Systems and synthetic biology in Strasbourg

March 26, 2015

This past week I was at a conference entitled ‘Advances in Systems and Synthetic Biology’ in Strasbourg. The first talk was by Albert Goldbeter and anyone who has read many of the posts on my blog will realize that I went there with high expectations. I was not disappointed. It was a broad talk with the main examples being glycolysis, circadian rhythms and the cell cycle. A lot of the things he talked about were already rather familiar. It was nevertheless rewarding to hear the inside story. There were also enough themes in the talk which were quite new to me. For instance he mentioned that oscillations have been observed in red blood cells, where transcription is ruled out. I enjoyed listening to him, perhaps even more than I did reading his book. Another talk on Monday was by Jacques Demongeot. I am sure that he is a brilliant, versatile and highly knowledgeable person. Unfortunately he made no concessions in his talk for the benefit of non-experts. He jumped into the talk without saying where it was going and I did not have the background knowledge to be able to supply that information on my own. I felt as if I was flattened by a blast wave of information and unfortunately I understood essentially nothing.

The first talk on Tuesday was by Nicolas Le Novère and it had to do with engineering-type approaches to molecular biology. This is very far from my world but gave me some fascinating glimpses as to how this kind of thing works. Incidentally, I found out that Le Novère has a blog with a number of contributions which I found enlightening. The next talk was by François Fages and was focussed on computer science issues. It nevertheless contained more than one aspect which I found very interesting. At this point I should give some background. There are influential ideas on the relation of feedback loops to the qualitative behaviour of the solutions of dynamical systems due to René Thomas. They have been developed over many years by several people and a number of them are at this conference (El Houssine Snoussi, Marcelle Kaufman, Jacques Demongeot) and today I attended a tutorial held by Gilles Bernot on related themes. The basic idea is ‘positive feedback loops are necessary for bistability, negative feedback loops for periodic solutions’. I will not get into this more deeply here but I will just mention that some of the conjectures of Thomas have been made into theorems over the years. For instance a rather definitive version of the result on multistability was proved by Christophe Soulé. In his talk Fages mentioned a recent generalization of this result due to Sylvain Soliman. In the past I had the suspicion that the interest of the conjectures of Thomas was severely limited by the fact that the hypotheses rule out certain configurations which are very widespread in reaction networks of practical importance. It seemed to me that Fages made exactly this point and was saying that the improved results of Soliman overcome this difficulty. I must go into the matter in more detail as soon as I have time. Another point mentioned in the talk was an automated way to find siphons. This is a concept in reaction networks which I should know more about and I have the impression that in a couple of cases I have discovered these objects in examples without realizing that they were instances of this general concept.

On Wednesday there was an extended presentation by Oliver Ebenhöh. One speaker had cancelled and Oliver extended his presentation to fill the resulting extra time. I felt that listening to the presentation was time well spent and I did not feel my attention waning. He explained many things related to plant science and, in particular, the use of starch by plants. One key topic was the way in which a particular enzyme acts on chains of glucose monomers (generalization of maltose, which is the case of two units). It creates a kind of maximal entropy distribution of different lengths. The talk presented both a theoretical analysis and precise experimental results. The theoretical part involved an application of elementary thermodynamic ideas. I liked this and it brought me to a realization about my relation to physics. In the past I have been exposed to too much theoretical physics of a very pure kind, remote from applications to phenomena close to everyday life. It was refreshing to see basic physical ideas being applied in a down to earth way to the analysis of real experiments, in this case in biology.

In his talk on Thursday Joel Bader talked about his work on engineering yeast in such a way as to find out which combinations of genes are essential for survival. The aim is to look for a kind of minimal genome within yeast. One of the techniques of gathering information is to do a random recombination using a Cre-Lox system and looking to see which of the mutants produced are viable. The analysis of these experiments leads to consideration of self-avoiding or non-self-avoiding random walks and at this point I had a strange feeling of deja vu. A few weeks ago I gave a talk in the Hausdorff colloquium in Bonn. In this event two speakers are invited on one afternoon and their themes are not necessarily correlated. On the day I was there the other speaker was Hugo Duminil-Copin and he was talking about self-avoiding random walks, a topic which I knew very little about. Now I was faced with (at least superficially) similar ideas in the context of DNA recombination. At the end of his talk Bader spent a few minutes on a quite different topic, namely bistability in the state of M. tuberculosis. I would have liked to have heard more about that. He is collaborating on this together with Denise Kirschner whose work on modelling tuberculosis I have discussed in a previous post.

