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Second Bonn conference on mathematical life sciences

March 20, 2026

I have just attended the conference mentioned in the title of this post. My general impression is that mathematics as I understand it is being more and more excluded by on the one hand masses of data and on the other hand by reliance on computers related to machine learning, AI etc. A cynical formulation would be to say that a research project is a machine for converting masses of data into complicated brightly coloured diagrams. The use of simple logical arguments to get real insights is becoming rarer. In my opintion this is not because such things are no longer possible or useful but decause they are no longer fashionable. Conversations with other older participants of the conference indicate to me that I am not alone in this opinion. Having got rid of some complaints let me now say something about some of the talks at the conference I liked best.

The first of these is a case where there were huge amounts of data involved and very complicated coloured pictures but there were also practical results which I found very impressive. The talk was by Bernd Bodenmiller from Zurich. In this work mass spectrometry techniques were used to produce very detailed pictures of the distribution of substances in slices of tumour tissue. I was surprised by one picture which showed the distribution of a conventional platinum-based chemotherapeutic agent within a tumour. While it was uniformly distributed through certain parts of the tumour it was more or less absent from others. Apparently cancer cells can develop methods to exclude this kind of drug from certain regions and thus survive. The one theme in the talk which caught my attention most was an application of this method to ovarial cancer. This is a very deadly cancer with frequent relapses after treatment. In the work reported on imaging techniques were use to distinguish different classes of patients and relate the differences between them to the rate of relapse. Beyond this predictions could be made which drugs might benefit which patients most. Patients were subjected to a kind of dual treatment strategy which would be illegal in Germany but which is fortunately legal in Switzerland. The idea is that on the one hand therapy decisions are considered in a conventional way and this information is given to the tumour board. Independently of this an analysis is done using the advanced imaging methods and this information also goes to the tumour board. These two sets of information are combined to make therapeutic decisions. In one case this method was applied to a patient already in palliative care, predicted to live for only a few more weeks. Five years later she is still alive and well. This is just one extreme case and the total sample size of patients is small. Nevertheless the preliminary conclusion is that this method leads to an large extension of the lifetime of the patients (I think a factor of four) in comparison to conventional approaches.

The second talk I want to mention is that of Becca Asquith. I had already heard a talk by her on a similar subject a couple of years ago and I wrote about it in a previous post. It has been observed that the KIRs an individual has can affect their ability to combat various infectious and autoimmune diseases, both positively and negatively, depending on the example. This is correlated to which MHC molecules the individual has. The subject of the talk was understanding the mechanisms behind these phenomena. One conclusion is that a determining factor is the typical lifetime of T cells. So how could KIRs modulate this lifetime? Two hypotheses are compared. One of these is that NK cells carrying the KIRs kill T cells, thus reducing their average lifetimes. Experiments were described which together with modelling, can decide between these two mechanisms. I find that this project was a beautiful combination of theory and experiment, exactly as I imagine such a project should ideally be. The whole thing, in particular the logical connections were very well described in the talk. At the end I asked the speaker why NK cells should kill T cells. Could this be of benefit to the organism or is it just a kind of collateral damage? My understanding of the answer, which I find plausible, is that any mechanism which can be used by the immune system to regulate its activity will be used.

The third talk was by Andreas Reichel, head of research at the company Bayer. He started off by mentioning a possible mechanism of action of a drug which is different to those commonly seen. This is to direct a certain protein to the proteasome so that it is destroyed. He then talked about the way in which candidate drugs are identified in the pre-clinical region. He mentioned a method in which a relatively simple ODE model can be used to obtain information. It can be used to find promising candidates. It can be used to suggest good doses for trials. (Sometimes increasing the dose produces no effect of the kind desired.) It can be used to choose optimal times for taking blood samples when testing candidates. Apparently it has been possible to convince decision makers that this theoretical work is something they can really profit from. For me this is a good example of how (relatively simple) mathematics can be used to make a significant contribution to a practical task such as drug discovery. If someone wants to develop models of this kind or apply them in an intelligent way then they need to things from analysis which I teach students on a day to day basis.

