Teaching students one often finds,<\/strong> as I have said before, that even ten years ago is viewed as \u201cfrom the ark\u201d<\/span>. 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.<\/p>\n

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,<\/a> who we have discussed before over at Stephen Curry\u2019s blog<\/a>.<\/p>\n

\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014<\/p>\n

\"\"<\/a>

AV Hill, probably photographed in his late 20s or early 30s.<\/p><\/div>\n

AV Hill (1910)<\/strong><\/big><\/p>\n

\u201cThe possible effects of the aggregation of the molecules of h\u00e6moglobin on its dissociation curves\u201d<\/big><\/p>\n

 <\/p>\n

 <\/p>\n

J Physiol<\/em> 40<\/strong> Suppl<\/a>, iv-vii<\/big><\/p>\n

First, a bit of background \u2013 The Physiological Society is famous, at least in part, for its meetings. And its dinners\u2026 In a post back in the Autumn<\/a> 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\u2019 dining club, with scientific papers being read before a substantial dinner at a London Club or restaurant.<\/p>\n

Almost all the meeting books of the Society survive, so that one can trace the activities of various scientists \u2013 both the then-famous, and the later to be so \u2013 through the pages. [Links to more (much, much more) history about the Society can be found here<\/a> ]. The Society also founded a journal \u2013 the Journal of Physiology<\/em>, first published in March 1878. The papers read to the society at the meetings appeared in a special supplementary volume called the Proceedings<\/em> .<\/p>\n

Anyway, enough preamble:<\/strong><\/p>\n

Let me take you to the Proceedings<\/span><\/em> for 1910, and a meeting of the Physiological Society that took place at King\u2019s College London on January 22nd 1910. <\/span>The meeting marks the first one attended, and first communication to The Society \u2013 one of only three papers in total read at the meeting! \u2013 of AV Hill<\/a> (1886-1977), Nobel Laureate, doyen of British biophysicists, and giant of 20th century physiology. And also, of course, the originator of the Hill Equation<\/a>, and the Hill coefficient, the guise in which non-physiologists are perhaps most likely to encounter him today.<\/p>\n

Hill (christened Archibald Vivian, though he disliked both names and was always known as \u2018AV\u2019) 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<\/em>. 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\u2019s meeting by his friend the respiratory physiology Joseph Barcroft<\/a>.<\/p>\n

Hill\u2019s main scientific interest through his career, and the one that was to earn him the Nobel prize<\/a>, 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\u2019s prot\u00e9g\u00e9 Bernard Katz<\/a> describes this in his Oxford Dictionary of National Biography entry on Hill:<\/p>\n

\u201d[Hill\u2019s] 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.
\n<\/span>
\nAlthough 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<\/a> 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.\u201d<\/span><\/p>\n

David Colquhoun, in an interesting article on the origins of quantitative approaches to drug-receptor interactions<\/a>, gives a nice account of Hill\u2019s December 1909 paper, which derived the Langmuir adsorption equation<\/a> some ten years before Langmuir, and the January 1910 communication.<\/p>\n

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\u2019s 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.<\/p>\n

Colquhoun notes that Hill (presciently?) did not attempt to ascribe precise physical meanings to the parameters in his equation:<\/p>\n

\u201cMy 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]\u201d.<\/span><\/p>\n

Colquhoun drily adds: \u201cHis caveat has often been forgotten since then.\u201d<\/span><\/p>\n

A.V. Hill \u2013 the man and his science<\/strong><\/p>\n

Speaking many years later<\/a> about how he had come to take up physiology, Hill said:<\/p>\n

\u201cA short answer\u2026 is, because Walter Morley Fletcher<\/a> 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.\u201d<\/span><\/p>\n

Fletcher persuaded Hill to complete his Mathematics degree before pursuing new directions. As Hill tells us:<\/p>\n

\u201cIn 1907 I took the Mathematical Tripos<\/a> [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<\/a> 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\u2019s advice again, and decided soon to become a physiologist.\u201d<\/span><\/p>\n

In the summer of 1910 Hill published the first instalment of his scientific life\u2019s work on muscle energetics (Hill, 1910). This work was to culminate in the Nobel Prize in 1923 \u2013 though \u2018culminate\u2019<\/span> 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.<\/em>, in 1961 and 1962, with his final PhD student Roger Woledge).<\/p>\n