This meeting had the advantages of relatively small conferences (in this case of the order of 50 participants) and has served the purpose of opening new perspectives for me.

Harald zur Hausen, colon cancer and MS

December 5, 2014

Having recently written about Harald zur Hausen I now had the opportunity to see him live since he gave a talk in Mainz today. On main theme of his talk was colon cancer. He discussed the different frequencies of this disease in different countries and how this is changing in time. The disease is increasing in Europe and decreasing in the US. He suggested that the latter is due to the increasing success of colonoscopy is identifying and removing pre-cancerous states. There has been a particularly strong increase in Japan and Korea which correlates with a much increased consumption of red meat. Places where this disease is relatively rare, despite considerable meat consumption, are Bolivia and Mongolia. One popular theory about the link between meat consumption and colon cancer is that the process of cooking at high temperatures produces carcinogens. A problem with this theory is that cooking chicken and fish at high temperatures produces the same carcinogens and that there is no corresponding correlation with colon cancer in that case. Thus there is no specificity of red meat. Zur Hausen’s suggestion is that the thing that favours the development of colon cancer is a combination of two factors. One of them is the carcinogens just mentioned but the other is specific to red meat. In fact the study of the geographical distribution suggests that it is even more specific than that. It is specific to cattle and even to the subtype of cattle common in Europe. The types of cattle or related animals in Bolivia and Mongolia do not have the same effect. The idea is that the causative agent could be a virus which is present just in that type of cattle prevalent in the ‘western’ countries. No specific virus has been incriminated but zur Hausen and his collaborators have isolated a lot of candidates from cattle. If this idea is correct then the highest danger would come from raw or lightly cooked meat and this is indeed popular in Japan and Korea.

Another main theme, which was quite unexpected for me, was MS. Here there is also a suggestion of a cattle connection. The idea is that consumption of cows milk at a young age and in particular consumption of non-pasteurized milk may carry a risk for getting MS. The model, at present rather speculative, is that there could be an interaction between some factor present in cows milk and some kind of virus, for instance EBV. Implication of virus infections in general and EBV in particular in causing MS is not new but here it is integrated into a more complicated suggestion. One problem with linking EBV and MS is that such a high percentage of the population has been affected with EBV. I cannot judge how solid these ideas about colon cancer and MS are but they are certainly interesting and original.

‘There but for the’ by Ali Smith

November 13, 2014

In a previous post I said that I might write something about my impressions of Ali Smith’s novels. Since I just finished reading ‘There but for the’ I thought that this was a good opportunity to do so. The other novels of hers which I have read (both a very long time ago) are ‘Like’ and ‘Hotel World’. I liked the first of these a lot and the second less. I no longer have many concrete memories of the contents of these books and I just want to mention one thing which sticks in my mind from ‘Like’. I am telling this story from memory and I did not go back to check the details. In one episode a young girl growing up in Scotland is alone at home when a woman comes to the door. This woman is of the exotic type called ‘English’. The girl asks her if she would like tea, according to the usual code of hospitality in that social context, which is the one I grew up in. The woman asks her what kinds of tea she has. This confuses the girl completely and would have confused me just as much in the same situation. For us drinking tea was very important and tea was tea. We knew nothing about herbal tea, fruit tea, green tea or special kinds of black tea. I only encountered Earl Grey, for example, as a student. In this context I remember one other experience I had while I was at university. I used to spend the summer holidays with my family. In general our dinner at home, the main meal of the day, always included potatoes. These potatoes grew on our farm and I was involved with planting and picking them as well as eating them. (I mentioned in a previous post how this encouraged my interest in metaphysics.) My grandmother, who lived with the family, loved eating potatoes, in particular potato soup, and towards the end of her life she sometimes said that that she would be quite happy to eat nothing else. The specific memory I wanted to mention is a comment she made on the eccentric habits I had picked up at university. She said, in the context of potatoes, ‘O, Alan he eats rice and pasta and ‘yin dirt’ (standard English translation ‘that rubbish’).