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Catch bonds and T cell activation

November 17, 2025

A frequent approach to studying T cell activation is based on the idea that properties of the chemical binding of the T cell receptor to an antigen determine whether the cell is activated or not. This applies in particular to the work I have written about here and here. An alternative idea is that mechanical properties also play a role in this process. We have studied this in a new preprint with Yogesh Bali and Wolfgang Quapp. What happens when two molecules are chemically (non-covalently) bound and we apply a force which tends to pull them apart? A simple scenario would be to assume that the greater the force the greater the chance the bond will break. This is what is called a slip bond. However there is also another possibility. It may be that in a certain range the applied force actually stabilises the bond. This is what is called a catch bond. It is related to what is called a Chinese finger trap. This is a toy with the following property. If you push a finger into it it is difficult to get it out again and pulling harder only makes it worse. The way to escape is to push instead of pull.

In this work we study a model with two mechanical degrees of freedom which are the extension of the bond between T cell and the pMHC and the angle between the T cell receptor and the cell membrane. The dynamics is described by a potential depending on these two variables. Stable and unstable bonds correspond to minima and saddle points of this potential. The potential depends on a constant external force as a parameter and varying this parameter leads to bifurcations. In the paper this behaviour is studied while trying to incorporate as much experimental data as possible related to this system.

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Mathematical models for T cell activation, part 2

April 12, 2025

In a previous post I discussed the topic of T cell activation and presented some results which Eduardo Sontag and I obtained on this subject. We studied a mathematical model of François et al. and found some interesting features of the solutions not previously known. We found that for some parameter values there exists more than one positive steady state. We also found that for some parameter values the response function describing the dependence of the activation on important parameters is non-monotone. It can happen that increasing the stimulation of the T cell decreases its level of activation. What we did not check was to what extent the parameter values for which these phenomena are observed are consistent with experimental measurements. Now in a paper of Yogesh Bali and myself we showed that they do occur for biologically reasonable parameter values. The paper also contains an extensive comparison of different models for the initial stages of T cell activation. In particular we give rigorous proofs of some properties of the solutions. We apply the Deficiency Zero Theorem in many cases. We also present simulations which allow comparisons of the predictions of different models with experimental results. A new discovery was that for one model the response function can have more than one maximum.

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Medicine must be defended

December 10, 2024

A key element of modern life is medicine. It has extended the lifespans of those with access to it enormously and also makes a huge contribution to the quality of the life we have. In my opinion it is the most important thing which science has done for society. For many decades the US has been a powerhouse in the progress of medicine. This was the result of a curious accident. The development of medicine in the US was stimulated in an essential way by the money pumped into it by J. D. Rockefeller. The strange thing is that Rockefeller himself did not believe in medicine. He preferred homeopathy and other superstitions. Because he did not have enough time to think carefully about distributing his money to deserving causes he hired someone else to do it for him. Fortunately that person, Frederick Taylor Gates, did understand the importance of medicine and gave the money correspondingly. Now medicine is under threat due to the nomination of Robert Kennedy to a position where he could control the US health system. He is an enemy of medicine. He claims that AIDS is not caused by HIV and is an anti-vaccine activist. In other words he denies fundamental facts of modern medicine. I was happy to see that 77 Nobel Prize winners now wrote a letter urging the Senate not to confirm his nomination. Of course there is no guarantee that anyone will pay attention to the letter. Maybe it will only serve to ruin the reputation of the Nobel Prize with a certain public. The NIH is probably the most prestigious medical research institution in the world. The damage likely to result from the nomination of Kennedy could be aggravated by the fact that Jay Bhattacharya, the nominee to head the NIH, also has views on COVID-19 which are, to say the least, highly controversial. Not only all those who believe in medicine should do all they can to oppose these nominations. Anyone who believes in science and in rational thought should do so. For these nominations would set a precedent in which control of science is given to people who openly oppose consensus judgments of science.

