Archive for the ‘books’ Category

Baruch Blumberg and Hepatitis B

August 6, 2014

This year, at my own suggestion, I got the book ‘Hepatitis B. The hunt for a killer virus.’ by Baruch Blumberg as a birthday present. Blumberg was the central figure in the discovery of the hepatitis B virus and was rewarded for his achievements by a Nobel prize in 1976. The principal content of the book is an account of the story leading up to the discovery. In fact the subtitle is a bit misleading since Blumberg was not hunting for a virus when he started the research which eventually led to it being found. He was interested in polymorphisms, differences in humans (and animals) which lead them to have different susceptibilities to certain diseases. Nowadays this would be done by comparing genes but at that time, before the modern developments in molecular biology, it was necessary to compare proteins. This was done by observing that antibodies in the blood of some individuals reacted with proteins in the blood of others. This is a mild version of what happens when someone gets a transfusion with an incompatible blood group.

Blumberg did a lot of work with blood coming from people living in unusual or extreme conditions. For this he travelled to exotic places such as Suriname, northern Alaska and remote parts of Nigeria. He seems to have had a great appetite for exciting travel and a corresponding dose of courage. He has plenty of adventures to relate. The second protein he found he names the ‘Australia antigen’ since it was common among aborigines. A good source of antibodies was the blood of people who had had many blood transfusions since their immune systems had been confronted with many antigens. In particular they often carried the Australia antigen.

Pursuing the nature of the Australia antigen led  to the realization that it was part of the hepatitis B virus, a virus which causes liver disease and can be spread by blood contact, in particular blood transfusions. The transfusion recipients had become infected with hepatitis B and had produced antibodies to it. Hepatitis B was the first hepatitis virus to be discovered and so why is it labelled ‘B’? In fact people had noticed cases of hepatitis after tranfusions and suspected two viruses, ‘A’ transmitted by contaminated food or water and ‘B’ transmitted by blood contact. There were researchers who had been ‘hunting’ intensively for these viruses and many of them were understandibly not happy when an outsider beat them to it.

For many years Blumberg worked at the Fox Chase Cancer Center in Philadelphia. It was generously funded and the fact that his research had little obvious relation to cancer was not a problem. Once the director of the institute warned that a serious funding cut might be coming. This led Blumberg and colleagues to the idea of developing a vaccine against hepatitis B as a way of making money. Just as Blumberg had not been a virologist when he discovered the virus he was not an expert on vaccines when he developed the vaccine. At that time the need for a vaccine did not seem so urgent since hepatitis B was known as an acute disease which was rarely life-threatening. Later the vaccine acquired a very different significance. There are very many chronic carriers (hundreds of millions worldwide) and a significant proportion of these develop liver cancer after many years. Thus, surprisingly, the hepatitis B vaccine has attained the status of an ‘anti-cancer vaccine’ and has had a huge medical impact.

This book has a very different flavour from the book of Francois Jacob I wrote about in a previous post. Blumberg gives the impression of being a highly cultured person but more than that of an adventurer and man of action. (Along the way he was Master of Balliol College Oxford and director of the NASA Astrobiology Institute.) Jacob also had enough adventures but appears to belong to a more intellectual type, concentrating more on his inner life. In his book Blumberg does not reveal too much which is really personal and always maintains a certain distance to the reader.



The life of François Jacob

August 19, 2011

I have just read the autobiography ‘La statue intérieure’ by François Jacob. I find that this is a book of high literary quality. An indication of this going beyond my personal judgement is that after the book came out Jacob was invited to talk about it by Bernard Pivot on his TV programme ‘Apostrophes’. I understand that at the time when Pivot was active an invitation from him was a kind of certificate of quality for any new book which appeared in French. Jacob is best known as a biologist but this book convinces me that he is also a very gifted writer. The book is not a monumental work, but rather a collection of anecdotes which illuminate many aspects of Jacob’s life and, more generally, many aspects of the human condition. I find it difficult to say what makes up the charm of his writing – I can only suggest reading the book in order to experience it at first hand.