Now let me finally come to ‘There but for the’, I enjoyed reading it a lot and it had the effect of a good novel of somehow modifying my feelings and mood in everyday life. Being confronted with and made to think about certain ideas helps with getting out of certain ruts. I have to say that I cannot recommend the book as bedside reading. I found that when I read it before going to bed it had the effect that my thoughts had such a momentum that they could not easily slow down. I would not advise reading it in public either, unless you are a real extrovert. At any rate I could end up laughing so much that it would make me embarrassed to do so in public.

The book is very up to date in the sense that it features a lot of aspects of our daily life which are very new. There are some things which can creep up on us so that they become familiar without our ever really being conscious that they are there. The book helps to reveal these hidden companions. It is full of humour and wordplay, much of which I appreciated. I imagine that I also missed a lot. I have lived outside Britain and even outside English-speaking countries for many years now and this is bound to mean that various jokes and references were lost on me. Many of the things in the book could be taken as comments on society but the interesting thing is that these comments come from inside. We receive them through a portrayal of the thoughts of individual characters including a young girl (who plays a central role) and an old woman approaching death. We also receive them by hearing the conversation between very different characters and seeing the misunderstandings which limit communication between them. In the end, while I appreciated the text ‘locally’ I was left  with the feeling that I did not understand its global structure. I could see that the snake bites its tail, the end connecting to the beginning, but I felt as if I was left facing a question mark. Was this the author’s intention? Or did I miss something essential? Whatever the answers to these questions I feel that the time I spent reading the book was time well spent.

Symposium in Mainz on controversies in biomedicine

October 26, 2014

Last Friday I attended a symposium on controversies in biomedicine at the Academy of Science and Literature in Mainz. There were a number of talks and a round table discussion at the end. The event itself was not the scene of much controversy. It seems that most of the people attending had a positive attitude to biomedical research. At least there was not much sign of the contrary in the questions after the talks. I thought that an event like this might have attracted more participants with a critical view of the subject but that does not seem to have been the case. The one vein of controversial discussion was between some journalists who had been invited for the round table (from Bavarian TV, Süddeutsche Zeitung and Frankfurter Allgemeine Zeitung) and the majority of the participants who were presumably scientific researchers in one form or another. The journalists expressed the opinion that scientists did not take part actively enough in public debates and the scientists suggested that journalists often sensationalized scientific subjects of public interest.

The first talk, by Christof von Kalle was about gene therapy. This taught me a number of things concerning this subject which I did not previously know much about. One example he discussed was that of X-linked SCID (severe combined immunodeficiency). The first choice of therapy for this fatal condition is a bone marrow transplant but this is dependent on the availability of a suitable donor. In other cases gene therapy was tried. It often cured the SCID but a high proportion of patients later got leukemia. A promoter in the inserted DNA had not only activated the gene it was supposed to but an oncogene as well. My one criticism of the talk is that the speaker packed in much too much information, sometimes flashing slides for just a couple of seconds. The next talk was by Bernhard Fleckenstein on pathogenic viruses. His main theme was biosecurity and biosafety. The first has to do with preventing voluntary misuse (such as bioterrorism) and the second with preventing accidents. I learned that this is still the subject of lively discussion. One amazing story is that there was an attempt to stop a paper written in Holland being published in the US by claiming that it was an export and that therefore an authority in Holland responsible for exports of goods had the right to forbid it. There is no doubt that experimental work on influenza viruses which are both highly virulent and highly infectious could be dangerous. However in my opinion it makes no sense to ban such research or to try to keep the results secret. This is because I think that somebody will do the research anyway, despite bans, and any important results will leak out. I think that the danger is minimized if the research is legal and open rather than illegal and secret. The next talk, by Martin Lohse, was on the necessity of animal experiments. One aspect which came out clearly was the tension between the legislation limiting research on animals and that requiring a certain amount of such research in the form of testing before a new drug can be approved.