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Biography of Paul Ehrlich

June 10, 2024

I have just read a biography of Paul Ehrlich by Ernst Bäumler. Ehrlich is one of the great heroes in the advances in medicine in the late nineteenth and early twentieth centuries. I liked the book not for any literary qualities but for the facts it contains. Here is one which is mentioned in the text and which I recommend to the consideration of those people who are against vaccinations. In the Franco-Prussian war the number of German soldiers who died of smallpox was 297, the number of French soldiers who died of smallpox 23400. This difference was due to compulsory vaccination on the German side. This book tells the story of Ehrlich’s life but also contains information about other notable figures in the history of medicine who he was in contact with, for instance Robert Koch, Emil Behring, Louis Pasteur, Emile Roux, Elie Metchnikoff and Joseph Lister. Another interesting fact is that at the time when Ehrlich won the Nobel Prize for medicine in 1908 more than half the prizes awarded up to that time had gone to Germans.

Ehrlich can be seen as the founder of modern immunology. If you open a textbook on immunology one of the first things you encounter is a list of different types of white blood cells. Many of these were discovered and named by Ehrlich, starting with the mast cells. Exceptions are the macrophages, discovered by Mechnikoff, and the different types of lymphocytes which could only be distinguished using techniques much more advanced than those available in Ehrlich’s days. Ehrlich was also the one who discovered and named the complement system. White blood cells all look rather similar under the microscope and the idea which allowed Ehrlich to make progress in distinguishing them was to stain them with various dyes. Ehrlich was known in younger years for the fact that his clothes and the laboratory in which he worked were covered with stains. What Ehrlich observed was that certain dyes were taken up preferentially by certain cells and certain substructures in those cells. This was useful for the study and classification of the cells. Ehrlich developed this further with the idea that dyes which were specific for certain cells, in particular unicellular pathogenic organisms, might be candidates for drugs which could affect those cells.

The first big practical medical success which Ehrlich was involved with was the development of serum treatment, in modern language antibody treatment, for diphtheria. The driving force in this development was Behring and he got a Nobel Prize for that. However without the contributions of Ehrlich this project might have failed. At least it would not have been successful so soon. The two men had a difficult relationship with Behring often being aggressive and Ehrlich forgiving. At Ehrlich’s funeral Behring had prepared a longer speech but in the end only managed to say the following, ‘Du hattest eine empfindsame Seele. Verzeih, wenn wir dir manchmal wehgetan haben’ [You had a sensitive mind. Forgive us if we often hurt you.] Incidentally, Ehrlich was the one to invent the idea of antibodies and that of a receptor in cell biology (Seitenkettentheorie).

Later Ehrlich started a big programme for synthesizing chemical substances and testing their effects on certain organisms, notably that which causes syphilis. A long list was tested, whereby a lot of the hard work leading to the final success was carried out by Sahachiro Hata. He was the one who discovered the effectiveness of the compound number 606 on the list against the causative agent of syphilis. This was later called Salvarsan and revolutionized the treatment of the disease. This was the first example of success of an artificially synthesised drug becoming a cure for a major illness. In this sense Ehrlich can be seen as the founder of chemotherapy, the development and use of chemicals to treat disease. Salvarsan was a tremendous success when it was introduced. It was later superceded by penicillin. Alexander Fleming gave a speech where he talks about how much he was influenced to do his work by what he knew about Ehrlich. Despite the success of Salvarsan it met with a lot of public opposition. It was the same kind of chorus we are familiar with from the reactions to the COVID-19 vaccines. It was claimed that the drug was dangerous, causing many deaths, that it was not effective and that it was too expensive and in fact had only been developed to make money. There are some sad constants in human nature. One positive thing is that one man who ran a campaign of lies about Salvarsan and slander of Ehrlich was sentenced to a year of prison for doing so.