The first three quarters of the book describe the part of his life before he began his career as a scientific researcher in his late twenties. He had started out studying medicine with the aim of becoming a surgeon. After less than two years this was interrupted by the outbreak of the second world war. Jacob, who is Jewish, fled France and joined the French army in exile led by de Gaulle. He spent a large part of the war in Africa. Shortly after his return to France he was very seriously wounded. This made it impossible for him to become a surgeon and left him somewhat at a loss what to do. An interesting point, which he does not emphasize in the book, is that in a sense his being wounded in this case was a result of a decision of his own. He was tending to an officer who had just been wounded when the group was bombed again. The officer could not be moved and begged Jacob not to leave him alone. Jacob could not do anything to protect the man but he nevertheless stayed with him instead of taking cover. As a result of this he was almost killed himself. His decision was very honourable but maybe not very reasonable. In any case, he ended up spending many difficult months in hospital.

Jacob’s way into research was quite indirect and dependent on a lot of chance factors. For some time he worked in an institute which was supposed to produce penicillin in France but never came close to doing so. He became involved in developing and marketing an antibiotic called tyrothricin. Somewhat later he was able to enter the research group of André Lwoff at the Institut Pasteur. This paved the way for the work for which he was awarded the Nobel prize for medicine with Lwoff and Jacques Monod. He describes how each year to commemorate the anniversary of Pasteur’s death everyone working at the institute (not just the scientists) would make a formal visit to the tomb of Pasteur in the basement of one of the buildings. This was made more vivid for me by the fact that I had visited this tomb myself a couple of years ago. I was at the Pasteur museum quite late in the afternoon when not many visitors were there. I was shown the tomb by a very friendly employee of the museum. It is an impressive structure with lots of marble. I remarked to her that Robert Koch did not have such an impressive mausoleum. She replied that the Germans do not honour their great scientists in the way the French do. I am not sure how true this is but it is at least food for thought.

A large part of the last quarter of the book is a description of the work with Monod. There are also a lot of general reflections on the way in which science is done and how the process by which scientific ideas are developed contrasts with the final product as found in research papers and textbooks. It also gives a good picture of who did what in this collaboration. A key mechanism was the interaction between what Jacob was doing on prophages and what Monod was doing on the lac operon. From a certain point on they were always looking for analogies between the two. This part of the book gives a vivid portrait of the early days of the discipline of molecular biology. It includes a description of Jacob working feverishly with Sydney Brenner at Caltech to establish the existence of messenger RNA, in an atmosphere of general scepticism. The narrative ends after the completion of the project with Monod. What happened afterwards in Jacob’s (scientific) life? According to the book ‘In the beginning was the worm’ by Andrew Brown, Jacob tried to work on Caenorhabditis elegans but without success and he failed to get funding to set up an ‘Institut de la Souris’. Jacob later wrote a book called ‘La souris, la mouche et l’homme’ and perhaps I will read that sometime. But since my summer holiday is at an end it will not be very soon.

The immortal Henrietta Lacks, part 2

January 12, 2011

I now read the book about Henrietta Lacks mentioned in a previous post. This book has perhaps three main aspects. One is the history of a scientific development. The second is the information about the family of Henrietta Lacks and the effects on them of her unusual type of fame. The third is a discussion (and some history) of medical ethics. My own bias is that I was most interested in the first point and less in the other two. Having read some reviews of the book I was not sure if I would like it. I was afraid that it might be too political in a direction I would not like, with overemphasis on polemical criticism of racism and hostility to the medical community. Fortunately my fears were not confirmed. In my opinion the intellectual quality of the book is a lot higher than that typical of the reviews I had read. The book tells many interesting stories and I recommend it to anyone with an inquiring mind.

One of the themes I found most interesting was that of contamination of human cell cultures by HeLa cells. This problem has been much more extreme in the past than I had known or expected. I did not get a picture of how it is today and I would like to read up on that sometime. The situation at one time was that it was uncovered that many cell cultures allegedly coming from different tissues and individuals had actually been colonized and taken over by HeLa cells. Embarrassingly, many papers had been published reporting experiments on the differences between the properties of cells coming from these ‘different’ cultures. I was struck by the horror story of a doctor who injected patients with HeLa cells to see if they would produce tumours. Sometimes they did. Sometimes these tumours were eventually eliminated by the patient’s immune system but sometimes they were not.