Over lunch I had some stimulating conversations with other participants. The first talk after lunch was by Jörg Michaelis on the benefit or otherwise of screening, in particular for cancer. He recounted his own experience in organizing a large study on the use of screening of small children for neuroblastoma, with negative results. He then surveyed what is known about the value of various other types of screening. In particular he stated that screening for skin cancer, as paid for by the German public health service is not justified by any scientific evidence. Nobody in the audience contradicted this. The last talk of the day, by Uwe Sonnewald was about green genetic engineering. Among other things he presented statistics on the huge difference in the level of the use of these techniques in the Americas and in Europe, particularly Germany. If the bar representing Germany had not been a different colour it would have been invisible. The meeting ended with the round table. I just want to mention one point which arose there. In a recent post I mentioned the negative attitude to science and technology, particular in the area of biomedicine, which I notice in Germany. (This was one motivation for me to attend the event I am writing about here, with the idea of collecting arguments in support of science.) Of course this was a recurrent theme in the symposium in one form or another, particularly during the round table. An idea which appeared repeatedly, implicitly or explicitly, during the day was that the troubled relationship of the Germans to this subject could have to do with thinking of the abuses carried out by certain German doctors during the time that the Nazis were in power. This is maybe an obvious point but in the discussion someone (I think it was Christof Niehrs) introduced another idea, one which was new to me. He asked if it was possible that this troubled relationship perhaps goes back much further, namely to the period of romanticism when there was a reaction in Germany against the rationalism of the Enlightenment. I found this symposium very informative and it provided me with a lot of material which I can use in the future in discussions on this type of subject.

Thoughts on Helen Keller

October 19, 2014

I must have seen something about Helen Keller on TV when I was a child. I do not exactly remember what it was and when her name recently came into my mind I could not remember what the story was. I just knew that she had an unusual handicap. Wikipedia confirmed my vague memory that she was deaf and blind. I saw that her autobiography is available online and I started to read it. I got hooked and having been reading a bit each evening I have now finished it. Actually the text is not just the autobiography itself but also has other parts such as some of her letters and text by her teacher Anne Sullivan.

Helen Keller, born in 1880, was left deaf and blind by an illness (it does not seem to be clear what, perhaps meningitis or scarlet fever) at the age of 19 months. Being cut off to such an extent from communication she lost some of the abilities she had already acquired as a small child, although she did invent her own personal sign language. The development was only turned around by the arrival her teacher in 1887. Anne Sullivan was not happy with the way in which people exaggerated when writing about the achievements of Helen and herself. She rightly remarked that what Helen did did not require extra embroidery – the plain truth was remarkable enough. It was claimed that she (Anne) had become Helen’s teacher as a selfless act. She writes that in fact she did so because she needed the money. She had herself been blind for some time before regaining her sight. On the other hand what she did for her pupil was in the end very remarkable. The first route of communication for Helen was through her teacher spelling into her hand. Later on Helen learned to type and read Braille, to write on paper (although in the latter form she could not read what she had written) and to speak (in several languages). She got a college degree despite the special difficulties involved. For instance in mathematics, which was not her favourite subject, there were difficulties for her to be able to understand the examination questions which were presented in a special form of Braille which she was not very familiar with.

I think that the story of Helen Keller can be an inspiration for the majority of us, those who do not have to struggle with the immense difficulties she was confronted with. If we compare then we may complain less of our own problems. Of course she did have one or two advantages. Her family must have been quite well off so as to pay for personal tuition so that she was freed from certain practical difficulties. She had great intellectual gifts which could develop vigorously once a sufficiently good channel of communication to the outside world (and, very importantly, to the world of books) had been established. The prose in her autobiography is of high quality. When she is describing some experience she often describes it as if she had seen and heard everything. This makes a strange impression when you realize that this had to be reconstructed from things her teacher had communicated to her, direct sensations such as smells and vibrations and memories from things she remembered from books. She seems to have had a remarkable talent for integrating all this information. I can only suppose that this integration was done not just for her writing but to create parts of her day to day experience.