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My life with multiple sclerosis

May 20, 2024

In this blog multiple sclerosis has come up as a theme from time to time. What I never said here was that I myself suffer from the disease. Now I want to write about this subject. Maybe this text will be helpful for someone with a recent diagnosis of MS who happens to come across it. I will start at the very beginning. I was born in 1963 in the Orkney Islands, which have one of the highest incidences of MS in the world. I started to study at the University of Aberdeen in October 1980. In the summer of 1980 I started having problems with one of my eyes. My vision rapidly got worse until that eye was almost blind. After some time I came into hospital in Aberdeen. There all kinds of tests were done on my eye. In particular, towards the end of my stay, a test called ‘visual evoked potentials’ was carried out. In this test the patient looks at certain patterns on a TV screen and nerve signals are measured. I think that at that point the doctors must have had a good idea what was wrong with me although they did not tell me. At that hospital, the only large one in the region, they must have had very many MS patients, in particular from the hot spots in Orkney and Shetland. I do not know how much they told my parents. With hindsight what was wrong with me was an ‘isolated optic neuritis’. MS is an autoimmune disease where the immune system attacks the myelin sheath of neurons in the central nervous system. In this way it damages or destroys the electrical insulation of the nerve cells and so reduces their capacity to transmit signals. In optic neuritis it is the optic nerve (which belongs to the central nervous system) which is attacked. An optic neuritis is often followed after many years by full MS. The doctors said something to me about a virus infection of the optic nerve. I do not know what they said to my parents. I think that in those days and in that place it was the strategy not to tell patients or their relatives too much so as to avoid causing unnecessary fear. In any case, after two weeks in hospital my sight had already improved spontaneously and I was able to go home. Things returned to normal. The episode seemed like a bad dream and I was able to go to university and forget it.

In 1994 I was living in Munich. I used to often go on long hikes with friends at the weekend. We would take one of the commuter trains (S-Bahn) which leave the city radially and then walk to the next radial line. At one point I noticed that towards the end of these walks my left foot was not working properly. It tended to come down hard with each step and make a noise and this was rather embarrassing. The effect increased with time and I stopped going on those walks. In October 1994 I moved to a new job in Paris and at that time things got much worse. From time to time I suffered from itching of my left arm and chest which was so intensive I could hardly bear it. This was particularly bad at night. I did not go to see a doctor about this. The effect was getting stronger and stronger and was close to forcing me to take action. However after some weeks the itching suddenly decreased in intensity although it did not go away completely. After a year I moved again, this time to Berlin. Then I started getting more and more symptoms, including difficulty in walking, itching, incontinence and numbness, particularly of the hands and feet. I was not sure if this numbness might be due to a neurological problem or a problem with the circulation. These symptoms were so varied that they made no sense to me. I was kept from going to a doctor because I thought he would think I was crazy if I told him these stories. I also thought that a lot of what I was experiencing could be psychosomatic and I was ashamed of that, as illogical as such a reaction may be. With time my symptoms got worse but not in a continuous way. Various things came and went. This is typical of the most common form of MS, the relapsing-remitting form. Of course I knew nothing about that at that time. Eventually I was forced to go to a doctor. In particular my state could no longer be hidden from the people around me. I once went for lunch with some colleagues. The place we used to go for lunch was a short walk (not more than ten minutes) from work. We would walk there, have lunch and walk back. On that day even this small amount of exertion was too much for me. On the way back I was walking like I was drunk.

After I went to a doctor (who I did not know previously) things went fast. He quickly sent me to a neurologist. On the referral I saw the diagnosis ED with the differential diagnosis CJD. Since that was the time of mad cow disease and I was from the UK the second alternative was perhaps not completely unreasonable. I found it rather amusing. Then I had to get informed and I went to a public library. I found out that ED stands for encephalomyelitis disseminata, a technical term for MS. From the books I read I discovered that on the basis of my symptoms the most probable diagnosis was MS and that the gold standard for confirming this diagnosis is an MRT. After examining me the neurologist sent me for an MRT. At this point it seemed to me that the two most serious hypotheses were MS or something psychosomatic (I still had not abandoned that alternative). After the MRT had been carried out the radiologist did not say much to me. She said that my neurologist would tell me more. Nevertheless it was clear to me at that moment that the suspected diagnosis had been confirmed – otherwise she would have behaved in a quite different way. On my way home it was clear to me that I was the subject of a great catastrophe. It seemed to me very improbable that this should be happening to me but I had no doubt that it was. I did not ask the question, which many people in this kind of situation do, why this had happened to me. I believe in chance and that not everything that happens must have a simple explanation. In any case that was the start of a period of fear about my future which lasted about a year. I think it is difficult for doctors to give patients this kind of diagnosis. In my case, for the reasons I have explained, it was not a surprise for me when the neurologist told me.