Another thing I would like to know more about after reading the book is what it is that makes HeLa cells so special. It is known that they have been genetically modified by one of the HPV, the viruses known to cause cervical cancer. What I did not see is what is known the status of these cells. How unique are they? Are there many other comparable human cell lines these days? If not, why not? As well as teaching me many facts the book has left me with a list of questions which I will try to keep in mind whenever I encounter information about human cell culture in the future.

Who’s afraid of Kurt Gödel?

July 20, 2010

When I was a schoolboy I was very interested in philosophy and, in particular, metaphysics. This interest continued to some extent when I went to university. I grew up on a farm where I had to do a lot of boring repetitive work to help my parents. For example there was planting potatoes. Behind the tractor was a machine whose central element, at least quantitatively, was a metal box full of potatoes. On each side sat a person facing the box. These two people were typically my mother and me. When you sat on one of the seats the person on the other side was not visible. A turning wheel caused a bell to ring at regular intervals and each time the bell rung you dropped a potato into a hole. Via a tube this deposited the potato at just the right place in a furrow made by the machine. The machine then immediately covered it up with earth. To get back to the main subject, while doing these and other similarly inspiring tasks, which I hated, I often thought about metaphysics. These thoughts were connected with my interest in fundamental physics which led me to devour all articles on particle physics in current and past issues of New Scientist and Scientific American I found in the school library. I can remember that at one time I was afraid that physics would be finished before I had a chance to make a contribution. At school we had to do a certain number of courses on religion. One teacher made the unfortunate mistake (unfortunate for her) of offering a course with the title ‘philosophy of religion’ and what was worse concentrating the subject of proofs of the existence of God. For me as an atheist with the enthusiasm of the fresh convert this was great. I thoroughly enjoyed knocking down one proof a week.

At university the attraction which philosophy exerted on me declined fairly rapidly. I came to the conclusion that a lot of what usually goes under that name is more about playing with words than making a connection with reality. I remember one incident which contributed to this, although I am sure there were many others. I once went to a talk given by a ‘philosopher’ in the university. I do not know what kind of a person he was, probably a philosophy professor who was visiting. There was an opportunity for discussion after the talk. I was convinced I had found a mistake in one of the arguments he had presented. He replied, ‘You are trying to catch me in a reductio ad absurdum’. In other words, instead of addressing the issue, and possibly admitting he was wrong, he used a formal device to divert the attention of the participants. By doing this he left me with a bad impression of himself and also of the field of philosophy.

What does all this have to do with Gödel? For my birthday I got a biography of Gödel by Rebecca Goldstein. I have not yet read enough of it to be able to judge whether I like it but it has had the effect of bringing back memories of the days when I was keen on philosophy. It has also made me come back to think about certain things and to test whether my philosophical convictions are really as solid as I imagine. When I was a student one of my mathematics lecturers told me about the book ‘Gödel, Escher, Bach’ by Douglas Hofstadter and that was exactly the right kind of thing to ignite my enthusiasm at that time. In particular, I learned about Gödel’s theorems. I rarely thought about the subject since. Now my general impression is that I am sad that these things are true. But should I really be afraid of them? I interpret the significance of the first theorem as being that some day I might come across a mathematical statement I am interested in which can be neither proved nor disproved. This sounds ugly, but I judge the probablity of it happening to be low, just based on the experience of countless mathematicians. The second theorem sounds worse since it says that someone might come across an inconsistency in mathematics which would bring down the whole house of cards. That sounds really serious but in the end I do not really believe it is going to happen. In a way it is comparable with the business about God. I am convinced that the existence of God can be neither proved nor disproved. Thus while not believing in the existence of God I have no foolproof argument which shows that he will not turn up on my doormat one day. I have lived quite happily with this danger now for the many years since I first thought about this kind of thing and the situation with Gödel and the threat of the internal inconsistency of mathematics is not much different. I also believe that the Sun will rise tomorrow.