The book was published in 1903 and so only contains information about Helen Keller’s life until about the turn of the century. She lived until 1968, was later a prominent public figure and wrote many books. Perhaps in the future accounts of her later life will cross my path.

Harald zur Hausen and the human papilloma virus

September 27, 2014

I just finished reading the autobiography ‘Gegen Krebs’ [Against Cancer] by Harald zur Hausen. I am not aware that this book has been translated into English. Perhaps it should rather be called a semi-autobiography since zur Hausen wrote it together with the journalist Katja Reuter. If I had made scientific discoveries as important as those of zur Hausen, and if I decided to write a book about it, the last thing I would do would be to write it with someone else. He made a different choice and the book also includes reminiscences by colleagues, even by some with whom he had controversies and who have a very different view of what happened. I have the impression that the amount of material on conflicts with colleagues is rather large compared to the amount of science. I think that many successful scientists tend to selectively forget the conflicts, even if these have taken place, and concentrate more on the substance of their work. Thus I ask myself if this slant in the book comes directly from zur Hausen, or if it comes from his coauthor, or if he himself really tended to get into conflicts more often than other comparable figures. In any case, this aspect tended to make me enjoy the book less than, for instance, the book of Blumberg I read recently.

Let me now come to the central theme of the book. Harald zur Hausen discovered that a type of viruses causing warts, the human papilloma virus (HPV), also cause the majority of cases of cervical cancer. He was also involved in the development of the vaccine against these viruses which can be seen as the second major cancer vaccine, following the vaccine against hepatitis B. For this work he got a Nobel prize in 2008. He pursued the idea that this class of viruses could cause cervical cancer single-mindedly for a long time while few people believed it could be true. The picture in the book is that while there were a number of people thinking about a viral cause for the disease they were fixated either on herpes viruses or retroviruses. Herpes viruses were popular in this context because the first human virus known to be associated with cancer was the Epstein-Barr virus (EBV) related to Burkitt’s lymphoma and EBV is a herpes virus. Early in his career zur Hausen worked in the laboratory of Werner and Gertrude Henle in Philadelphia. I studied (among other things) zoology in my first year at university and part of that, which appealed to me, was learning about anatomical structures and their names. From that time I remember the ‘loop of Henle’, a structure in the kidney. The Henle of the loop, Jakob Henle, was the grandfather of Werner. As I learned from a footnote in Blumberg’s book, the elder Henle was also the mentor of Robert Koch. Incidentally, Blumberg worked in Philadelphia starting in 1964 while zur Hausen went there in 1966. I did not notice any personal cross references between the two men in their books.

It seems that Gertrude Henle ruled with a strong hand. Once when a laboratory technician was ill for a few days she put on so much pressure that the young woman came into the lab one day just to show how ill she was. She did look convincingly ill and while she was there a blood sample was taken. This turned out to be a stroke of luck. Everyone in the lab had been tested for EBV as part of the research being done there and the technician was one of the few who had tested negative. After her illness she tested positive. In this way it was discovered that glandular fever, the illness she had, is caused by EBV. At that point it is natural to ask why EBV causes a relatively harmless disease in developed countries and cancer in parts of Africa. I have not gone into the background of this but I read that the areas where Burkitt’s lymphoma occurs tend to coincide with areas where malaria is endemic, suggesting a possible connection between the two.

One of the key insights which led to progress in the research on HPV was the recognition that this was not just one virus but a large family of related viruses. Those which turned out to be the biggest cause of cervical cancer are numbers 16 and 18. (After some initial arguments the viruses were named in the order of their discovery.) To obtain this insight it was necessary to have sufficiently good techniques for analysing DNA. The book gives a clear idea of how the progress in understanding in this field was intimately linked to the development of new techniques in molecular biology.