This is enough for today but I just want to say a few things for any newly diagnosed patient who is reading this. MS is a horror diagnosis and when you get it you may interpret it as meaning that your life has been destroyed. That is the way I experienced it and I think that that reaction is quite typical. You should realize that when you hear about MS you usually hear the worst stories and many of the negative statements you hear are thoughtless, misleading or simply false. I can say due to my own example that MS is not always so bad as the stories you hear. It does not have to be the end of a good life. Since I got my diagnosis in 1997 I have been able to meet the woman of my life and win her love (2000), marry her (2008) and obtain a full professorship in the area of my choice (2013). To be continued …

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Nobel lecture of Harvey Alter

March 1, 2024

In 2020 the Nobel prize for medicine was awarded to Harvey Alter, Michael Houghton and Charles Rice for their role in the discovery of the hepatitis C virus. I now watched the videos of the corresponding Nobel lectures. For my taste the lecture of Alter was by far the most interesting of the three. I think that he was also the one who played the most fundamental role in this discovery. At the beginning of his lecture he emphasizes the point that the most important discoveries in science often come as a complete surprise and not as a result of planned research programmes. Alter was 85 when he got the prize and so he had to wait a long time for it. The papers documenting his fundamental contributions were published in 1989. A central part of this work was the collection and preservation of blood samples from patients undergoing open heart surgery. Why was this group chosen? One of the most important modes of infection with hepatitis B and C used to be blood transfusions. This continued to be the case until tests were available to screen donors for these diseases. This kind of surgery involves extensive blood transfusions and so the chances of infection were relatively high in these patients. Also these patients suffered from relatively few other diseases which could have been confounding factors. These blood samples were an invaluable resource in the search for the virus. They were the basis of painstaking analysis over many years.

One important feature of hepatitis C is that it becomes chronic in 70 per cent of cases. This looks like a failure of the immune system to handle this disease. What are the reasons for this failure? One concerns quasispecies. The hepatitis C virus has an RNA genome and the copying of RNA is very error-prone. This leads to a huge variety in the genomes of virions in a single patient. This in turn results in rapid mutations of the virus. If an antibody has developed to combat the virus then selective pressure will quickly cause a new form to become dominant which is not vulnerable to that antibody. It seems to me that if this type of effect is to be captured using mathematical model it will require a stochastic model. Deterministic models of the type I have studied in the past are probably not helpful for that. In the lecture it is also mentioned that the number of T cells (CD4+ and CD8+) declines very much in chronically infected hepatitis C patients. No explanation is offerred as to why that is the case. Deterministic mathematical models might be able to contribute some understanding in that case.

The lecture contains the following interesting story. There was a time at which liver cancer was much more common in Japan than in the West. The reason for this was that that cancer was in many cases a late stage effect of hepatitis C. During wars in the early part of the 20th century many Japanese soldiers injected drugs with shared needles and this was what spread the disease. It was observed that there were many cases of jaundice (the most striking symptom of hepatitis) on the battlefield. Decades later many of these men developed serious liver disease, including cancer. Japanese doctors predicted that a similar phenomenon would be seen in the West when the effects of recreational drug use became manifest. They were right.

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Nobel lectures of Katalin Karikó and Drew Weissman

December 10, 2023

Yesterday I listened to the Nobel lectures of Katalin Karikó and Drew Weissman, describing their work on mRNA vaccines. The lecture of Karikó mainly described the history of their discoveries while that of Weissman went into more technical details and discussed the prospects for the future applications of this technology. One interesting aspect of Karikó’s lecture was what she said about the difficulties she experienced during her scientific career. She was repeatedly unable to obtain funding for her research and lost several jobs due to her lack of success in this endeavour. For many years her work was supported by sympathetic colleagues. She could not afford assistants and had to do the menial jobs in the lab herself, down to thawing out the fridge where she kept her samples. In her talk she did not complain loudly about the injustice done to her in this way but restricted herself to making brief comments along the way. Eventually her career was saved when she was given a good job at the then obscure company Biontech.