The immortal Henrietta Lacks

January 23, 2010

I find immortal cell lines a fascinating topic and I mentioned the subject in a previous post on influenza vaccines. From time to time I had heard about HeLa cells. I knew that this was a cell line derived from tissue taken from a tumour in the 1950’s. I also knew that the name was an abbreviation of the name of the woman who was the donor of the cells. Now, while wandering through the internet, I discovered the blog ‘Culture Dish‘ of the science writer Rebecca Skloot. My attention was immediately attracted by an advertisement for her forthcoming book ‘The Immortal Life of Henrietta Lacks’. This is the story of the woman who ‘gave’ the world HeLa cells, and how this was not exactly voluntary. Now this is the most important cell line in medical research and has become notorious for contaminating other cell lines. I will say no more about this since of course I have not seen the book yet. If I read it, which I probably will, I may write about it in a future post. The abbreviation was not very successful in assuring the anonymity of Henrietta Lacks.

How to be unhappy

August 16, 2009

There are many books on the market which give advice as to how to improve your life. I feel attracted to this kind of book, which of course shows something about how satisfied I am with my own life. I particularly like the classic ‘How to stop worrying and start living’ by Dale Carnegie which I have read several times. This is an old book, going back to 1944, but this does not matter. Circumstances change but human nature, which is at the centre of this type of book, does not. I like Carnegie’s down to earth approach. I also like the fact that he makes clear that the main things he has to say are not new – his purpose is to remind us of things which in principle we already know but which are all too often forgotten. I feel that I have really profited from reading that book.

The reason I am writing this post is that I just read a book called ‘Anleitung zum Unglücklichsein’ by Paul Watzlawick, which I came across in the public library. I found this book very amusing and entertaining. The title can be translated as ‘Guide to being unhappy’. I am not aware that it has been translated into English. The list of references includes a book called ‘How to make yourself miserable’ by Dan Greenburg, which may be similar.Returning to the book of Watzlawick, it is not likely to make its readers unhappy. It is full of biting humour. It is a kind of parody of the self-help books I mentioned above but in a sense it can have similar effects. It lays bare certain mechanisms in human thinking and in the communication between individuals. This is not a easy book to read. It is necessary to pay careful attention so as not to occasionally take what is written there literally. Reading the book is a rewarding experience. It underlines the fact that the meaning of the word ‘happiness’ (Glück) is not so obvious as is generally assumed.

H1N1 and the influenza pandemic of 1918

May 15, 2009

A few years ago I read the book ‘Flu. The story of the great influenza pandemic of 1918 and the search for the virus that caused it’ by Gina Kolata. (Actually it happened to be the German translation.) I found it very interesting and a pleasure to read. The recent public interest in the outbreak of influenza of type H1N1 in Mexico led me to take up the book again. I found it just as fascinating as the first time around and I ended up rereading the whole book. Things I had learned in the meantime allowed me to appreciate more aspects of the subject. In what follows I will describe some of the highlights.

The main subject of the book is the influenza pandemic of 1918. According to conservative estimates this killed 50 million people, more than died in combat in the First World War. In view of the magnitude of the catastrophe it is surprising that it is not more widely known. In 1951 Johan Hultin travelled to Brevig in Alaska and obtained samples from the remains of victims from 1918 which had been relatively well preserved in the permafrost.He had hoped that the virus might have survived but this was too optimistic. He could not do much with his samples at that time. Later it was clear to him that with more recent developments in molecular biology there were new possibilities of using this kind of material. Independently of this, in 1995 Jeffery Taubenberger and his colleagues at the Armed Forces Institute of Pathology started to try to obtain information about the 1918 influenza virus from remains of soldiers who had died at that time which were archived at the institute. They were able to determine part of the genetic sequence of the virus but the quantity of material they had was so small as to limit the possibilities. Hultin read their first publication on the subject in Science in 1997 and contacted Taubenberger, offering to return to Brevig to obtain more material. He was successful and this finally allowed Taubenberger’s team to determine the whole genome of the virus. This was completed in 2005. A few months later the virus was reconstructed at the Centers for Disease Control and Prevention (CDC).