When zur Hausen won the Nobel prize it seemed that the German press and parts of the medical establishment had nothing better to do than to attack him, instead of celebrating his success. From the beginning it was suggested that he only got the prize because a member of the prize committee was on the board of one of the companies producing the vaccine and so would have a personal advantage from the publicity. It was also suggested that the vaccine was ineffective and/or dangerous. (The latter point actually led to a decrease in the number of people getting vaccinated and so, presumably, will mean that in the future many women will get a cancer that could have been prevented.) I do not believe that there was any justification for any of the criticism. So why did it happen? The explanation which occurs to me is the (latent or openly expressed) negative attitudes to science and technology which seem rather widespread in the German press and in German society. I find this surprising for a country which has contributed so much to science and technology and derives so much economic benefit from it.

After finishing the book I decided to try to get a small personal impression of Harald zur Hausen by watching the video of his Nobel lecture. It is untypical for such a lecture in that it contains relatively little about the work the prize was given for and instead concentrates on future research directions. According to the book zur Hausen’s co-laureate Luc Montagnier was suprised by that. The subject is zur Hausen’s lasting theme, the relation between infection and cancer. I found a lot of interesting ideas in it which were new to me. I mention just one. It is well known that there are statistics relating to a possible increase in the incidence of leukemia near nuclear power plants. Whether or not you find this data a convincing argument that there is an increased incidence it is fairly certain that you will link the increase in leukemia in this case (if any) to the effects of radiation. I was no exception to the tendency to make this connection. In his talk zur Hausen says that there are similar statistics showing an increase in leukemia near oil drilling platforms. So how does that fit together? If you cannot think of an answer and you would like to know then watch the video!

My connection to literature

September 23, 2014

When I was at school I had mixed feelings about the English class. One of the things we had to do was to write essays, which was enjoyable for me. Another was to study Shakespeare plays and I got nothing positive out of that. The teacher once asked in class who did not like Shakespeare. I was the one who was brave enough to stand up and say that I did not like it. I am sure I was not the only one who thought so. More generally I had no interest in ‘literature’. The person I have to thank for changing that is Vivia Leslie, my English teacher in my last year at school. In that year each of us was supposed to choose an author and read some of their books and write about them. At that time my main fictional reading was science fiction and so I wanted to choose a writer of that kind, such as Isaac Asimov. Mrs Leslie was rightly not prepared to allow that and in the end the compromise we found was Aldous Huxley. After all, ‘Brave New World’ is a kind of science fiction. When I then came to read other novels of Huxley it was strange at first and difficult to appreciate. With time this changed and Huxley became the first ‘serious author’ who I liked. In the following years I read more or less all of his novels and became a fan. One thing led to another and at the end of my time in school I was reading a lot of classical literature. When I went to university I had much better access to books and I spent a lot of my time reading the classics.

The one modern foreign language I studied at school was French and I liked that a lot. The system was that at the age of sixteen everyone chose between sciences and languages. I could not give up science and so I had to give up French after four years. At least officially. In my fifth and last year of secondary school I used to spend my lunch breaks with two girls, Ingrid and Joy, who were still studying French. Since I had been relatively far advanced I could help them with their homework and this naturally caused me to continue learning some more French. Apart from an intrinsic appreciation for the beauty of the French language which I already had then the association with spending time with two attractive girls certainly increased my interest further. After I went to university I started reading French literature and getting more and more into that. The culmination of this was ‘A la recherche du temps perdu’ and since then Proust has always been the author I appreciate most. Over the years I read the whole novel twice and parts of it more often. I would like to read it again but at some time (a long time ago now) I decided to put that off until my retirement.