Now let me come to the science, following Karikó’s account. After mRNA was discovered it took about twenty years before it could be synthesized artificially. mRNA is the template for the production of proteins and this gives rise to the idea that it might be made to cause cells to produce desirable proteins, for instance drugs. It turned out that there are several problems with this. The first is that within a living organism mRNA is attacked by the immune system and destroyed. The second is that artifical mRNA seemed to give poor protein yields. The third is that mRNA is a rather unstable molecule and thus only survives for a short time after it has been introduced into the body. Artificial mRNA is like the molecule is described in the textbooks. It consists of a string of nucleotides each of which contains one of the bases adenine, cytosine, guanine and uracil. Natural mRNA as it occurs in the human body is very different since many of the nucleotides containing the bases have been chemically modified. At the beginning of the work described in the lecture the enzymes responsible for these modifications were not known so that this process could not be understood, let alone controlled. A key type of experiment done by Karikó and Weissman was to feed dendritic cells with nucleotides, natural or modified, and look at whether they showed an inflammatory reaction, producing cytokines. It turned out that the dendritic cells reacted much less strongly to mRNA including certain modified nucleotides occuring naturally than to the textbook mRNA. It is easy to guess why this should be the case. (This is my speculation, not a statement from the lecture.) mRNA occurring in the body could be from a pathogen such as a virus and then the immune system should eliminate it. The modifications could be a way the body could signal to the immune system that an mRNA molecule is made by the host and should be left alone. In any case it was found by trying many examples that one powerful way of suppressing the immunogenicity of the RNA was to replace uridine by the modified molecule pseudouridine. This provided an avenue to removing the first of the difficulties in applying RNA therapeutically. It turns out that the modified RNA produces higher protein yields and is more stable than the textbook RNA. In other words, it can contribute to the solution of the other two problems as well.

If RNA is to be used as a vaccine then while the immune system should ignore the RNA it should react strongly to the corresponding protein. This seemed to work well in the case of RNA vaccines but this was paradoxical. Normally a protein is not enough to make a vaccine. It must be accompanied by another substance, an adjuvant, which activates the innate immune system. The RNA vaccine contained no known adjuvant. The solution to this problem is as follows. In order to get the RNA into a cell it has to be coated in lipids. It turns out that these lipids act as an adjuvant. In the end they activate the so-called follicular helper T cells. This kind of vaccine is remarkable in that it can stimulate the immune system more strongly than the pathogen it is intended to be a vaccine against. For instance the RNA vaccines against COVID-19 cause a production of antibodies which is several times higher than an infection with the virus itself.

Now a lot is known about the use of different kinds of RNA to achieve different effects. Various aspects of this were explained in the lecture of Weissman. He discussed a variety of different applications which appear within reach: improved vaccines against infectious diseases, vaccines against cancer, production of drugs. Appart from their flexibility and effectiveness the RNA techniques have the potential to replace the extremely expensive processes required for the therapy of certain diseases by rather cheap ones. Weismann’s talk gave the impression that the RNA techniques could soon lead to revolutionary advances in medicine. He is not at all the type of person who comes across as an advertiser. Instead he makes an impression of someone who is modest and trustworthy. He discussed a wide variety of examples. Let me concentrate on one. This is the idea of a universal influenza vaccine. The influenza virus mutates frequently with the result that it is necessary to develop a new vaccine each year to be effective for the new dominant variant. A dream is to develop a vaccine which would be effective for all types. It has been found that RNA vaccines can be effective against many antigens simultaneously, for instance for all types of influenza. This is being tested in practice now. I was excited by what I heard in this lecture. Of course there will no doubt be many unexpected difficulties in implementing these ideas but I think that there is a good chance that they could bring a major improvement in medicine as a whole.

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Is mathematics being driven out by computers?