There were two parts of the book which I liked less. This was not because the writing was any less good in those parts – what I did not like was aspects of the content. The first of these two parts concerned the fears of a pandemic in 1976 and the reactions to it. At that time a mass vaccination was carried out which was very expensive and probably not necessary. This just shows how difficult decision making can be in this kind of situation. The thing which I find disturbing is that the costs of this were dwarfed by a sum of over three billion dollars which the government had to pay to people who claimed to have suffered adverse consequences from being vaccinated. This is of course likely to affect decisions of this kind in the future. My conclusion
from this is that the worst virus is probably less dangerous than the mechanisms which take place within human society and prevent mankind from reacting to the threat of a virus in the most effective way. The second part concerns another expedition to obtain material from the influenza victims of 1918, this time in Spitzbergen. It was the idea of Kirsty Duncan. Here I want to describe my personal reactions. From the beginning I felt admiration for the efforts of Hultin and of Taubenberger and his team. In contrast, my attitude to Kirsty Duncan was immediately negative. The sequel only strengthened this impression. The expedition set up by Duncan was a failure – that could have happened to anyone. What I dislike most is the combination of a facade of integrity with the refusal to admit the truth. I find it impressive when people achieve something remarkable by working discretely and quietly rather than thriving on and exploiting publicity. I am happy that in this case luck was on the side of those who deserved it.

One interesting effect of the affair concerning the pandemic scare and the vaccination campaign of 1976 was that the idea came up that a rare side effect of the vaccination might be the disease called Guillain-Barre syndrome. This is a demyelinating disease of the peripheral nerves. It seems that at least some types of this disease are related to molecular mimicry, a subject mentioned in a previous post. In this case the disease can be triggered by the bacterium Campylobacter pylori. Perhaps this disease could be a valuable model for autoimmunity in general.

The progress of the present H1N1 epidemic can be followed in daily reports on the web page of the World Health Organization. Today (15th May) the official number of cases is 7520.

A text of Grothendieck

February 6, 2009

Starting in the autumn of 1994 I spent a year at the Institut des Hautes Etudes Scientifiques (IHES) in Bures sur Yvette near Paris, which for me at that time was an institution which seemed almost mythical. While there I discovered a bound volume of more than 1000 typewritten pages in the library. I do not know why I opened it – perhaps in those days I was tempted to open any thick book in a good library. In any case, once I had opened it I was soon captured by the text. I did not read it all, but I read most of it. The text was ‘Récoltes et Semailles’ by Alexandre Grothendieck. (This is not exactly the text occurring in the title of this post.) In English the title is ‘Reaping and Sowing’. From time to time in what follows I give English versions of text where the original is in French. These are my spontaneous translations, and I have tried to convey the essential meaning as I understand it rather than to be absolutely literal.

Recently, during a conversation with David Klawonn, we got talking about Grothendieck and memories of my time at IHES naturally came back to me. David asked me if I knew why Grothendieck changed subject from functional analysis to algebraic geometry. I did not know and I was surprised that I had never asked myself this before. I was led to do a little research in the Internet and found some things contributing to an answer although I still feel that there is a lot I do not know. While I was doing this I came across another text with the title ‘Promenade à travers une oeuvre ou L’enfant et la Mère’ (Stroll through a work or The child and the Mother). I started reading and was rapidly absorbed by the prose, just as I had been by ‘Récoltes et Semailles’ so many years before. I am not sure of the relation
between the two texts – the one I am talking about here may even be a part of (a version of) the other. A large selection of writings by Grothendieck can be found at In this text Grothendieck describes his career as a mathematician, but with a wealth of digressions. Among these I found many fascinating, both due to the content and due to the wonderful use of language. I will only discuss a couple of them here.

At one point Grothendieck describes his passage from analysis to geometry in 1955. The reader should be warned that Grothendieck’s definitions of ‘analysis’ and ‘geometry’ may not be those commonly used. Among other things he says that it was as if he was leaving arid and harsh steppes to suddenly find himself in a kind of promised land. He wants to describe the experience by the German word ‘überwältigend’ and has difficulty finding a satisfactory French translation. I personally cannot imagine experiencing a transition in that direction in this way. Nevertheless at this point, and in many other cases, I found it difficult to avoid being carried along by Grothendieck’s language even when not naturally inclined to share his point of view on the subject in question. And in a way I wanted to be carried along. Grothendieck’s judgement of himself and his own work is a curious mixture of modesty and pride. On the one hand he emphasizes his lack of talent while at the same time suggesting that he finds his own work tremendously important. His idea of his own greatest strength seems to be that he has looked carefully at things which others regarded as too unimportant to merit their attention.