At university I was a member of the Creative Writing Group. I wrote some poetry and short pieces of prose but nothing has remained of that. It was a chance to meet interesting people. For certain periods Bernard MacLaverty was writer in residence and part of the duties associated with that was to take part in the Creative Writing Group and give the students advice. I remember him arriving to meet us for the first time with a bottle of Scotch whisky as a present. Among the members of the group were Alison Smith and Alison Lumsden (commonly referred to by us as Ali Smith and Ali Lum). I recently saw that Alison Lumsden has gone back to Aberdeen University (where we studied) as professor of English. As for Ali Smith, she was clearly the most talented writer in the group and later she became a successful novelist. I last saw her quite a few years ago at a reading she gave in Berlin. Perhaps I will write something about my impressions of her novels in a later post. I recently remembered a story associated to another member of the group, Colin Donati. I was once visiting him in his flat in Aberdeen and I found a single loose page of a novel lying on the floor. Of course I was curious to read it and see if I could identify the author. It was not something I had read before but I thought I recognized the style as that of one of my favourite authors. Despite that I would not have been certain if it had not been for one specific subject mentioned on the page which appeared to me conclusive: rooks. These birds occur in several places in the writings of Virginia Woolf (the errant page was from her novel ‘Jacob’s room’), notably in ‘To the Lighthouse’. At the moment I am living in a small furnished flat until our house is built and the final move to Mainz can take place. Near that flat there is a roost of Jackdaws and Rooks and I enjoy hearing them through the open window in the evenings. It occurres to me that I will probably miss those pleasant companions when I move to the house.

These days I do not find much time for reading novels. The last one I can remember reading which I really liked is ‘Ungeduld des Herzens’ by Stefan Zweig. That was about a year ago. Perhaps I should take some time again for reading beyond the confines of science.

The existence proof for Hopf bifurcations

September 22, 2014

In a Hopf bifurcation a pair of complex conjugate eigenvalues of the linearization of a dynamical system \dot x=f(x,\alpha) at a stationary point pass through the imaginary axis. This has been discussed in a previous post. Often textbook results (e.g. Theorem 3.3 in Kuznetsov’s book) concentrate on the generic case where two additional conditions are satisfied. One of these is that the first Lyapunov coefficient is non-vanishing. The other is that the eigenvalues pass through the imaginary axis with non-zero velocity. The existence of periodic solutions can be obtained if only the second of these conditions are satisfied. This was already included in the original paper of Hopf in 1942. Hopf states his results only in the case of analytic systems but this should perhaps be seen as a historical accident. A similar result holds with mucher weaker regularity assumptions. It is proved under the assumption of C^2 dependence on x and C^1 dependence on \alpha in Hale’s book on ordinary differential equations. This has consequences for the case where the second genericity assumption is not satisfied. Let \lambda be an eigenvalue which passes through the imaginary axis for \alpha=0 and suppose that the derivatives of {{\rm Re}\lambda} with respect to \alpha vanish up to order 2k for an integer k but that the derivative of order 2k+1 does not vanish. Then it is possible to replace \alpha by \alpha^{2k+1} as parameter and after this change the second genericity assumption is satisfied. Even if the original right hand side was analytic in \alpha the transformed right hand side is in general not C^2. It is, however, C^1 and so the version of the theorem in Hale’s book applies to give the existence of periodic solutions. This theorem applies to a two-dimensional system but it then also evidently applies in general by a centre manifold reduction.

The theorem is proved as follows. The problem is transformed to polar coordinates (\rho,\theta) and then \rho is written as a function of \theta. In this way a non-autonomous scalar equation with 2\pi-periodic coefficients is obtained and the aim is to find a 2\pi-periodic solution. The first step is to reformulate the task as a fixed-point problem with the property that if a fixed point is periodic it will be a solution of the original problem. Then it is shown using the Banach fixed point theorem(in a minor variant of the local existence theorem for ODE using Picard iteration) that there always exists a fixed point depending on a certain new parameter. This fixed point is only periodic if the result of substituting it into the right hand side of the original equation has mean value zero. This condition can be written as G(\alpha,a)=0. Applying the implicit function theorem to G shows the existence of a solution of G(\alpha(a),a)=0 for a small. This completes the proof.

Summing up, there are two types of theorem about Hopf bifurcation, a ‘coarse’ theorem of the type just sketched with weak hypotheses and a weak but still very interesting conclusion and a ‘fine’ theorem which gives stronger conclusions but needs a stronger hypothesis (non-vanishing of the Lyapunov coefficient and its sign). In his original paper Hopf proved both types. Are there also ‘rough’ versions of theorems about other bifurcations?