September 28, 2022

In the past two weeks I attended two conferences. The first was the annual meeting of the Deutsche Mathematikervereinigung (DMV, the German mathematical society) in Berlin. The second was the joint annual meeting of the ESMTB (European Society for Mathematical and Theoretical Biology) and the SMB (Society for Mathematical Biology) in Heidelberg. I had the impression that the participation of the SMB was relatively small compared to previous years. (Was this mainly due to the pandemic or due to other problems in international travel?) There were about 500 participants in total who were present in person and about another 100 online. I was disappointed with the plenary talks at both conferences. The only one which I found reasonably good was that of Benoit Perthame. One reason I did not like them was the dominance of topics like machine learning and artificial intelligence. This brings me to the title of this post. I have the impression that mathematics (at least in applied areas) is becoming ever weaker and being replaced by the procedure of developing computer programmes which could be applied (and sometimes are) to the masses of data which our society produces these days. This was very noticeable in these two conferences. I would prefer if we human beings would continue to learn something and not just leave it to the machines. The idea that some day the work of mathematicians might be replaced by computers is an old one. Perhaps it is now happening, but in a different way from that which I would have expected. Computers are replacing humans but not because they are doing everything better. There is no doubt there are some things they can do better but I think there are many things which they cannot. The plenary talks at the DMV conference on topics of this kind were partly critical. There occurred examples of a type I had not encountered before. A computer is presented with a picture of a pig and recognizes it as a pig. Then the picture is changed in a very specific way. The change is quantitatively small and is hardly noticeable to the human eye. The computer identifies the modified picture as an aeroplane. In another similar example the starting picture is easily recognizable as a somewhat irregular seven and is recognized by the computer as such. After modification the computer recognizes it as an eight. This seems to provide a huge potential for mistakes and wonderful opportunities for criminals. I feel that the trend to machine learning and related topics in mathematics is driven by fashion. It reminds me a little of the ‘successes’ of string theory in physics some years ago. Another aspect of the plenary talks at these conferences I did not like was that the speakers seemed to be showing off with how much they had done instead of presenting something simple and fascinating. At the conference in Heidelberg there were three talks by young prizewinners which were shorter than the plenaries. I found that they were on average of better quality and I know that I was not the only one who was of that opinion.

In the end there were not many talks at these conferences I liked much but let me now mention some that I did. Amber Smith gave a talk on the behaviour of the immune system in situations where bacterial infections of the lung arise during influenza. In that talk I really enjoyed how connections were made all the way from simple mathematical models to insights for clinical practise. This is mathematical biology of the kind I love. In a similar vein Stanca Ciupe gave a talk about aspects of COVID-19 beyond those which are common knowledge. In particular she discussed experiments on hamsters which can be used to study the infectiousness of droplets in the air. A talk of Harsh Chhajer gave me a new perspective on the intracellular machinery for virus production used by hepatitis C, which is of relevance to my research. I saw this as something which is special for HCV and what I learned is that it is a feature of many positive strand RNA viruses. I obtained another useful insight on in-host models for virus dynamics from a talk of James Watmough.

Returning to the issue of mathematics and computers another aspect I want to mention is arXiv. For many years I have put copies of all my papers in preprint form on that online archive and I have monitored the parts of it which are relevant for my research interests for papers by other people. When I was working on gravitational physics it was gr-qc and since I have been working on mathematical biology it has been q-bio (quantitative biology) which I saw as the natural place for papers in that area. q-bio stands for ‘quantitative biology’ and I interpreted the word ‘quantitative’ as relating to mathematics. Now the nature of the papers on that archive has changed and it is also dominated by topics strongly related to computers such as machine learning. I no longer feel at home there. (To be fair I should say there are still quite a lot of papers there which are on stochastic topics which are mathematics in the classical sense, just in a part of mathematics which is not my speciality.) In the past I often cross-listed my papers to dynamical systems and maybe I should exchange the roles of these two in future – post to dynamical systems and cross-list to q-bio. If I succeed in moving further towards biology in my research, which I would like to I might consider sending things to bioRxiv instead of arXiv.

In this post I have written a lot which is negative. I feel the danger of falling into the role of a ‘grumpy old man’. Nevertheless I think it is good that I have done so. Talking openly about what you are unsatisfied with is a good starting point for going out and starting in new positive directions.