I am not qualified to give an assessment of the importance of Grothendieck’s work – my own interests in mathematics are too far away from his. I do, however, have the impression that he overrates the importance of his own discoveries for mathematics as a whole. At least I can appreciate his idea of ‘ordinary’ cohomology as a derived functor. This is a case where simplicity is impressive. Grothendieck’s ideas on the central importance of his work, in particular for geometry and topology, are now vulnerable to comparisons with the work of Hamilton and Perelman leading to the proof of the Poincaré conjecture, which are of a very different kind. In this context I could not help thinking of certain parallels between Grothendieck and Perelman. I now list some. Both of them
1. are exceptionally gifted mathematicians.
2. have had difficult relations with the mathematics community and have questioned the morality of that community.
3. have refused prestigious prizes (Grothendieck the Crafoord prize, Perelman the Fields medal).
4. isolated themselves from the mathematical community at some point.
5. are uncompromising about standing up for what they believe in.
6. have a considerable charisma.
In Grothendieck’s case I could only experience the charisma through his writings; in Perelman’s case I was fortunate enough to hear the seminar in Berlin where he first talked about ideas related to his now famous work on the Poincaré conjecture. Of course the points on the above list are not all independent. Perelman has not been isolated so long and we may yet be fortunate enough to see him present us with a new breakthrough.

It is important to mention that in his writings Grothendieck sometimes seems to leave the region which most of us would call sanity. In saying this I am thinking less of the text I am discussing here than of ‘Récoltes et Semailles’ and others. When reading ‘Récoltes et Semailles’ I could not help thinking of Rousseau’s ‘Confessions’. It has a similar attractiveness for me in its earlier parts and seems to go off the rails (as seen from a frame of reference of ordinary everyday life) towards the end.

The fact that I am writing about this subject here is certainly not just due to the mathematical content of the text in question. It affected me on an emotional level and shook the limits within which my thinking usually takes place. This is not an accident. Grothendieck writes: If in ‘Récoltes et Semailles’ I am addressing someone other than myself it is not a ‘public’. I am addressing you who are reading me as a person and as a person who is alone.

Schrödinger’s ‘What is life’

October 12, 2008

After writing the previous post I discovered a web site where Sydney Brenner talks about his life on video. He discusses many interesting things which I cannot go into here. I just want to concentrate on one subject which he mentions there, Schrödinger’s book ‘What is life’. A large part of this book, which was published in 1944 and is available online, is concerned with the mechanism of heredity. It had a strong influence on a number of important biologists, including Francis Crick and James Watson. Thus it may be said that, at least on the level of motivation, the book made an important contribution towards the discovery of the structure of DNA. Brenner’s attitude to Schrödinger’s book is rather negative. He is of the opinion that the one who really gained important insights into heredity from the point of view of mathematics or physics was John von Neumann, following up on ideas of Alan Turing on computing. Unfortunately the biologists payed little attention to (or simply did not know about) this work of von Neumann.

Most of Schrödinger’s book is about heredity. He starts by pointing out that because of the universal presence of fluctuations in the real world a mechanical system cannot work in a reliable way unless it consists of a very large number of atoms. A system consisting of only a few atoms is too sensitive to random disturbances. This Schrödinger presents as the answer to the question why living organisms are so big on the atomic scale. Although the fluctuations arise from quantum phenomena this is not crucially important for the discussion. What is important is that there is some prolific source of fluctuations. Now a gene can be estimated to consist of a number of atoms which is not enormous. The question then is how genetic information can be passed on so reliably from one generation of cells to the next. The answer (in my words) is that it is a digital system. The information is stored in discrete pieces and these cannot be routinely affected by small fluctuations. This has to do with quantum theory and the presence of potential barriers which must be overcome to change from one state to another. The information in the chromosomes is encoded (in Schrödinger’s picture, which we of course now know to be correct) in chemical bonds. The stability of this system rests on the stability of the chemical bond and this in turn is really a consequence of quantum nature of atoms.