SIAM Conference on the Life Sciences in Charlotte

August 7, 2014

This week I have been attending the SIAM Conference on the Life Sciences in Charlotte. Here I want to mention some highlights from my personal point of view. First I will mention some of the plenary talks. John Rinzel talked about mathematical modelling of certain perceptual phenomena. We are all familiar with the face-vase picture which switches repeatedly between two forms. I had never considered the question of trying to predict how often the picture switches. Rinzel presented models for this and for other related auditory phenomena which he demonstrated in the lecture. I find it remarkable that such apparently subjective phenomena can be brought into such close connection with precise mathematical models. Kristin Swanson talked about her work on modelling the brain cancer known as glioma and its various deadly forms. I had heard her talk on the same theme at the meeting of the Society for Mathematical Biology in Dundee in 2003. Of course there has been a lot of progress since then. This was long before I started this blog but if the blog had existed I would certainly have written about the topic. I will not try to resurrect the old stories from that distant epoch. Instead I will just say that Kristin is heavily involved in using computer simulations to optimize the treatment (surgery, radiotherapy, chemotherapy) of individual patients. One of the main points in her talk this week is that it seems to be possible to divide patients into two broad categories (with nodular or diffuse growth of the tumour) and that this alone may have important implications for therapeutic decisions. Oliver Jensen talked about a multiscale model for predicting plant growth, for instance the way in which a root manages to sense gravity and move downwards. This involves some very sophisticated continuum mechanics which the speaker illustrated by everyday examples in a very effective and sometimes humorous way. The talk was both impressive and entertaining. Norman Mazer talked about the different kinds of cholesterol (LDL, HDL etc.). According to what he said lowering LDL levels is an effective means for avoiding risks of cardiovascular illness but the alternative strategy of raising HDL levels has not been successful. He explained how mathematical modelling can throw light on this phenomenon. My understanding is that the link between high HDL level and lower cardiovascular risks is a correlation and not a sign of a causal influence of HDL level on risk factors. The last talk was by James Collins, a pioneer of synthetic biology. The talk was full of good material, both mathematical and non-mathematical. Maybe I should invest some time into learning about that field.

There was one very interesting subject which was not the subject of a talk at the conference (at least not of one I heard – it was briefly referred to in the talk of Collins mentioned above) but was a subject of conversation. It is a paper called ‘Paradoxical Results in Perturbation-Based Signaling Network Reconstruction’ by Sudhakaran Prabakaran, Jeremy Gunawardena and Eduardo Sontag which appeared in Biophys. J. 106, 2720. It suggests that the ways in which biologists deduce the influence of substances on each other on the basis of experiments are quite problematic. The mathematical content of the paper is rather elementary but its consequences for the way in which theoretical ideas are applied in biology may be considerable. The system studied in the paper is an in vitro reconstruction of part of the MAP kinase cascade and so not so far from some of my research.

Among the parallel sessions those which were most relevant for me were one entitled ‘Algebra in the Life Sciences’ and organized by Elisenda Feliu, Nicolette Meshkat and Carsten Wiuf and one called ‘Developments in the Mathematics of Biochemical Reaction Networks’ organized by Casian Pantea and Maya Mincheva. My talk was in the second of these. These sessions were very valuable for me since they allowed me to meet a considerable number of people working in areas close to my own research interests, including several whose papers were well known to me but whom I had never met. I think that this will bring me to a new level in my work in mathematical biology due to the various interactions which took place. I will not discuss the contents of individual talks here. It is rather the case that what I learned form them will flow into my research effort and hence indirectly influence future posts in this blog. I feel that this conference has gained me entrance into a (for me) new research community which could be the natural habitat for my future research. I am very happy about that. The whole conference was an enjoyable and stimulating experience for me. I noticed no jet lag at all but I must be suffering from a lack of sleep due to the fact that the many things going on here just did not leave me the eight hours of sleep per night I am used to.

 

 

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.

 

 


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