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Another conference on biological oscillators at EMBL in Heidelberg

March 11, 2022

I recently attended a conference at EMBL in Heidelberg and I very much enjoyed experiencing a live conference for the first time in a couple of years. I heard similar sentiments expressed by many of the other participants at the meeting. This conference at EMBL was a sequel to one which I previously wrote about here. The present event was in hybrid form with many of the speakers remote. There were nevertheless more than a hundred people attending on site. The conference started with a presymposium. This was intended to teach some mathematics to biologists. I attended it since I saw it as an opportunity to learn more about what kind of mathematics is really of interest to biologists. Among the main themes discussed were the relationships between positive feedback and multistability and between negative feedback and oscillations. First there was a one-hour talk by Hanspeter Herzel. Then there was a practical part where we were supposed to play with a computer programme. I had downloaded the necessary programmes (R and RStudio) as recommended but this part of the event was a failure for me. I am simply lacking in basic computer competence. It was not explained to us how to begin using the programme and I was not able to supply this missing information on my own. The first part, the lecture, was more interesting for me. The speaker mentioned a paper which he wrote with others about circadian oscillations in the number of lymphocytes in different tissues (D. Druzd et al., Immunity 46, 120). I had previously wondered about the possible roles of oscillations in immunology but I never thought of that direction. I spoke to Herzel about this in a coffee break. This demonstrates a huge advantage of live versus online conferences. I am sure that the information he and I exchanged over coffee would never have been communicated if the conference had been only online. There is a standard picture in immunology in which antigen is being continuously transported to lymph nodes, where it can activate lymphocytes. A key point of the paper is that this does not happen at a constant rate. Instead the process is highly oscillatory. Lymphocytes reach their highest level in the lymph nodes mainly at the beginning of the active phase  (i.e. the beginning of the dark phase in the mice in which these observations were carried out). This means that the effectiveness of a vaccination or another chemical intervention may depend strongly on the time at which it is administered. Herzel told me about an example where this has been seen in practise in cancer immunotherapy. I decided that I wanted to investigate this more closely. Before I could do that I heard the talk of Francis Levi, which was exactly on this topic. Returning to the paper quoted above, according to Herzel the mathematical content was very elementary, using a linear model. I am happy that simple mathematical models and ideas can lead to useful biological insights. What I do not find so good is that the information on the mathematics presented in the paper is so minimal, even in the supplementary material. There is one aspect of this story which is unclear to me. It is important for the functioning of the immune system that a given T cell visits many lymph nodes in a day. Thus the delays to the entrance or exit from lymph nodes which are supposed to implement the rhythm must act in some kind of averaged sense.

I also had a chance to talk to Levi over coffee and get some additional insights about some aspects of his lecture. He has been working on chronotherapy in oncology for many years. This means the idea that the effectiveness of a cancer therapy can be very dependent on the time of day it is administered. He has applied these ideas in practise but the ideas have not gained wide acceptance in the community of oncologists. There is a chance that this may change soon due to the appearance of two papers on this subject in the prestigious journal ‘The Lancet Oncology’ in November 2021. One of the papers (22, 1648) is by Levi, the other (22, 1777) by Qian et al.

Now let me mention a couple of the other contributions I liked best. On Monday there was a (remote) talk by Albert Goldbeter on the coupling between the cell cycle and the circadian clock. Here, as elsewhere in this conference, entrainment was a central theme. There was a discussion of the role of multiple limit cycles in these models. There was also a (remote) talk by Jim Ferrell. His subject was cataloguing certain aspects of an organism called the mouse lemur. The idea was to have a list of cell types and hormones and to know which cell types produce and are affected by which hormones. There is a preprint on this subject on BioRxiv. One feature of these primates which I found striking is the following. They are much fatter in winter than in summer and this is related to a huge difference in thyroid hormones. If I remember correctly it is a factor of ten. For comparison, in humans thyroid hormones also vary with the time of year but only on the scale of a couple of per cent. In a talk by Susan Golden (live) on the Kai system in cyanobacteria I was able to experience one of the pioneers in that field.

Posted in diseases, dynamical systems, immunology, life, mathematical biology | Leave a Comment »

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