Brenner’s objection to Schrödinger’s presentation is that while in reality the genetic material only contains the information needed to make a new individual Schrödinger does not clearly distinguish between the information and the machinery required to implement that information to replicate the cell. In modern terms, he does not distinguish between the role of DNA and that of such things as messenger and ribosomal RNA. This, apparently, von Neumann did without of course knowing anything about the detailed mechanisms. I would tend to say that Schrödinger’s picture was not wrong, its disadvantage being that it is at too low resolution.

I enjoyed reading most of Schrödinger’s book but I felt less well when I got to chapter 6 where the concept of entropy takes center stage. Schrödinger writes (on p. 30 of the online text) ‘Let me first emphasize that it [entropy] is not a hazy concept or idea …’ This is not enough to reassure me. I often feel that even if entropy is not ‘hazy’ in principle it often does have that character in the way it is used by many physicists, not to mention others. When in the seventh and last chapter Schrödinger seems to leave the realm of science in the direction of religion I feel that it does not concern me any more. Chapter 6, on the other hand, does seem to concern me and leaves me with an uneasy feeling. There may be some unfinished business for me there.

Mouse fur

October 1, 2008

The Turing instability has been a popular theme in mathematical biology. There is no doubt that it is nice mathematics but how much does it really explain in biology? Recently a detailed proposal was made by researchers from the Max Planck Institute of Immunobiology and the University of Freiburg to explain the development of hairs in mice on the basis of a Turing mechanism. (S. Sick, S. Reinker, J. Timmer and T.Schlake. WNT and DKK determine hair follicle spacing through a reaction diffusion mechanism. Science 314, 1447.)

Here I want to take this as a stimulus to think again about the status of these ideas. On my bookshelf at home I have the biography of Turing by Andrew Hodges (‘Alan Turing: the enigma’). I now reread the parts concerning biology, which are not very extensive. On the basis of thistext it seems that one of the things in biology that fascinated Turing most was the occurrence of Fibonacci numbers in plants. This seems to have little to do with the contribution to biology for which he became famous. He himself seems to have hoped that there would be a connection. I looked at the original paper of Turing (‘The chemical basis of morphogenesis’) but I did not learn anything new compared to modern accounts of the same subject I had seen before. The basic mathematical input is a system of reaction-diffusion equations, as described briefly in a previous post. A homogeneous steady state is considered which is stable within the class of homogeneous solutions. Then a growing mode is sought which describes the beginning of pattern formation. This is similar to what is done for the Keller-Segel system. There is a mouse in Turing’s paper but it has nothing to do with the mouse in the title of this post. Its role is to climb on a pendulum and thus illustrate ideas about instability.

Another book I have at home is ‘Endless forms most beautiful‘ by Sean Carroll. In this book, which appeared in 2005, the author explains recent ideas about embryonic development and their connections to the evolution of organisms on geological timescales. Turing is mentioned once, on p. 123, but only to dismiss the relevance of his ideas to embryology, the central theme of his paper. Carroll writes, ‘While the math and models are beautiful, none of this theory has been borne out by the discoveries of the last twenty years’. As a remaining glimmer of hope for the Turing mechanism, the diagrams on pp. 104-105 of the book might fit a Turing-type picture but concern small-scale structures. The large-scale architecture of living bodies is claimed to arise in a quite different way. The picture of the development of individual organisms presented by Carroll has a character which strikes me as digital. I do not find it attractive. I should emphasize that this is an aesthetic judgement and not a scientific one. I suppose I am just in love with the continuum.

Now I return to the article of Sick et. al. A key new aspect of what they have done in comparison to previous attempts in this direction is that they are able to identify definite candidates for the substances taking part in the reaction-diffusion scenario and obtain experimental evidence supporting their suggestion. These belong to the classes Wnt and Dkk (Dickkopf). An accompanying article by Maini et. al. (Science 314, 1397) is broadly positive but does also add a cautionary note. It is pointed out that similar predictions can be produced by different mathematical models. A model of Turing type may produce something that looks a lot like what is provided by a model involving chemotaxis. This is a generic danger in mathematical biology. In a given application it is important to be on the lookout for experimental data which can help to resolve this type of ambiguity.

The reaction-diffusion model used for modelling and numerical simulation is related to a classical model of Gierer and Meinhardt. The original paper from 1972 and a great deal of information on related topics are available from this web page.


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