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 \u2018oxygen debt\u2019.<\/a><\/p>\n

Hill married into the Keynes academic dynasty<\/a> (his wife Margaret was the sister of the economist John Maynard Keynes, and aunt to Professor Richard Keynes). Among Hill\u2019s four children, his son David or \u2018DK\u2019 Hill (1915-2002) followed in his father\u2019s footsteps to become a muscle physiologist, Professor and FRS. Nicholas Humphrey, Hill\u2019s 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.<\/em><\/a><\/p>\n

Outside the laboratory<\/strong><\/p>\n

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 \u2018operational\u2019 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 \u2018extracurricular\u2019 activity for which he is most remembered is his leading role in the 1930s in the Academic Assistance Council<\/a> which helped Jewish academics flee from the Nazis.<\/p>\n

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<\/em> in early 1934, with the German physics Nobelist Johannes Stark<\/a> who had become an enthusiastic Nazi. Stark insisted that Jews were not being persecuted, only people guilty of \u201chigh treason\u201d<\/span> against the Nazi state. Hill\u2019s response was withering:<\/p>\n

\u201cWith Prof. Stark\u2019s political anti-Semitism I need not deal\u2026 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 \u2026 No doubt in Germany, after this reply, my works in the Journal of Physiology and elsewhere will be burned.\u201d<\/span><\/p>\n

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\u2019s cause \u2013 but he felt he could not really take the credit, as the donors\u2019 generosity surely owed something to Stark\u2019s (racist-ideological) arguments. Bernard Katz, himself a Jewish refugee from the Nazis, sought Hill out partly because of the correspondence (see e.g. here<\/a>, and would later write that the letters:<\/p>\n

\u201cGave me the first glimpse of A.V. Hill\u2019s personality\u2026[which] I found\u2026 so attractive that I made every effort to go and work with him\u201d.<\/span><\/p>\n

Katz also quoted a favourite saying of Hill\u2019s:<\/p>\n

\u201cLaughter is the best detergent of nonsense\u201d.<\/span><\/strong><\/span><\/p>\n

The definitive scientific biographical source on Hill is Bernard Katz\u2019s monumental (78 page!) Royal Society Biographical Memoir; for a shorter introduction Katz\u2019s DNB entry is a useful starting point.<\/p>\n

References<\/strong><\/p>\n

Colquhoun D (2006). Trends Pharmacol Sci 27, 149-157.<\/p>\n

Hill AV (1909). J Physiol 39, 361-373.<\/p>\n

Hill AV (1910). J Physiol 40, 389-403.<\/p>\n

Hill AV (1969). J Physiol 204, 1-13.<\/p>\n

Katz B (1978). Biogr Mem Fellows R Soc 24, 71-149.<\/p>\n","protected":false},"excerpt":{"rendered":"

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, … Continue reading →<\/span><\/a><\/p>\n","protected":false},"author":13,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[8,22],"tags":[17],"class_list":["post-126","post","type-post","status-publish","format-standard","hentry","category-history","category-physiology","tag-history-physiology-hill-equation-av-hill-100-yrs-ago"],"_links":{"self":[{"href":"https:\/\/occamstypewriter.org\/notranting\/wp-json\/wp\/v2\/posts\/126","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/occamstypewriter.org\/notranting\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/occamstypewriter.org\/notranting\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/occamstypewriter.org\/notranting\/wp-json\/wp\/v2\/users\/13"}],"replies":[{"embeddable":true,"href":"https:\/\/occamstypewriter.org\/notranting\/wp-json\/wp\/v2\/comments?post=126"}],"version-history":[{"count":0,"href":"https:\/\/occamstypewriter.org\/notranting\/wp-json\/wp\/v2\/posts\/126\/revisions"}],"wp:attachment":[{"href":"https:\/\/occamstypewriter.org\/notranting\/wp-json\/wp\/v2\/media?parent=126"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/occamstypewriter.org\/notranting\/wp-json\/wp\/v2\/categories?post=126"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/occamstypewriter.org\/notranting\/wp-json\/wp\/v2\/tags?post=126"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}