## Archive for September, 2014

### 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

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?